Ultrafast Gas-Phase Electron Diffraction Citation Williamson, Joseph Charles (1998) Ultrafast Gas-Phase Electron Diffraction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8kj6-m794. https://resolver.caltech.edu/CaltechTHESIS:11112025-231937152 Abstract The temporal resolution of pump-probe, gas-phase electron diffraction (GED) has been extended to the picosecond time scale, a three order-of-magnitude improvement. With such resolution, GED can now be applied to structural studies of fundamental chemical dynamics, providing complementary information to conventional ps and fs spectroscopy techniques. This thesis gives a thorough theoretical and experimental treatment of ultrafast gas-phase electron diffraction (UGED). Classical Monte-Carlo simulations of coherent chemical dynamics were used to demonstrate that the evolution of molecular spatial coordinates can be determined with fs GED. Similarly, ps GED can reveal the structure of short-lived intermediates in kinetic processes. The circular symmetry of GED patterns was predicted to break during ps rotational coherences, revealing additional structural detail such as bond angles. Instrumentation for UGED was almost entirely home-built. Femtosecond laser pulses were generated in a colliding-pulse, mode-locked ring dye laser and amplified with a four-stage dye cell arrangement pumped by a Nd:YAG laser. The 620-nm output (2 to 3 mJ, 300 fs uncompressed; 30 Hz) was split into pump and probe arms and frequency-doubled. 95% of the laser intensity was focused onto a molecular beam. The remaining 5% was directed onto a back-illuminated 450-A silver cathode, where ultrafast electron pulses were created via the photoelectric effect. The electrons were accelerated with an 18-kV electron gun and focused to a 300-μm diameter. Space-charge effects forced a compromise between electron number density and temporal resolution: streaking experiments revealed that a 1-ps pulse contained 1,000 electrons and a 10-ps pulse contained 10,000 electrons. Thirty centimeters downstream from the exit of the gun, the electrons intersected the pump laser at a 90° angle, directly underneath the molecular beam orifice. A theoretical analysis of the crossed-beam geometry showed that velocity mismatch between the pump photons and the probe electrons also affected the temporal resolution of UGED, making a 3-ps contribution. Approximately 10% of the electrons scattered elastically from sample molecules within the interaction region, and the resulting diffraction pattern was recorded with a scintillator / fused fiber optic / image intensifier / charge-coupled device imaging system housed in a separate vacuum chamber. Single-electron sensitivity across two-dimensions was necessary because of the extremely low electron flux, and the estimated detective quantum efficiency of the imaging system was better than 0.5. Ground-state GED patterns of CCl 4 , SF 6 , CF 3 I, CH 2 I 2 , and C 2 F 4 I 2 were recorded using ps electron pulses. The diffraction data were processed with a software package developed in the laboratory, and the resulting modified molecular scattering curves agreed well with theory. Radial distribution functions were also calculated. Time zero for the pump-probe experiment was identified to within 1 to 2 ps using photoionization-induced lensing (PIL) of the unscattered electron beam. The excitation laser ionized a small fraction of the molecular beam sample, and a cylindrical coulombic lens developed within ps as the nascent photoelectrons escaped the interaction region. The effects of this lens on the incident 18-ke V electron beam shape was detected by direct-bombardment on a charge-coupled device located inside the scattering chamber; high spatial resolution of ~ 15-μm was necessary to observe PIL-induced changes in the electron beam. Diiodomethane was selected as the prototype molecule for the first ultrafast GED investigation. After establishing time zero with PIL, diffraction patterns were recorded at several time steps around t 0 . The transients showed that approximately 10% of the CH 2 I 2 dissociated into CH 2 I and an iodine atom following excitation with the 310-nm pump laser. The estimated temporal resolution was 5 to 10 ps. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Zewail, Ahmed H. Thesis Committee: Rees, Douglas C. (chair) Zewail, Ahmed H. McKoy, Basil Vincent Okumura, Mitchio Defense Date: 21 August 1997 Record Number: CaltechTHESIS:11112025-231937152 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11112025-231937152 DOI: 10.7907/8kj6-m794 ORCID: Author ORCID Williamson, Joseph Charles 0000-0002-3711-1682 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17757 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 14 Nov 2025 18:13 Last Modified: 14 Nov 2025 18:13 Thesis Files PDF - Final Version See Usage Policy. 275MB Repository Staff Only: item control page

Ultrafast Gas-Phase Electron Diffraction Volume One Thesis By J. Charles Williamson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1998 (Submitted August 21, 1997) Ultrafast Gas-Phase Electron Diffraction ii Ultrafast Gas-Phase Electron Diffraction iii The universe is no narrow thing and the order within it is not constrained by any latitude in its conception to repeat what exists in one part in any other part. Even in this world more things exist without our knowledge than with it and the order in creation which you see is that which you have put there, like a string in a maze, so that you shall not lose your way. For existence has its own order and that no man's mind can compass, that mind itself being but a fact among others. Blood Meridian Cormac McCarthy Ultrafast Gas-Phase Electron Diffraction iv Acknowledgments As my graduate student years at the California Institute of Technology come to a close, I would like to take this opportunity to acknowledge the network of collaborators and friends who have bolstered, assisted, and cheered me, helping me bring this thesis into being. First of all, I thank Dr. Ahmed Zewail, my research advisor, for his support and enthusiasm, for his scientific insight, and for providing me with the opportunity to contribute to ultrafast gas-phase electron diffraction techniques. I doubt any other research project would have been better suited towards my own interests and skills. I also greatly appreciate Dr. Zewail's patience, and the trust he showed me and my co-workers in the instrument's long construction phase, when data were slow to appear and the likelihood of experimental success remained uncertain. I was extremely fortunate to interact with many talented scientists during my years at Caltech. Dr. Marcos Dantus and Dr. Scott Kirn were my partners for the development and testing of the first-generation instrument, and they also were my role models as I made the adjustment from college life to graduate research. After Marcos and Scott departed the group, I had the pleasure of assisting Dr. Christoph Lienau for a few months on a high-pressure cell FTS experiment. The second phase of UGED began in earnest with the arrival of Dr. Hans Frey. Hans and I had a fantastic time working together, designing and building the second-generation instrument, and annoying people in the neighboring conference room with our (loud) stereo. No wonder the UGED lab was later moved to a room with 12"-thick concrete walls. Hakno Lee worked with Hans and I for awhile Ultrafast Gas-Phase Electron Diffraction V before switching research advisers to go tackle "bigger molecules," and then Hyotcherl Ihee joined the project as characterization tests of the new instrument began. Hyotcherl rapidly learned the experiment's complexities, and he has continued developing UGED as part of his own quest for a Ph.D. Dr. Stefan Preuss helped put the final touches on the instrument, and a sudden influx of enthusiasm, energy, and ideas came with the arrival of Dr. Jianming Cao - just what the project needed to get those first time-resolved, CH2 l 2 diffraction transients. In the year I have spent out of the lab writing my dissertation, Jim and Hyotcherl have successfully applied UGED to a number of molecular systems, and I wish them and others who pursue this challenging experiment the best. My thanks, also, to Jim, Hyotcherl, and K~n Cooper for critiquing some of the chapters in this text. The Caltech Support Staff were of course invaluable to the UGED experiment: Guy Duremberg, Ray Garcia, and Mike Roy made the Chemistry Instrument Shop our "lab away from lab," taught us how to machine the things we needed, and made those items for us that required special expertise. Likewise, Tom Dunn guided us in solving our electronics dilemmas, and Steve Gould, Elly Noe, and Ruth Brambila in Purchasing and Receiving somehow never tired of us always marking our order forms as "Urgent." The Zewail and Weitekamp community made the subbasement an enjoyable place to be. Thanks to S¢ren Pedersen for dragging many of us up and out into the light of day to play soccer, and to Ahmed Reik.al, Hansi, and others for post-group-meeting pool games. Jennifer Herek was and continues to be an amazing friend, commiserator, and conspirator. Thanks again, Jen, for all the rides to the airport, your help at Jeanine's and my wedding, and our assorted misadventures ("$20 for building a little, paper model? We'll be rich!"). Ultrafast Gas-Phase Electron Diffraction vi Thanks to Manish Gupta, Mike Machczynski, Joel Jones, and Jen Ottesen for letting me crash on their floor for a few days each month over the past year, although I will never recover from the deluge of pop culture they forced on me. Other friends near and far: Jim Kempf, Mark Minto, Nie Close and Lori Pollock, Torsten Kimura, Luke Burke, and of course Patrick McGraw, Grant Nebel, and the Banzai Institute. Unqualified support and love always flows from my parental units, Ted and Eileen Williamson, a:nd my sister Lee Ann McKelvey and her husband David. And the genetic link extends eerily into my research interests, too. Imagine my surprise to recently discover that part of my father's dissertation work was on the theory of neutron diffraction with delta-function pulses ... Finally, all my love and thanks to my wife, Jeanine. We have both made personal sacrifices for our respective paths into higher education, but if we can survive four years of a long-distance relationship, then we can make it through anything. Thanks for being my best friend, and for the Tater Tot! And I must thank Mr. Flibbert and Atlas for their company while I was at home alone all day writing, even if they did glibly eat my shoelaces and a few of my references. Ultrafast Gas-Phase Electron Diffraction vii Abstract The temporal resolution of pump-probe, gas-phase electron diffraction (GED) has been extended to the picosecond time scale, a three order-of-magnitude improvement. With such resolution, GED can now be applied to structural studies of fundamental chemical dynamics, providing complementary information to conventional ps and fs spectroscopy techniques. This thesis gives a thorough theoretical and experimental treatment of ultrafast gas-phase electron diffraction (UGED). Classical Monte-Carlo simulations of coherent chemical dynamics were used to demonstrate that the evolution of molecular spatial coordinates can be determined with fs GED. Similarly, ps GED can reveal the structure of short-lived intermediates in kinetic processes. The circular symmetry of GED patterns was predicted to break during ps rotational coherences, revealing additional structural detail such as bond angles. Instrumentation for UGED was almost entirely home-built. Femtosecond laser pulses were generated in a colliding-pulse, mode-locked ring dye laser and amplified with a four-stage dye cell arrangement pumped by a Nd:YAG laser. The 620-nm output (2 to 3 mJ, 300 fs uncompressed; 30 Hz) was split into pump and probe arms and frequencydoubled. 95% of the laser intensity was focused onto a molecular beam. The remaining 5% was directed onto a back-illuminated 450-A silver cathode, where ultrafast electron pulses were created via the photoelectric effect. The electrons were accelerated with an 18-kV electron gun and focused to a 300-µm diameter. Space-charge effects forced a compromise between electron number density and temporal resolution: streaking Ultrafast Gas-Phase Electron Diffraction viii experiments revealed that a 1-ps pulse contained 1,000 electrons and a 10-ps pulse contained 10,000 electrons. Thirty centimeters downstream from the exit of the gun, the electrons intersected the pump laser at a 90° angle, directly underneath the molecular beam orifice. A theoretical analysis of the crossed-beam geometry showed that velocity mismatch between the pump photons and the probe electrons also affected the temporal resolution of UGED, making a 3-ps contribution. Approximately 10% of the electrons scattered elastically from sample molecules within the interaction region, and the resulting diffraction pattern was recorded with a scintillator / fused fiber optic / image intensifier / charge-coupled device imaging system housed in a separate vacuum chamber. Single-electron sensitivity across two-dimensions was necessary because of the extremely low electron flux, and the estimated detective quantum efficiency of the imaging system was better than 0.5. Ground-state GED patterns of CC4, SF6, CF3I, CH2h, and C2F4Ji were recorded using ps electron pulses. The diffraction data were processed with a software package developed in the laboratory, and the resulting modified molecular scattering curves agreed well with theory. Radial distribution functions were also calculated. Time zero for the pump-probe experiment was identified to within 1 to 2 ps using photoionization-induced lensing (PIL) of the unscattered electron beam. The excitation laser ionized a small fraction of the molecular beam sample, and a cylindrical coulombic lens developed within ps as the nascent photoelectrons escaped the interaction region. The effects of this lens on the incident 18-keV electron beam shape was detected by direct-bombardment on a charge-coupled device located inside the scattering chamber; Ultrafast Gas-Phase Electron Diffraction ix high spatial resolution of ~ 15-µm was necessary to observe PIL-induced changes in the electron beam. Diiodomethane was selected as the prototype molecule for the first ultrafast GED investigation. After establishing time zero with PIL, diffraction patterns were recorded at several time steps around t0 . The transients showed that approximately 10% of the CH2Ii dissociated into CH21 and an iodine atom following excitation with the 310-nm pump laser. The estimated temporal resolution was 5 to 10 ps. Ultrafast Gas-Phase Electron Diffraction X Table of Contents Volume One ACKNOWLEDGMENTS ..................................................................................................................... iv ABSTRACT .......................................................................................................................................... vii TABLE OF CONTENTS ........................................................................................................................ X LIST OF ABBREVIATIONS .............................................................................................................. xvi FUNDAMENTAL CONSTANTS ....................................................................................................... xvii LIST OF SYMBOLS ......................................................................................................................... xviii CHAPTER ONE: TIME-RESOLVED DIFFRACTION STUDIES ..................................................... I 1.1 FEMTOSECOND TRANSITION-STATE SPECTROSCOPY .. .... ......... ............ ........ ... .. ... . ........... ... .. .. .. .... .. .. 1 1.2 EXTRACTING R(t) FROM FTS TRANSIENTS ...... .......................... ... .. ........... .... ... ................ .... ...... .. .. 6 1.3 STRUCTURE DETERMINATION WITH DIFFRACTION TECHNIQUES ........... .. .... .. .... .. .. .. .. . ............ ........ 16 1.4 PICOSECOND X-RAY DIFFRACTION .. ..................... .. .................... .... ... .... ... ..... ............ .......... ... ...... 24 1.5 PICOSECOND ELECTRON DIFFRACTION : SURFACES AND FILMS .... ...... ...... .......... .. ................. ... ....... 27 1.6 TIME-RESOLVED GAS-PHASE ELECTRON DIFFRACTION .... .......... ................................................... 31 1.6.1 Long-Lived Reaction intermediates 1.6.2 The Millisecond and Microsecond Time Scales 1.6.3 The Nanosecond Time Scale 1.7 ULTRAFAST GAS-PHASE ELECTRON DIFFRACTION .. .... .. .. ... ... .. .. ................... ... .. .. .................. .... .... 38 CHAPTER TWO: GAS-PHASE ELECTRON DIFFRACTION THEORY ..................................... 43 2.1 DIFFRACTION FROM ISOTROPIC SAMPLES .. .. ......... .................................................. .. ............ ....... .. 44 2.1.1 Defining The Theoretical Model 2.1.2 The First Born Approximation: Deriving f(s) 2.1.3 Diffraction From A Rigid Molecule 2.1.4 The Second Born Approximation: Deriving 1J(s) 2.1 .5 The Method Of Partial Waves 2.1.6 Diffraction From A Vibrating Molecule 2.1. 7 The Radial Distribution Curve 2.1.8 Additional Corrections 2.2 DEFINITIONS OF INTERNUCLEAR SEPARATION ....... .. ........... ............. .... .. ....... .. .............. .. ........... .. .. 74 2.2. 1 Physical Definitions Of r Ultrafast Gas-Phase Electron Diffraction xi 2.2.2 Operational Definitions Of r 2.2.3 Geometrical Considerations 2.3 DIFFRACTION FROM SPECIALLY-PREPARED GAS SAMPLES ............................ ................................. 79 2.3.1 Spatially-Oriented Molecules 2.3.2 Rotationally-Selected Or -Excited Molecules 2.3.3 Vibrationally-Excited Molecules 2.4 ROTATIONALLY COHERENT SAMPLES ........................... ............ .. ................. ................. ................ 85 2.4.1 Rotational And Spatial Coherence 2.4.2 Theoretical Framework 2.4.3 Diffraction From Perfectly Aligned Diatomic Molecules 2.4.4 Diffraction When The Laser Polarization Vector ls Parallel To k0 2.4.5 Diffraction When The Laser Polarization Vector ls Perpendicular To k0 2.4.6 Experimental Applications 2.4. 7 Diffraction From Nonlinear Molecules 2.5 VIBRATIO NALLY COHERENT SAMPLES .......... ....... ....... ................... .. .............. ... .... ... .......... ......... 120 2.5.1 Basic Principles 2.5.2 The Molecular Dynamics Simulation 2.5.3 Coherent Dissociation 2.5.4 Coherent Vibrations 2.5.5 Ultrafast Kinetic Dynamics CHAPTER THREE: LASERS, VACUUMS, AND THE COMPUTER .......................................... 134 3.1 THE FEMTOSECOND LASER SYSTEM .... ................ ... ... .. .. .. ............................... ... ........ ......... .......... 135 3.1.1 The Colliding-Pulse, Mode-Locked Ring Dye Laser 3.1.2 The Pulsed Dye Amplifier 3.1.3 Autocorrelation Measurements and Pulse Compression 3.1.4 Wavelength Generation 3.2 THE GAS-PHASE ELECTRON DIFFRACTION VACUUM SYSTEM ......................... ...... ....................... 143 3.2.1 The Electron Gun Chamber 3.2. 2 The Scattering Chamber 3.2.3 The Detector Chamber 3.3 THE SAMPLE INLET SYSTEM .... ..... ...................... .. .............. ... ...................... .. ...... ......... .............. 158 3.3.1 The input Manifold 3.3.2 The CW Free-Jet Expansion Nozzle 3.3.3 The Piezoelectric Pulsed Nozzle 3 .4 THE MET AL-EV APO RATION VACUUM CHAMBER ......................................... .. .... ....... ................... 163 3.5 THECOMPUTERSYSTEM ............... ............................................................................. ........ ........ 165 CHAPTER FOUR: ULTRAFAST ELECTRON PULSE GENERATION ...................................... 168 4.1 METHODS OF GENERATING FREE ELECTRONS FROM METALS ... .. ..... .................................. .......... 169 4.1.1 Thermionic Emission 4.1.2 Field Emission 4.1.3 Photoemission 4.2 THEPHOTOCATHODE ...... ...... ........ ....... . ....... ................................... ...... . .... ... ... ...... ....... .... ......... 180 4.2.1 Photocathode Selection Criteria 4.2.2 Choosing and Testing the 450-A. Silver Photocathode 4.3 THE UGED ELECTRON GUN······················································ ········ ·· ······ ·· ·········· ··· ·············· ··· 192 4.3.1 The High-Voltage Power Supply 4.3.2 The Photocathode and Extraction Pinhole Ultrafast Gas-Phase Electron Diffraction xii 4.3.3 The Electron Gun Body and Focusing Electrodes 4.3.4 The Final Pinhole and Deflection Plates 4.3.5 The Electron-Generating Laser 4.3.6 Estimations of Temporal Coherence 4.3. 7 Estimations of Spatial Coherence 4.4 MEASUREMENT OF THE ELECTRON PULSE WIDTH ....................................................................... 217 4.4. I A Theoretical Model of Streaking Experiments 4.4.2 The UGED Streaking Experiment CHAPTER FIVE: REAL-TIME, SINGLE ELECTRON DETECTION ACROSS TWO DIMENSIONS ........................................................................................... 228 5 .1 Ev ALUATION OF ELECTRON FLux ................................................ ... .... ....................................... 228 5.1.1 Comparison With Standard GED Electron Flux 5.1.2 Estimation of the Signal-to-Noise Ratio 5.2 REAL-TIME ELECTRONIC METHODS OF GED DETECTION ................................................ ...... .. .... 237 5.3 CHARACTERIZING Two-DIMENSIONAL IMAGING SYSTEMS .......................................................... 241 5.3.J Gain 5.3.2 Pulse-Height Distribution 5.3.3 Response Time, Readout Time, and Gating 5.3.4 Dynamic Range 5.3.5 Linearity and Uniformity 5.3.6 Distortion 5.3. 7 Point Spread Function and the Limit of Spatial Resolution 5.3.8 Detector Area 5.3.9 Modulation Transfer Function 5.3. IO Detective Quantum Efficiency 5.3. I I Durability 5.4 ELECTRON IMAGING COMPONENTS ... .. ...... ........ ........ .............. ............... .... ..... ................ ...... ..... 256 5.4. I Two-Dimensional Electron Detectors 5.4.2 Photon Imaging Optics 5.4.3 Two-Dimensional Amplifiers 5.4.4 The CCD Storage Device 5.5 DESIGN EXAMPLES AND DETECTIVE QUANTUM EFFICIENCY .... .................. .................................. 277 5.5. I Direct Bombardment of a Charge-Coupled Device 5.5.2 Scintillators 5.5.3 Direct Bombardment of a Microchannel Plate 5.5.4 Scintillators With Amplification 5.5.5 Conclusions CHAPTER SIX: THE UGED IMAGING SYSTEM ........................................................................ 288 6.1 THE FUSED FIBER OPTIC COMPONENTS .............................................. ........ .. .............................. 291 6.2 ASSEMBLY OF THE SCINTILLATOR-BASED IMAGING SYSTEM ....................................................... 292 6.3 THE ALUMINUM BEAM STOP ... ...... .......... ........ ............ ......................................... .............. ........ 300 6.3. I Aluminum Transmission Characteristics 6.3.2 Preparation of the Beam Stop 6.4 THE P20 PHOSPHOR SCINTILLATOR ........... ............................................... ... ... ........ ..... ... ............ 303 6.5 THE PROXIMITY-FOCUSED IMAGE INTENSIFIER .......... .. ..... ............................................ ... ....... .. .. 305 6.5.1 The Power Supply 6.5.2 The Controller Unit Ultrafast Gas-Phase Electron Diffraction xiii 6.5.3 Triggering the Image Intensifier 6.5.4 Setting the Image Intensifier Gate Delay 6.5.5 Setting the Image Intensifier Gate Width 6.6 THE CHARGE-COUPLED DEVICE ............................................................ ............. ... ..................... 313 6.6.I Basic Principles 6.6.2 The S/Te CCD 6.6.3 The TI CCD 6. 7 THE SPECTRASOURCE CAMERA HEAD ................ ... .................................................. ··············· .... 328 6. 7. I The Timing Board 6.7.2 The Voltage Generation Board 6.7.3 The A~D Conversion Board 6. 7.4 The Optical Isolator Board 6.7.5 Generation of the TI CCD's SRG Signal 6. 7.6 Summary of Modifications Made to the SpectraSource Camera Head 6 .8 THERMOELECTRIC COOLING SYSTEMS .. .......... .... ................. ........ ....................... .. ............... ... .... 355 6.8.1 Cooling the S/Te CCD 6.8.2 Cooling the TI CCD 6.9 CHARACTERIZATION OF THE DETECTORS .......... .......................................... ... ........................... .. 361 6.9.1 Single-Electron Pulse-Height Distribution and Gain of the TI CCD 6.9.2 Single-Electron Detective Quantum Efficiency of the TI CCD 6.9.3 Single-Electron PHD and Gain of the Scintillator Detector 6.9.4 Single-Electron Detective Quantum Efficiency of the Scintillator Detector 6.9.5 Readout Noise and Thermal Noise 6.9.6 The Point Spread Function 6.9.7 The Modulation Transfer Function REFERENCES ................................................................................................................................... 371 Volume Two TABLE OF CONTENTS ....................................................................................................................... iii LIST OF ABBREVIATIONS ................................................................................................................ ix FUNDAMENTAL CONSTANTS ........................................................................................................... X LIST OF SYMBOLS ............................................................................................................................. xi CHAPTER SEVEN: METHODS OF DIFFRACTION DATA ANALYSIS .................................... 392 7 .1 EXTRACTION OF RAW INTENSITY CURVE: RADAR2 ................. ....... .... .... ................................... 393 7.2 BACKGROUND CORRECTION TECHNIQUES .................................................... ................. ........... ... 405 7.3 DETERMINATION OF THE CAMERA CONSTANT ......... ...... .................................... ........... ............ ... 414 Ultrafast Gas-Phase Electron Diffraction xiv CHAPTER EIGHT: GROUND-STATE ELECTRON DIFFRACTION DATA ............................. 421 8.1 THE EXPERIMENTAL METHOD .............................. ..................................................... ... .... ... ....... 422 8.2 CARBON TETRACHLORIDE •••••••••••••••••••···· ····· ·· · ..................... ..... .... .. ................................... ....... 427 8 .3 TRIFLUOROMETHYL IODIDE .......................................... ...... ............ ......... .. .......... .... ........ .... ...... 430 8.4 SULFUR HEXAFLUORIDE ........ ··············· ···· ··· ··· ·· ... .. ........ ... ..................... .. ................................... 433 8 .5 DIIODOMETHANE ............. ....... ....... .......... ....... ...... ............ .. ............. ........ ....... .... .. .. .. .............. ... 436 8.6 DIIODOTETRAFLUOROETHANE .... .... ...... ....................................... ............... .... ......... .. ................. 439 8 .7 PHOTODISSOCIATION OF TRIFLUOROMETHYL IODIDE ........ ........ ... ..... ............. ... .. ...... ... ...... ... .. ..... 441 8.8 POSSIBLE SOURCES OF ERROR ........................ ..... ..... ...... ................... ... ............ ...... ........... ....... .. 443 CHAPTER NINE: TOTAL EXPERIMENTAL TEMPORAL RESOLUTION AND ESTABLISHMENT OF TIME ZERO ...................................................... 448 9 .1 VELOCITY MISMATCH ... .. .. .... ..... ....................... ...... ..... ...................... ....... ... .. .. ..... ............. .... ... 450 9.2 PURE ELECTRON-PHOTON INTERACTIONS ....... ............... ... ............. ........... .. ......... ...... ......... ........ 461 9 .3 ELECTRON-PHOTON INTERACTIONS VIA INTERMEDIARIES ..... .... ... .............. .................... .. .......... . 4 72 CHAPTER TEN: ULTRAFAST GAS-PHASE ELECTRON DIFFRACTION ............................... 486 10. 1 SELECTION OF THE PROTOTYPE MOLECULE: CHJ2 .... .. ........... .......... ......... ... ............................ 487 10.2 EXPERIMENTAL SETUP AND METHOD ............ ............. .... ......... ...... .............. ........... ....... .. ........ . 490 10.3 DATA ANALYSIS ANDTHEFIRSTUGED TRANSIENTS ................................. .... ... ........... ....... .... .. 494 CHAPTER ELEVEN: CONCLUSIONS AND FUTURE DIRECTIONS ........................................ 512 11.1 SUMMARY OF RESULTS ..... .... .. ........ .... .. ....... ............... ............... ....................... ....... ........ ...... .. 512 11 .2 THE THIRD-GENERATION UGED INSTRUMENT ................ .. ................ ........ ............... ........ ...... .. 514 APPENDIX A: DERIVATION OF ELECTRON WAVELENGTH ................................................ 527 A.1 INTRODUCTION ....... .... .... .. .............................. ........ .... ... ...... ........... ............................. ... ........ .. 527 A.2 NONRELATIVISTIC ELECTRON WAVELENGTH ....... .... .... .. ... .. .. .. ... .... ................. ... ...... ...... ...... ..... . 528 A.3 RELATIVISTIC ELECTRON VELOCITY ....... ................... ... ..................... .. ... ...... ... .. ... ..... ...... .... ...... 528 A.4 RELATIVISTIC ELECTRON WAVELENGTH .. ........................... .............. .......... .. ..... ......... ............... 529 APPENDIX B: DERIVATION OF ROTATIONAL COHERENCE DIFFRACTION INTEGRALS .............................................................................................. 531 B.1 INTRODUCTION AND PRELIMINARY MATHEMATICS .. ...................................... .......................... .. 531 cos l/f + ib sin l/f )dl/f ..... ............... .... ...... ........ ............ .. ............. .... ...... ...... 534 B.2 ~ s:ir exp(ia 2 B .3 2 2~ s:ir COS l/f exp(iaCOSl/f B.4 ½J;(sin0)"+ Jn(bsinO)exp(iacosO)d.Q .. .................................................................. 539 1 + ibsinl/f)dl/f ... ............. ........ .... .... .... .... ..... ... ...... ............. 536 Ultrafast Gas-Phase Electron Diffraction xv APPENDIX C: INTERPOLATING THE SCATTERING FACTORS ............................................ 543 C.1 INTERPOLATION ALONG ENERGY .................... .......................................................................... 544 C.2 INTERPOLATION ALONG MOMENTUM TRANSFER .............................................. ........... .... .. ......... 545 APPENDIX D: SOFTWARE DEVELOPED FOR ULTRAFAST GAS-PHASE ELECTRON DIFFRACTION ......................................................................................... 547 D.1 INTRODUCTION .............................. .......................... ............................. ... ....... ..... .. .. ... .............. 547 D .2 READING AND WRITING CCD IMAGES ............... ...................................................... ..... ... ... ...... 554 D.3 RADAR2 .. .. ........................................ .. ................ ...... .. .................... ........ .... ........ .. ................. 557 D.4 PROC5 ...................... ............................. ..... .................. .............. .......... ... ............................... 582 D.5 ADDER ............. ................. .. .... ..... .... .......... ... ................. ... ........ .. ..... ... ................... ................ 624 D.6 PROFILE ......... .................. .. ................................. ............................................................. ..... 639 D.7 STREAK .................. .......... ..................... .. ..................... .. .... ................... ................................ 654 D.8 PROC4 ..................................... .. .......... ........ ............. .............. ........ ........... .. .. .... .. ............... .... 665 D.9 R-K ... .. ........... .................... ........... .. ......... .......... ..... ... .. ....... ... ...... .... ............... .. .. .. ... .......... .... . 668 D.10 PROC3 ......... ..................... ............... ................. ..... .............. .. ......................... ..... ....... .......... 679 D.11 CONV .......... ......................................................... .... ......... .... ............... ..... ...... ....... ..... ..... .... 689 D.12 CIRC ........... .. .. ...... ... ................................................. ....... ....... ..................... ............. ... ...... ... 691 D.13 AUTOHOME AND AUTOSCAN ... ... .... .................. .. .......................................... ..... ... ...... .. ... . 703 APPENDIX E: EXCEL MACROS FOR AUTOMATING UGED EXPERIMENTS ...................... 706 E. l INTRODUCTION ..... ............. ..... ... ... ... .... ... .................. .......... ...... ...... .. ....... .. .. ... ......... ... ..... .... ..... 706 E.2 MACROFOREXAMINATIONOFCCD IMAGES .............. ...... ..... .. ... .. ... ........................................ .. 707 E.3 MACRO FOR THE UGED EXPERIMENT .. ... ... ... ............. ........ .... ..... ..... .. ......... .. ..... ... ... ............... .. 709 E.4 MACRO FOR DETERMINATION OF TIME ZERO ... ... .... .. .. .... .... .. .. .. .............. .. ........ ........ .... .... ..... .... 712 APPENDIX F: CLOCKING TRANSIENT CHEMICAL CHANGES BY ULTRAFAST ELECTRON DIFFRACTION ................................................................... 716 REFERENCES ................................................................................................................................... 720 Ultrafast Gas-Phase Electron Diffraction List of Abbreviations A➔D ADU APS ASE ATI CCD CCE CDS CTE CFF CPM csv DQE DSCS EBS EHP EMF e-p EPH FTS FWHM GED 1AM ID LEED LIF MAV MOSFET MS MTF Nd:YAG Nd:YLF OAR OD ODE OM PC PCS PDA PES analog to digital A➔D conversion unit active pixel sensor amplified spontaneous emission above-threshold ionization charge-coupled device charge-collection efficiency • correlated double sampling charge-transfer efficiency Conflat flange colliding-pulse, mode-locked, ring dye laser comma-separated variables detective quantum efficiency differential scattering cross section electron-bombarded semiconductor cascade process electron hole pairs electromagnetic fields encoder pulses extraction pinhole femtosecond transition-state spectroscopy full-width at half-maximum gas-phase electron diffraction independent atom model inner diameter low-energy electron diffraction laser-induced fluorescence mean amplitude of vibration metal-oxide-semiconductor field-effect transistor molecular scattering modulation transfer function neodymium yttrium aluminum garnet laser neodymium yttrium lithium fluoride laser open area ratio outer diameter ordinary differential equation order of magnitude photocathode photoconductive switch pulsed dye amplifier potential energy surface xvi xvii Ultrafast Gas-Phase Electron Diffraction PGF PHD PIL pix pixel PLE PLU PPE PPU PSF RAM RD RHEED RMS SITe SNR sr SSD TEC TI TOF UGED YAG ZEKE probability generating function pulse-height distribution photoionization-induced lensing see "pixel" picture element; the smallest unit of resolution of a CCD parallel / excited parallel / unexcited perpendicular / excited perpendicular/ unexcited point spread function random access memory radial distribution •reflection high-energy electron diffraction root mean square Scientific Imaging Technologies, Inc. (CCD manufacturer) signal-to-noise ratio steradian (unit solid angle) sum of the square of the differences thermoelectric cooler Texas Instruments (CCD manufacturer) time of flight ultrafast gas-phase electron diffraction yttrium aluminum garnet zero electron kinetic energy Fundamental Constants Bohr radius speed of light charge of electron permittivity of vacuum Planck's constant Boltzmann constant mass of electron electron mass energy mass of neutron Avogadro's number ao C e co h k me 2 m eC mn NA gas constant R classical electron radius Thomson cross section <JT re 5.29177 X 10-ll m 299792458 ml s 1.602189 X 10- 19 C 8.854188 X 10- 12 F/m 6.626176 X 10-34 Js 1.38066 X 10-23 J /K 9.109534 X 10-3 l kg 511.003 keV 1.674929 X 10-27 kg 6.022045 X 1023 #/mol 0.08206 ,e atm / mol K 8.3145 JI mol K 2.817938 X 10-lS m 6.652448 X 10-29 m2 List Of Symbols xviii List of Symbols a ae ~ r r( ) y ~£ ~Tl ~v ~cr ~t ~tt.t: ~t8 ~te ML ~tTo, ~tvM o o( ) 08 or E Eo angle; rotational angle of ru about the excitation axis during integration of Fu( ) vibrational-rotational interaction constant velocity ratio volume Euler's gamma function constant; relativistic constant; Keldysh parameter FWHM of initial electron energy distribution difference in elastic scattering phase factors frequency bandwidth scattering cross section difference time delay between pump and probe laser pulses temporal broadening due to initial electron energy distribution temporal broadening due to pumpprobe geometry temporal pulse width (FWHM) of the electron beam temporal pulse width (FWHM) of the laser total temporal resolution of UGED experiment temporal broadening due to velocity mismatch phase shift; mean number of secondary electrons Dirac delta function transverse displacement shrinkage of internuclear separation centrifugal distortion energy; radiant efficiency; KapitzaDirac theory constant permittivity of vacuum 0 e es K p p() pt cr <>eb <>et C>inel 't Fermi energy quantum efficiency; probability phase of electron elastic scattering factor for element a Euler angle angle; scattering angle Bragg scattering angle internuclear separation asymmetry constant wavelength electron de Broglie wavelength neutron de Broglie wavelength probe laser wavelength pump laser wavelength reduced mass frequency density; potential density function density distribution mass-thickness parameter standard deviation; scattering cross section standard deviation of single electron pulse-height distribution; elastic scattering cross section standard deviation of electron beam pulse width elastic electron scattering cross section second harmonic generation cross section inelastic electron scattering cross section molecular electron scattering cross section time; kinetic time constant; Kapitza-Dirac theory constant; photoelectric absorption cross section List Of Symbols temporal resolution combining electron pulse width and velocity mismatch ionization potential rotational angle of detection (relative to x-axis); metallic work function azimuthal Euler angle X wave function; azimuthal angle of internuclear separation (relative to x-axis) incident wave function scattered wave function solid angle; altitude angle of internuclear separation (relative to z-axis) angle between internuclear separation rij and excitation axis (i) spatial or vibrational frequency fundamental vibrational frequency ffie constant; rotational constant; area; A Richardson constant constant; anharmonicity constant; a atomic element; acceleration; pixel dimension Bohr radius ao rotational constant B Bon() row-dependent background offset function of CCD image change of background offset from top to bottom of CCD image; also range of pulse-height distribution background offset value at top of CCD image constant; atomic element b constant; rotational constant; flow C conductance CI() x-y array of CCD pixel count values after A~D conversion Cloff pixel count value offset CP() average profile of CCD pixel array speed of light C rate of background noise accrual D D() radial distribution function "' xix dissociation energy diameter; distance differential solid angle energy; electric field one-half potential energy change of bringing atoms to molecular positions energy of wavelength A photon E'A. binding energy Eb correlation energy Ecorr total energy E10 1 charge of electron e e() edge spread function internuclear force constant; Fano F factor F() generic function; Fowler function Fu() spatial orientational average of scattering function for internuclear separation rij Fx() x-ray scattering function focal point distance; fraction f f() generic function; modified radial distribution function electron elastic scattering factor for element a lfa( )I amplitude of electron elastic scattering factor for element a probability generating function; G() Green's function gain g generic function; normalization g() function; spin-flip scattering amplitude scaling factor between experimental and theoretical sM(s) curves user-defined rescaling factor for CCD pixel intensities relative gain variation between top and bottom of CCD image relative CCD gain as a function of row number Planck' s constant h point spread function h() current; intensity I intensity distribution I() xx List Of Symbols la IA() Is() IE() IM() IT() i J KE k k ko ko ks L LAe l Im M() MW moment of inertia about axis a atomic scattering intensity background scattering intensity experimental scattering intensity molecular scattering intensity theoretical scattering intensity integer index; H rotational quantum number; current Bessel function of integer order integer index Bessel function of fractional order transverse displacement of thermally-averaged internuclear separation; time-bandwidth product kinetic energy scattered electron beam wave vector integer index; Boltzmann constant; optical extinction coefficient; wave constant incident electron beam wave vector magnitude of incident electron beam wave vector damping constant used during the generation of a radial distribution curve voltage sweep rate length; camera length camera constant integer index; mean amplitude of vibration; length line spread function mean amplitude of vibration of lowest vibrational state mean amplitude of vibration of harmonic oscillator mean amplitude of vibration between atoms i and j effective mean amplitude of vibration modified molecular scattering function; modulation transfer function molecular weight m m p P() P,/) p Q q R R R() r ro integer index integer index mass of electron mass of neutron relativistic mass number number of CCD images number of different internuclear separations in a molecule number of regions selected from a CCDimage number of trajectories integer index; refractive index population distribution number of internuclear separations with atoms a and b pressure; probability; point of detection probability distribution Legendre polynomial momentum; probability flow throughput momentum transfer magnitude; Kapitza-Dirac theory constant detection vector reflectance; distance to point of detection; gas constant set of molecular coordinates; radial probability function radius; repetition rate distance determined from groundstate rotational constants distance between average nuclear positions at thermal equilibrium structure defined with rg bond distances and ra bond angles internuclear separation determined with electron diffraction equilibrium internuclear separation; classical electron radius thermal average of internuclear separation vector from atom i to atomj distance between atoms i and j List Of Symbols s S() s s Smin Smax T T() t to U() Vo u u() V V() V distance determined from spectra with Kraitchrnan's method distance between average nuclear position at vibrational level v distance between two CCD pixels distance between average nuclear positions at T = 0 K. pumping speed or flow rate; signal molecular sample spatial distribution function electron inelastic scattering factor for element a momentum transfer vector momentum transfer magnitude lowest s position containing valid experimental scattering data largest s position of scattering data used during radial distribution transformation period; temperature molecular trajectory array (internuclear coordinate versus time) molecular trajectory array convoluted with electron pulse width time; thickness zero of time modified potential function ponderomotive potential variable axis modified radial probability function voltage; volume potential energy function velocity; vibrational quantum number electron velocity relativistic velocity xxi streak velocity well depth WB() Windows bitmap x-y array of pixel count values w weighting constant; width width of electron beam W eb pre-alignment window width in Wp PROFILE software CCD pixel width Wpix X coherence length X variable axis x-axis position on CCD of unscatXeb tered electron beam x-coordinate from lower-right corXt ner selected region on CCD x, x-axis range of selected region on CCD x-coordinate from upper-left corXu ner of selected region on CCD anharmonicity constant x~ Y() angular probability function Dunham coefficient Yu variable axis y y-axis position on CCD of unscatY eb tered electron beam y-coordinate from lower-right corner of selected region on CCD y, y-axis range of selected region on CCD y-coordinate from upper-left corYu ner of selected region on CCD atomic number z variable axis z position of ith zero in modified Z; molecular scattering curve Vs w 1 Chapter One Ti me-Resolved Diffraction Studies Nothing exists except atoms and empty space; everything else is opinion. Democritos 1. 1 Femtosecond Transition-State Spectroscopy A new era of time-resolved spectroscopy began one decade ago following publication of the first femtosecond transient of a molecular system [Dan87]. The authors of this paper studied the photodissociation of iodocyanide into an iodine atom and a CN radical, a process representative of the general class of elementary reactions known as half-collisions: A-B hv [A-··BJ* ~ A + B ( 1.1) Dantus, Rosker, and Zewail wanted to observe a chemical reaction's transition state the period of time during which reacting molecules exist as an activated complex en route to product formation (Figure 1-1). An extremely fast "camera" is required to make such Chapter One: Time-Resolved Diffraction Studies 2 an observation. The time scale of the transition Transition State [A · .. 8]+ ~ state can be estimated by assuming that the ___ t ____ _ 0) dissociation is a direct process in which the <D ~ A-8 reaction coordinate of the half-collision lies A+ B along the A-B bond, i.e., the A-B internuclear separation increases continuously until A and B no longer interact. Molecular translational velocities are on the order of 1 km/s; therefore, Products Reaction Coordinate Figure 1-1: Potential energy diagram of an exothermic reaction. Reactants require an activation energy Ea to reach the activated complex in the transition state. the distance between A and B will grow by several Angstr¢ms within a few hundred femtoseconds (1 fs = 10- 15 s). To resolve classical and quantum details of this motion, the transition-state camera would need to have a temporal resolution on the order of 50 fs . The authors of the ICN study attained this resolution with a pump-probe experiment built around a single femtosecond laser system [RoM88] . The general scheme of ultrafast pump-probe spectroscopy experiments is shown in Figure 1-2. Pulsed output BS Amplified Femtosecond Laser M TS ~ 0 ( .) Ql M Ql 0 ,,,., M OM Sample Figure 1-2: Experimental schematic for femtosecond transition-state spectroscopy. BS: beamsplitter; M: mirror; WG: wavelength tuning optics; TS: computer-controlled translation state; OM : dichroic mirror; L: lens. Chapter One: Time-Resolved Diffraction Studies 3 from the laser system is directed into a Mach-Zehnder interferometer. One arm of the interferometer corresponds to the pump laser, which initiates the chemical reaction, and the second arm corresponds to the probe laser, which monitors the progress of the reaction. The wavelengths of pump and probe lasers can be adjusted independently using nonlinear optical techniques such as second-harmonic generation, continuum generation, and sum- or difference-frequency mixing. The relative time delay lit between pump and probe laser pulses must be varied to obtain a transient; this can be done by changing the optical path length of one interferometer arm using a computer-controlled translation stage (light travels 3 µm in 10 fs). The pump and probe lasers are recombined with a dichroic mirror, completing the interferometer arrangement, and then focused into the sample. Several types of signals can be detected. A representation of the ultrafast pump-probe experiment m terms of chemical potentials is shown in Figure 1-3. The pump laser (/1,p,,) excites molecules from the ground-state electronic potential energy surface V0 up to an intermediate PES. The intermediate PES might be dissociative (V1a), as in the case of a half-collision, or else perhaps a stable bound state (V,b)- The energy bandwidth of transform-limited 50-fs laser pulses is on the order of 36 meV (300 cm- 1) [Gre74], [Fle86]. As a result, the pump laser transfers ground state population on V0 to a range of excited states on the intermediate PES, creating a wave packet. The excited states could be part of a continuum (V,a), or, in the case of a bound PES (V1b), discrete vibrational eigenstates. The nascent wave packet then evolves along the PES. The probe laser (A,p,) arrives at a time lit after the pump laser and further excites molecules up to the electronic state Vi. molecules which reach Vi. Signal is collected from Chapter One: Time-Resolved Diffraction Studies 4 V2 APr1 APr2 >, - V1a w v1b O') Q) C Pu If Vo -3 Reaction Coordinate Figure 1-3: Potential energy diagram for a model pump-probe spectroscopy experiment. A fs pump laser (APu) excites ground-state population on Vo up to dissociative state V1aThe wave packet created on Via evolves with time and is excited to upper state V2 by a fs probe laser (Apr1 or Apa). The population of V2 is monitored. Only certain regions of the PES are suitable for a vertical transition from Via ( or Vib) to Vi, as determined by Ap, and its bandwidth. The likelihood of the transition depends on the probability density of the wave packet within these regions. For example, Chapter One: Time-Resolved Diffraction Studies 5 Figure 1-3 shows Apu creating a wave packet on the dissociative state Via• As the molecule breaks apart, this wave packet will evolve over time out to greater and greater R. If the probe laser has wavelength Ap,i, then the transition from Via to Vi is most likely to occur when the en C Q) +--' pump and probe lasers overlap temporally; the detector c registers signal only around lit = 0 (time zero, to) because C ctS 0) the wave packet moves away from the vertical transition Cf) I Apr= Apr2 region accessible by Ap,i (Figure 1-4, Top). On the other hand, if the probe laser has wavelength Ap,2 , then vertical transitions can be accessed only after the molecule has to dissociated. The rise in detector signal occurs at some lit after to, corresponding to the time required for the wave packet to move out to greater R (Figure 1-4, Bottom). The temporal-resolution of the pump-probe experiment depends on three factors: (1) the pulse widths of the pump and probe lasers, (2) velocity mismatch across the sample, and reproducibility of varying lit. (3) the accuracy and Molecules which reach state Vi are already encoded for a specific set of Apu, Ap,, De Ia y T i m e ~t Figure 1-4: Probe wavelength dependence of FTS transients for the model potentials shown in Figure 1-3. Pump and probe laser pulses overlap at time to. (Top) The redder wavelength (Apr1) excites from the inner turning point of Via, so signal is centered at to. (Bottom) The bluer wavelength (Apr2} excites final products. Signal takes time to rise, but then remains constant. (Middle) Ap, is in between Apr1 and Ap,2. Signal reaches a maximum some time after to and then declines to an asymptotic value. and lit, so measurement of the Yi-state population is not restricted by the speed of the detector system. In the ten years since the inception of FTS, transients have been Chapter One: Time-Resolved Diffraction Studies 6 recorded with powerful techniques such as laser-induced fluorescence (LIF), multiphoton ionization coupled with mass spectrometry, absorption and depletion, four-wave mixing, and many others [Che96], [Man95], [Zew94], [Man93]. Femtosecond studies have also been conducted on most forms of matter, including gases, liquids, solids, molecular clusters, condensed phases, and biological systems [Zew96] . The next section reconsiders FTS studies of "simple" prototypical diatomic systems, and explores how the evolving internuclear coordinate, R(t), is contained within the transient data. 1.2 Extracting R(t) From FTS Transients Excitation with the probe laser pulse samples the wave packet density present across a region of the intermediate potential energy surface. To further illustrate the correlation between wave packet motion and transient signal intensity, studies of three diatomic (or pseudodiatomic) molecules are described below. This research was carried out in the Zewail laboratories at Caltech using a colliding-pulse, mode-locked, ring dye laser (CPM) pumped by an argon-ion laser. The CPM produced 50-fs pulses centered at 620 nm, and the pulse energy was -300 µJ after further amplification with a Nd:YAGpumped pulsed-dye amplifier (PDA) operating at 20 Hz [RoM88]. Dantus et al. 's inaugural fs chemical study [Dan87] investigated the dynamics of a pseudodiatomic molecule on a dissociative PES [Dan88]. ICN stored in a slow-flow sample cell was excited from the ground state up to the A continuum using a Ap" of 306 nm. Probe wavelengths around 390 nm transferred the wave packet to a higher-energy dissociative PES, and LIF signal of free CN was collected from this state. With Apr tuned Chapter One: Time-Resolved Diffraction Studies 7 to the red, 391.4 nm, the probe laser sampled the A continuum near the ground-state internuclear separation of the I and CN species (2. 7 5 A). The Ff S transient showed a fast rise and complete decay centered near t0 , indicating that the wave packet was present in the sampled region immediately after the pump laser excitation, but did not remain there. (This transient is similar to the example in Figure 1-4 with Ap, equal to Ap,1.) When A,p, was tuned to 388.5 nm (the CN bandhead, analogous to AM in Figure 1-4), the rise of the FfS transient was delayed 205 fs after t0 , and it did not decay. The wave packet needed time to evolve into the sampled region of the PES, but then remained there as a stable product since R(I· •-CN) remained large. Transients from probe wavelengths between 388.5 nm and 391.4 nm had a starting delay shorter than 205 fs, and the sharp rise was followed by a decay to an asymptotic intensity level (Figure 1-4, Middle). In these cases, the bandwidth of the probe laser was wide enough to sample some of the stable CN product, but the signal intensity was greatest at an intermediate time, when the wave packet passed through an R(l··•CN) between 2.75 Aand ~4 A. Studies of ICN provided direct evidence of wave packet motion along the dissociative channel of the A continuum. The time scale of this half-collision reaction (Eq. 1.1) was found to be ~200 fs, and the lifetime of the [l··•CN] t transition state was estimated to be ~50 fs from additional experiments and analysis [Dan88] . Bound diatomic systems, like V1b in Figure 1-3, have also been studied. For example, a pump wavelength of 620 nm excites ground-state molecular iodine up to the B-state potential well [Bow89], [Dan90]. After probing the B-state in the near UV, fluorescence emission from higher PESs serve as the FfS signal. Experiments were conducted on Ii both in a cell and a Chapter One: Time-Resolved Diffraction Studies 8 a Experimental - Molecu lar Iodine molecular beam. --l 1- 300 Is As shown in Figure 1-5, when Ap, is 310 nm, the transient exhibits strong oscillations with a period of 300 fs. For the FfS signal to 5 ps oscillate, the wave packet must be moving in and out of the probe-sampling region on the E- h Theoretical - Two Vibrational Motions ~ I- 300 Is state: the classical interpretation is that the iodine molecule is vibrating. The 10-ps periodic envelope also seen in Figure 1-5 is a Time dela y (fs) result of imperfect phase matching between the excited vibrational states. The PES is not a true harmonic oscillator, and frequencies are quite not the vibrational Figure 1-5: (Top) FTS transients showing real-time vibrational motion of molecular iodine. Apu = 620 nm; Ap, = 310 nm. (Bottom) Calculated results using the same vibrational frequencies. This figure was borrowed from [Dan90]. commensurate because of the asymmetry. Shifting Ap11 to the blue creates a wave packet from vibrational states of higher v, and the period of the FfS signal is longer, again due to asymmetry. Spectral analysis on the vibrational (and also rotational) transients from a range of Ap11 can reveal the shape of the intermediate PES [BeR89], [Gru90], [Gru93]. Shifting the probe wavelength does not alter the period of the oscillations, nor should it be expected to since the probe pulse merely samples the dynamical process initiated by the pump pulse. Although the dynamics are unchanged, the form in which they are presented is affected by choice of Ap,. Shifting Ap, to 390 nm produces molecular iodine oscillations with deeper amplitudes [Bow89]; at 390 nm, the FfS signal samples the edge of the B-state potential well, and the wave packet can move almost completely Chapter One: Time-Resolved Diffraction Studies 9 4 out of the probe window. Similar oscillatory transients have been observed with Na*+I pump-probe 2 experiments of sodium iodide in a heated cell [RoT89]. The ground ionic Nal state intersects the lowest (dissociative) covalent state ·at 7 A. The two PES have a strong, adiabatic interaction, making an -2 avoided crossing, and the covalent and ionic PESs mix to form a long, flat, partially-bound potential well -4'-------'----L.---....L..--20 10 15 5 o Internuclear distance (A) approximately 3 eV (24,200 cm- 1) above the bottom of the ground ionic state (Figure 1-6). Rosker and co-workers, using pump wavelengths between 310 and 390 nm and probe wavelengths Figure 1-6: Potential energy surfaces of sodium iodide. The ground-state ionic PES intersects the lowest covalent state at 7 A, creating an avoided crossing with -10% leakage. +: Inter-nuclear separations accessed by pump laser A1. •: Internuclear separations accessed by probe laser A-2- ◊: Outer turning points obtained from FTS transients. This figure was borrowed from [Mok90]. between 590 and 700 nm, detected LIF from free sodium atoms (the D line, 589 nm). Transients showed regular oscillations with gradually decaying amplitudes: 10% of the wave packet "leaked" through the avoided crossing during each pass. As with Ii, the period of the Nal wave packet motion increased when A pu was shifted to the blue due to asymmetry in the potential. With sufficient temporal resolution, however, new features were observed as a function of Ap,. Oscillations in the transient split into doublets, with Chapter One: Time-Resolved Diffraction Studies the separation between 10 doublets ~ !!l increasing as Apr decreased (Figure 1- ·g 7) fi [Mok90], [Con96]. Probe c wavelengths on the order of 620 nm -~ ] sample the intermediate PES in the ~ ,_J reg10n of 4-7 A (Figure 1-6), and 0.0 longer wavelengths access regions closer to the ionic turning point. The doublets in Figure 1-7 therefore show the back-and-forth passage of the 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 Time Delay (ps) Figure 1-7: Experimental FTS transients of sodium iodide for different pump and probe wavelengths. (a) Pump wavelength varies while AQ = 605 nm. Oscillation period increases as 11,1 shifts to the blue. (b) Probe wavelength varies while 11,1 = 391 nm. Doublet splitting increases as AQ shifts to the blue. This figure was borrowed from [Con96]. wave packet during each cycle. The doublet separation is smaller when the probe-sampling window is closer to the outer limit of the oscillatory motion. Part of the appeal of FTS data for diatomic systems is the ease with which the transients lend themselves to classical dynamics interpretations. With each peak and valley in the transient, one can envision a pair of atomic nuclei undergoing one vibration, like two balls connected by a spring. Furthermore, the Nal studies have hinted that complete R(t) surfaces might be generated to show the evolution of the internuclear coordinate as a function of time (Figure 1-8). As described above, varying Apr yields temporal slices at different R(Na-I) with a spatial resolution 11R on the order of 0.5 A [Mok90], [Con96]. A complete R(t) surface could be pieced together by varying Apr and amassing a set of these temporal slices. Chapter One: Time-Resolved Diffraction Studies 11 The tremendous power of FfS resides in its ability to time-resolve the many facets of energy transfer, and the extrapolation dynamics into of R(t) diatomic measurements represents but a small part of the information obtained through timeresolved spectroscopy. Complete R(t) surfaces would help complex interaction dynamical processes, show the between energy, and structure, and might serve as maps for controlling reaction products with laser-selective chemistry (see, for Figure 1-8: (Top) Classical mechanics simulation of sodium iodide wave packet motion showing R(t) . (Bottom) Examples of R(t) slices obtained with FTS spectroscopy by varying the probe wavelength. This figure was borrowed from [Mok90]. example, [War93], [Kaw95]). But in order to pursue this tangent of ultrafast structure determination further, new time-resolved techniques must be developed. Experimentalists invoking FfS for the measurement of R(t) face a number of difficulties. Spectroscopic transients show how a molecule interacts with energy as a function of time. When a molecule absorbs a photon of energy hcf')..,Pu at time to, the FfS signal reports the probability that the molecule will absorb a second photon of energy hc!APr at some later time t + t0 . For diatomic systems, the pump and probe laser pulses link one-dimensional potential energy surfaces, and energy can be Chapter One: Time-Resolved Diffraction Studies correlated with specific R. 12 The spatial resolution till depends on the probe laser >, O') ,_ (]) energy bandwidth and the slope of the C w ('CS V2 :;:::; potential energy difference curve, C (]) +-' 0 d(V2 -v1 )/dR, so till is not easy to control. CL V1 As an extreme example, probing Nal at the sodium D-line transition samples all R(Na-1) on the lowest covalent state from ~8 A out to oo (Figure 1-6), and therefore till is infinite. However, when probing the outer ionic surface in the same region of R(Na-1), till is only a fraction of an Angstr0m because d(V2 -v1 )/dR is large. .. - E' lJ.J -<l Internuclear Separation (A) Figure 1-9: (Top) Model potential energy surfaces. Wave packet dynamics on Vi are probed by excitation to V2. (Bottom) Energy difference, t,,.E = V2 - Vi. Probe photon with energy E? would transfer wave packet population from two different regions of internuclear separation. Figure 1-9 shows that even for a simple diatomic system, the mapping between energy and R is not necessarily one-to-one. According to the difference curve, M, a transient recorded with a probe laser pulse of energy E' would mix wave packet densities from two different regions along V 1. In addition, one transient does not necessarily show all the wave packet density for a given R. In the Nal system, part of the wave packet leaks through the avoided crossing during each cycle, and at least two different probe wavelengths must be used to sample the populations of both the ionic and covalent states in order to collect the total wave packet density beyond 7 A. Finally, assignment of absolute amplitudes to FTS R(t) surfaces depends on many factors , such as laser intensity, Chapter One: Time-Resolved Diffraction Studies 13 't (CH3I) = 175 ± 10 fs 't (CD3I) = 325 ± 15 fs -500 0 500 1000 1500 2000 Time Delay· (fs) Figure 1-10: FTS transients of methyl iodide after two-photon excitation at 315 nm to a dissociative Rydberg state. Population was probed by ionizing the Rydberg state with 618 nm and monitoring the parent mass. The decay of CD3I is almost twice as slow as CH 3I. This figure was borrowed from [Dan91 a]. bandwidth, and Franck-Condon overlap between the two states. All these factors vary with Ap,. For a molecular system of higher complexity, the mapping between probe laser energy and R is no longer one-to-one, or even two-to-one. (Now R represents the set of all internuclear coordinates.) Instead, for a given Ap, there are continuous ranges of different molecular configurations linked by vertical transitions because the potential energy surfaces are multi-dimensional. An excellent example of the interpretational puzzles which can result is found in the FfS studies of methyl iodide. CH3I in a molecular beam was excited into Rydberg states by two-photon absorption, with "-Pu between 275 nm and 315 nm [Dan91a]. Parents and products were probed at 620 nm and detected through TOF mass spectrometry. The pump laser initiated a half-collision (Eq. 1. 1), in Chapter One: Time-Resolved Diffraction Studies which the CH 3I molecule dissociates directly into an iodine atom and a methyl radical. 14 3.5 3.0 When monitoring the CH3I+ mass, the FfS signal 2.0 showed a sharp buildup at to followed by a fast decay with a 1.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7 .0 R(C-I) lifetime 't of 175 fs (Figure 1-10). If methyl iodide is treated as a pseudodiatornic, like ICN, then the Figure 1-11 : Two-dimensional quantum calculation of methyl iodide wave packet dynamics approximately 30 fs after excitation. Motion proceeds first along the C-H coordinate, and then along the C-1 coordinate. This figure was borrowed from [Guo94]. signal decay can be interpreted as the motion of the wave packet passing through the probe-sampling window as the CHr ••I stretch increases. But Dantus et al. repeated their experiment with a deuterated sample, which changed the mass of the methyl moiety by 33%. The time constant of the CD 3I+ decay increased to 325 fs, almost doubling, an indication that other reaction coordinates had to be involved in the dissociation process. Two-dimensional quantum calculations combined with additional experiments showed that the reaction may actually start along a C-H stretch (Figure 1-11) before progressing down the CH 3 .. ·1 coordinate [Jan93], [Guo94] . This would explain the strong dependence of 't on the hydrogen and deuterium masses. So while the FfS signal clearly revealed changes in the CH3I and CD 3I Rydberg state populations, their energies, and the time scale of the transition states had never been obtained before - a description of the reaction mechanism which it was also true that a key aspect of the mechanism was not immediately apparent: how the methyl iodide structure responded during dissociation. Chapter One: Time-Resolved Diffraction Studies 15 Explicit determination of R(t) surfaces with ultrafast temporal resolution would complement the varieties of data obtained by femtosecond transition-state spectroscopy. To do this, a new experimental approach must satisfy four conditions: 1. The experiment must yield structural parameters at the microscopic level. 2. The experiment must have general application to a variety of chemical species. 3. The experiment must be applicable to the study of isolated molecular systems (gas-phase or clusters). 4. The experiment must be time-resolved, and the temporal resolution should approach the fs regime. Creation of the wave packet with a pump laser pulse would still be an integral part of any ultrafast structural-determination experiment; fs time resolution is useless unless some form of coherent behavior has been initialized. The question then remains of how to find the structure of molecules on the intermediate potential V 1 without inviting the aforementioned difficulties of exciting to V2 using a probe laser pulse. In effect, the structural measurement itself must be ultrafast. Although mass spectrometry has proven invaluable in many FTS experiments (see, e.g., [Ped94]), separating and detecting positively-charged ions takes microseconds or longer; furthermore, the structural data returned by MS is qualitative. Other common non-spectroscopic techniques, like nuclear magnetic resonance and molecular dipole measurements [Dom92], [RoB87], [Whe59] are also either "slow" processes (unsuitable as a probe) or provide limited structural information. Diffraction methods have the unique ability of revealing a complete set of internuclear coordinates with very high spatial resolution (<0.01 A) [Dom92], [Sim73], Chapter One: Time-Resolved Diffraction Studies 16 [Wor73] . In these techniques, a monochromatic particle beam elastically scatters from the sample (gas, liquid, or solid), and microscopic dimensions are magnified to the macroscopic level through interference effects. Since the time scale of the scattering process is on the order of attoseconds (10- 18 s), diffraction is at least theoretically fast enough to replace the probe laser mechanism in FfS and yield R(t) with ultrafast resolution. This is, of course, contingent on generating an ultrafast pulse of scattering particles synchronized to the excitation laser pulse. The next section provides a brief, phenomenological description of how diffraction "works," its historical development, and a few introductory details on the feasibility of determining R(t) with an ultrafast diffraction experiment. 1.3 Structure Determination With Diffraction Techniques The Van Nostrand Scientific Encyclopedia defines diffraction as: In any wave disturbance, the interference pattern resulting from the rays passing through different parts of an opening, or coming from different points around an opaque object, as they unite at each point. [CoD83] The definition of diffraction is narrower in the context of structure determination, referring to the interference pattern created by the overlap of scattered intensity from two or more openings or objects. Most physics students are introduced to multi-body diffraction through Young's classic double-slit experiment [Sha59], [Hal78]. beam of visible light with wavelength Ao= A monochromatic 2n/!k ! is incident on a screen containing two 0 slits ("openings") separated by a distance d (Figure 1-12). The slit widths are much smaller than Ao, so both slits diffract the incident light, acting like a pair of phase-matched Chapter One: Time-Resolved Diffraction Studies 17 point sources. The diffracted light is detected at a distance L from the slits, L >> d. The difference in optical path length U from each slit to the detector varies as a function of position along the detector screen. Since the sources are coherent (phase-matched), the continuous change in U correlates to a periodic change in phase: when M.., is an integer multiple of Ao, the electric field vectors from the two sources add, but when M.., is equal to (n + ½)Ao (n an integer), the electric field vectors cancel. As a result, the total light intensity I on the screen cycles through maxima and minima, and I can be related to the scattering angle 0 by: 1(0) = F(0)cos'( ~ sin0J where F(0) is the diffraction intensity from a single-slit. (1.2) As shown in Eq. 1.2, the frequency of the oscillations depends on the distance separating the two slits and the wavelength of the light, so d can be determined by analyzing /(0) if Ao is known. In addition, the ratio d!Ao must not be either too small or too large. If d < Ao/2, then the interference pattern will not extend out to the first minimum; if d >> Ao, then measurement of the fringe spacing may be limited by the resolution of the detector. The physical principles intrinsic to Young's experiment apply at the microscopic level, too. An atom can take the role of an "opaque object" and diffract an incident, mono-chromatic wave. Interference effects in the intensity scattered from two neighboring atoms (Figure 1-12) can be detected in the far field, provided that the wavelength A is the same order of magnitude or smaller than the internuclear separation r. If A is known, then r can be determined from the intensity scattered by the atomic pair, just like d is determined from the light intensity scattered by a pair of slits. Chapter One: Time-Resolved Diffraction Studies To resolve internuclear 18 Young's Double-Slit Experiment Scattered Light Intensity distances, A should be on the order of 1 A or less, which corresponds to the x-ray electromagnetic region of the spectrum (-10 keV / photon or greater). Max Incident Visible Light u von Laue recognized that this <I> • <I> 0 wavelength was comparable to theoretical estimates for interplanar spacing of the single Atomic Scale Diffraction Incident Beam crystals, and he predicted that crystals might serve as x-ray diffraction gratings. Laue and coworkers subsequently recorded the first x-ray diffraction pattern in 1912 using CuSO4 -5H2O [Bij69]. a crystalline sample [Fri12], ➔ <( Figure 1-12: Examples of diffraction with two scattering centers. (Top) Young's classic double-slit experiment. Visible monochromatic light creates an interference pattern after scattering from two slits. (Bottom) Similar interference patterns are created when a particle beam (x-rays, electrons, neutrons) with 'A, on the order of 1 A scatters from two atoms. Because of the long- range order present in the crystal, the diffracted intensity formed a pattern of isolated spots (a Laue pattern) rather than the oscillatory signal found in Young's experiment. Shortly after Laue' s work was published, Bragg identified the simple mathematical relationship which must be satisfied for diffraction to occur [BrW12] : Chapter One: Time-Resolved Diffraction Studies 2d sin0 19 = nA (1.3) In Eq. 1.3, d is the interplanar spacing, n is an integer, and 0 is the angle between the incident x-ray beam and the crystal surface. Debye and Scherrer, and also Hull, demonstrated that diffraction images could be detected from powder samples containing a random mix of crystal orientations [Debl6], [HuAl 7] . Powder samples do have longrange order, in the sense that the microcrystals which make up the powder are large regions of regular structure on the microscopic scale. However, unlike a single crystal, a powder sample is orientationally isotropic with respect to the incident x-rays. As a result, the diffraction images (called Debye-Scherrer patterns) are concentric, sharp rings rather than discrete spots. Each ring corresponds to a different interplanar spacing, and the ring diameter can also be found using Bragg's equation (Eq. 1.3). In 1915, Debye predicted that structural information would be present in the diffraction images of amorphous samples, too [Deb15], [Deb88]. Even though an amorphous sample, such as a gas, has neither orientational nor long-range order, Debye showed mathematically that the intramolecular order would still lead to an interference pattern. The nature of these patterns would be similar to the diffraction fringes formed with Young's double-slit experiment (Figure 1-12). Debye proved himself correct fourteen years later by diffracting Cu-Ka x-ray radiation ( 1.54 A) with carbon tetrachloride vapor [Deb29] . From the spacing of the gently oscillating rings in the diffraction pattern, the Cl·• •Cl internuclear separation was estimated to be 3.3 A (accepted value today: 2.888 A [Mor6Oa]): The technique was applied to several other molecules [Deb3O] even though exposure times of many hours were required to record one image. Nearly all present day x-ray diffraction experiments involve solid or liquid phases Chapter One: Time-Resolved Diffraction Studies 20 where the scattering efficiency is high [Klu74], [Lad93], [Glu94]. Elastic scattering occurs when an incident x-ray initiates a nonresonant oscillation in an unbound atomic electron (bonded hydrogen atoms do not scatter x-rays). The oscillator re-emits an x-ray of the same wavelength, but not necessarily in the same direction - the atom is similar to a point source. Elastic scattering cross sections <ie depend on A and increase strongly with Z: at 1.2 A (10 keV), <ie for oxygen (Z =8) is 6.8 barns• and <ie for manganese (Z =25) is 100 barns [Hub79]. Note that the photoelectric absorption cross section 't for x-rays is a few orders of magnitude greater (102- 104 barns) than the elastic scattering cross section [Hub80]. X-ray beams are created with plasmas, radioactive materials, and particle accelerators, but the most common laboratory sources are peak emission lines generated by bombarding metals with high-energy electrons (x-ray diodes). Diffraction effects are not confined to photon beams. In 1925, de Broglie published his theory that particles with momentum p have wavelengths given by [BrL25]: A = h/p = h/mv = h/.J2mKE (1.4) According to Eq. 1.4, a beam of electrons with 150 eV of kinetic energy has an atomicscale wavelength of 1.0 A. The wave nature of electrons was unequivocally demonstrated in 1927 by both Thomson and Reid [Tho27], and Davisson and Germer [Dav27]. Thomson and Reid diffracted high energy electrons (10 keV, Ae = 0.12 A) from a celluloid film; Davisson and Germer used a lower energy range (up to 370 eV, Ae = 0.64 A) and a thin nickel single crystal target. Subsequent high-energy experiments on metal foils • 1 barn = 10·28 m 2 = 10·24 cm2 = 10·8 A2 Chapter One: Time-Resolved Diffraction Studies 21 produced ring images analogous to Debye-Scherrer patterns, and the measured interplanar spacings were in agreement with results from x-ray experiments [Tho28a], [Tho28b]. Thin samples were necessary because the elastic scattering cross section for electrons is much larger than for x-rays. An incident electron interacts directly with the atomic nucleus, diffracting due to the Coulombic attraction between the negativelycharged electron and the positively-charged nucleus. Repulsion between incident electrons and the atomic and molecular electron clouds only affects small-angle scattering, where the impact parameter distance relative to the nucleus is large. As with x-rays, ae for electrons depends on Ae and Z; at 10 ke V (Ae = 0.12 A), cre for oxygen is 7x 106 barns and 7 cre for manganese is 4x10 barns [Bon74], [lti90]. (See Eq. 2.55a in 2.1.4 for a method of estimating cre.) In 1930, Hermann Mark, an x-ray crystallographer for the German chemical company Farben, juxtaposed Debye's recent CCLi-vapor x-ray patterns with the experimental evidence for the wave-nature of electrons. Mark wrote: It occurred to me that the scattering of fast electrons from gases should lead to much shorter exposure times, to a much better control of the experimental conditions, and to the possibility of longer systematic studies of the interatomic distances. When I asked Dr. Raimund Wierl of his opinion he agreed that such experiments would be very interesting but certainly not easy. [Mar88] Together, Mark and Wierl recorded the first gas-phase electron diffraction pattern in 1930 [Mar30]. Their experiment used 36-keV electrons (Ae = 0.064 A), a carbon tetrachloride sample, and a three-second exposure time (as compared with the 20-hour exposure time for Debye's first x-ray experiment [Deb29]). Mark and Wierl initially reported a Cl·· -Cl distance of 3.14 A, and later studies improved the value to 2.98 A [Wie31]. But Mark and Wierl's employer, Farben, felt that GED was unprofitable and discontinued their Chapter One: Time-Resolved Diffraction Studies 22 experiments. Mark passed the details of their technique on to Linus Pauling, visiting from the United States, and upon returning to the California Institute of Technology, Pauling promptly built an apparatus to further his research on the nature of the chemical bond [Pau95]. Other physical chemistry laboratories rapidly invested in the technique as well. The third particle commonly used for diffraction experiments is the neutron, whose wave nature was confirmed in 1936 [HaH36], [Mit36]. Molecular structure studies with low-energy neutron beams have been found to complement data provided by x-ray and electron diffraction because neutrons interact primarily with the atomic nuclei, colliding like hard spheres (although there can be penetration of the neutron into the nucleus) [Lov84], [Dac78], [Bac77]. The elastic scattering cross-section is on the order of 10 barns with almost no dependence on An, Part of the interest in neutron diffraction is that cre varies strongly and unsystematically with Z, even between isotopes of the same Z. For example, hydrogen (which does not scatter x-rays) has a cre of 1.8 barns, while cre for deuterium is 5.6 barns, and cre for oxygen is 4.2 barns [Lov84], [Bac77]. Most diffraction experiments use thermalized neutrons emitted from nuclear reactors with kinetic energy of -0.025 eV (An= 1.8 A). At these energies the neutron translational velocity is 2.2 km/s, and neutron diffraction experiments can reveal intramolecular atomic velocities through Doppler shift measurements. X-ray, electron, and neutron diffraction certainly satisfy the first two of the four requirements identified in 1.2 as necessary for successful determination of R(t): scattered particle intensities reveal internuclear separations for both bonded and non-bonded atoms, and any molecule will serve as a scattering center. Collectively, diffraction techniques using the three particles can be applied to most chemical systems, which satisfies the third Chapter One: Time-Resolved Diffraction Studies 23 BS Amplified Femtosecond Laser TS M M 6L t Scatterer Source Sample Detector Figure 1-13: Experimental schematic for pump-probe time-resolved diffraction. BS: beamsplitter; M: mirror; WG : wavelength tuning optics; TS: computer-controlled translation state; L: lens. requirement. Electron experiments are better suited for gases, thin films, and surfaces because of the high electron scattering cross section; m contrast, x-ray and neutron diffraction are better for liquids and solids, although gas-phase experiments are possible if the particle flux is very large. The remaining criterion m 1.2 demands ultrafast temporal resolution from the experiment, which means incorporating the diffraction method into a pump-probe type of arrangement. A general scheme for time-resolved diffraction is shown in Figure 1-13. Output from an amplified femtosecond laser is split into a Mach-Zehnder-like optical arrangement. Just as in the FTS scheme (Figure 1-2), one arm serves as the pump laser and initiates coherent behavior in the sample. The second arm, however, generates an ultrafast pulse of either x-rays, electrons, or neutrons. This pulse flies towards the laserexcited sample, scatters, and the scattered particles are detected. The relative time delay 11t between the arrival of the pump laser and the scatterer pulse is adjusted with an optical delay line. Generation of the scatterer pulse is of key importance. Despite the interesting structural and dynamical information neutron diffraction provides, the technique is Chapter One: Time-Resolved Diffraction Studies 24 unsuitable for time-resolved structural measurements. Even if an ultrafast neutron source were available (the nuclear femto-reactor?) and synchronized with the pump laser, the experimental temporal resolution would be limited to nanoseconds because of severe velocity mismatch between the pump laser and the neutron pulse [WiT68], [Wil93]. Ultrafast pulses of x-rays and electrons, on the other hand, have seen much development, and the next section (1.4) relates the state-of-the-art in time-resolved x-ray experiments. Unfortunately, the flux from most x-ray sources is not high enough for gas-phase structural determination (the third and fourth criteria of 1.2). Electron scattering is the remaining diffraction option. Compared with x-rays, electron pulses are simple to generate and focus, but their temporal resolution is limited by space-charge effects. Most of the ultrafast electron diffraction experiments have been performed on solids where scattering probabilities are high (discussed in 1.5), but several groups have worked towards improving the speed of gas-phase electron diffraction. The evolution of timeresolved GED, from long-lived reactive intermediates out to the nanosecond time scale, is described in 1.6. Finally, as prologue to the remainder of this thesis, 1.7 presents the topic of ultrafast gas-phase electron diffraction and its initial development in the Zewail laboratories. 1.4 Picosecond X-Ray Diffraction X-rays are obtained from radioactive materials, plasmas, particle accelerators, and electron-bombarded metals [Klu74], [Glu94]. Radioactive decay is the only x-ray source which does not depend on an outside triggering event; as a result, all sources except 25 Chapter One: Time-Resolved Diffraction Studies radioactivity have been successfully adapted to ultrafast experiments. Bergsma et al. calculated theoretical time-resolved x-ray diffraction patterns for iodine in solution shortly before the first FfS transient was reported [Ber86]. They proposed making ps x-ray pulses with a laser-triggered x-ray diode: a fs laser pulse would generate an ultrafast electron pulse through the photoelectric effect; this electron pulse would be accelerated towards a metal target, creating characteristic x-rays upon collision. The emitted x-rays should have a temporal resolution similar to the electron pulse. Early x-ray diodes achieved pulse widths of 100 ps, although the results were unpublished [Ber86], [WiS--]. Anderson and co-workers created 20-ps x-ray pulses with a similar arrangement [And93]. A 10-ps laser pulse (2.5 mJ, 193 nm, 300 Hz) generated electrons from an aluminum photocathode. These electrons then bombarded a copper anode at 70 ke V, and the resulting Cu Ka flux was ~ 100 photons / cm2 / shot, as measured 40 cm from the source. The x-ray pulses have been diffracted from Pt(l 11) and Au(l 11) crystals in laserheating experiments with a total temporal resolution of 50 to 100 ps [Tom95a]. Recently, the researchers have shortened the x-ray pulse duration by using 1-ps laser pulses [Tom95b]. Faster x-ray pulses have been created from plasmas. A high-intensity fs laser superheats and ionizes a target (usually a metal surface), and the resulting plasma emits a burst of broadband x-ray radiation before being quenched by temperature and pressure gradients [Mur94]. Pico second and subpicosecond pulses have been reported in the soft x-ray region (~300 eV, 'A= ~40 A) using silicon [Mur89], gold [She93], and liquid gallium targets [ScJ94], and Murnane et al. created x-rays with nearly 1.9 keV ('A = 6.5 A) of energy using a porous aluminum target [Mur94]. Other researchers have generated hard Chapter One: Time-Resolved Diffraction Studies 26 x-rays of 4 to 5 keV (A = 2.5 A) by multiphoton ionization of xenon van der Waals clusters with a 300 fs laser [McP94]. In this approach, the rapid excitation forms some xenon ions with inner-shell vacancies, which, when filled, cause the x-ray emission. The temporal duration of the emitted x-rays was not reported. Raksi and co-workers have conducted an ultrafast near-edge x-ray absorption study of gaseous SF6 molecules using a plasma source [Rak96]. Molybdenum or tantalum metal targets were illuminated with intense 400-fs laser pulses (500 mJ, 530 nm, 0.02 Hz) to create plasma-emitted x-rays around 2.5 keV (A= 5 A) . The x-ray pulses had durations of 1.5-3 ps as determined with a streak camera. A second high-intensity laser pulse photodissociated SF6 into fragment atoms and ions; Raksi et al. observed this process by monitoring the transmission of x-rays near the sulfur K edge at 2.48 keV. More x-rays were transmitted following dissociation because destruction of the molecule breaks the absorption resonance, and the rise in transmission took place within ~2 ps. Typically 1020 photons were detected per shot over the bandwidth of the absorption region. The temporal resolutions of x-ray pulses created from ultrafast diodes and plasmas are limited by the intermediaries of their generation: space-charge effects in the intense electron pulse of the x-ray diode broaden the pulse width [And93], and plasma x-ray pulses are only as fast as the quenching time of the plasma [Mur94], [Rak96]. Schoenlein et al. have recently reported the creation of 300-fs x-ray pulses by Thomson-scattering 50- fs laser pulses (100 mJ, 800 nm, 2 Hz) off of 50-MeV electrons in a linear accelerator [ScR96]. Since the, interaction time between an incident photon and an electron is instantaneous, the temporal resolution is limited only by the geometry of the collision the best resolution comes when the focused beams intersect at 90° [Kim94]. The x-ray Chapter One: Time-Resolved Diffraction Studies 27 4 flux was ~5x10 per shot, spanning a broad energy range of 20 to 30 keV (A= 0.6 to 0.4 A). The authors have obtained a static diffraction pattern from a Si(l 11) surface, recording one diffracted x-ray per shot. Zholents and Zolotorev have proposed a method for generating ultrafast x-ray pulses from a synchrotron source [ZhA96]. They suggest using an intense 50-fs laser to transversely displace a portion of the electron pulse circulating within the storage ring. Their calculations show that the radiation emitted by the displaced electron bunch will have a pulse width of 100 fs, although difficulties in synchronizing this radiation with an external pump laser may limit the actual experimental temporal resolution. Between x-ray diodes, laser-induced plasmas, and high-energy particle accelerators, ultrafast soft and hard x-ray pulses are available for experiments. At present, however, the faster sources (plasmas and accelerators) emit only broadband radiation, and not the monochromatic beam desired for diffraction. Furthermore, all sources produce xray fluxes around 102 to 104 photons per shot or less, and often with low repetition rates. While this flux is sufficient for surface diffraction and absorption experiments, orders of magnitude more intensity would be required to study isolated molecular systems. Application of ultrafast x-ray pulses to gas-phase diffraction experiments does not seem possible with current technology. 1.5 Picosecond Electron Diffraction: Surfaces and Films Electron beam generation methods include the photoelectric effect, thermionic emission, and field emission, all of which can be adapted into time-resolved pump-probe Chapter One: Time-Resolved Diffraction Studies 28 experiments. The most common approach is to illuminate a photocathode (metal or alkali) with a low-intensity laser pulse (µJ) and extract the photoelectrons with an accelerating potential. The photon-to-electron conversion process is thought to be extremely fast fast enough that the electron pulse should have the same temporal and spatial intensity profiles as the incident laser pulse, even on the fs time scale. This fact motivated some of the earliest research involving ultrafast electron pulses: streak camera technology. Standard ultrafast autocorrelation techniques require multiple laser pulses, and the true temporal profile cannot be observed (although single-shot measurements are becoming more common [Bru91], [Kan93]). The streak camera is an instrument which directly measures the duration of individual ultrafast laser pulses. A laser pulse illuminates the streak camera's photocathode, creating a photoelectron duplicate which is accelerated towards a detection screen [Men92b], [RoP92]. Before the electrons reach the detector, however, a fast, high-voltage ramp converts the temporal profile into a spatial profile. The detected image shows both the temporal width and the shape of the electron pulse, and therefore characterizes the original laser pulse. Streak cameras with resolutions of a few picoseconds were developed over a quarter century ago [Bra71], [ScM71], and subpicosecond resolution was achieved a few years later [Bra75]. The temporal resolution of streak cameras, or any time-resolved electron experiment for that matter, is limited by space-charge effects. Unlike a pulse of photons, a pulse of electrons is self-dispersing because Coulombic repulsion spatially broadens the electron pulse along all axes, including the temporal axis. Ultimately there is a tradeoff between electron number density and temporal pulse width; subpicosecond pulses typically contain fewer than 103 electrons (see, e.g., [Suy88]). This is comparable to the flux from Chapter One: Time-Resolved Diffraction Studies 29 the ultrafast x-ray sources described in 1.4. Given that ultrafast electron and x-ray fluxes are essentially equal, a time-resolved gas-phase diffraction experiment has a much better likelihood of succeeding if electrons are used rather than x-rays. Certainly the electron source is more straightforward and less expensive, requiring neither state-of-the-art, high-intensity lasers nor large-scale accelerators. Collimating and focusing electron beams is simpler, too, and monochromaticity is often better than 0.01 %, as determined by the stability of the voltage sources and the initial electron energy distribution [Har88a], [Cow90]. This monochromaticity translates as a de Broglie bandwidth of less than 1x10-5 A at 15 keV (Ae = 0.10 A), in contrast to reported x-ray bandwidths of ~0.1 A (1.4). Most importantly, the atomic elastic scattering cross sections of electrons are five orders of magnitude greater than those of x-rays, and the probability of electron attachment is very small. (Recall T.!cre for x-rays is ~ 100.) Thus, even when sample thickness is adjusted to compensate for CTe, an x-ray diffraction experiment would still require 102 to 105 times more particles to generate the same elastically scattered flux than in an electron diffraction experiment. Diffraction studies with picosecond electron pulses have a history extending back at least to 1982, when Mourou and co-workers modified a streak camera to record the static transmission diffraction pattern of an aluminum foil [Mou82], [WiS82]. The authors illuminated an Al photocathode with the fourth harmonic of an Nd:YAG laser (266 nm), generating a single, 100-ps electron pulse. The electron pulse was accelerated to 20 ke V and directed at the 150-A foil, whose thickness was chosen to average one elastic collision per incident electron. The streak camera's deflection plates were disabled. Scattered Chapter One: Time-Resolved Diffraction Studies 30 electron intensity was detected on the streak camera's phosphor screen and amplified by 104 with an image intensifier. Analysis of the ring pattern yielded a lattice constant in good agreement with the known value. Two years later, the authors reported the first time-resolved electron diffraction experiment with picosecond resolution [WiS84]. Using a gold photocathode and an acceleration voltage of 25 keV, Williamson et al. created 20-ps electron pulses with approximately 104 electrons per pulse. Single-shot transmission patterns of Al foils were recorded as a function ohime delay between the electron pulse and a 1064-nm laser pulse incident on the foil. Each foil was used only once. At a laser fluence of 13 mJ/cm2 , the foils melted within the time resolution of the experiment (the Debye-Scherer diffraction rings disappeared due to the phase transformation). The authors then varied the laser fluence and measured the time-dependence of melting on superheating. In order to study isothermal melting dynamics at the surfaces of bulk materials, the electron beam must be directed towards the sample at a grazing angle of a few degrees using a technique known as reflection high-energy electron diffraction (RHEED). Some authors have reported RHEED experiments with temporal resolutions of a few nanoseconds [Kit93], [Sai88], but over the past ten years Elsayed-Ali and co-workers have pushed the temporal resolution into the picosecond regime [Els95]. Electron pulses with energies of 15 to 20 ke V were created in a home-built electron gun based on conventional streak cameras [Els88], [Els90]. The gold photocathode was illuminated with 200-ps, 266-nm output from a Nd:YAG laser, and each electron pulse, also 200 ps, contained approximately 105 electrons. After scattering from the surface of a single crystal target mounted on a rotatable, temperature-controlled positioning stage, the Chapter One: Time-Resolved Diffraction Studies 31 diffracted electrons activated a P47 phosphor. Fluorescence emission from the phosphor was amplified by an image intensifier, collected on a linear diode array, and digitized. The authors monitored RHEED spot intensities as a function of time delay between the electron pulse and a 1064-nm laser pulse which heated the crystalline sample. Correlation between the time-resolved melting dynamics and surface temperatures were made by recording the static RHEED patterns from stage-heated samples [Els95]. Recently the apparatus has been redesigned for experiments with resolution of a few picoseconds [Aes95a], [Aes95b]. Improvements include a new 2-ps dye laser pumped by a Nd:YLF master oscillator, a redesigned electron gun with a 400-A silver photocathode, and a single-electron detection system based on direct-bombardment of microchannel plates and two-dimensional CCD imaging. A static RHEED pattern from Ni(l00) has been recorded using 5-ps electron pulses containing~ 104 electrons per pulse. 1.6 Time-Resolved Gas-Phase Electron Diffraction Pioneering ultrafast x-ray and electron diffraction experiments both suffer from low incident particle flux, and the selection of surfaces and foils as scattering targets is logical for such studies. Elastic scattering cross sections can approach unity, and the signal-to-noise ratio of the interference patterns is high because of the long-range order intrinsic to a solid sample. In order to obtain R(t) surfaces for fundamental chemical processes, though, the target molecules ought to be isolated chemical systems; the techniques of time-resolved diffraction must be applied to gas-phase samples. This section narrates the historical progression of gas-phase electron diffraction towards faster and Chapter One: Time-Resolved Diffraction Studies 32 faster time scales. 1.6.1 Long-Lived Reaction Intermediates Rudiments of time-resolved GED appeared in the literature over thirty years ago. In 1965, Andersen heated samples of hexaphenylethane and recorded GED patterns from the reversible dissociation product, triphenylmethyl free radical [AnP65]. This was the first reported diffraction study of long-lived intermediates, those species which are highly reactive but can survive repeated collisions with other molecules or the walls of the nozzle system. Other long-lived intermediates whose structures have been determined by shifting reaction equilibria through heat include di-t-butylnitroxide radical, (C4H9)2NO [AnB66a], [AnB66b], and difluoroamino radical, NF2 [Boh67]. Structures of intermediates formed after irreversible thermal decomposition have also been recorded with GED. Schafer identified the indenyl radical (C9H7) while trying to study the parent molecule, diindenyl cobalt [Sch68]. Leggett and co-workers obtained diffraction patterns from the mix of fragments generated by heating tetrahalide methanes to temperatures on the order of 1000 °C [Leg73], [lve74]. Intermediate species in the bromination of ethylene were also observed [Leg74]. While introducing their investigation of CChBr fragmentation products, Leggett et al. noted that: In order to study short-lived species it is necessary to initiate the reaction very close to the scattering volume. [Leg73] They designed a special nozzle which provided thermal energy only to those sample molecules within a few millimeters of the exit orifice. The intent was to preserve the population of highly reactive, intermediates by limiting the number of collisions occurring before diffraction took place. Extrapolating from the statement quoted above, the ideal Chapter One: Time-Resolved Diffraction Studies 33 trigger for a decomposition process would apply energy to the sample molecules during the expansion from the needle tip into the scattering volume so that there would be no post-reaction collisions with the nozzle walls, and collision frequencies between reactive products could be controlled. A laser could approach this experimental ideal. Arvedson and Kohl were the first to impart gas-phase electron diffraction sample molecules with energy using laser excitation [Arv79] . A continuous CO2 laser tuned towards the asymmetric-stretch absorption resonance of sulfur hexafluoride crossed a 38.9-keV electron beam just beneath the exit orifice of the SF6 nozzle system. Diffraction patterns, recorded on photographic plates, showed definite increases in the mean amplitude of vibration of the S-F and F·· •F (cis) stretches. Bartell and co-workers continued with more exhaustive studies of laser-pumped sulfur hexafluoride using a similar apparatus, [Bar80], [Bar81a], [Bar81b] . The authors positioned the electron beam / molecular beam intersection ~300 µm downstream of the laser / molecular beam intersection, allowing 1 µs of flight time for additional intermolecular energy transfer through collisions. They correlated even greater changes in both mean amplitudes of vibration and internuclear separations to the vibrational temperatures, and observed the dependences on laser wavelength and sample pressure (collisional frequency) [Bar84b]. Various theoretical methods were developed to treat the data [Bar84a], [Isc90]. Monts et al. conducted laser-pumped GED experiments similar to the early thermal decomposition studies. 1,2-Dichloroethylene, either cis or trans, was photodissociated in a flow cell using 193-nm output from an ArF excimer laser (10 mJ, 195 Hz) [Mon87]. The flow cell had a retention time of 20 ms, allowing an average of four laser shots during passage. Upon exiting the nozzle, reaction products scattered a Chapter One: Time-Resolved Diffraction Studies 34 continuous 40-keV electron beam, and diffraction intensities were recorded with a linear photodiode array optically coupled to a phosphor screen. The authors found evidence of both isomers in the laser-pumped diffraction patterns, regardless of whether the initial sample was pure cis or pure trans. Isomerization occurred within at least 20 ms following excitation. 1.6.2 The Millisecond and Microsecond Time Scales Gas-phase electron diffraction experiments have the potential for µs temporal resolution without any special modifications to the apparatus because the time required for gas molecules to flow through the electron beam: is on the order of 1 µs. If some type of dynamical behavior is initiated in the sample molecules by a µs event, such as passing them through the focal point of a laser, then the GED experiment can have µs temporal resolution simply based on time-of-flight principles. Bartell et al., and also Arvedson and Kohl, had essentially attained this resolution in their experiments, but they studied only one time point, l::,,.t = 1 µs [Bar84b] and M =0 [Arv79], respectively. To achieve even faster time resolutions (or to reduce background intensity when the excitation source is pulsed), the electron beam must be pulsed. The first GED apparatus with a pulsed electron source was reported by Golubkov et al. [Gol83]. Their thermal-emission electron beam was swept across an aperture by applying a square-wave voltage signal to deflection plates. Electron pulses were as short as 100 ns. The detection scheme was also novel: the authors scanned diffracted electron intensity across a secondary electron multiplier, varying the gain to compensate for the fall off of scattered intensity with angle 0. This apparatus was used to study the dissociation of Chapter One: Time-Resolved Diffraction Studies 35 trifluoromethyl iodide into CF3 radical and an iodine atom following multiphoton absorption in the infrared [Isc83]. Diffraction patterns of CF3I molecules were recorded both with and without the presence of a CO2 laser tuned to the v1 stretch (300 mJ, 1 µs, 100 Hz). Although the diffraction data was not formally analyzed because of detector calibration problems, the two scattering curves were different and the authors felt confident ascribing the changes to formation of the CF3 radical. Mastryukov has questioned these conclusions after analyzing Ischenko et al.' s published scattering curves with conventional methods [Mas91]. Mastryukov found no evidence of photodissociation in the data, and hypothesized that the observed changes were most likely instead due to vibrational excitation, as in the SF6 experiments. Ischenko et al. have responded by pointing out that the total scattering intensity decreased in the presence of laser excitation, evidence that high kinetic energy fragments were formed and left the scattering volume [Isc93]. Other authors have also observed such an effect [Ewb92]. Despite this debate, Ischenko and co-workers did demonstrate that gas-phase electron diffraction patterns could be generated using a pulsed electron source. Rood and Milledge conducted the first GED studies in which scattering images were actually recorded as a function of time [Roo84]. Electron pulses of 0.1 to 4.0 ms were created by stroboscopic deflection of a 30-keV thermal-emission electron gun, and reactions were initiated in the sample by flash photolysis with xenon flash lamps (0.2 ms). Scattered electron intensity was amplified with a customized microchannel plate assembly and detected on a phosphor screen coupled to photographic plates. In their first experiment using 400-µs electron pulses, the authors photodissociated chlorine dioxide (ClO2), and diffraction patterns showed a marked, reproducible change in the first Chapter One: Time-Resolved Diffraction Studies millisecond immediately following dissociation. 36 Diffraction patterns of the parent compound were obtained at longer delays, presumably due to the refresh of the sample volume with unirradiated molecules. In their second experiment, Rood and Milledge photoexcited biacetyl, CH3(CO)2CH3. Short-time diffraction patterns (< 1 ms) were different from ground-state diffraction patterns but did not match the theoretical intensities predicted for biacetyl's triplet-state structure. Additional changes in the scattering pattern occurred in the 1 to 2 ms following excitation. As with Ischenko et al.' s data, Rood and Milledge did not conduct a complete least-squares analysis on either the ClO2 or biacetyl data, and exact conclusions on the product compositions could not be reached. A third research group has constructed a time-resolved GED apparatus using stroboscopic deflection of the electron beam. Bartell and Dibble have combined 200-µs electron pulses with a pulsed Laval nozzle (20 Hz) designed to create supersonic expansions [Bar89]. Nucleation dynamics of clusters were followed as a function of time by changing the time-of-flight distance from the nozzle to the electron beam; as in other TOF experiments, the temporal resolution was on the order of 1 µs. In this case, the electron beam was pulsed to match the nozzle frequency and reduce background scattering in the Debye-Scherrer-like diffraction patterns. The authors observed that carbon tetrachloride (CCLi) clusters formed in the jet with a neon carrier gas were initially liquid but froze within 40 µs of the start of the expansion [Bar90]. Clusters of selenium hexafluoride, SeF6, and of trimethyl chloride, (CH3)3CCl, underwent crystalline phase transformations over the course of 40 µsand 150 µs, respectively [Dib92]. Chapter One: Time-Resolved Diffraction Studies 37 1.6.3 The Nanosecond Time Scale In order to reach time scales faster than 1 µs, a time-resolved GED instrument must satisfy a number of additional constraints. First of all, the electron beam must be pulsed; temporal dynamics can no longer be resolved by TOF because the molecular beam velocity is too slow. Secondly, the use of a pulsed laser to initiate a chemical reaction becomes ubiquitous because few other techniques exist for perturbing molecular systems in less than 1 µs, aside perhaps from fast potential gradients. Thirdly, the electron beam, excitation laser, and molecular beam must all spatially overlap, again because the molecular beam flow rate becomes negligible. This volume of overlap is often called the interaction region. Fourthly, photoemission electron beam sources become the more favorable choice rather than stroboscopic thermal emission sources. A photoemission source has fewer "moving parts" (no oscillating high-voltage ramp is required) and is easily synchronized with the excitation laser. Finally, special attention must be paid to the detection system. Space-charge effects begin limiting electron flux, and in order to keep exposure times on the order of miutes, the detector's efficiency must be high. Ewbank and co-workers have constructed a 15-ns GED apparatus based on these principles [Ewb92], [Ewb90]. The instrument was driven by two synchronized excimer lasers. One laser (30 mJ, 15 ns, 193 nm, 20-40 Hz) was focused onto the tantalum or titanium photocathode of a Pierce-type electron gun. The emitted photoelectrons were accelerated to 40 ke V, had a pulse width of 15 ns, and had a number density of ~ 10 10 electrons per shot. The second excimer laser (70 mJ, 15 ns, 193 nm, 20-40 Hz) photoinitiated a chemical reaction at the exit orifice of the molecular beam. Electrons scattered from the interaction region were detected on a phosphor screen fiber-optically Chapter One: Time-Resolved Diffraction Studies 38 coupled to a linear photodiode array, and exposure times were typically 30 s, or ~ 1000 shots. The authors have also tried amplifying the phosphor signal with an image intensifier, and this approach reduced the integration time to just 10 shots [Ewb93]. Quantitative least-squares analysis was performed on all diffraction data. Detailed studies of two chemical systems have been conducted with this apparatus. First, the authors returned to the photodissociation of the cis and trans isomers of 1,2dichloroethylene (C2H2Ch). Recall in earlier work with 20-ms resolution (1.6.1), excitation of either isomer led to the production of both isomers [Mon87]. On the nanosecond time scale, however, only fragmentation products were observed, confirming that the isomerization process occurs after many collisions following the formation of C2H2Cl radicals [Ewb93]. The authors estimated that the number of collisions per molecule in the new experiment was less than 102 , as compared with estimates of 106 collisions per molecule in the original study. Their second reported experiment was a time-resolved study of the photodissociation of carbon disulfide into a sulfur atom and a CS radical [Isc94c]. A series of diffraction patterns recorded over 100 ns showed that the CS fragment becomes vibrationally hotter with time, which the authors identified as evidence for electronic-to-vibrational energy transfer following collision of the fragment with excited-state sulfur atoms. 1. 7 Ultrafast Gas-Phase Electron Diffraction The transition from the nanosecond time scale to the femtosecond time scale requires a major interpretive change in data analysis. The diffraction patterns no longer Chapter One: Time-Resolved Diffraction Studies 39 represent a series of static structures, transforming step-wise from state to state or parent to fragments. Instead, ultrafast diffraction patterns record the fundamental mechanism of chemical change, the R(t). This approach was first proposed in 1991 [Zew91], [Wil91]. The success of the experiment hinges on detection of the total electron flux, since subpicosecond electron pulses are composed of only ~ 103 particles. Comparison with Ewbank et al.' s nanosecond experiments shows that not one electron can be wasted. Using their most sensitive detector, Ewbank and co-workers found that 1011 incident electrons were necessary to record a diffraction pattern, but their detection system only sampled a thin diameter of the scattered image and 99% of the flux was undetected. If all scattered electrons were detected, then only 109 would be needed. At 30 Hz, ten hours of exposure time using subpicosecond pulses would be necessary, and less if either the repetition rate was higher or the electron pulses were slightly longer in time. In 1992, the Zewail group recorded the first GED pattern using electron pulses of a few ps duration [Wil92]. A CPM/PDA laser system created 300-fs pulses (620 nm, 0.5 ml, 30 Hz) which were wavelength-tuned through continuum generation and frequency doubling to 255 nm (<10 µJ). The gold photocathode of an electron gun was illuminated with this laser output, and 15 keV electron pulses of 1-10 ps duration were generated. Single scattered electrons were detected by directly bombarding a two-dimensional CCD chip. Reasonable diffraction patterns of CCli, lz, and CF3I were recorded with exposure times of about an hour. In addition, CF3I molecules were dissociated by pumping with synchronized 266 nm from an Nd:YAG laser (~l rnJ, 30 Hz). Changes in the diffraction pattern following laser illumination corresponded to a nearly 25% dissociation of the parent into CF3 radical and an iodine atom. Chapter One: Time-Resolved Diffraction Studies 40 A more complete description of the apparatus and experimental results was reported in 1994 [Dan94], along with a theoretical treatment on the ramifications of vibrational and rotational coherence on GED [Wil94]. These experiments proved that ultrafast gas-phase electron diffraction was feasible, and with additional work it might be possible to record R(t) surfaces. The prototype apparatus, though, was in need of an overhaul. The highly-sensitive, scientific-grade charge-coupled device was located directly in the scattering chamber and cooled to temperatures of -120 °C, a natural attractor for stray corrosive molecules from the sample beam. The detector lifetime was also reduced by the high-energy electrons, and other experimental features demanded refinement before a true time-resolved ultrafast diffraction study could be attempted. This thesis discusses the second-generation UGED apparatus developed in the Zewail laboratories. The suitability of this instrument for ultrafast chemical investigations is demonstrated by the presentation of the first set of GED data ever recorded with a temporal resolution of a few picoseconds. The thesis is broken into two volumes and organized as follows: Chapter Two presents the basic elements of gas-phase electron diffraction theory, including the various interpretations of the internuclear coordinate, r. The theoretical effects of nonisotropic samples, prepared by rotational excitation, hexapole alignment, or rotational and vibrational coherence, are also considered. Chapter Three describes laboratory components which are not unique to UGED. These include the femtosecond laser system, the vacuum chambers, the sample inlet system, and the computer system. A brief overview of electron emission sources and photocathode selection is accompanied by details on the construction and testing of the ultrafast electron gun in Chapter Four. The temporal response of the electron gun, measured with a Chapter One: Time-Resolved Diffraction Studies 41 streaking experiment, is also reported. Chapter Five presents the theoretical basis for the dual-CCD single-electron detection system built for the second-generation UGED apparatus. A variety of possible detector schemes are compared. Construction, operation, and characterization of the detector and its components occupies Chapter Six. Volume Two opens with a description of the GED data extraction and analysis techniques in Chapter Seven. Ground-state diffraction studies of CCLi, CF31, SF6 , C2F4Ii, and CH2 h recorded in the UGED instrument are summarized in Chapter Eight. Chapter Nine takes another look at ultrafast timing and resolution for GED, and it is found that a fundamental limit to the temporal resolution is set by velocity mismatch between the pump laser and probe electron pulses. Various methods for establishing the location of time zero in the pump-probe experiment are considered, and the technique actually used, photoionization-induced lensing, is described. Chapter Ten begins with a justification of the selection of diiodomethane, CH2l 2 , as the prototype molecule, and then presents the results from the first two successful picosecond gas-phase electron diffraction studies ever recorded. General conclusions and future directions for the laboratory are summarized in Chapter Eleven. The reference list appears at the conclusion of both volumes. A collection of six appendices has been provided to round out the discussion of UGED. Equations for relativistic electron velocities and de Broglie wavelengths are derived in Appendix A, and key integrals needed in the calculation of orientationally isotropic diffraction patterns are derived in Appendix B. Appendix C lists the Mathematica routines used to interpolate electron scattering factors from published data. The body of software written for the various aspects of UGED are described in the bulky Appendix D, and Appendix E explains the Excel 4.0 Macros which control the CCD Chapter One: Time-Resolved Diffraction Studies 42 camera and computer-controlled translation stage over the course of an experiment. Finally, Appendix F presents the latest publication from this laboratory [Wil97]. 43 Chapter Two Gas-Phase Electron Diffraction Theory As the impact of the significance of [electron diffraction] burst upon me I could not contain my enthusiasm, which I expressed to [Hermann] Mark -- my feeling that it should be possible in a rather short time, perhaps ten years, to obtain a great deal of information about bond lengths and bond angles in many different molecules. Linus Pauling [Hag95] This chapter provides a theoretical basis for time-resolved gas-phase electron diffraction. Traditional GED theory is reviewed in the first section, 2.1, starting from the Schrodinger equation for an electron interacting with an atomic potential. The theory moves from a simple model of atomic scattering to greater and greater levels of complexity, eventually reaching a molecular scattering equation commonJy used by diffractionists today for isotropic gas-phase samples. Analyzing GED patterns with this equation yields molecular structure, but 2.2 points out that the definition for an internuclear distance takes many forms. Theoretical definitions of r can have any of several physical interpretations, and furthermore experimental methods such as GED and rotational spectroscopy yield so-called operational definitions of r which must be converted to physical definitions using correction terms. Chapter Two: Gas-Phase Electron Diffraction Theory 44 If the gas-phase sample is prepared with rotational, vibrational, or orientational anisotropy, the diffraction patterns may contain additional structural information. Timeinvariant preparation methods, such as laser excitation to specific rotational or vibrational states, or orientational alignment with a hexapole magnet, are discussed in 2.3. The remaining two sections of this chapter investigate ultrafast time-resolved GED experiments. Rotational coherences can be created in the molecules by excitation with a picosecond laser, and the sample becomes orientationally anisotropic during the rotational recurrences which follow. As discussed in 2.4, this anisotropy can be detected in twodimensional diffraction images, yielding bond angles and moments of inertia. Vibrational coherences can be created if the pulse width of the excitation laser is on the order of tens of femtoseconds. 2.5 presents simulations of the diffraction patterns which result when the total experimental resolution is also in the femtosecond regime. Semiclassical trajectories of molecular iodine excited to the B-state with various electronic energies, above and below the dissociation limit, were calculated and several R(t) surfaces are presented. A simulation of the diffraction patterns from an ultrafast kinetic process is also shown. 2. 1 Diffraction From Isotropic Samples The theoretical derivation of gas-phase electron diffraction scattering equations has been presented from several different scientific perspectives in varying degrees of detail. For this thesis, the mathematical model is constructed by amalgamating the viewpoints of both physicists and chemists in order to focus on those aspects particularly Chapter Two: Gas-Phase Electron Diffraction Theory 45 relevant to ultrafast GED and molecular dynamics.* For example, some of the corrections chemists employ when refining internuclear separations to thousandths of an Angstrszsm are unnecessary during UGED analysis because the experimental precision is not as high as in static studies. The theoretical derivation results in two key equations. The first equation is for the molecular scattering electron intensity, IM, which contains intramolecular interference terms and hence structural parameters. Other intensity contributions, such as atomic scattering and inelastic scattering, contain no interference terms and are removed en masse from the experimental data during UGED analysis (Chapter Seven). The molecular scattering intensity is written as a double sum: (2.1) where N is the number of atoms in the molecule, rij are the internuclear separations, lij are the corresponding mean amplitudes of vibration, and f; and 11; are element-dependent scattering amplitudes and phase factors. IM is a function of s, the magnitude of momentum transfer between incident and scattered electrons. The momentum transfer depends on the scattering angle e and has units of inverse Angstrszsms (A- 1). IM(s) can also be written as a single sum over the number of unique internuclear separations N1s in the molecule: (2.2) • The primary sources for the derivation presented here are [Sei67], [Bon74], and [Har88a] . Other references for scattering theory and GED include [MaH32], [Bro36], [WuT62], [Mot65], [Sei73], [Cow90], and [Har92]. Chapter Two: Gas-Phase Electron Diffraction Theory 46 The number of times a specific atom pair occurs in the molecule (containing the same elements i andj, the same r, and the same l) is given by nk. Figure 2-1 shows JM(s) for carbon CC4 tetrachloride. has two umque internuclear separations: four C-Cl atom pairs (r = 1.765 A) and six Cl···Cl atom -- x100 ► Cl) :!: pairs (r = 2.886 A) [Mor60a] . According to Eq. 2.2, the molecular scattering intensity contains two sinusoidal components. The ' ov oscillations are rapidly damped, however, because the scattering factors f;(s) decrease like s2, but the modified molecular scattering I 20 Molecular scattering intensity /~s) for carbon tetrachloride using structural parameters from [Mor60a] . Figure 2-1: function, sM(s), can be plotted instead to bring out the oscillatory features. One form of sM(s) is: sM(s) (2.3) = where a and b correspond to two elements found in the molecule. A plot of sM(s) for CC14 is shown in the top of Figure 2-2. The second key equation borne of gas-phase electron diffraction theory is the radial distribution function, f(r). This function is obtained from the sine transform of sM(s), and approximates the combined internuclear probability distributions of all atom pairs in the molecule: Chapter Two: Gas-Phase Electron Diffraction Theory 47 smax JsM(s)sin(sr)exp(-kds2)ds f(r) (2.4) 0 Ideally the upper limit on the integral should be 00 , but this is not experimentally possible; diffraction data are typically recorded out to an Smax on the -- order of 40 A- 1. The exponential Cl) :E term with coefficient kd is included t--,t--,t--+-,l-rr-rl,--trlr-tt-lr--+--,f--1--l-----.¼--T-h--h-fi+,~f-J-~-\----.1--,41 Cl) to damp spurious oscillations in f(r) caused by cutting off the integration at Smax • Figure 2-3 presents of a distribution pair functions 1 radial derived from the sM(s) curve for CC4 0 shown in Figure 2-2. The leftf(r) spunous oscillations introduced --.... A2 30 Figure 2-2: (Top) Modified molecular scattering curve sM(s) for carbon tetrachloride (a, b = Cl) using structural parameters from [Mor60a]. (Bottom) Plot of the radial distribution curve damping function exp(-kds2) with kd = 0.002 A2. curve is not damped and the kd = 0.000 RD Damping Curve Cl•• •CI kd = 0.002 --.... C-CI C-CI L., L., 0 1 2 3 Internuclear Separation {A) 4 Cl·••CI A2 0 1 2 3 Internuclear Separation {A) Figure 2-3: Radial distribution curves for carbon tetrachloride calculated from sM(s) curve shown in Figure 2-2. (Left) kd = 0 A2. (Right) kd = 0.002 A2. 4 Chapter Two: Gas-Phase Electron Diffraction Theory 48 by a finite experimental range of sis clearly seen; the rightf(r) curve uses a kd = 0.002 A2 (this exponential damping function is plotted in the bottom of Figure 2-2). The f(r) curves have two peaks, one corresponding to the C-Cl atom pair and one corresponding to the Cl·• -Cl atom pair. Radial distribution curves have more intuitive appeal than modified molecular scattering functions. Each unique internuclear separation yields one peak in the f(r) curve, and the area under each peak is approximately proportional to: Peak Area oc n Z;Z j / r;j (2.5) when kd is equal to zero. The FWHM of each _peak is related to the mean amplitude of vibration lu, and also Smax (see Figure 2-3). Since f(r) is related to internuclear probability distributions, the measurement of molecular scattering intensities offers a direct method of observing the evolution of a wave packet. For example, if one chlorine atom were to dissociate from CC4, one-fourth of the C-Cl peak would "break away," moving out to greater r with time, and one-half of the Cl·· ·Cl peak would do the same. The radial distribution curve as a function of time, f(r, t), is almost equivalent to the R(t) surfaces discussed in Chapter One. The derivation of the molecular scattering and radial distribution functions is developed throughout the remainder of this section in the following way. First, a theoretical model of atomic scattering is introduced, leading to a differential equation which, once solved, yields the probability amplitude of atomic scattering. Several approximations will be made to solve this differential equation, and later calculated solutions are discussed. The solutions are then applied to molecular scattering, first by assuming that the molecular structure is rigid, and then by considering a structure Chapter Two: Gas-Phase Electron Diffraction Theory undergoing vibrational motion. 49 Equations for /M(s) will be derived. The relationship between /M(s) and internuclear probability II~ ol I I I I I i 1 1 amplitudes is reconsidered, leading to a definition of the radial distribution function. Finally, additional refinements and higher Figure 2-4: Atomic scattering geometry. Incident electron beam propagates along the z-axis and scatters off an atom at the origin. Scattered intensity, detected in the far field at R, is a function of the angle e. orders of correction are outlined. 2.1.1 Defining the Theoretical Model A simple picture of atomic scattering is .shown in Figure 2-4. An electron beam travels along the z-axis, encounters the electric field of an atom centered at the origin, and scatters in all directions. Three initial assumptions are made about this interaction: 1. The electrons scatter elastically, without exchanging energy with the atom. 2. The atomic potential does not change with time. 3. The atomic potential has spherical symmetry. One consequence of the third assumption is that the scattered electron intensity must have cylindrical symmetry about the z-axis and depend only on the angle 0. Schrodinger's wave equation must be solved to find the probability amplitude of the scattered electrons. As a result of the second assumption, the time-independent equation can be used: (2.6) where Eis the sum of the kinetic and potential energies of an electron and \j/ is the wave function. If V describes the atomic potential energy, then the Hamiltonian operator is: Chapter Two: Gas-Phase Electron Diffraction Theory _.!t__V 2 + V A H 50 (2.7) 2m. In the absence of the potential (i.e., before scattering occurs, at a position -z far from the origin), the incident electron beam can be described as a plane wave: (2.8) The wave vector ko is directed along the z-axis towards positive z, and the magnitude of ko is given by: 2 = .J2m.c KE + KE 2 lie (2.9) .. where KE is the kinetic energy and Ae is the relativistic de Broglie wavelength (see derivation in Appendix A). The electron beam's current density (or Schrodinger current) is calculated from: (2.10) where mR is the relativistic electron mass, and so: (2.11) gives the initial incident current, where VR is the relativistic velocity (Eq. A.8). The atom located at the origin is assumed to have a spherically-symmetric potential V(R), and for convenience U(R) will be defined as: u(R) = 2 ~R v(R) Ii (2.12) In the asymptotic limit of large R, the atom will appear as a point source of spherical waves with some functional dependence on 0. The wave amplitude of the scattered Chapter Two: Gas-Phase Electron Diffraction Theory 51 electrons must also have a 1/R dependence in order to conserve electron density, so the functional form of the scattered wave amplitude is chosen to be: l/f s(R) In this equation, f(8) is called the scattering amplitude and jkj (2.13) = jk 0 I because the scattering process is elastic. if (0 )12 is the differential scattering cross section dcr for unit solid angle dQ. According to Eqs. 2.10 and 2.13, the intensity of the scattered wave is equal to: (2.14) so an equation forf(S) must be derived in order to predict the scattered intensity. The total wave function is a sum of the incident and scattered waves: l/f(R) (2.15) and \j/(R) must satisfy Schrodinger's equation. Inserting Eq. 2.7 into Eq. 2.6 yields: (2.16) which, with Eqs. 2.9 and 2.12, simplifies to: (2.17) The problem to be addressed is how to solve Eq. 2.17 under the boundary condition in Eq. 2.15, and then derive an equation for \j/(R) such that the formula for the scattering amplitude f(8) can be found. Chapter Two: Gas-Phase Electron Diffraction Theory r 52 p R - r - r0 \ e \ z Figure 2-5: Atomic scattering geometry. The incident electron beam propagates along the z-axis and scatters from an atom displaced from the origin by ro. Scattered intensity is measured in the far field at point P. The scattered intensity is integrated over all infinitesimal volume elements dr. 2.1.2 The First Born Approximation: Deriving/(s) As a first step in solving Eq. 2.17, a more detailed illustration of the scattering center is required (Figure 2-5). In this figure, the atomic potential with volume r is displaced from the origin by r0 , so Schrodinger' s equation is modified to be: (2.18) The scattered intensity is detected at point P at the end of R, and r points to an infinitesimal volume element dr of the potential. To aid in the analysis, a mathematical "crutch" will be constructed: the Green's function G(R, r + r0 ) is defined to provide a function of -4n8(R - r - r0 ) when operated on by the Hamiltonian: (2.19) A particular solution for \j/(R) is therefore given by: Chapter Two: Gas-Phase Electron Diffraction Theory 53 (2.20) To see this, apply the Schrodinger equation (Eq. 2.17) to 'l''(R), moving the Hamiltonian operator inside of the volume integral, and integrating over r using the properties of the Dirac delta function. 'l''(R) is not really a solution to Eq. 2.17 because Eq. 2.20 is recursive ('lf'(R) appears in the integral) However, Eq. 2.20 can be used as the starting point for approximating a solution. The general solution to the homogeneous Schrodinger equation (when V = 0) can be added into the particular solution 'l''(R) to give the general solution of Eq. 2.17: lfl(R) = Aexp(ik z) 0 - - 1 fG(R,r+r )U(r)lfl(r+r )dr 4n v:0 0 0 (2.21) The Green's function can be derived using complex variables analysis (see [Bon74] for specific details): = exp(i k!R - r - r0 I) IR- r-rol (2.22) In the asymptotic limit of R >> lrol ""lrl, the Green's function is equal to: (2.23) where IR - r - r 0 j "" R has been used in the denominator of Eq. 2.22 and: (2.24) has been used in the exponential to preserve the phase (see Figure 2-5). After substituting Eq. 2.23 into Eq. 2.21, the asymptotic form of \jl(R) becomes: Chapter Two: Gas-Phase Electron Diffraction Theory 54 (2.25) or: lfl(R) = Ae 1 koz - iU [ Jexp(-ik ·r-ik·r )U(r)lfl(r+r )dr ] _e_ 0 0 4nR v.0 (2.26) Comparing Eq. 2.26 with Eq. 2.15 shows that the scattered wave \j/s is equal to the second term of Eq. 2.26. In order to evaluate the integral, it is assumed that the scattered wave amplitude is negligible compared with the incident wave: \j/s << \j/I• This is the first Born approximation, which has the additional physical interpretation that only single-scattering events occur. (Note that higher order solutions for \j/(R) can be .. generated iteratively - e.g., the second Born approximation.) To make the first Born approximation, the displacement z from the origin to the scattering element dr is written in terms of the projections of r0 and r (see Figure 2-5): (2.27) and \jli is inserted for \j/ in the integral of Eq. 2.26: (2.28) The scattered wave is given by: lfls(R) A iU 1 ] = _e _exp(i(k 0 -k)·r0 ) [ --Ju(r)exp(i(k 0 -k) ·r)dr R (2.29) 4n v.0 The momentum transfer vectors for the scattered electron is: s -- k0 - k (2.30) Chapter Two: Gas-Phase Electron Diffraction Theory 55 Since k0 and k have the same magnitude, the triangle formed by k0 , k, and s is isosceles (Figure 2-5) and s has a magnitude given by: (2.31) Note that some diffractionists describe the magnitude of the momentum transfer with the variable q instead of s (see, e.g., [Bon59]): (2.32) Substitution of s into Eq. 2.29 gives: AeikR 1/f s (R) = --exp(i s •r0) R [ l •• ] --f U(r )exp(i S • r)dr 4n-v (2.33) 0 After recognizing that the exp(is·ro) term in Eq. 2.33 is merely a phase shift due to the displacement of the atom from the origin by the vector r0 , it is apparent that the portion of \j/s(R) in square brackets is equal to f(8) in Eq. 2.13; therefore, a first-order approximation of the elastic electron scattering amplitude has been derived: f (s) = - - 1 fU (r )e; dr (2.34) s-r 4Jr V 0 A potential function U(r) is required in order to evaluate f(s). The Coulombic potential for an atom can be written as a sum of the attractive point-charge-like potential of the nucleus and the repulsive diffuse potential of the electron cloud distribution p(r'): V(r) = - Ze2 + e2 r f p(r'), dr' vJr - r I Using this potential, it can be shown that [Bon74], [Sei67]: (2.35) Chapter Two: Gas-Phase Electron Diffraction Theory f(s) 56 (2.36) where Fx(s) is the x-ray scattering function: Fx(s) = ~ J sin(sr) 4n rp(r)-~dr 0 s (2.37) The elastic electron scattering amplitude depends on Z and decreases with scattering angle like s2. To summarize, under the first Born approximation the elastic electron scattering amplitude from a spherically-symmetric atom at position r0 is found to be: A ikR lfls(R) = _e-f(s)exp(is·r0) R (2.38) 2.1.3 Diffraction From a Rigid Molecule A rigid molecule can be described as a collection of atoms whose positions are defined by the vector set {r 1, r2, ... , rN}. The atoms are "glued" together by the overlap of valence electron orbitals, and clearly this chemical binding removes spherical symmetry from the potential functions of individual atoms. Nevertheless, assuming that the molecule is composed of non-interacting atoms still proves to be a remarkably robust approximation for diffraction theory. The Independent Atom Model (1AM) succeeds in part because most diffraction data is recorded over larger scattering angles, typically 5-40 A- 1. Momentum transfer is large when an electron passes close to an atomic nucleus, where the electric field from core electrons and nuclear charge is still spherically symmetric. The weaker asymmetric field due to molecular orbital electrons is significant only when the impact parameter is large, and the momentum transfer is small. Chapter Two: Gas-Phase Electron Diffraction Theory 57 Using 1AM, the scattered electron wave amplitude from a molecule is written as a sum of Eq. 2.38 over each atom: (2.39) The intensity of scattered electrons is again calculated usmg the equation for the Schrodinger current (Eq. 2.10): (2.40) This multiplication of two series can be reindexed as a double summation of a product: (2.41) Eq. 2.41 shows that the scattered intensity depends on the internuclear separation vector rij = r; - r1 for all atom pairs in the molecule, bonded and non-bonded. This double sum can be broken apart into an atomic contribution containing no structural information, and a molecular contribution containing the interference terms: (2.42) Usually the incoherent inelastic scattering terms are included in /A(s): (2.43) where S;(s) are the inelastic scattering factors and a0 is the Bohr radius. Theoretical discussions of inelastic scattering are found in [Mot65] and [Bon74]. The molecular scattering intensity /M(s) of Eq. 2.42 results from just one rigid Chapter Two: Gas-Phase Electron Diffraction Theory 58 molecule with a specific orientation defined by {r 1, r 2, ... , rN}- To model experimental data, IM(s) must be averaged over all the distributions of whatever physical parameters describe the sample molecules (e.g., orientation, electronic state, vibrations): N IM (s) N = CL LJ; (s)Jj(s) \exp(i S • rij ))M_ole_cular i=I j=I (2.44) D1stnbut10n ;,,,j At this point m the analysis, the molecules are described as "ground-state" rigid structures, but the sample is still an unordered gas, and so the molecules have an isotropic distribution of spatial orientation. -- One method of averaging over this distribution is to consider that the directions of possible ru map out the surface of a sphere relative to each s (Figure 2-6). If a is the angle between ru Figure 2-6: Method of integrating exp(is-rij) for an isotropic molecular distribution of spatial orientation. and s, and P(a) is the probability distribution, then the average value of exp(is·ru) is found by integrating over a : rr: ( exp(i s • rij )) Sptl fexp(i s •rii )P(a )da (2.45) 0 Within an angular element da, the probability distribution is the area of strip with width ruda, normalized for the total surface area of the sphere: P(a)da [2nh sina)hda Carrying out the integration: 4m;} sin ad -- a 2 (2.46) Chapter Two: Gas-Phase Electron Diffraction Theory ( exp(i s •r;j))SptI gives: 59 (2.47) (2.48) for the isotropic spatial-orientation distribution function. The elastic electron scattering intensity from an unordered gaseous sample of rigid molecules is therefore: (2.49) 2.1.4 The Second Born Approximation: Deriv~_ng T1(s) The precision of experimental GED techniques dramatically improved in the twenty years following Mark and Wierl' s first diffraction pattern, and the approximations behind Eq. 2.49 required further refinement. Chemists certainly knew that molecules were not rigid structures, and by 1950 GED data analysis methods regularly incorporated vibrational corrections (see 2.1.6 below). Other errors in the theory were more subtle. For some molecules containing atoms of large Z, the structures determined by diffraction did not agree with the conclusions of spectroscopic analysis. The spectra of uranium hexafluoride, for example, pointed to octahedral symmetry, but the electron diffraction radial distribution curve showed two distinct U-F distances, separated by ~0.3 A [Bau50]. Schomaker and Glauber showed that the splitting could be explained as an artifact due to atom-dependent phase shifts [ScV52], [Gla53]. An incident electron accelerates as it approaches an atomic nucleus and the de Broglie wavelength contracts. After the electron leaves the influence of the atomic potential, Ae returns to its original value, but the Chapter Two: Gas-Phase Electron Diffraction Theory 60 phase of the scattered wave differs from that of a wave traveling the same path with constant Ae. While the first Born approximation gives only real scattering amplitudes, the second Born approximation yields complex amplitudes containing a phase shift, and Schomaker and Glauber defined the complexf(s) to be: (2.50) where 11(s) is the argument ofJ(s). Tl is positive for an attractive potential and negative for a repulsive potential. The correction to the magnitude is small enough that the first Born approximation can still be used for IJ(s)I (Eq. 2.36). The new phase term is the more important result, and the authors derived an equation for 11(s) [Gla53]: (2.51) Eq. 2.51 shows that the phase shift is more pronounced at larger scattering angles and depends on Z. A new formula for the molecular scattering intensity must be derived from Eq. 2.10 iff(s) is complex: I M(s) = ct,t,Re[J,(s)Ji(s)(exp(is r, l)r,::~b~:::,J (2.52) it,j Substitution with Eq. 2.50 and averaging over an isotropic sample gives: I M(s) = ct, t,Re[lf (s)ll!h)lexp(i(11,(s )-11 Js) it,j which simplifies to: Jit:tr;1) (2.53) Chapter Two: Gas-Phase Electron Diffraction Theory 61 (2.54) Thus, the scattering intensity from two atoms of very different Z, such as U and F, . contains an additional interference term which causes splitting in the radial distribution curve peak. Using Eq. 2.54, Schomaker and Glauber duplicated the U-F splitting distance found in the experimental UF6 diffraction data and resolved that the molecule did in fact have octahedral symmetry. As a side note, the authors pointed out the first Born approximation fails to account for scattered electron flux. According to the optical equation, the elastic electron scattering cross section is zero if the scattering amplitude is not complex [Gla53], [WuT62], [Bon74]: (2.55a) cre1 is explicitly calculated by integration of the differential scattering cross section: 2ir tr flJ(e)i1 dQ = f fIJ(e)\2 sin0d0d</J 0 (2.55b) 0 Ir (jel = 2n fIJ(e)i1 sin0d0 (2.55c) 0 2.1.5 The Method of Partial Waves More accurate values of f(s) are obtained by solving the Schrodinger equation exactly with a computer using the method of partial waves [Fax27], [Hoe53]. The Schrodinger is rewritten in terms of spherical coordinates; if the atomic potential is still assumed to have spherical symmetry, then the wave function can be separated into angular Chapter Two: Gas-Phase Electron Diffraction Theory 12 r I (40 keV) -- 62 3 ( /) --.... C: 8 .!2 I(18keV) Cl) 'C 2 ca 0:: 4 Cl) 1 I=" C (18 keV) 0 0 15 5 20 0 5 10 15 20 s cA· ) 1 Figure 2-7: Magnitude lf(s)I of atomic elastic scattering factors for carbon and iodine. Figure 2-8: Phase 11(s) of atomic elastic scattering factors for carbon and iodine. For 18 keV electrons, scattering from C and I are 1 90Q out of phase at s"" 11.2 A- . and radial components: lfl(r,8,¢) = R(r)Y(8,</J) = u(r) Y( e' </>) (2.56) r The asymptotic solution leads to a complex scattering amplitude as an infinite sum: (2.57) where the Pn terms are Legendre polynomials. Several different mathematical methods have been used to estimate the phase shift term, bn, such as [lbe74]: (2.58) Tabulated values of IJ (s )I, 11(s), and the inelastic scattering factor S(s) are available in the literature as functions of s, Z, and electron kinetic energy.• Figure 2-7 plots IJ (s)I for carbon and iodine; note the rapid, s2 decay. Figure 2-8 compares the phase factors for • See, for example, [Tav67], [KiM67], [Haa70a], [Haa70b], [Tan71], [Sch71], [Ibe74], [Sel78], [RoA92] , and [Smi94]. Chapter Two: Gas-Phase Electron Diffraction Theory 63 carbon and iodine as a function of s. For 18 keV incident electrons, the carbon and iodine 11(s) terms are 90° out of phase at s""' 11.2 A- 1 ; at this position in the diffraction pattern, all C···I atom pairs make zero contribution to the molecular scattering intensity. 2.1.6 Diffraction From a Vibrating Molecule Nuclear coordinates are frozen on the attosecond time scale, the time scale of high-energy electron scattering, and an incident electron scatters from a target molecule as if the molecule was in fact rigid. Because of random vibrational motion, however, molecules are frozen in different internuclear configurations throughout the sample, and the ensemble is represented by an average structure, not an absolute structure. To account for vibrational motion in the diffraction pattern, the "Molecular Distribution" average occurring in Eq. 2.44 must include a vibrational average in addition to the spatialorientation average: IM (s) = ct, t,11,IIJ;lcos(1J, - 1J;) ( ( exp(i s r, )),,,, t (2.59) ;,,,j The scattering factors f and Tl are understood to be functions of s in Eq. 2.59. Since a molecule's spatial orientation is considered independent of its vibrational motion, the spatial-orientation average can be carried out first as in 2.1.3: (2.60) To average over vibrational motion, each internuclear separation ru is assigned a probability Pu(r)dr of having ru between rand r + dr. Eq. 2.60 becomes: Chapter Two: Gas-Phase Electron Diffraction Theory 64 (2.61) An analytical description of the distribution function is required to carry out the integration. As an initial approximation, each atom-atom pair can be thought of as a perfect harmonic oscillator (even the non-bonded pairs). For an ensemble of harmonic oscillators in equilibrium at temperature T, the average over all vibrational states \jlv gives a gaussian probability distribution as a function of the variable x: 2 = Iexp(-Ev/kT) 1 ( x ) l1z ✓'brexp - 2!; (2.62) Y=O where x is the displacement from the equilibrium distance, x = r - r.. The variable l1z is the mean amplitude of vibration of a harmonic oscillator at T. (Recall that in general: (2.63) and la = n/ ,J2µm. for the ground vibrational state of a harmonic oscillator.) Using the gaussian probability distribution from Eq. 2.62, the integral in Eq. 2.61 becomes: s= ( 2 1 x ) sin[ s(re + X)] exp - - - - - - - d x l1z ✓'2n ~ 2!; s(r. + x) (2.64) The vibrational probability distributions are highly localized around re, so the lower integration limit can be extended to -oo in order to simplify the math. Nevertheless, the integral in Eq. 2.64 does not have an analytical solution and further approximations must be made. The denominator can be written as a binomial expansion: Chapter Two: Gas-Phase Electron Diffraction Theory 65 (2.65) Since x is small compared to re, the first two terms of the expansion are the most significant. Rewriting Eq. 2.64 with this substitution gives: (2.66) The integral in Eq. 2.66 is evaluated by expanding the sine functions using angle-sum relations and then integrating with Eqs. 3.952-9 and 3.952-10 of [Gra80] to get: exp(-.1s2z2) [ 2 _ ___;__- - h ~ s~ sI2 sin( sr,) - _ h cos( sr,) ] (2.67) ~ Eq. 2.67 can be further simplified by noting that sl; /r, << 1. For small y it is true that sin y "'"y and cosy "'" 1, so the portion of Eq. 2.67 written in square brackets can be simplified using an angle-difference relation: (2.68) Thus if all atom-atom pairs are modeled as harmonic oscillators, the elastic electron scattering intensity from an unordered gaseous sample of vibrating molecules is: (2.69) where the effective internuclear separation ra is related to the equilibrium internuclear separation r, by the mean amplitude of vibration (MAV): (2.70) Conventional GED experiments can determine structural parameters with a Chapter Two: Gas-Phase Electron Diffraction Theory precision on the order of 0.001 A. 66 The harmonic oscillator model has proven to be inadequate at this level of precision, and the influence of anharmonic effects on the probability distribution must be accounted for as well. Kuchitsu and others considered an expansion about the harmonic oscillator gaussian distribution [Kuc61], [Kuc67]: If(x) (2.71) where en are expansion coefficients and the normalization constant Ap is close to unity: (2.72) Again, the choice of variable is the vibrational displacement x: x = r-r-8r e (2.73) although now x incorporates corrections for centrifugal distortion, 6r. Kuchitsu showed that the elastic electron scattering intensity now incorporates an asymmetry constant K in the sine term [Kuc67]: (2.74) In Eq. 2.74, lm is an effective MAV close in value to lh, and ra and Kare series expansions including weighted terms of l/. Often the ground-state of the Morse anharmonic oscillator provides sufficient precision [Bar55a]. The Morse oscillator expansion coefficeients for Eq. 2.71 are: C 2 = O·' (2.75) where a is the anharmonicity constant and all other c,, are equal to zero. With these Chapter Two: Gas-Phase Electron Diffraction Theory 67 parameters, ra and Kare approximated by: r;, rg - l; /r, (2.76) rg = + or r, + J.a/2 2 h (2.77) 1( = alt /6 (2.78) Values of a for different atom-atom pairs are tabulated in [Kuc65] and [Kuc88], although often diffractionists set a equal to 2 A- 1 for all bonded atom pairs and a equal to 0 A- 1 for all non-bonded atom pairs. At present, UGED provides a precision on the order of 0.01 diffraction data is recorded out to an Smax of only 15 A- 1 at best. A- 1 because Even with large vibrational motion (lh ""'0.1 A), the anharmonicity term K.s2 in Eq. 2.74 is never more than 0.001 A and can be neglected. Replacing the rigid molecule model with a harmonic oscillator model is still an important correction for the JM(s) curve measured with UGED. Although the difference between ra and r, is usually less than 0.01 A (Eq. 2.70), the exponential damping term exp(-½ s2 z;) alters the molecular intensity by 10% or more at a 1 scattering position of s = 10 A- • 2.1.7 The Radial Distribution Curve As derived in the previous section, the molecular scattering intensity from vibrating molecules with isotropic spatial orientation is: (2.79) Pu(r) is a radial distribution function: the normalized probability density that atoms i and j are separated by a distance r . Pauling and Brockway recognized that qualitative Chapter Two: Gas-Phase Electron Diffraction Theory 68 interpetation of diffraction data is simplified by transforming the reciprocal-space data to yield a distribution function D(r) related to Pu(r) [Pau35]. Instead of comparing experimental /M(s) curves with theoretical calculations for different structural models (a tedious process in 1935), Pauling and Brockway suggested that internuclear separations could be read directly from the maxima in D(r). To obtain D(r), a modified scattering intensity M(s) is derived from Eq. 2.79: (2.80) where g(s) is a levelling function and D(r) is defined as the sum: (2.81) If gk is independent of s, then D(r) is a true sum of all radial distribution functions Pk(r) weighted by 1/r and the constant terms gk, After substituting in D(r) and multiplying bys, Eq. 2.80 becomes: = sM(s) = Cf D(r)sin(sr)dr (2.82) 0 and thus D(r) and sM(s) are related by a sine-transform: = D(r) f = C' sM(s)sin(sr)ds (2.83) 0 Pauling and Brockway chose gk(s) = s4f(k/j(k) to compensate for the s2 fall off in the scattering factors (recall that the phase factors 11(s) were not introduced until 1952). Debye pointed out that if the scattering effects from planetary electrons are ignored (Fx = O in Eq. 2.36), then their gk is a constant equivalent to [Deb41] : Chapter Two: Gas-Phase Electron Diffraction Theory 69 (2.84) Debye's definition aids in the interpretation of D(r) because the area under the curve: (2.85) can be simplified by recalling that the Pk(r) are highly localized about re,k and are normalized to have unit area: (2.86) So by assuming that gk(s) are constant and that nuclear scattering dominates GED, the area under a peak in the distribution curve is proportional to the atomic numbers of the atoms involved, and inversely proportional to their internuclear separation (Eq. 2.5). Two formulations of gij(s) are commonly used in modem GED analysis [Sei73], [Sch76] , [Har88b]. The "Norwegian school" writes gij(s) as [Vie47] : (2.87) where a and b are two atoms in the molecule. With this version, D(r) is truly proportional to P(r)lr for homonuclear diatomic molecules because gu(s) becomes 1. The "American school" writes gij(s) as [Bar55b]: (2.88) on the grounds that the resulting distribution curve has a flatter baseline. For the UGED analysis techniques used up to this point in the Zewail laboratory, however, Eq. 2.87 has consistently provided better results. Figure 2-9 compares three forms of gu(s) for the C-C Chapter Two: Gas-Phase Electron Diffraction Theory 70 and C· •-Cl atom pairs in carbon tetrachloride. The D(r) distribution curve defined m Eq. 2.83 cannot be calculated from experimental scattering intensities because the data is recorded over a finite range of s. A modified radial distribution curvef(r) (also called cr(r)/r) is calculated instead: Smax J(r) C' J sM(s)sin(sr)exp(-kds 2 )ds (2.89) 0 The exponential damping function reduces the ringing in f(r) caused by the cut off at Smax (see Figure 2-3) [Kar49], [Deg37] . If kd is sufficiently large,f(r) and D(r) are related by: 1 J(r) 00 = 2.[,if; J D(p) exp[-(r- p)2../4kd]dp (2.90) -oo which shows that f(r) is the convolution of D(r) with a gaussian, smoothing D(r) and broadening the peaks. In practice, kd is chosen such that exp(-kdsma/ ) z 0.1. 2.1.8 Additional Corrections The molecular scattering intensity equation derived in 2.1.6 (Eq. 2.74) has been successfully applied to the determination of hundreds of structures. Still, this equation results from a series of assumptions, and its failures are evident under certain conditions [Bon65c], [Sei67] , [Sei73], [Har88a]. For example, early calculations of the atomic scattering factors assumed that \j/s << \j/1, implying that the likelihood of a doublescattering event was negligible (2.1.2). The inadequacy of the first Born approximation becqme clear after several years of experimentation, and f(s) were subsequently derived using the method of partial waves to account for the effects of intraatomic multiple scattering. However, the first Born approximation is still made in molecular scattering Chapter Two: Gas-Phase Electron Diffraction Theory theory because the contributions from intramolecular multiple scattering 1 71 Pauling and are Brockway neglected. Theory has shown that electrons .,· ,,.,, ___ ... -···-···- ... --·· _, .• •• ,."· which scatter first from one atom and then from a second atom in the same molecule do not affect the scattered molecular intensity. 1 .·-·. ·-· .·-·. ·-·. ·-·. ·-·. ·-·. ·-·. ·-·. ·-·. ·-·. ·-· Norwegian Format Additional terms do appear in IM(s) due to interference effects between single-scattered waves and doubly-scattered waves, and the contributions are greatest 0 +--,---,,-,------.-+---.----,---,,-,--+--.--.---.--r---1 1 /" for slow electrons and molecules with atoms of high Z [Bon65c]. --··-···-··· American Format Evidence of three-atom scattering effects have been observed in the diffraction pattern obtained 0 30 from rhenium hexafluoride, ReF6 [Jac70], and similar molecules. In the RD curve, the two peaks comprising the Re-F doublet have different amplitudes, whereas they are Figure 2-9: Normalized representations of g;is) for C-CI and c1 ... c1 distances in CCl4. 4 (Top) Multiplication by s [Pau35]. Complex scattering factors are used. (Middle) The Norwegian format: division by lfallfbl with a= b = Cl. (Bottom) The American format: division by /A(s). expected to have nearly equal heights according to Eq. 2.74. Application of an intramolecular multiple scattering theory developed by Glauber [Gla58], [Yat72] to the ReF6 system accounts for more than eighty percent of the observed discrepancy [Bar72], -[Won73]. Extensions of Glauber theory predict that the Chapter Two: Gas-Phase Electron Diffraction Theory 72 intensity from intramolecular multiple scattering interference terms is upwards of four percent of the total molecular scattering intensity at electron energies of 10 ke V and greater [Mil80], [Koh80], [Nag82]. Recently, Meier et al. have measured intramolecular multiple scattering contributions from fluoromethyl halides to be as large as eight percent using 1 keV electrons [Mei94]. Careful studies of diffraction from sulfur hexafluoride show that corrections for multiple scattering change internuclear separations by ~0.001 A, and the MAV are affected even more [Mil81], [MiJ92]. Failure of the Independent Atom Model in regions of small s (< 10 A- 1) has already been mentioned. Chemical binding disrupts the symmetry of the valence electrons, reducing the total experimental scattered electron intensity If,n{s) [Kon88]. The change o l can be as large as ten percent for s < 3 A [Nag82]. Tavard and others have shown that the molecular binding energy Eb can be derived from lio 1 (s) according to: 1 ~ = lla(s)ds + El + Ecorr 2n 0 f (2.91) (2.92) where: E 1 is one half the potential energy change of bringing all the independent atoms (with infinite separation) to their molecular positions, and Ecarr is a sum of correlation energies [Tav65b], [Tav66], [Koh67]. The constant ai/4 rescales the electron scattering factors in /(s) to match x-ray scattering factors (Eq. 2.36). intensity based on IAM, The total theoretical scattered I;,: (s) , should also be corrected for multiple scattering effects. Table 2-1 lists some of the molecules whose binding energies have been derived from absolute measurements of total elastic scattering intensity at small angles. Structure Chapter Two: Gas-Phase Electron Diffraction Theory determination may also be affected by chemical binding because ~cr(s) oscillates due to electron density shifts within the molecule. For example, 73 Molecule Reference [Bon63b], [Bon65a], H2 [Tav65a], [Koh67] N2 [Koh67], [Bon69], [Eps77], [Fin79] 02 [Koh67], [Eps77] ~cr(s) for CC4 has a strong oscillation corresponding co [Eps77] to r = 2.9 A (the Cl·· -Cl internuclear separation) CH4 CS2 H20 H2CO H2CCO CCl4 SF6 [Fin70a] because the electronegative chlorine atoms pull charge density away from the central carbon atom [Nag82]. The atomic charge distribution can be distorted by the incident electron as the electron passes the atom. [Nag73], [Nag82] [Tak86] [Sas92] [Sas92] [Nag73], [Nag82] [Pul83], [MiJ92] Table 2-1: Partial list of smallscattering angle GED chemical binding studies. Bonham has accounted for polarization effects in the atomic scattering factors by usmg the second Born approximation, and the perturbations are largest for small scattering angles, slow incident electrons, and particularly atoms with large Z [Bon65c]. In general, though, the changes are both smooth and small enough to be neglected from structure determination. Bonham has also explored the ramifications of the implicit diffraction theory assumption that the incident electron is distinguishable from molecular electrons [Bon62] . Exchange effects were shown to be negligible, except for low electron kinetic energies (< 1 ke V). At high electron kinetic energies, an additional term appears in the atomic electron scattering intensity equation due to relativistic effects [Sei73]: I(s) = ;~ (IJ(s)i2 + Jg(s)i2) (2.93) where f(s) is the direct scattering amplitude and g(s) is the spin-flip scattering amplitude. Chapter Two: Gas-Phase Electron Diffraction Theory 74 Both f(s) and g(s) can be determined using the method of partial waves [RoA88] (the formula for f(s) is similar to Eq. 2.57), but as with polarization and exchange effects, calculations show that the impact of relativistic scattering amplitudes on structure determination is very small [Yat68], [Yat69]. 2.2 Definitions of Internuclear Separation Three different kinds of internuclear separation (re, ra, rg) have been encountered in 2.1 during the discussion of gas-phase electron diffraction theory, but many others are also found in the literature. t This section compares eight definitions of r for polyatomic molecules (Table 2-2). Some r, such as re and rg, correspond to physical definitions of molecular structure; other r, like ra, are directly measured by experiment but are called operational definitions because they have no true physical counterpart. 2.2.1 Physical Definitions of r re is the distance between nuclear equilibrium positions, i.e., the location of the potential well minimum. Theoretical structure calculations usually report re distances, but re generally is not determined by diffraction experiments alone. rz is the distance between the average nuclear positions of the ground vibrational state. These distances are equivalent to ra (defined below) at T = 0 K. If the z-axis links the nuclei in their equilibrium positions, then rz is related to re by: t See, for example, [Kuc72b], [Sei73] , [Sch76], [HaM79], [Har88a], and [Kuc92] . Chapter Two: Gas-Phase Electron Diffraction Theory r 75 Definition Distance between equilibrium internuclear positions. re 0 rz, ra Distance between average nuclear positions of the ground vibrational state (V=O). rv Distance between average nuclear positions of vibrational state v. ra Distance between average nuclear positions for thermal equilibrium at temperature rg Thermal average of internuclear distances. Center of gravity of P(f'J. ra Distance measured with gas-phase electron diffraction. Center of gravity of P(t)/r. ro Distance determined from ground-state rotational constants. rs Distance determined from rotational constants using isotopic substitution and Kraitchman's method. rr Structure defined with r9 bond distances and ra bond angles. T. Table 2-2: Definitions of internuclear separation . (2.94) where the displacements relative to re are averaged for v = 0. Expanding Eq. 2.94 gives: (2.95) ~ Since the average transverse displacements (&)o and (!iy)o are small, the third term in Eq. 2.95 is negligible compared with (11:z.)o and can be dropped: (2.96) The rz distance has special importance because it may be measured both by GED and by spectroscopic analysis [Kuc88]. rv is the distance between the average nuclear positions of vibrational state v. As with rz, rv is related to the equilibrium distance by: (2.97) Chapter Two: Gas-Phase Electron Diffraction Theory 76 ra. is the distance between the average nuclear positions in thermal equilibrium at temperature T. ra. is related to the equilibrium distance by: (2.98) If ra. is measured at different temperatures, then r2 can be determined by extrapolation: (2.99) rg (sometimes called rg(O)) is the center of gravity of the probability distribution P(r). This is the thermal average of internuclear distances, as opposed to ra. which is the internuclear distance between the thermally-averaged atomic positions. Differences between rg and ra. are due to transverse displacement of atomic positions and centrifugal distortion. rg is related to re by: = \✓(re + Llz)2 + (&)2 + (!1y)2}T + Or (2.100) = ((re+ Llz) 1 + (&)2 + (!1;)2) (2.101) (r, + Llz) + Or T (2.102) (2.103) Unlike with ra., the transverse term K in Eq. 2.103 is not negligible because K is the thermal average over the square of the displacement, as opposed to the square of the thermally averaged displacement (see, e.g., Eq. 2.95). K = 0 in diatomic molecules. br is the increase in internuclear distance due to centrifugal distortion, and for a diatomic molecule the distortion can be approximated by [Toy64]: (2.104) Chapter Two: Gas-Phase Electron Diffraction Theory 77 where F is the force constant of the bond. Or is most significant at high temperatures. As discussed in 2.1.6, r 8 for a diatomic molecule can be approximated by: (2.105) using a Morse-like anharmonic oscillator potential [Bar55a], [Bon63a], [Kuc67], [Fin88]. Note that for harmonic oscillators, re= rz =rv =ra = r8 (neglecting Or). 2.2.2 Operational Definitions of r Gas-phase electron diffraction experiments yield ra, the center of gravity of the probability distribution P(r)lr. (ra is also called rg(l)). If P(r) is determined from a Morse-like anharmonic potential (2.1.6), then ra and r8 are approximately related by: (2.106) where the mean amplitude of vibration h is also measured in the GED experiment. The difference between ra and r8 is on the order of 0.002 A. Using Eqs. 2.98, 2.103, and 2.106, ra can be derived from ra by estimating K: (2.107) and rz can be determined with Eq. 2.99 if measurements versus temperature. r0 is an operational internuclear distance determined from ground-state rotational constants. For a diatomic molecule with rotational constant Bo: (2.108) but this equation is not valid for polyatomic molecules because of Coriolis effects. Table 2-3 compares re, r0 , ra, and r8 for several diatomic molecules. Often rs is determined from spectroscopic data (instead of r 0 ) using Kratichman's method for analyzing rotational Chapter Two: Gas-Phase Electron Diffraction Theory constants from molecules with different isotopic substitutions [Kra53], [Cos66]. This method is favored because re and rz can be calculated from 78 co r HCI re 1.2746 1.1282 1.9878 2.6666 ro 1.2839 1.1309 1.9907 2.6678 ra 1.2870 1.1316 1.9931 rg 1.2915 1.1326 1.9942 2.6746 Cb 12 2.6734 rs [Kuc72b]. 2.2.3 Geometrical Considerations Table 2-3: Values of re, r0 , ra, and rq (in A· 1) for several diatomic molecules at 300 K [Kuc67]. The internuclear distances determined from average nuclear positions are geometrically consistent. Non-bonded values of re, rz, rv, and ra. can be found directly from bond distances if the structural symmetry is known. This is not true for rg and ra distances because transverse displacements "shrink" the measured internuclear separations between non-bonded atoms by an amount ◊g- Ignoring centrifugal distortion, ◊g for a linear ABC molecule is: (2.109) (2.110) because the z-axis terms cancel. This effect, known as Bastiansen-Morino shrinkage [BaO60], [Mor60b], was seen in CO2 as early as 1949, although ◊g was less than the experimental uncertainty [Kar49]. Early confirmatory experiments studied linear carbon chains like allene, H2CA=Cn=CcH2, where ◊g(CA .. ·Cc)= 0.006 A [Alm59], and butatriene, rg and ra are "better" measures of internuclear separation because those r based on average nuclear positions, like ra. and rz, project transversely displaced distances onto the z-axis. In contrast, bond angles obtained from rg and ra distances are less accurate because of the shrinkage effect; for example, the rg values reported for allene predict a LCACnCc Chapter Two: Gas-Phase Electron Diffraction Theory angle of 172°. 79 Angles determined from geometrically consistent structures are more reliable. Often molecules are defined by an "ry" structure which combines rg internuclear distances with ra bond angles. 2.3 Diffraction From Specially-Prepared Gas Samples The molecular scattering intensity equation derived in 2.1.6 (Eq. 2.74) represents standard GED experimental conditions: an isotropic gaseous sample in thermal equilibrium, with vibrational population concentrated in the lowest-lying states. As reviewed in Chapter One, there has been considerable interest in applying GED to the study of molecules existing under non-standard conditions. Special methods of sample preparation include high temperature nozzles, electromagnetic fields, and photoexcitation. Clearly all perturbations of the sample must be accounted for in the theoretical model by averaging over a description of the molecular distribution: IM (s) = ct,!JJ: llt Re[exp(i (7/, - 7/ 1)) (exp(i s r,J)~,::7,~'::;J 11 (2.111) i7'j Various parameters relevant to electron diffraction include the vibrational population, the rotational population, spatial orientation, and composition. This section reviews recent theoretical models for systems that are either static (within the temporal resolution of the experiment) or governed by kinetic processes. In ultrafast GED, molecular samples can be prepared with coherent vibrational and rotational motion. Theoretical descriptions of electron diffraction from coherent samples are presented in 2.4 and 2.5. Chapter Two: Gas-Phase Electron Diffraction Theory 80 2.3.1 Spatially-Oriented Molecules Fink et al. have considered the impact of a well- ;:;- - - - - k defined molecular spatial orientation on scattering patterns [Mih89], [Fin89]. <I> The standard equation for ~,' IM(s) assumes that molecules are randomly oriented - I \ 0 \ ko within the sample beam, but under ideal conditions a specific orientation might be selected by using the Stark effect and a hexapole magnet [Par89], or by scattering molecules from a surface [Sit87a], [Sit87b]. Figure 2-10: The scattering geometry for a spatiallyoriented molecule as defined in [Mih89]. For an atom pair A-B positioned relative to the incident electron beam as shown in Figure 2-10, the dot product in Eq. 2.111 becomes: s-rAB = srA 8 (sin(0/2)cosQ - cos(0/2)sinQcos¢) (2.112) where Q is the angle between fAB and ko, and <j> is the azimuthal angle of detection. With this geometry, Fink and co-workers calculated the ratio of scattering cross sections for specific orientations relative to the isotropic model. The cross sections were evaluated for a symmetric-top molecule, methyl iodide, using incident electron kinetic energies ranging from 200 eV to 40 keV. As a first observation, if the internuclear axis is not parallel to the electron beam (Q -:;: 0°, 180°), then the diffraction pattern no longer has cylindrical symmetry because of the cos<j> term. The degree of asymmetry correlates to the molecular orientation. Furthermore, the difference between oriented and isotropic scattering is significant enough across the first 25 A- 1 of momentum transfer that the authors have proposed using GED to characterize the degree of spatial orientation in a molecular beam. Chapter Two: Gas-Phase Electron Diffraction Theory 81 Mihill and Fink also considered the effects of molecules which either "cartwheel" or "helicopter" relative to the electron beam by integrating the scattering intensity over angles <I> (Q = 90°) or Q, respectively [Mih89]. These calculations are equivalent to classically averaging over rotational motion for high J states with a well-defined angular momentum vector. The authors again see marked differences in the scattering intensities dependent, in this case, on the direction of the rotational axis. The topic of diffraction from spatially oriented samples will be explored in greater detail in 2.4 within the context of rotationally coherent laser-excited molecules. 2.3.2 Rotationally-Selected Or -Excited Molecules Kohl and Shipsey developed a theoretical treatment of the scattering intensity from molecules prepared in specific ro-vibrational states [Koh92a], which is a more realistic description of the sample distribution created with the Stark effect. For a symmetric top molecule with quantum numbers J, K, and M, the molecular scattering intensity is: N IJKM (0,0 s,X,) = C(J N 11 + ½)L Llf l\fj\L CJKMn Re[exp(i (77; -17 j )) Fnij(s)] (2.113) i=l j=l i~j 11 = 1 where 0 s is the angle between ko and the electric field vector, Xs is the azimuthal angle of detection, and CnCMn are coefficients given by Choi and Bernstein [Cho86]. The function F 11 ij(s) in Eq. 2.113 is: (2.114) where: cosa = cos(0/2)sin0s cosx s + sin(0/2)cos0s (2.115) P II are Legendre polynomials, the jn are spherical Bessel functions, Zij is the projection of internuclear separation rij onto the molecular symmetry axis, and Ov is a vibrational Chapter Two: Gas-Phase Electron Diffraction Theory 82 amplitude operator. Based on these equations, Kohl and Shipsey have shown that specific rotational states could be identified by the anisotropy and amplitudes in the twodimensional diffraction pattern. GED should be sensitive enough to characterize the relative populations of a mixture of rotational states, even in the presence of an isotropic background signal. The authors have also derived a Fourier-Bessel transform for converting the · asymmetric scattering pattern into a 2-D radial distribution curve [Koh92b]. Of particular interest is the possibility of obtaining additional structural information using the GlauberSchomaker phase shift term. Because Fnu(s) is complex, with real terms dependent on even powers of cosa and imaginary terms dependent on odd powers of cosa (Eq. 2.114), the imaginary components of ln<M can be extracted from the observable if the atom pair is heteronuclear and has a complex phase shift. Heteronuclear and homonuclear atom pairs which happen to have similar r can be distinguished because the homonuclear atom pair will not contribute to the detectable imaginary portion of the observable. Volkmer, Bowering, and others have tested Kohl and Shipsey's equations on diffraction data recorded from state-selected, oriented symmetric top molecules. A beam of methyl iodide was created with a supersonic expansion, state-selected with an electrostatic hexapole lens, and oriented with a linear electric field [Vol96], [Vol92]. A 1 ke V electron beam intersected the molecular beam at right angles, and scattered electrons were detected at specific angles with a rotatable energy analyzer / channeltron. The molecules were oriented either parallel or antiparallel to the electron beam (0s = 0°, 180°), so the diffraction pattern was expected to be cylindrically symmetric. Deviations from the isotropic diffraction pattern were on the order of 5%, and showed qualitative agreement Chapter Two: Gas-Phase Electron Diffraction Theory 83 with Kohl and Shipsey's theoretical predictions. Note that hundreds of rotational states were expected in the sample, and the relative populations could only be approximated using estimates of the molecular beam rotational temperature, expansion conditions, and the lensing properties of the hexapole. Similar results were obtained in a study of methyl chloride [Bow94]. In one experiment, methyl chloride molecules were oriented perpendicular to the electron beam, and an azimuthal scan of the scattering intensity showed the expected asymmetry in the diffraction pattern [Bow95]. 2.3.3 Vibrationally-Excited Molecules The formalism for the scattering intensity from molecules in specific vibrational states is a simple extension of the equation for a vibrating molecule: (2.116) where Pu.v(r) is the probability distribution of vibrational state v for atom pair i, j, and Wv is a weighting coefficient. Simulation of the MS curve from molecules in specific vibrational levels is straightforward if the potential energy surface is known [GeA81], [Isc95]. Ischenko et al. have determined the vibrational-state population distribution of C=S photo fragments based on GED patterns [lsc94c]. The authors used spectroscopic parameters for the PES, and assumed that the vibrational distribution was a Poisson curve. The analytical challenges posed by diffraction patterns of high-temperature samples has been reviewed by Fink and Kohl [Fin88]. One approach is to report the temperature dependence of r8 values and MAV using the scattering equation derived from the groundstate Morse-like anharmonic oscillator (Eq. 2.74). The moment method is a more Chapter Two: Gas-Phase Electron Diffraction Theory 84 sophisticated technique in which perturbation theory is used to find the thermally-averaged moments of normal coordinates. Another approach is the cumulant method, which begins much like traditional analysis for a vibrating molecule by writing instantaneous r as re + x: sin(sr)) ( Sr = Vib (sin(s(re + x))) s(re + X) Vib (2.117) After expanding about lire and using angle-sum relations, the average over displacement can be separated out as (eisx) [lsc88], [Spi81], [Ogu77]. Only the first two terms of the expansion are shown here: According to Kubo, (eisx) can be written as a series expansion [Kub62]: (2.119) where ( xn) c are called the cumulant averages, and the first three terms are: (x)c = (x) (x 2\ = (x 2) - (x)2 (x 3 )c = (x 3 ) - 3(x)2(x) + 2(x)3 (2.120) (2.121) (2.122) For a harmonic oscillator, the only non-zero cumulant average is n = 2, so that: (2.123) and Eq. 2.118 leads to Eq. 2.67 derived in 2.1.6. Chapter Two: Gas-Phase Electron Diffraction Theory 85 The cumulant method has been tested with temperature-dependent SF6 diffraction data and has been found to converge faster than the moment method, usually requiring no more than the first four terms of Eq. 2.119 [Isc89], [Isc88]. An additional advantage of the cumulant method is that diffraction data can be analyzed directly for the equilibrium geometry, re. The complete approach is calculation-intensive, requiring spectroscopic information about potential constants, and therefore may not have wide applicability [Isc94b], but recently a simplified cumulant method has been developed for temperatureequilibrated systems which yields re without spectroscopic data [Isc96b]. 2.4 Rotationally Coherent Samples§ Excitation with an ultrafast laser creates coherent behavior across a molecular sample. The formation of vibrational wave packets has already been introduced in Chapter One; coherent rotational states are also created, with less stringent demands on temporal resolution since rotational motion is slower than vibrational motion. Following ultrafast excitation, the presence of rotational and vibrational wave packets imposes a degree of order on the previously isotropic molecular sample. The nature of the structural and dynamical information that can be obtained from an experiment which combines high temporal resolution with high structural resolution must be established, both in the regime of coherent elementary dynamics and also afterwards, when coherence is lost. This section discusses the diffraction patterns which result when rotational coherence is § An earlier version of 2.4 was published in [Wil94] . Similar ideas were later discussed in [lsc96a] . Chapter Two: Gas-Phase Electron Diffraction Theory induced or recovered. 86 During rotational recurrences, the molecular sample has an anisotropic distribution of spatial orientation, and more structural information, including bond angles and rotational constants, is available than in a conventional GED experiment. These points are illustrated in this section by first considering the structural changes in diatomics, and then examining the impact of rotational coherence on the analysis of dissociation products and molecules with more structural complexity than a diatomic. The effects of vibrational coherence are considered in 2.5. 2.4.1 Rotational And Spatial Coherence To first approximation, the spatial-orientation distribution of laser-excited molecules has a simple dependence on the polarization of the laser and the type of transition accessed. For example, if n is defined as the angle between the dipole transition moment and the polarization vector of the laser (linearly-polarized), then immediately following a parallel-dipole transition, the number of excited molecules at angle Q is proportional to cos2Q. This approximation assumes that the molecular sample is not saturated with laser radiation. If the excitation probability is unity, then 1/3 of the molecules are pumped into a higher state, and the remaining unexcited molecules must have a sin2Q spatial-orientation distribution. In effect, the pump laser converts the isotropic sample into an anisotropic mixture of excited and unexcited molecules with welldefined spatial orientations. The duration of the anisotropy, however, lasts only until rotational motion randomizes spatial orientation: after several picoseconds the sample will again be isotropic, albeit a mixture of excited and unexcited molecules. Rotational motion is quantized and the rotational frequencies are commensurable Chapter Two: Gas-Phase Electron Diffraction Theory (or nearly so). 87 Barring any collisions, there will be some later time at which all the molecules return to their original spatial orientation. The short-lived anisotropic distribution will therefore appear again and again over the course of many nanoseconds [Fel87]. This phenomenon, known as rotational recurrence, has been extensively studied in the context of time-resolved spectroscopy experiments to determine the geometry of large molecules [Bas87], [Bas89], [Bas94], [Man95]. The period of the recurrence in a symmetric top molecule is equal to l/(2B) where B, the rotational constant, is: (2.124) and h is the moment of inertia about the b-axis. For asymmetric tops, there are three key observables: A, B, and C. The temporal width of the recurrence, /::..t, is proportional to the temperature T and the rotational constant [Fel87], [Man95]: (2.125) In Eq. 2.125, B has units of cm-' and Tis in Kelvin. For example, the first recurrence oftstilbene (B = 0.252 GHz) occurs 1.95 ns after excitation and has a full width at half maximum (FWHM) of 21.0 ps at 5 K, and 6.8 ps at 50 K [Fel87]. These estimates have been experimentally verified [Bas86], [Bas87]. Kohl and Shipsey showed theoretically [Koh92a] that the diffraction patterns from molecules in specific rotational states, with well-defined nutation axes, are not cylindrically symmetric and contain extra clues about the molecular structure (2.3.2) . The molecular sample in an ultrafast GED experiment, however, gains a different type of rotational order. Instead of single-state excitation, many rotational states are coherently populated by the ultrafast laser. By combining high temporal resolution with quantized rotations and a Chapter Two: Gas-Phase Electron Diffraction Theory 88 dipole transition, a succession of brief (M) well-ordered spatial-orientation distributions should be observable. In keeping with the discussion of other specially-prepared samples (2.3), diffraction patterns from spatially-anisotropic distributions might contain more structural information than conventional GED patterns. Fink et al. provided an introductory treatment of spatial orientation for molecules prepared in a hexapole field [Fin89], [Mih89]. More degrees of freedom are necessary for modeling the experimental arrangement discussed here than in Fink's model (Figure 2-10). Eq. 2.111 must be evaluated to ascertain the impact of anisotropic spatial-orientation distributions, formed by ultrafast laser excitation, on scattering intensities. These effects must be considered at short times, immediately after excitation, and over longer times, when the recurrences take place and the anisotropic distribution reappears. The methodology is outlined in 2.4.2. 2.4.3 follows with an exploration of the diffraction patterns generated by molecules with perfect spatial alignment; this synopsis will assist in interpreting the more complicated patterns from laser-excited samples. The theoretical diffraction equations for the molecular subset selected by linearly-polarized lasers in parallel and perpendicular configurations (relative to ko) are established in 2.4.4 and 2.4.5, and their application to UGED rotational recurrence studies of molecular iodine is discussed in 2.4.6. Finally, 2.4.7 concludes this section by evaluating the structural information present in the anisotropic diffraction pattern from more complicated molecules, using trifluoromethyl iodide as an example. To emphasize the changes in the diffraction patterns, the excitation probability is assumed to be unity with no saturation. (Of course in an actual experiment stimulated emission and saturation effects will limit the probability to one-half at best, unless the Chapter Two: Gas-Phase Electron Diffraction Theory 89 upper state is dissociative or Rabi cycling is introduced.) All molecular scattering and radial distribution curves presented in this section were calculated for an incident electron energy of 40 keV, and scattering factors were interpolated from published tables as described in Appendix C. Two-dimensional sM(s) and f(r) surfaces were generated with the program PROC3 (D.10); for radial distribution curves, Smax was set at 15 A- 1, and the 0 2 damping constant (kd) was set to 0.01 A . 2.4.2 Theoretical Framework The elastic molecular scattering intensity, IM, from a laser-excited sample must be averaged over the rotational and vibrational probability distributions: I M(s) - ct,t,1t,llt;IRe[exp(iL\1J,) ((exp(is r, )).JJ (2.126) i*j In the context of UGED, though, the average over rotational states can be evaluated as an average over spatial orientation since. Many rotational states are populated, and the important perturbation is the initial (and recurring) spatial orientation distribution which has been selected with the excitation laser's polarization vector. According to this interpretation, Eq. 2.126 may be rewritten as: N I M(s) = N C:L L IJ;IIJjj Re[exp(i ~1Jij) (F:is))vJ (2.127) i=l j=I i j * where: Fij . ( exp(i s • r;j )) Spatial (2.128) contains the spatial average of the scattering function for a specific internuclear separation. Note that Fij is a function of the momentum transfer vector s, and not just its magnitude. To simplify the derivation, only those position vectors rij which are parallel to Chapter Two: Gas-Phase Electron Diffraction Theory -~:J r ,,.,,--- - - - - 90 Plane Of Detector l) X ~ Scattering Center Figure 2-11: Electron scattering geometry used in the text. The incident electron beam travels towards the scattering center along the z-axis with wave vector ko. The position vector between atoms i and j, rii, is defined by altitude angle .Q (relative to the z-axis) and azimuthal angle 'I' (relative to the x-axis). Electrons scatter at angle e with wave vector k and intersect the x-y plane of the detector at angle qi (relative to the x-axis). The momentum transfer vectors connects the z-axis to the inner surface of the sphere swept out by k. the molecular dipole transition axis will be considered at first. This is sufficient for calculating /M(s) for all diatomics and linear molecules; more complicated molecules with non-parallel position vectors will be evaluated in 2.4.7. Figure 2-11 presents the geometrical frame of reference chosen to evaluate F iJ· The incident electron beam travels along the z-axis, and the position vector riJ is oriented relative to the z- and x-axes by an altitude angle Q and an azimuthal angle \jf, respectively. Diffracted electrons strike the flat, two-dimensional detector at a position determined by the scattering angle 0 and the rotational angle <j> (defined relative to the x-axis). In this coordinate system, the incident electron wave vector ko is: (2.129) Chapter Two: Gas-Phase Electron Diffraction Theory 91 and the scattered electron wave vector k is: k = k0 {cosq>sin0, sinq>sin0, cos0} (2.130) so the momentum transfer vectors is written: s = k0 {- cos q> sin 0, - sin </> sin 0, 1 - cos 0} = s {-cosq>cos(0/2), -sinq>cos(0/2), sin(0/2)} (2.131) There will be frequent reference to two-dimensional scattering intensity surfaces, JM(s). Note that the momentum transfer vectors connect the detector origin to the surface of the sphere swept out by k (relative to the scattering center origin). An x-y coordinate system of s vectors, (sx, Sy) in Figure 2-11, is a map of the distances from the detector origin to the sphere, and not simply an x-y coordinate system projected onto the surface of the sphere. To complicate matters, the angle <j> is defined in the x-y coordinate system of the flat detector. Cos<j> in Eq. 2.131 can be written in terms of sx using: cosq> = Proj[xs]/Proj[s] (2.132) where Proj[] refers to the projection of the s-coordinate system onto the flat detector. The projection relation is derived in D.4.1 (Eq. D.14) and can be rewritten as: Proj[s] = L tan( 2 arcs in( s/2k0 )) (2.133) Therefore: 2 - X S cosq> - s 2 (2.134) and the formula for sin<j> in terms of Sy is similar. Following the geometry in Figure 2-11, the internuclear separation vector ru is written: Chapter Two: Gas-Phase Electron Diffraction Theory rij 92 = rij (sin n cos lf/, sin n sin lf/' cos n) (2.135) To simplify the presentation, the subscripts i and j will be temporarily dropped. The dot product of sand r is equal to: s·r = sr(sin(0/2)cosn - cos(0/2)sin0cos(¢-lfl)) (2.136) In order to derive various F(s), the scattering function exp(s·r) must be integrated over the surface of the sphere defined by Q and \jf. The anisotropic spatial orientation is included by multiplying the scattering function with an appropriate distribution function, S(Q,\jf), before integration: 1 11: 211: F(s) = J fS(O,lfl) exp(is •r )sinO dlfl dQ - .. (2.137) 4n o o For the case of an isotropic distribution (S(Q,\jf) = 1), the integral with respect to \jf can be analytically evaluated using Eq. B.29 derived in Appendix B, yielding: F(s) = _!_ f exp(i srsin(0/2)cosn) J (srcos(0/2)sinO)sinQ dQ 0 2 0 (2.138) The integral with respect to Q is evaluated with Eq. B.59: F(s) = J0 (sr) (2.139) giving the same result as derived earlier in 2.1.3 (Eq. 2.48). A two-dimensional plot of the Norwegian school's M(s) curve (Eq. 2.87) for isotropic molecular iodine in the ground vibrational state is presented in Figure 2-12. The harmonic oscillator formulation, Eq. 2 2.69, was used Cra = re - I Ire), with re = 2.6664 A and l = 0.03519 A [Luc80]. The 0 frequency of the oscillations in this familiar ring pattern is equal to ra12rc. 0 Chapter Two: Gas-Phase Electron Diffraction Theory 93 -10 -5 0 5 5 - .... I )<( o)( (/) -5 y -10 Figure 2-12: Electron scattering from an isotropic sample of molecular iodine. The spatial-orientation probability distribution, S(Q, 'I'), is a sphere: the orientation of the '2 axis has equal probability of being in any direction. The molecular scattering pattern M(s) consists of damped cylindrical oscillations with frequency rJ2n. 2.4.3 Diffraction From Perfectly Aligned Diatomic Molecules Anisotropic electron diffraction patterns from laser-prepared molecular samples can be calculated using Eqs. 2.127 and 2.137. Before generating /M(s) for various S(Q,\jf) which might be encountered in experiment, it is useful to first consider the scattering patterns from diatomic molecules with perfect spatial alignment. The functional forms of these patterns require no integration about Q or 'I' and can be derived directly. Two basic arrangements are possible: ( 1) all molecules are oriented parallel to the direction of the incident electron beam, and (2) all molecules are oriented perpendicular to the direction of Chapter Two: Gas-Phase Electron Diffraction Theory 94 the electron beam. In the first case (Q = 0, the bond axis is parallel to the z-axis), the dot product s-r simplifies as: s ·r = sr sin(0/2) = s 2 r/2k0 (2.140) If the potential energy surface is assumed to be harmonic, then the vibrational average can be written as an integral over the displacement x from the equilibrium position, just like in the treatment of an isotropic sample (2.1.6, Eq. 2.64): (2.141) (2.142) Integration about the sine term evaluates to zero because the function is odd, so, using Eq. 3.952-9 of [Gra80], the vibrational average becomes: (2.143) Substituting Eq. 2.143 into Eq. 2.127, the molecular scattering intensity for diatomic molecule A-B aligned perfectly parallel to ko is: IM (s) 2C If, II!Blexf ;;i) Re[exp(i Al) AB )exp(i ~~:)] (2.144) = 2CIJAIIJslexp(- s l{Jcos(11A - 11s + s 2 r)2k0 ) (2.145) = 4 or: 8k 0 The diffraction pattern is cylindrically symmetric, and its profile is an oscillatory function that changes slowly withs at small scattering angles (ko >> s). As shown in Figure 2-13 for Ii, the modified molecular scattering pattern M(s) is an order of magnitude more Chapter Two: Gas-Phase Electron Diffraction Theory - - - Isotropic - - Parallel • • • • • • Perp. x-axis 95 - - - Perp. y-axis 2 -----~--=-~-~------~---------------------------------.·: ,' .. . .. ...... '• .. '• 1 .-. Cl) .._. 0 ~ 0 I 5: . 10 ' 20 -1 \. -2 .... .. ....., .. ,, .. ., Figure 2-13: M(s) scattering profiles from molecular iodine in three different spatial distributions: (1) isotropic, (2) perfect parallel alignment with ko (the z-axis), and (3) perfect perpendicular alignment to ko (along the x-axis). The scattering intensity from the isotropic sample is an order of magnitude less than the perfectly-aligned samples. The oscillation frequency of interference fringes from the parallel configuration begins very 1 slowly; the first cycle finishes at s = 22.2 A" . Scattering from the perpendicular configuration is not cylindrically symmetric. The interference fringes along the x-axis are strong and have a frequency similar to the isotropic pattern, but the corrected scattering intensity along the y-axis is constant. intense than electron scattering from an isotropic distribution, but the oscillation frequency is initially very slow. This has a physical interpretation - since the molecules are struck by the electrons end on, the second atom is "hidden" by the first atom along ko and interference fringes are muted. Although the number of cycles increases with the square of s, there is little structural information present in the range of s available to UED. A two-dimensional plot of M(s) is shown in Figure 2-14. In the second case, when all molecules are spatially-oriented perpendicular to the electron beam (Q =n/2, \j/ =0, the bond axis is parallel to the x-axis), s-r is: Chapter Two: Gas-Phase Electron Diffraction Theory 96 -10 10 S(Q,'I') 5 - ► -5 y -10 Figure 2-14: Electron scattering from molecular iodine when all internuclear axes are aligned parallel with ko. The spatial-orientation probability distribution, S(Q, \JI), is a deltafunction along the z-axis. The molecular scattering pattern M(s) consists of slowly-varying cylindrical oscillations with frequency srJ41tk. s·r = -srcos(8/2)cos</> = ~cos<f>.J4kg - s 2k 0 2 (2.146) The mathematics for evaluating (F(s))vib is identical to the parallel case, and the molecular scattering intensity is found to be: IM (s) = 2Clf Ills !exp(-½( slh cos</Jcos(8/2 ))2) A x (2.147) cos(7JA - 1J 8 + srecos<f>cos(8/2)) The presence of the cos<)> term destroys the cylindrical symmetry usually observed in GED patterns. There are no oscillations along the y-axis, where <I> = '±TC/2 (Figure 2-13), and the Chapter Two: Gas-Phase Electron Diffraction Theory 97 -10 -5 0 5 10 10 5 -5 y -10 Figure 2-15: Electron scattering from molecular iodine when all internuclear axes are aligned perpendicular to ko and parallel with the x-axis. The spatial-orientation probability distribution, S(.Q, 'l'), is a delta-function along the x-axis. The molecular scattering pattern M(s) consists of parallel fringes with frequency recos(8/2)/2n. vibrational damping term has only an x-axis dependence, as would be expected from the experimental geometry. The oscillations along the x-axis have a period similar to the interference fringes from an isotropic distribution, but are an order of magnitude larger in amplitude. A two-dimensional plot of M(s) for the perpendicular configuration, shown in Figure 2-15, clarifies the connection between the horizontal and vertical profiles presented in Figure 2-13. The diffraction pattern from molecules perfectly aligned parallel to the xaxis forms a series of linear fringes, as opposed to concentric rings. This figure is similar Chapter Two: Gas-Phase Electron Diffraction Theory 98 to the interference pattern from Young's double-slit light scattering experiment [Hal78]; in fact, the scattered electron intensity of Eq. 2.147 for a rigid diatomic molecule can be put in a form analogous to the equation for the diffracted light intensity from a pair of slits separated by a distance d. Along <1> = 0: IM(e) oc cos(sr,cos(8/2)) IM (e) oc 2 cos ( / Double Slit ( 8) oc ni = 4 co{ ;, sin(8/2)cos(8/2)) (2.148) 2 sin 8) - sin ( :, sin 8) (2.149) ~ (2.150) 2 COS ( sin 8) The potential wells of the two atoms function as a pair of "slits" for the incoming electrons, and the pattern shown in Figure 2-15 results from interference between the electrons diffracted by these two scattering centers. Perfect alignment of the sample molecules affects both the amplitude and the frequency of the interference fringes in the diffraction pattern. The amplitude increases by an order of magnitude, which implies that the signal-to-noise ratio for molecular scattering from spatially-oriented molecules should be larger than from isotropic scattering. This increase in signal-to-noise might counterbalance the more realistic expectations of the percentage of molecules actually contributing to the anisotropic diffraction pattern in an experiment. For both parallel and perpendicular configurations, the oscillation frequency depends on r,, and not the ra value which appears in the isotropic equation. This is because the vibrational average takes place about P(r), instead of the function P(r)/r. Still, the oscillation frequency of the diffracted intensity from the parallel configuration is Chapter Two: Gas-Phase Electron Diffraction Theory fundamentally different from that of the perpendicular configuration. 99 Structural information is more difficult to obtain in the first case because the initial oscillations are very slow; the diffraction pattern would have to be measured out to large values of s. In the perpendicular configuration, however, the oscillation frequency along the x-axis is re .J 1 - (s I 2k0) /2n, which approaches the frequency of the isotropic distribution, ra12TC, 2 at high electron energies where ko is large. The diffraction pattern from the perpendicular configuration also potentially contains information about bond angles. Figure 2-15 tells the experimentalist that the iodine bond axis is parallel to the x-axis; if \j/ were non-zero, then the interference fringes would be similarly r.otated on the detector by angle \j/ relative to the x-axis. The diffraction pattern from more complicated molecules is a sum of contributions from individual atom pairs, and interference fringes in the diffraction pattern will reflect the differing spatial directions of the various ru. This topic will be developed further in 2.4. 7. 2.4.4 Diffraction When The Laser Polarization Vector Is Parallel To k0 The laser beam, electron beam, and molecular beam are all mutually orthogonal in the Zewail laboratories' UGED experiment. The experimental design is motivated by ease of construction and a desire to reduce velocity mismatch broadening in the total temporal resolution [Wil93]. With reference to Figure 2-11, the laser travels towards the scattering center along the y-axis, and the polarization vector can be oriented in one of two ways relative to the electron beam. This section considers the diffraction patterns which result when molecules are excited by a linearly-polarized laser where the polarization vector is parallel to the wave vector ko. Scattering is assumed to occur before the molecules rotate Chapter Two: Gas-Phase Electron Diffraction Theory 100 out of their initial distribution; diffraction patterns at later times are considered in 2.4.6. For a parallel-dipole transition in this geometry, the spatial orientation distributions of both excited and unexcited molecules will be cylindrically symmetric about ko, and the diffraction pattern should reflect this symmetry. The orientation of the excited molecules' internuclear axis will have a spatial distribution of S(.Q,\j/) = cos2.Q, and the spatial distribution of the unexcited molecules will therefore be S(.Q,\j/) = sin2.Q. As in the discussion of perfect alignment, all position vectors are assumed to be parallel to the transition-dipole excitation axis, and the excitation probability is unity with no saturation. Integration of Eq. 2.137 about \j/ is identical to the isotropic distribution, giving: F(s) = f .!_ exp(isrsin(0/2)cosn) 10 (srcos(0/2)sinO)sin 3 .Qd.Q (2.151) 2 0 for the parallel / excited (PLE) spatial distribution. Eq. 2.151 can be integrated analytically about .Q using Eq. B.60 to give: PLE: (2.152) The parallel / unexcited (PLU) spatial distribution function is equivalent to the isotropic F(s) minus the PLE F(s): PLU: (2.153) Calculating ( F(s ))vib for the harmonic oscillator model requires the same mathematics and approximations that were presented in 2.1.6. Recall that for the isotropic F(s): (2.154) Chapter Two: Gas-Phase Electron Diffraction Theory 101 where r = r,, - I;, /r, . In a similar way it can be shown that: 0 _ - j 1 (sr )) ( sr 1;· (sr)) 2 Vib \ Vib exp (-.l 2 2 )[sin(s(,;,-2/;,/r,)) cos(s(r0 -z;,/r,))] 2 s lh 3 3 2 2 sr, sr, = exp(- -21 s2 lh2 ) (2.155) x (2.156) Typically the correction term I;,/r, is on the order of 0.002 A or less, well below the expected resolving power of ultrafast GED. Using just ra in all the sine and cosine terms of Eqs. 2.155 and 2.156 is not an unreasonable approximation, and the equations can be simplified in terms of the spherical Bessel functions. As expected from the experimental geometry, the F(s) for PLE and PLU are independent of <p. Profiles of the modified molecular scattering function for these two distributions (using ground-state iodine) are compared with the isotropic distribution in Figure 2-16. The scattering contribution from the PLE subset of molecules is relatively weak; evidently the strong scattering signal observed in 2.4.3 (when all molecules are oriented parallel to the electron beam - Figure 2-13 and Figure 2-14) is rapidly washed out by interference with the scattered intensity from molecules slightly off-axis to the electron beam. Because this contribution is weak, the oscillation frequency of the scattering intensity from the PLU subset is nearly identical to the isotropic distribution. The oscillation frequency from the PLE subset is similar, but phase-shifted by ~rc/2. Since all distributions are calculated for the same species, the sum of the two scattering signals is equal to the diffraction signal from the isotropic distribution. Consequently, if the excited Chapter Two: Gas-Phase Electron Diffraction Theory 1 ---Isotropic 102 - - - Parallel/ Excited ······Parallel/ Unexcited .-. Cl) -o ~ Cl) 0 -1 l 10 s (A- 1) Figure 2-16: Modified molecular scattering intensities of ground-state molecular iodine in three spatial distributions: (1) isotropic, (2) parallel / excited (PLE), and (3) parallel / unexcited (PLU). Note that these are sM(s) curves, not M(s) curves. The intensity of interference fringes from the PLE distribution is weak - nearly an order of magnitude less than the other two patterns. The oscillation frequency is similar to the isotropic and PLU distributions but ~rr/2 out of phase. species is structurally identical to the unexcited species, the diffraction pattern will not change. No additional structural information was present in the diffraction pattern from a sample with perfect parallel alignment (2.4.3); in fact, the internuclear separation is more difficult to extract because the interference terms varied slowly with s across usual detection ranges. The same principles are true for the diffraction signal from the PLE subset. Like the isotropic pattern, the PLE signal depends only on the magnitudes of the position vectors, but determination of the excited-state molecular structure would be difficult because the signal amplitude is so low. The PLE scattered intensity would be overwhelmed by the diffraction signal from unexcited molecules. 2.4.5 Diffraction When The Laser Polarization Vector Is Perpendicular To ko Significantly different effects are observed when the polarization vector of the laser is parallel to the x-axis and perpendicular to ko. As with perfect perpendicular alignment, Chapter Two: Gas-Phase Electron Diffraction Theory 103 the scattering pattern loses its cylindrical symmetry because the spatial orientation distribution selected with the polarized laser is not symmetric about the z-axis. With an excitation probability of unity, the distribution of the excited molecules is defined by S(Q, 2 2 2 2 \j/) = sin Qcos \j/ and the distribution of the unexcited molecules is (1 - sin Qcos \j/) . For the perpendicular / excited (PPE) spatial distribution function, the double integral is: 2 F(s) = l 1r: sin Q [ J 1r: cos 1f1 exp(i s •r) dlfl ] d.Q -J 4n o o 3 2 (2.157) Integration of Eq. 2.157 over 'I' makes use ofEq. B.46 in Appendix B, yielding: F(s) = ~] sin 3 Qexp(isrsin(0/2)cosn.) x 0 (2.158) li(srcot?tnD.) - cos' c/J J 2 (srcos(0/2)sinQ)] d.Q [ srcos 0 2 smQ Integration over Q using Eq. B.59 gives the following equation for the PPE F(s): PPE: (2.159) The perpendicular / unexcited (PPU) spatial distribution function is found by subtracting the PPE F(s) from the isotropic F(s): PPU: (2.160) Averaging over harmonic vibrations is the same as for PLE and PLU. The presence of the cos2cp term in Eqs. 2.159 and 2.160 means that both functions are not cylindrically symmetric. A two-dimensional plot of M(s) where all ground-state iodine molecules are in a PPE distribution (3xPPE) is shown in Figure 2-17. Figure 2-18 compares sM(s) surfaces of the isotropic and PPU distributions. Both the PPE and PPU Chapter Two: Gas-Phase Electron Diffraction Theory 104 -10 S(Q,'I') 10 5 X -5 z y -10 Figure 2-17: Electron scattering from a perpendicular / excited (PPE) distribution of molecular iodine when the polarization vector lies along the x-axis. The spatial-orientation 2 probability distribution, S(.Q, \Jf), is equal to 3xsin .Qcos2\j/ (the factor of three is a normalization constant). The molecular scattering pattern M(s) resembles a cross between the isotropic pattern (Figure 2-12) and the perfect perpendicular alignment pattern (Figure 2-15). The interference fringes along the x-axis are enhanced compared with the isotropic pattern. patterns appear to be a cross between isotropic scattering and the scattering from a sample with perfect perpendicular alignment (Figure 2-15). Ignoring any structural changes due to excitation, the PPU distribution is actually a mathematical mixture of a parallel / excited distribution and a perpendicular / excited distribution (in which the laser polarization vector lies along the y-axis). Since the PLE distribution contributes little to molecular scattering (Figure 2-16), the strong interference fringes in the PPU distribution are generated by only 1/3 of the original molecular Chapter Two: Gas-Phase Electron Diffraction Theory population (Figure 105 2-18). Furthermore, the <I> dependence of the fringes indicates the directionality of r1_1, as mentioned -10 in2.4.3. Two-dimensional distribution functions radial of the isotropic and PPE distributions are shown in Figure 2-19. As might be expected from the appearance of the PPE sM(s) surface, the corresponding radial distribution function also indicates the -10 directionality of the iodine-iodine internuclear separation during the experiment. The disappearance of the 2.7 A peak along the y-axis reflects the fact that most molecules oriented parallel to the laser beam axis are not in the perpendicular / excited subset after a parallel dipole transition. Figure 2-18: sM(s) patterns from ground-state molecular iodine. (Top) Isotropic distribution. The M(s) isotropic pattern was shown in Figure 2-12. (Bottom) The perpendicular / unexcited (PPU) pattern. The internuclear axes of unexcited molecules tend to lie along the y- and z-axes, so interference fringes are strong along the detector's y-axis and weak along the xaxis. Chapter Two: Gas-Phase Electron Diffraction Theory 106 The radial distribution function to corresponding the perpendicular / unexcited subset (not shown) contains a peak along the y-axis and no peak along the x-axis. I I I Admittedly, the sine transform of Eq. 2.127 using the y - Axis 0.0 0 .0 x - Axis function in Eq. 2.159 generates only a crude approximation of D(r) (see 2.1.7), which is reflected in the fluctuating baseline of the surface (Figure 2-19). appropriate techniques More for extracting f(r) will be considered in the future (perhaps based on Kohl and Shipsey's work [Koh92b]), but for now the sine transform is sufficient to provide excellent qualitative information. When molecular scattering from trifluoromethyl iodide is y - Axis x - Axis In tern uclear Separation (A) Figure 2-19: One quadrant of 2-D radial distribution curves tor ground-state molecular iodine. (Top) f(,) from an isotropic sample. The ring has a radius of ~2.7 A. (Bottom) f(,) from a perpendicular / excited (PPE) distribution. The intensity at 2.7 A is strong along the xaxis and weak along the y-axis, which reflects the physical orientation of the iodine molecules in the laboratory reference frame. Chapter Two: Gas-Phase Electron Diffraction Theory 107 considered in 2.4. 7, the radial distribution function is still seen to provide a structural description that is easier to interpret by visual inspection than the molecular scattering function. 2.4.6 Experimental Applications The diffraction pattern from laser-prepared molecules differs from the isotropic pattern because the excitation-process is spatially selective, dependent on the orientation of the transition dipole. The expectation, of course, is that structural parameters change following excitation - otherwise the total scattering pattern (PLE + PLU or PPE + PPU) merely sums to the isotropic formj 0(sr). The excited-state structure usually differs from the ground state structure to some degree, and electron diffraction is quite sensitive to small changes. Figure 2-20, for example, compares isotropic sM(s) curves for the lowest vibrational levels of ground-state iodine and of B-state iodine. The next few paragraphs discuss how rotational coherence effects can be combined with the diffraction patterns discussed in 2.4.4 and 2.4.5 such that more structural information --XState - - - - - - B State I about the scattering molecules can be extracted than in conventional GED. With distribution, an isotropic the signal-to-noise ratio of the sM(s) curve can be improved by averaging the total Figure 2-20: Comparison of sM(s) curves for isotropic distributions of ground-state and B-state molecular iodine, both in the v = O vibrational level. Structural parameters are from [Luc80]. Chapter Two: Gas-Phase Electron Diffraction Theory scattering intensity at a constant value of s around the detector. 108 When the laser polarization is parallel to the electron beam, the diffraction patterns from excited and unexcited subsets are cylindrically symmetric and can therefore be averaged in a similar way. The parallel arrangement, however, only leads to subtle changes in the diffraction pattern, and these patterns do not contain extra structural information (2.4.4). Instead, full attention will be turned to the scattering patterns formed when the laser polarization vector is perpendicular to ko. In this case, the diffraction pattern loses cylindrical symmetry and the signal cannot be averaged over the entire detector. Variations in the diffraction pattern must be particularly distinct, and ideally there would be some way to separate the scattering signal of the excited species from the unexcited species. The scattering pattern at early times, in the instant after the molecular sample has been excited by the polarized laser, will be considered first. The excited and unexcited molecules have not had a chance to rotate out of their anisotropic spatial distributions, although they will have undergone several vibrations. A simple experiment of this type is excitation of iodine from the X state to the bound B state (a parallel dipole transition). For demonstration purposes, the influence of Franck-Condon overlap will be ignored, and it is assumed that the excitation laser places ground state molecules into the lowest vibrational level of the B state. The ground state molecules are also assumed to be in the lowest vibrational level. (A more detailed investigation of the B<c--X transition must account for the impact of overlap and vibrational motion.) The resulting diffraction pattern is a sum of the PPE distribution (Eq. 2.159) evaluated for the B state (re = 3.0267 A, la = 0.04598 A) plus the PPU distribution (Eq. Chapter Two: Gas-Phase Electron Diffraction Theory 109 2.160) evaluated for the X state (re = 2.6664 A, la = 0.03519 A) [Luc80]. The modified molecular scattering pattern from this system -10 (Figure 2-21) reflects the anisotropy of the sample. The oscillation frequencies along the x and y-axes are clearly different, but extracting information on the excited-state species is non-trivial because the background signal from the unexcited molecules also depends on <j>. Other possible -10 approaches should be considered, as discussed below. Iodine can be excited to a dissociative state instead of a bound state. The dissociation Figure 2-21: sM(s) patterns from a mixture of ground-state (2/3) and B-state (1/3) molecular iodine. (Top) Scattering pattern immediately after excitation. B-state iodine is in a PPE distribution and X-state iodine is in a PPU distribution. The oscillation frequency along the x-axis is slightly greater than along the y-axis, which reflects that B-state molecules (re = 3.027 A) are parallel to the x-axis and the unexcited molecules (re = 2.667 A) remain in the y-z plane. (Bottom) Scattering pattern a few picoseconds after excitation. Spatial anisotropy has been lost due to rotational motion, and the diffraction pattern now corresponds to an isotropic mixture of the two species. Chapter Two: Gas-Phase Electron Diffraction Theory time is very fast - within a few hundred femtoseconds [Bow89] - 110 so shortly after excitation the molecular sample will consist of atomic iodine in the PPE distribution and molecular iodine in the PPU distribution. The diffraction pattern will therefore be equivalent to Figure 2-18. The change in the diffraction pattern is distinct, and additional structural information about the ground state species has been determined: the directionality of r,_,. Over longer times, the anisotropic distribution of the unexcited iodine molecules will be lost due to rotational motion, and the electron diffraction pattern will correspond to an isotropic distribution. The amplitude of the rings will be 2/3 of the early-time amplitude along the x-axis, assuming that the excitation laser has dissociated all of the molecules in the perpendicular / excited subset. Approximately 1/2B picoseconds after laser excitation, however, a rotational recurrence will take place and the anisotropic distribution will appear once again. (A half-recurrence will also occur earlier at 1/4B picoseconds [Fel87] .) By taking a series of diffraction patterns in time, it will be possible to mimic the spectroscopic rotational recurrence experiments of Felker et al. , and determine the rotational constant with UED. The experimentalist looks for those times at which the isotropic distribution changes to the anisotropic pattern. Rotational recurrence studies of the ground-state species are therefore possible with UED. Observing rotational recurrences with UED is a time-domain technique for measuring rotational constants, but rotational recurrences can also be used to distinguish between the structures of ground-state and excited-state species. The early-time diffraction pattern from excitation of the B(-X transition was anisotropic, but did not Chapter Two: Gas-Phase Electron Diffraction Theory distinguish well between 111 the excited and ground-state species (Figure 2-21). This will not be the case at later times because the -10 rotational constants of the ground and excited-state species are different, and the recurrences will be separate and distinct. As an example, with ground-state iodine (v = 0), Bx = 0.0373 cm- 1 and 1/2Bx = 447 ps; for iodine in the B state (v = 0), B 8 1 = 0.0289 cm- and 1/2Bs = 577 ps [Luc80] . -10 These recurrences are well-resolved in time, and the scattering pattern at each recurrence will correspond to a sum of one species in an isotropic Figure 2-22: sM(s) patterns from mixtures of ground-state and 8-state molecular iodine during subsequent rotational recurrences. The laser polarization vector is parallel to the xaxis. (Top) At 447 ps the ground-state molecules recur. 2/3 of the molecules are X-state in a PPU distribution and 1/3 are B-state in an isotropic distribution. (Bottom) At 577 ps the B-state molecules recur. In this example the sample has been excited along both the x- and y-axes, so 1/3 of the molecules are X-state in an isotropic distribution and 2/3 are 8-state in a mixture of PPE and PLE distributions. Chapter Two: Gas-Phase Electron Diffraction Theory 112 distribution and the second species in an anisotropic distribution. Studies of excited-state species are best conducted with a pair of ultrafast laser pulses which have orthogonal polarization vectors, such that the diffraction signal for the excited species is a sum of the parallel and perpendicular distributions. Although the parallel contribution does not add much to the scattering pattern, the isotropic background signal from the unexcited molecules would be reduced by a factor of two. The excited pattern is easier to discern because only 1/3 of the sample remains unexcited. Scattering patterns for molecular iodine at 447 and 577 ps are presented in Figure 2-22. At 447 ps, the interference fringes corresponding to ground-state iodine are enhanced along the y-axis; in contrast, at 577 ps the interference fringes of excited-state iodine are enhanced along the x-axis. In both figures, the x and y-axis scattering profiles are different in frequency and amplitude; separation of the ground and excited-state scattering patterns has been accomplished by exploiting the differences in the period of the rotational recurrences in UED. 2.4.7 Diffraction From Nonlinear Molecules The enhancement of the interference fringes shown in Figure 2-22 is perhaps a little misleading because iodine is a simple diatomic molecule. In general, the scattering pattern of a molecule with many atoms is a sum of different frequency components from the various internuclear separations, and therefore the total signal results from a combination of constructive and destructive interference between these different components. Furthermore, the scattering theory developed in 2.4.2 does not adequately describe nonlinear molecules because only position vectors parallel to the transition dipole Chapter Two: Gas-Phase Electron Diffraction Theory 113 axis have been considered. To correct this, the scattering pattern from all \ II fl II \ position vectors will now be \ \ V \ usmg considered 1:;QF F trifluoromethyl iodide as an example. The transition dipole is assumed to lie parallel to the C-1 bond. rF.. ·F ~---,.,----,Iii?) ' rC-1 Figure 2-23: (Top) Structure of trifluoromethyl iodide. (Bottom) Spatial distributions of the four CF3 1 position vectors after a parallel-transition dipole along the C-1 bond axis has been excited. The three remaining position vectors (rc-F, rF .. .F, rF ... ,) sweep out cones defined by Qii, where Qii is the r1 angle between rc-1 and ~ii- The structure of CF3I is shown in Figure 2-23. Excitation of a dipole transition parallel to the C-1 bond is independent of the angular position of the fluorine atoms around the C-1 axis, and the scattering pattern must account for an average over all possible rotational orientations of the other internuclear separations. As demonstrated in Figure 2-23, each position vector rij sweeps out a cone about the C-1 axis; the angle between the C-1 axis and each cone is defmed by Qij, using the r 1 structure (2.2.3). The geometry of this arrangement is shown in Figure 2-24, where the angle a defmes the angular position of rij about the excitation axis. In the primed coordinate system, riJ is: (2.161) where Qij is the angle between rij and the excitation axis. The primed coordinate system can be transformed into the unprimed coordinate system according to: Chapter Two: Gas-Phase Electron Diffraction Theory 114 X Figure 2-24: Scattering geometry for a position vector rii that is not parallel to the excitation axis. The excitation axis i is defined by altitude angle .Q and azimuthal angle 'I' (see Figure 2-11). The angle between rii and i is .Qii· The position vector sweeps out a circle in the primed coordinate frame where a is defined relative to the x'-axis. Calculation of the scattering pattern requires a triple integration over a, n, and '1'· To simplify the illustration, the x'- and y'-axes are shown intersecting the i-axis at r;pos.Qii and not i = 0. x] y [z = [sinQcoslfl] [cosQcoslfl ru cos Q ij sin Q sin lfl + cos~ sin lf/ cosQ -smQ -sin lfl COSlf/ 0 sin Q cos lfl][x'] sin Q sin lfl y' cosQ (2.162) z' Application of this transform to Eq. 2.161 leads to: (sin Q ii cos a cos Q + cos Q ij sin Q) cos lfl - sin Q ij sin a sin lf/l ru = ru ( sin Qij cos a cosQ + cosQ;j sin Q) sin lfl - sin Qu sin a cos lfl [ (2.163) cosQu cosQ- sinQ;j cosasinlfl Note that if ru is parallel to the excitation axis (Ou = 0) then Eq. 2.163 simplifies to the earlier definition of ru (Eq. 2. 135). The momentum transfer vectors is independent of Ou and a, but Fu(s) must now include a third integration about the circle defined by a and Chapter Two: Gas-Phase Electron Diffraction Theory 115 rijsin.Qij to average over different rotational positions about the excitation axis: 2 F;/s) = 2 -f f -f 1 n: n: [ 1 n: ] s(n,l/f) exp(is·r;j)da sin.Qdl/f d.Q 4n O O 2n 0 (2.164) Note that the weighting distribution Sis independent of .Qij because S depends only on the angle between the excitation axis (the C-1 bond in the example discussed here) and the laser polarization axis. The inner integral can be evaluated analytically using Eq. B.29 in Appendix B. The resulting double integral was integrated numerically with Mathematica, and analysis of the calculated molecular scattering curves led to the following equation for the perpendicular/ excited spatial distribution when .Qij is arbitrary: F"(s) = j, ::r") - (sin Q" + (2- 3sin n,; )cos'~ cos (0/2)/ ~Y;;) 2 2 2 2 (2.165) I} This equation agrees with the numerical integration results to at least ten decimal places, and reduces to Eq. 2.159 when .Qij = 0. The structural constants ra, l, and nu for CF31 are summarized in Table 2-4 [Typ78], [AnA72]. Figure 2-25 plots the sM(s) surfaces for isotropic and PPU distributions of CF3I, and the corresponding two-dimensional Pair # ra (A) l (A) na C-F C-I F···F F·•·I 3 1 3 1.3314 2.1409 2.1535 2.8916 0.0510 0.0465 0.0547 0.0812 110.82 0.0 2 90.02 154.62 3 Table 2-4: Structural parameters of CF3 1obtained from [Typ78]. radial distribution curves are presented in Figure 2-26. The isotropic pattern f(r) consists of three rings: the inner ring corresponds to the C-F atom pairs, the middle ring is an overlap of the C-1 and the F-· ·F atom pairs, and the outer ring corresponds to the F-··1 atom pairs. A profile of this cylindrically symmetric pattern is shown in Figure 2-27. All three rings are present in the perpendicular / unexcited distribution, but now Chapter Two: Gas-Phase Electron Diffraction Theory 116 the amplitude of each ring varies with the angle <p. The order in the molecular sample (imposed by the excitation laser) provides more structural information m -10 the diffraction pattern because atom pair components are separated as a function of q>. The amplitude of the middle ring is approximately half as large as the isotropic distribution since the C-I and the F-··F components are orthogonal. -10 The C-I scattering contribution should be similar to the molecular iodine pattern in Figure 2-18; rc.r contribution from F· ••F atom pairs is closer to the pattern in Figure 217. The sum of the two contributions leads to a complete ring at ~2.15 A. The area of a Figure 2-25: sM(s) patterns from trifluoromethyl iodide. (Top) Isotropic sample. (Bottom) A PPU distribution where the laser excites a parallel transition along the C-1 bond axis and the polarization vector is along the x-axis. Dissociation products are not included. The pattern loses cylindrically symmetric but interpretation is less straightforward because three of the rij are not parallel to rc.1. Chapter Two: Gas-Phase Electron Diffraction Theory 117 radial distribution curve peak is proportional to nuZ;Z/ru (Eq. 2.86), where nu is the number of identical atom pairs present in the molecule and Z; is the atomic number of atom i. In many cases it would be possible to identify y - Axis x - Axis overlapping components because their maximum peak areas would be different, but in this example it happens that ZcZ1 ::::: 3Zl Still it is possible to distinguish the components, because the C-1 interference fringes are damped 4.0 by the cos(T\c-T\ 1) phase term and the F···F interference fringes are not damped. Consequently, the y - Axis 0 .0 x - Axis Internuclear Separation (A) Figure 2-26: One quadrant of 2-D radial distribution curves for trifluoromethyl iodide. (Top) f(r) from an isotropic sample. The inner ring corresponds to the C-F separation, the middle ring is a sum of C-1 and F- --F separations, and the outer ring corresponds to the F-. -I separation. (Bottom) transform of the PPU distribution in Figure 2-25. The inner ring is most intense along the x-axis because rc-F is almost perpendicular to rc-1. The outer ring is most intense along the y-axis because rF ... 1 is almost parallel to rc.1. The two components of the middle ring have been separated along the x- and y-axes because rc.1 .l rF ... F. Scattering from rc.1 is found along the y-axis and scattering from rF ... F is found along the x-axis. Chapter Two: Gas-Phase Electron Diffraction Theory F· ··F peak is expected to be 118 F·••I narrower and taller than the C-1 peak, and this is confirmed in the profiles (Figure 2-27). a.. ;;::- The PPU radial Isotropic distributions in Figure 2-26 and in the profiles of Figure 2-27 provide qualitative information about the 0 angles nc-F and nF···l· A quick glance at the inner ring shows that the C-F bond is almost orthogonal to the C-1 bond because the peak is larger on the x-axis than on the 1 2 3 Internuclear Separation (A) 4 Figure 2-27: Radial distribution curve profiles of isotropic and PPU CFsl distributions. The curves have been baseline-corrected to emphasize the changes in each peak (compare with the uncorrected surface in Figure 2-26). As discussed in the text, the C-1 and F·· ·I peaks are most intense along the y-axis and least intense along the x-axis. The C-F and F···F peaks are most intense along the x-axis. y-axis. Conversely, the amplitude distribution of the outer ring shows that n f...1 must be closer to 0° (or 180°) than 90°. It should be possible to determine n uwith great precision by carefully fitting the x and y-axis molecular scattering curves, providing another link between r8 and ra• In x-ray crystallography, the entire structure of the unit cell is mapped out by taking a series of diffraction patterns using different crystal orientations. This process can be imitated in UED to some extent by exciting different dipole transitions - the perpendicular / unexcited radial distribution of CF31 will be different if the excitation axis is parallel to a C-F bond. These diffraction patterns thus contain information about the nature of the excited transition (perpendicular versus parallel, etc.), in addition to Chapter Two: Gas-Phase Electron Diffraction Theory 119 Spatial Orientation Distribution S(Q,\j/) f F;1{s) Isotropic 1 1 j 0 (sr) PLE cos Q 2 1/3 j,(sr) - sin 2 (0/2)j2 (sr) sr PLU sin Q 2 2/3 j 0 (sr) - j 1(sr) + sin 2 (0/2)j2 (sr) sr PPE sin Qcos '1' 1/3 j 1 ( sr) - - cos 2 ¢cos 2 ( 0/2 ) j 2 ( sr ) PPU 1 - sin 2Qcos2\j/ 2/3 2 PPE, 2 arbitrary Q;i 2 sin Qcos2'1' 1/3 sr j 0 (sr) - ji(sr) + cos 2 ¢cos 2 (0/2)j2 (sr) sr 11 ~;r) - (sin 2 Q ii +(2-3sin 2 nii)cos 2 ¢cos 2 (0/2)) 1 2 ~r) Table 2-5: Spatial distribution functions F;i{s) for various S{Q,\j/). f is the fraction of molecules in the sample which comprise that spat_ial distribution. All r;i have been written as just r. structural details. Finally, rotational recurrence UED provides a unique opportunity for determining the rotational constants and structure of radicals and other dissociation products. If the dissociation takes place more quickly than the duration of the rotational recurrence, then the dissociation products will have anisotropic spatial orientation distributions. For example, CF3l readily dissociates into CF3 and atomic iodine when excited by a 266 nm laser pulse. The CF3 radicals will take on a PPE distribution at each rotational recurrence. Since the moment of inertia of CF3 is not equal to the moment of inertia of CF3I, the rotational recurrence times of CF3 will be different and potentially observable if the experimental temporal resolution is high enough. A summary of the spatial orientation distribution functions, Fu(s), derived in this section is presented in Table 2-5. Chapter Two: Gas-Phase Electron Diffraction Theory 120 2.5 Vibrationally Coherent Sample~ In the previous section it was shown that additional structural and spectroscopic information can be obtained by observing the diffraction pattern of a laser-excited molecular sample during rotational recurrences. The experimental factors that enable this are the ultrafast laser pulse, which creates a coherent superposition of rotational states, and the ultrafast electron pulse, which has sufficient time resolution (a few picoseconds) to record the diffraction pattern of the molecular sample during the rotational recurrence window. -· This section investigates the impact of vibrational coherence on gas-phase electron diffraction patterns. A femtosecond laser pulse creates the coherence by exciting a superposition of vibrational eigenstates. In FfS, the time evolution of this wave packet on unbound, bound, and quasi-bound potential energy surfaces is monitored with a second femtosecond laser pulse. As discussed in Chapter One, ultrafast GED can provide complementary information about the dynamics and PES' s of molecular systems. Less preliminary spectroscopic information is required than in most FfS studies because the ultrafast electron probe interacts only with the state of interest, and not with some second, higher state. Furthermore, the dynamics along the reaction coordinate can be extracted for complex systems because UGED records all structural changes - the R(t) surface. To demonstrate time-resolved GED studies of vibrational coherences, diffraction patterns have been determined as a function of time by calculating the electron scattering § An earlier version of this section was published in [Wil94] . Chapter Two: Gas-Phase Electron Diffraction Theory from classical trajectories of molecular iodine excited to the B state. 121 The scattering patterns were calculated for two different values of the electron pulse / velocity mismatch temporal resolution ('te), 50 and 500 fs. 2.5.1 introduces the molecular scattering equation used in conjunction with the trajectory calculations, and the trajectory calculations themselves are then described in 2.5.2. The results are broken up into a discussion of the case when B-state iodine dissociates (2.5.3), and the case when B-state iodine is trapped within the potential well (2.5.4). This section concludes by examining the experimental applications of UGED to molecular dynamics studies on longer time scales. 2.5.1 Basic Principles To emphasize the role of vibrational coherence in the diffraction patterns, the effects of anisotropic spatial orientation distributions in the scattering sample are ignored and the excited molecules are assumed to have an isotropic distribution. The diffraction patterns will therefore be cylindrically symmetric and consist of sums of the zero order spherical Bessel function, j 0 . This accounts for the rotational averaging shown in Eq. 2.126, but vibrational averaging must be considered differently. The classical trajectory calculation consists of a molecular ensemble in which the initial conditions of each trajectory are randomly determined with a Monte Carlo technique according to some probability distribution. The total number of trajectories, NT, must be sufficiently large such that the macroscopic dynamics emerge by averaging the behavior of the individual trajectories. Consequently, if the molecular scattering curve is calculated from a large number of trajectories, then the total scattering should automatically account for vibrational averaging. Chapter Two: Gas-Phase Electron Diffraction Theory 122 The modified molecular scattering intensity from a set of NT trajectories for molecular iodine condenses to: (2.166) where rn(t) is the evolution of the internuclear separation of the nth trajectory in time. Two-dimensional diffraction plots with the modified molecular scattering along the abscissa (in A- 1) and time along the ordinate (in fs) have been created. Generating radial distribution curves from these plots is straightforward. Similar ultrafast GED simulations of coherent vibrational dynamics have been calculated for Nal, IBr, and ICN [Ewb94], [Isc94a]. 2.5.2 The Molecular Dynamics Simulation With molecular dynamics simulations of solutions, Bergsma et al. have shown the calculated vibrational dynamics of iodine in different solvents following x-ray diffraction [Ber86]. Here, the trajectory calculation was designed to mirror the UGED experimental excitation process, where the pump laser excites isolated molecular iodine and creates a wave packet on the B state. The evolution of the wave packet was recorded for each trajectory in a one-dimensional array, rn(t), and the diffraction pattern at a specific time ts was obtained by summing the scattering contributions from all rnUs) (Eq. 2.166). The diffraction patterns from several different excitation energies are compared: 2000, 3000, and 4000 cm- 1, which are below the dissociation energy, and 4750 cm- 1, which is above the dissociation energy. These energies are relative to the bottom of the B-state potential well [Luc80]. The molecular dynamics simulation program written for this task is called R-K Chapter Two: Gas-Phase Electron Diffraction Theory 123 (D.9 in Appendix D). One thousand trajectories were used for the bound systems, and ten thousand trajectories were used for the dissociative system. The initial ground-state molecular iodine was assumed to be vibrationally cold, with the initial energy and probability distributions corresponding to v = 0. The excitation laser pulse had a Gaussian temporal profile (FWHM = 50 fs), and the energy bandwidth was determined by assuming that the pulse was transform limited. The goal of the trajectory calculation was to generate a two-dimensional array containing internuclear separation probabilities as a function of time (an R(t) surface). The size of each position element was 0.01 A and the size of each temporal element was 5 fs. The initial conditions of each trajectory were determined using the Monte Carlo technique. The initial energy was equal to the excitation energy (e.g., 3000 cm- 1) plus an offset determined by the laser bandwidth, and the initial position was determined from the probability distribution of ground-state iodine. Several iterations were sometimes necessary to establish a valid combination of initial energy and position, particularly at lower energies where the Franck-Condon overlap between the X state and the B state is poor. The initial velocity was calculated from the initial energy and the B-state potential surface, and a randomly determined direction for the velocity (i.e., bond contracting or expanding) was assigned. After defining the initial conditions, the evolution of each trajectory on the B-state potential surface was calculated. R-K employed a Hulburt-Hirschfelder potential energy surface [Hul41], [Hul61]: V(r) = Yoo((1-e-xr + b0 x3e-2 x(l+b 1x)) (2.167) Chapter Two: Gas-Phase Electron Diffraction Theory where: 124 ho = 1 + al"/Yoo/ao (2.168) bl = 2 - 7a 0 - (2.169) ao = Yi~/41;;1 (2.170) al 12Yo0a 2 12a0b0 Yi1Yio _ 1 6Yo~ (2.171) (2.172) The Dunham coefficients were provided by Gerstenkorn and Luc [Ger85] and are shown in Table 2-6. Dunham Spectro. Coeff. Term Yoo .. De Yo1 New positions and velocities were calculated every 5 fs using an embedded Runge-Kutta integration Be Y10 ffie Y11 -ae Y20 -Xffie X{1:Eg) B(3Tiu) State State 12547.2 0.037368 214.529 4381.8 0.029001 125.669 -1.1138x10· 4 -1.4944x10· 4 -0.612973 -0.750400 1 Table 2-6: Dunham coefficients (in cm- ) for molecular iodine. Source: [Ger85]. scheme designed to conserve the total energy of each trajectory [Pre92]. The calculation began at -0.5 ps (with the static ground state distribution) and continued out to +2.5 ps. The zero of time, t = 0, corresponded to excitation of the molecular sample with the pump laser. The duration of the pump laser pulse was included by offsetting time zero for each trajectory by a random amount determined with a Monte Carlo technique on the pump laser temporal profile. Prior to to,n, the two-dimensional array was filled with the probability distribution of ground-state iodine normalized to unit area. Evolution of the trajectory after to,n was modeled by adding one to the array element corresponding to the current time and calculated position. The temporal profile of the electron pulse (including Chapter Two: Gas-Phase Electron Diffraction Theory 125 velocity mismatch effects) was assumed Gaussian. the to be The duration of electron pulse was included in the calculation 2.0 by convoluting the temporal behavior of a specific internuclear distance (one Time (ps) row in the array) with the temporal profile of electron pulse. The final result array of was internuclear an 8 the 10 distances 2.0 ranging in time from 0 ps to 2 ps. The program Time (ps) PROC3 (D.10) converted these arrays into modified molecular scattering curve using Eq. 2.166. The sM(s, t) curves were calculated o over a range of 0 to 15 A I Internuclear Separation (A) 10 Figure 2-28: Molecular dynamics of B-state iodine excited to 4750 cm- 1 above the bottom of the potential well. Iodine dissociates at this energy. Electron pulse temporal resolution: 'Ce = 50 fs. (Top) Modified molecular scattering curve as a function of time. (Bottom) Radial distribution curve as a function of time. The hump at 400 fs appears because the wave packet slows down as it climbs the outer potential wall before dissociation. Chapter Two: Gas-Phase Electron Diffraction Theory 126 (in 0.02 A- 1 steps), and each time interval was transformed into an f(r) curve using kd = 2.5.3 Coherent Dissociation The first system of interest was iodine excited to 4750 cm- 1 above the bottom of the B-state potential well. The dissociation threshold of the B-state is located at 4381.8 cm- 1, and it is expected that the diffraction patterns will reflect a continuous increase in the internuclear separation of the molecule with time. The modified molecular scattering curve and radial distribution curves with 'te = 50 fs are presented in Figure 2-28. The radial distri- bution curve shows that iodine molecules traverse the potential well within the first 500 fs and subsequently dissociate. The position of 2.0 the radial distribution peak increases in distance with time, and the peak also Time (ps) flattens out as the wave packet gradually disperses 10 across the potential surface. The modified molecular scattering curve presents the Figure 2-29: Modified molecular scattering curve for 8-state 1 iodine dynamics after excitation to 4750 cm- above the bottom of the potential well. Electron pulse temporal resolution: 'te = 500 ts. The oscillations damp out much more quickly than when 'te = 50 ts (Figure 2-28). Chapter Two: Gas-Phase Electron Diffraction Theory same information, reciprocal-space but domain. m 127 the t = 0 fs (50 fs) The - - - t = 1 ps (50 fs) frequency of oscillation increases with time as r1_1 increases, and the amplitude of the oscillations • • • • • • t = 1 ps (500 fs) -a.. ..... ., ., diminish rapidly as the wave packet ---------------------------- spreads; .. ··--· .. ---- .. ---- .. ---- .. ---- .. ----. ·---· ..• -•·. scattering contributions from a wide range of internuclear 0 ,..,- .... '' ~------ --- •·----. ··--. 2 4 6 8 Internuclear Separation (A) 10 separations lower the molecular scattering intensity. The calculated behavior of Figure 2-30: Comparison of radial distribution cuNes at selected times for 8-state iodine dynamics after 1 excitation to 4750 cm- above the bottom of the potential well. iodine is similar to observations of dissociating Ii and ICN made with FfS [Bow89], [Dan88], and to the corresponding quantum mechanical wave packet calculations of the FfS experiment [Gru93], [WiO88]. UGED provides the actual dynamical trajectory of the fragments. Also, by taking diffraction patterns at various times after laser excitation and calculating the change in the internuclear separation, it should be possible to determine the kinetic energy distribution of the fragments, and deduce the dissociation energy. Such measurements require femtosecond time resolution, however, as is shown by the molecular scattering curve for 't e = 500 fs in Figure 2-29. The interference fringes are almost completely washed out after the first 400 fs and the molecular scattering intensity is very small. A comparison of the radial distribution curves at 1 ps for 'te = 50 fs and 'te = 500 fs (Figure 2-30) shows that the Chapter Two: Gas-Phase Electron Diffraction Theory 128 peak flattens significantly as the temporal resolution changes by an order of magnitude. 2.0 2.5.4 Coherent Vibrations dynamics Molecular calculations were also performed Time (ps) for iodine at three energies (2000, 3000, and 4000 cm- 1) below the Internuclear Separation (A) 8 10 dissociation energy of the B-state. The radial distribution curves are plotted as a function of time in Figure 2-31 and Figure 2-32. 2.0 When the temporal resolution is high ('te = 50 fs), the vibrational motion is clearly present, even for Time (ps) fast oscillations at 2000 cm- 1. Close examination shows that Internuclear Separation (A) 10 vibrational dephasing occurs, and one can expect that vibrational quantum coherence would be apparent if a quantum mechanical wave packet calculation was Figure 2-31: Radial distribution curves for dynamics of B-state iodine excited below the dissociation energy (4381 .8 cm-1)_ Electron pulse temporal resolution: 'te = 1 1 50 fs. (Top) 2000 cm· . (Bottom) 3000 cm- . In both graphs the peak intensity at the inner and outer turning points decreases as a function of time, which shows that the classical wave packet is spreading and approaching a static (incoherent) distribution. Chapter Two: Gas-Phase Electron Diffraction Theory 129 As with FTS, a conducted. Fourier analysis of this oscillatory motion should yield the spacing 2.0 between the vibrational energy levels [Gru93]. The oscillation period at Time (ps) 4000 cm· 1 is long enough that the vibrational motion may still be resolved when 'te = 500 fs (Figure Internuclear Separation (A) 8 10 2-32), although there appears to be rapid vibrational dephasing. motion at The lower 2.0 energies is not resolved, and the diffraction pattern is static after the first 500 fs. This static pattern represents a weighted sum of the Time (ps) 2 position probability amplitudes of the vibrational states excited within the laser bandwidth, and therefore these diffraction patterns Internuclear Separation (A) 10 Figure 2-32: Radial distribution curves for dynamics of 1 8-state iodine excited to 4000 cm· above the bottom of the potential well. (Top) Electron pulse temporal resolution: 'te = 50 fs. (Bottom) 'te = 500 fs. are useful for determining the shape of the potential energy surface. Figure 2-33 shows the 2 ps radial distribution Chapter Two: Gas-Phase Electron Diffraction Theory functions (with 'te = 500 fs) for all 130 5000 three energies overlaid on the E4000 state potential energy surface. Note that the curves for 2000 and 3000 cm- 1 are static and represent >c, the average vibrational motion, w but the 4000 cm- 1 curve is still evolving in time. aiC: 2000 1000 This type of 1 experiment was already mentioned 2 3 4 5 Internuclear Separation (A) 6 in 2.3.3; there is actually no need for ultrafast time resolution, and lasers that have longer-pulses or are cw might be superior because Figure 2-33: Radial distribution curves at 2 ps from molecular dynamics of B-state iodine excited below the dissociation energy. The RD curves are shown superimposed over the B-state potential energy surface. Electron pulse temporal resolution: 'te = 500 ts. With this 1 1 'te, the 2000 cm- and 3000 cm- trajectories are static after the first 500 ts, but vibrational oscillations at 4000 cm- 1 can still be resolved (see Figure 2-32). the bandwidth would be narrow enough to pick out specific vibrational states. 2.5.5 Ultrafast Kinetic Dynamics The most important characteristic of gas-phase electron diffraction is that the scattering patterns are extremely sensitive to small changes in internuclear separation. Conventional GED experiments typically report internuclear separations to within 0.005 A or less [Har88a]; so far, a limited range of sis detected in UGED (15 A-1, as opposed to ~40 A- 1 in GED), and the precision is more on the order of 0.05 A. This sensitivity is still sufficient to distinguish between different vibrational states (Figure 2-33) as well as Chapter Two: Gas-Phase Electron Diffraction Theory between different electronic states ~. 0 g 2-20). UGED therefore . .} _,•. :· '·::, (r*l !,l•~ ."'- ·_," ,).·~···/· ,.- . C (Figure 131 ., • ,:· .i If) C Q (l) provides another detection scheme for C "O 0 T=32 ± I Ops monitoring ultrafast decay processes, either when the products dissociate or when they merely change to a different 0 20 40 60 Time (ps) 80 100 vibrational or electronic state. Such an avenue of detection is, of course, particularly useful when spectroscopic Figure 2-34: Reaction dynamics of C2F4l2 photofragmentation shown as ground and excitedstate iodine atom signal [Kne85]. The first iodine atom dissociates coherently within 0.5 ps. The second iodine atom dissociates with 't2 = 32 ps. data about higher excited states is not available or is too complicated. The three-body photofragmentation process of C2F4I2 is considered as an example of how UGED might be applied to ultrafast kinetic studies. Time-resolved spectroscopic studies have shown that excitation around 250 nm causes photofragmentation in a twostep process where both iodine atoms dissociate, leaving tetrafluoroethylene [Kne85], [Khu90], [Zho97]: (2.173) (2.174) The primary C-I bond breakage is very fast (-c 1 = 200 fs), while the secondary bond breakage results from internal energy redistribution and is significantly slower ('t2 "" 32 ps at a given energy). The dynamics of the two steps depend on the total energy and have been probed by measuring the rises of excited-state atomic iodine (i*) and ground-state Chapter Two: Gas-Phase Electron Diffraction Theory 132 0 1 Internuclear Separation (A) Time (ps) 5 6 Figure 2-35: Evolution C2F4l2 photofragmentation dynamics as shown in radial distribution curves. At time zero the molecular sample is pure C2F4l2. After time zero, the sample is a mixture of C2F4I radical and F2C=CF2. Compositions were obtained from experimental values of 't1 and 't2. atomic iodine (a biexponential; see Figure 2-34). The corresponding time evolution of the radial distribution curve is shown in Figure 2-35. The molecular scattering curve is a the molecular sample was calculated as a function of time using measured values of 't 1 and 't2. Structural parameters for C2F4l2 and F2C=CF2 were obtained from the literature [ThH92], [Car74], and the structure of the radical component was assumed to be identical to C2F4li with one iodine atom missing. The radial distribution curve highlights the dynamical changes of the fragmentation process. The primary bond breakage is shown by the rapid disappearance of the peak at Chapter Two: Gas-Phase Electron Diffraction Theory 5.0 A, which corresponds to the l···l internuclear separation. 133 The subsequent transformation of the radial distribution curve over the next 100 ps characterizes the secondary bond breakage; note that the intensity of the first peak at 1.3 A (C-C, C-F) does not change because all carbon and fluorine atoms remain in the molecule, although the position of the peak shifts inward slightly as the C-C bond changes to a double bond. The primary and secondary bond breakages in C2F4 h are very different processes and help illuminate the distinctions between monitoring vibrational coherence versus following dynamical decays. Loss of the first iodine atom is a direct process and very fast; if the molecule is excited with a femtosecond laser pulse, a wave packet is formed on the dissociative potential energy surface. With a 50-fs electron pulse, it would be possible to monitor this dissociation process in time, and the diffraction patterns would be similar to those shown in Figure 2-28. The J... J separation would rapidly move outward from 5.0 A, and one set of C-1, C-··I, and F··l peaks would shift outward as well. Loss of the second iodine atom, however, is not a coherent process. The individual C2 F4 I radicals dissociate independently of each other, with the behavior of the entire population characterized by the decay constant 't2 . Trajectory calculations are unnecessary to model this type of dynamical process because the loss of the second iodine is very fast compared to the uncertainty in the onset of the dissociation. Thus the diffraction pattern may be calculated as a sum of scattering from each of the three components weighted by their relative populations. 134 Chapter Three Lasers, Vacuums, and the Computer The focus of this thesis is directed towards the more exotic instrumentation of the UGED laboratory, such as ultrafast electron pulse generation and single-electron detection across two-dimensions. This particular chapter, however, describes the UGED versions of "basic" equipment - lasers, vacuum chambers, and computers - which are fundamental to nearly all time-resolved investigations. An amplified, colliding-pulse, mode-locked ring dye laser provided a reliable, stable stream of femtosecond laser pulses (3.1). Ultrafast electron pulses were then generated, scattered, and detected within a three-chamber vacuum system (3.2), and the molecular sample was introduced through either a continuous-flow jet or a pulsed nozzle (3.3). 3.4 discusses the metal evaporation chamber, a one-chamber vacuum system in which the electron-gun photocathode and other thin metal films were prepared. Finally, 3.5 describes the computer system. The Chapter Three: Lasers, Vacuums, and the Computer 135 laboratory computer controlled several instruments, automated experiments, and provided the mathematical muscle necessary for processing diffraction data. 3. 1 The Femtosecond Laser System The UGED experiment used visible or ultraviolet femtosecond laser pulses to (1) create ultrafast bursts of photoelectrons and (2) initiate a chemical reaction within the molecular beam. In the first process, only a few microjoules of laser energy were needed to make a sufficient electron flux. A high rep~tition rate was also desired because the number of electrons per pulse had to be kept very low to avoid temporally broadening the pulse through space-charge effects. The second process, however, required millijoules of energy in order to excite at least ten percent of the molecular sample (GED data are not background free). Generally, laser pulse energy and repetition rate are inversely proportional to each other and a practical compromise must be reached. The prototype UGED experiments reported here used a 30-Hz laser system which produced 2-3 mJ of 620-nm light. The primary emission source was a colliding-pulse, mode-locked ring dye laser (CPM), the second such laser constructed in the Zewail laboratories, and pulse energies were enhanced with a pulsed dye amplifier (PDA). Other femtosecond sources, such as synchronously-pumped dye lasers or solid-state titanium sapphire lasers, could be readily substituted into the UGED experiment. 3.1.1 The Colliding-Pulse, Mode-Locked Ring Dye Laser The CPM was a ring-cavity laser composed of two dye jets, seven mirrors, and Chapter Three: Lasers, Vacuums, and the Computer From Argon Ion Laser (All Lines) 136 To PDA 620 nm Output oc Synchronizing Photodiode Gain Jet Figure 3-1: The colliding-pulse, mode-locked ring dye laser (CPM) which generates femtosecond laser pulses for the UGED laboratory. SA: saturable absorber; OC: output coupler (2 %); G: refraction grating for observing laser pulse spectrum. four Brewster-angle prisms (Figure 3-1) [For81], [For83], [Dan91b]. All mirrors were specially coated with single-stack dielectrics to give high reflectivity and rrunlilllZe wavelength-dependent phase shifts. Most optics were purchased from CVI. The gain medium of the dye laser was rhodamine 6G (Exciton) solvated in ethylene glycol. The jet of dye emerged from a 300-µm nozzle (Coherent; 406-224-02), crimped to a width of less than 100-µm such that the central region of the jet stream was only -10-µm thick. The backing pressure of the jet was -22 psi. The gain medium was pumped with an Innova 310 argon ion laser (Coherent) running all lines at a few watts of power, and fluorescence was collected by two curved mirrors with focal lengths of 10.0 cm. The second dye jet contained a saturable absorber, 3,3'-diethyloxadicarbocyanine iodide (DODCI) in ethylene glycol, and the backing pressure of the jet was -32 psi. In the presence of the saturable absorber, lasing action within the ring cavity became mode locked: the phase difference between all viable cavity modes was zero. The absorber Chapter Three: Lasers, Vacuums, and the Computer 137 transmitted light only if the incident intensity surpassed a saturation threshold, which naturally reinforced the occurrence of a temporally short, intense pulse. The tailing end of the pulse was also cut by saturation of the gain medium, and the presence of two pulses in the ring cavity, traveling in opposite directions and overlapping at the saturable absorber, further improved the temporal resolution. The separation between the gain jet and the saturable absorber jet was approximately one-fourth of the cavity path length, which provided equal gain-medium recovery times after each pulse passed through the gain jet [Fle86] . Four Brewster-angle prisms were included in the ring cavity to correct for groupvelocity dispersion [For84]. Optical pulses in the CPM passed through two streams of ethylene glycol and interacted with thin coatings on seven mirrors during each trip around the cavity. The pulse width broadened because different frequencies within the optical wave packet traveled at different velocities due to the wavelength-dependence of refractive index. Refractive indices are higher for shorter wavelengths, so the bluer portion of the wave packet lagged behind the redder portion and the pulse duration increased. This effect is known as group-velocity dispersion (GVD). Careful adjustment of the prism positions could compensate for GVD by spectrally separating the pulse such that the redder wavelengths traveled longer distances, and the bluer wavelengths "caught up." The prism positions could be adjusted to overcompensate for GVD in anticipation of the dispersive components within the PDA. This adjustment also increased the total output power by as much as a factor of five [VaJ86]. Output pulses from the CPM had a repetition rate of 100 MHz (as determined by the cavity length), a temporal width of -60 fs, and a wavelength centered between 610 and 138 Chapter Three: Lasers, Vacuums, and the Computer 620 nm, depending on the fine-tuning of the cavity. The bandwidth was several nanometers, the energy was approximately 200 pJ per pulse, and the laser was polarized in the plane of the optical table. The ring cavity had two output couplers (Figure 3-1), each coated for two percent transmittance, and two beams emerged from each output coupler. One beam from the left-hand-side output coupler of the CPM triggered a fast photodiode circuit (EG&G; FND-100) with a 1-GHz bandwidth [McC72]. Signals from individual CPM pulses could be resolved on an oscilloscope and had amplitudes of 100 to 200 mV. The second beam of the left-hand-side output coupler was not used. One beam from the right-hand-side output coupler refracted off of a grating, providing a qualitative spectral diagnostic of the CPM' s operation. The second beam passed up through a mirror elevator and across into the pulsed dye amplifier. The laser polarization vector was rotated 90° by the elevator, and the CPM output was therefore vertically polarized within the PDA. 3.1.2 The Pulsed Dye Amplifier The energies of laser pulses emitted directly from the CPM were too low for most experiments, so the output was amplified in a four-stage pulsed dye amplifier following the design of Fork et al. [For82], [Dan91b] . The CPM laser passed through four dye cells within the PDA (Figure 3-2). The first stage contained kiton red in water, and the remaining stages contained sulfarhodamine 640 in water. All stages were pumped by the doubled output (532 nm; -5 ns) of a neodymium: yttrium aluminum garnet (Nd:YAG) laser (Spectra Physics; GCR-4) operating at 30 Hz. The Nd:YAG and CPM pulses were temporally overlapped by amplifying the CPM photodiode output and sending the signal through a synchronization unit (Spectra Physics; SM-1) to trigger the Nd:YAG laser. Chapter Three: Lasers, Vacuums, and the Computer 139 From CPM Output (620 nm) PH Figure 3-2: The pulsed dye amplifier (PDA) for amplifying the output of the CPM. SA: saturable absorber; BS: beam splitter; C#: dye cell; PH: pinhole spatial filter; CL: cylindrical lens; F: filter; CM: dichroic mirror; S: beam stop. The first three dye stages were transversally-pumped by the Nd:YAG laser, with approximately 5% of the 532-nrn light split between the first two stages and 25% incident on the third stage. The beam diameter of the CPM output was then expanded to 1 cm and made two passes through the longitudinally-pumped fourth stage (pumped with the remaining 70% of the 532-nm light). This design was different from the original Zewail laboratory CPM / PDA [Dan91b], and yielded a total pulse energy of 2 to 3 mJ instead of -300 µJ [RoM88]. One consequence of pumping the fourth stage so intensely was that the dye degraded rapidly and needed replenishment after about one day of operation. Several optical elements were included in the PDA to reduce amplified spontaneous emission (ASE). Pinhole spatial filters (Fort Wayne Wire Die) were positioned between the first and second stages and the third and fourth stages (Figure 32). A saturable absorber jet containing malachite green in ethylene glycol was placed between the second and third stages. Following the four stages of amplification, the total Chapter Three: Lasers, Vacuums, and the Computer 140 PDA gain was on the order of 107, and the repetition rate was reduced to 30 Hz. The amplified CPM output descended to the main optical table through a second mirror elevator, which rotated the polarization vector back to the horizontal direction. The relative output power from the PDA was continuously monitored with a home-made power meter. A photodiode (United Detector Technologies; lODP-SB), enclosed in a light-tight box with a 1-cm aperture, was placed behind the first mirror at the output of the PDA. The residual transmission through this mirror was large enough that several NG-9 filters were still required to prevent the photodiode from saturating. The photodiode signal was integrated using a simple operational amplifier circuit, and the total was displayed continuously on a digital meter for easy reference. 3.1.3 Autocorrelation Measurements And Pulse Compression Since the PDA contained nearly 20 cm of glass and liquid, the output pulses were broadened by GVD and had a FWHM of 250 to 350 fs. The pulses could be recompressed to less than 100 fs using double-passage through a pair of prisms [For84], [Lie93], but pulse lengths of 300 fs were sufficient for most UGED experiments. Shorter laser pulses did not improve the temporal resolution of the electron pulses, and introduction of the prisms reduced the total laser intensity by as much as a factor of two. The temporal width of the fs laser pulses was determined with a background-free autocorrelation measurement [lpp75], [Fle86]. The laser was split in a Michelson- interferometer-like arrangement where the recombined arms were not quite collinear (Figure 3-3). Each arm was focused by the same lens and the two paths intersected within a KD*P doubling crystal. The path length of one arm was varied with a computer- Chapter Three: Lasers, Vacuums, and the Computer controlled translation stage; when the path lengths of both 141 PDA Output Boxcar Ave rag er F F arms were equidistant (such I- A~D Converter that the pulses overlapped temporally at the crystal), the second harmonic Computer was generated along the bisector of the trajectories due to Figure 3-3: Experimental setup for background-free autocorrelation experiment. F: filter; BS: 50/50 beamsplitter; SHG: second harmonic generation crystal; PMT: photomultiplier tube. momentum conservation. The fundamental wavelength was blocked with an iris and filters, and the second harmonic signal was detected on a room-temperature photomultiplier tube (Hamamatsu; R1527), integrated with a boxcar averager (Stanford Research Systems; SR250), and transferred to the computer with an A➔D converter (Stanford Research Systems; SR245). Interfacing between the computer, translation stage, and A➔D converter was handled by the program CIRC (D.12). After converting the abscissa of the autocorrelation transients from encoder-pulses to time (100 e-p = 10 µm = path length change of 66.71 fs - see D.12.1), the data were fit with commercial software analysis packages such as Scientist. The pulse width Pulse Shape Correction Factor K Rectangular Gaussian Lorentzian Squared sech 1 0.7071 1/2 0.6482 0.8859 0.4413 0.3148 0.2206 Table 3-1: Autocorrelation fwhm correction of the laser, 11ti, was then calculated by multiplying the measured autocorrelation factor and time-bandwidth product K for various pulse shapes [Sal80]. Chapter Three: Lasers, Vacuums, and the Computer 142 fwhm of the transient, MAc, by a correction factor under o the assumption that the pulse was transform limited [Sal80], [Fle86]. The correction factor (Table 3-1) depends upon the laser pulse shape, which is generally thought to be squared hyperbolic secant -1.5 -1 -0.5 0 0.5 1 1.5 Time Delay (ps) Figure 3-4: Autocorrelation transient of uncompressed PDA output. The temporal pulse width is 296 fs. for femtosecond lasers. Figure 3-4 shows a slightly noisy autocorrelation transient of the PDA output in which !itL is equal to 295 fs . 3.1.4 Wavelength Generation Different wavelengths of ultrafast light can be generated by frequency-doubling, sum- or QC difference-frequency F generation, generation [Fle86], [Dan91b]. or continuum In the UGED C1 BS experiments, the pump laser was either left at 620 nm or frequency-doubled to 310 nm with a 2-cm c2 KDP crystal and compensator (Quanta-Ray; Crystal Module 1). The portion of the laser beam directed toward the electron gun photocathode was either left at 620 nm, frequency-doubled to 310 nm with an 0.5-mm KD*P crystal (Cleveland Crystals), or Figure 3-5: Continuum generation scheme with two-stage amplification. QC: quartz crystal; F: filter; C#: dye cell; CL: cylindrical lens; PH: pinhole spatial filter: SHG: second harmonic generation crystal. Chapter Three: Lasers, Vacuums. and the Computer 143 converted to other wavelengths using continuum generation. An example of the continuum generation setup is shown in Figure 3-5. A new wavelength was created by focusing the 620-nm light into a quartz crystal and selecting a portion of the continuum spectrum with a 10-nm bandpass filter (Schott). The pulse energies of the selected wavelength were increased in a two-stage pulsed dye amplifier pumped by tripled (355 nm) or quadrupled (266 nm) output from the Nd:YAG laser. The amplified ultrafast pulses could be frequency-doubled to create ultraviolet wavelengths. 3.2 The Gas-Phase Electron Diffraction Vacuum System The design and construction of vacuum systems suitable for gas-phase electron diffraction measurements has been discussed by various authors.* The background chamber pressure is usually between 10-6 and 10-4 torr, which is not a severe experimental constraint although often high speed oil diffusion or turbo pumps (1500 f./s or more) are required because the chemical throughput is large. The Zewail laboratory's UGED apparatus was divided into three separate vacuum chambers in order to protect sensitive instruments from potentially corrosive sample molecules (Figure 3-6). The electron gun and scattering chambers were differentially pumped; in this way the pressure in the electron gun chamber remained at 10-6 torr or below, preventing electrical arcs and contamination of the photocathode. Sample molecules flowed directly into the scattering chamber, where the background pressure • See, e.g., [Fin70b], [Kon72], [Sch76], [Tag84], [Tre88], [Moo89], [HaB91a], and [Ewb92] . Chapter Three: Lasers, Vacuums, and the Computer Electron Gun Chamber 144 Scattering Chamber Detector Chamber fs fs Laser --A,,;_>-~-----,r, Figure 3-6: The second-generation ultrafast·· electron diffraction apparatus. The apparatus is divided into three chambers: one for electron beam generation, one for electron scattering from a molecular beam , and one for the single-electron detection system . The pump laser, electron beam , and molecular beam intersect along three perpendicular axes near the center of the scattering chamber. during an experiment was approximately 10-4 torr. The image intensifier, charge-coupled device, and other detection components were housed in their own chamber, isolated from the scattering chamber by a fiber-optic window with an O-ring seal. The pressure in the detection chamber was kept at 10-2 torr to avoid condensation on thermoelectricallycooled devices. Most pieces of the vacuum system were joined with Conflat-flange-type connections, although a few ASA flanges were used if Conflat was unavailable. Frequently-opened flanges were sealed with viton O-rings, and the remainder were sealed with copper gaskets. Foreline connections were either Qwik Flanges, Swagelok fittings, or vacuum tubing crimped with hose clamps. The following sections describe the electron gun chamber, scattering chamber, and detector chambers in greater detail. Chapter Three: Lasers, Vacuums, and the Computer 145 Butterfly Valve Flange Adapter Flange Water Baffle t HS-2 Diffusion Pump To Alcatel 2010 Mechanical Pump Figure 3-7: End-on view of the electron gun chamber, looking from the scattering chamber towards the mouth of the electron gun. The electron beam exits the electron gun chamber through the central gap created by opening the off-axis butterfly valve. TCG: thermocouple gauge. 3.2.1 The Electron Gun Chamber The ultrafast electron gun was mounted within an 8" Conflat flange (CFF) Tshaped chamber (Figure 3-7 and Figure 3-8). The inner diameter (ID) for 8" CFF nipples was 6", and the length of each arm of the Twas 6.5". The Twas modified by adding a 6" CFF half-nipple (4" ID), welded at right angles to the two axes of the T, and two sections Chapter Three: Lasers, Vacuums, and the Computer of 0.5'' -OD stainless steel tubing connected to valves were welded onto the half-nipple. One line could be opened to air to vent the electron gun chamber, and the other line was connected 8" CFF T-Tube • / ·1Electr'n Guni Half Nipple mechanical pump for roughing Adapter out the chamber. As shown in Water Baffle Figure 3-7, beneath the half- HS-2 Pump CFF-to-ASA adapter flange I~: \ PEc(J --- - - •. ---- _________________-::::::---:·--s-E;/t Gate Valve valve (HVA; 125-0400), a 6"- ,, ,, ,, \' _,.9 T _j---------------'._\·------------: through vacuum tubing to the nipple was a pneumatic gate 146 ! ! CHN Figure 3-8: Side view of the electron gun chamber showing the pumping volume and the molecular flow conductance labels for each segment (see text). PEc: pressure in the electron gun chamber; Psc: pressure in the scattering chamber. (machined from a 6" CFF), a water-cooled baffle (Varian; 332), and a 285-f/s oil diffusion pump (Varian; HS-2). The HS-2 diffusion pump was filled with Santovac-5 oil (Duniway). The recommended roughing speed for the HS-2 is 5 cfm (ft 3/min); an Alcatel 2010 mechanical pump, rated at 6.8 cfm, was used to back the HS-2 diffusion pump. A pneumatic right-angle valve (Nor-Cal; KF25) separated the diffusion and mechanical pumps, and a thermocouple gauge (Duniway; DST-06M) was included on the mechanical pump side for monitoring the foreline pressure. The electron gun was mounted on a customized 8" CFF and directed along the long axis of the T. The customized flange had five 30 kV / 1 A feedthroughs (MDC) for the electron gun bias Chapter Three: Lasers, Vacuums, and the Computer 147 voltages and a central port with 2.75" CFF attachments on both sides. The electron gun was attached to the inner fitting (see 4.3.3), and a 2.75" CF window flange (MDC; VP150) was installed on the outer fitting to allow the ultrafast laser to enter and strike the photocathode. The inner walls of the T's long axis were lined with 0.02"-thick µ-metal (Magnetic Shield Corp.) to reduce the effect of earth and laboratory magnetic fields on the electron beam trajectory. The opposite end of the T was sealed with a customized 8" CFF containing a 1" butterfly valve (Figure 3-7). Butterfly valves rotate around a central axis, and the center region is always blocked. For this reason, the valve door was offset by 0.25" along the horizontal axis of the flange in order to provide a 85 mm2 half-moon window, centered in the 8" CF flange, through which electrons could pass into the scattering chamber. The butterfly valve did not perturb the electron beam path when open. The 8" CFF also had centered attachments for 2.75" CFFs on both sides; a flange for mounting apertures was installed on the outer side (the scattering chamber) and the inner fitting was not used. When the butterfly valve was closed, the scattering chamber could be brought up to atmospheric pressure without disturbing the vacuum in the electron gun chamber. A three-port 8" CFF (MDC; CF800-3-275) was installed on the third arm of the T. A Bayard-Alpert ionization gauge (Duniway; I-100-KF) was mounted on one of the three 2.75" CFF ports, and flanges with high-voltage BNC feedthroughs (e.g., MDC; MHV275-2) were put on the other two ports. These feedthroughs were used to transmit deflection plate voltages and streak plate voltages to the end of the electron gun. The foreline pressure was continuously monitored with a pressure gauge controller (Granville-Phillips; Model 307), and the unit also displayed ionization gauge readings. An Chapter Three: Lasers, Vacuums, and the Computer 148 interlock circuit was installed to protect the diffusion pump and the vacuum chamber in the event that the mechanical pump broke down or other potential disasters occurred, and a flow switch (Proteus Industries; lO0Ll 10) was put in the cooling water line. If the foreline pressure rose above 1.0 torr or the flow of cooling water stopped, the gate valve would automatically close and the diffusion pump would shut off. An override switch was installed on the pressure interlock so that the chamber could be roughed out without shutting down the diffusion pump. In the event of a power failure, a breaker would trip such that the diffusion pump would remain off even when power returned. Similar interlocks were installed for the scattering chamber (3.2.2) and are shown in Figure 3-12. The first-generation UGED vacuum system housed the electron gun, molecular beam, and a liquid-nitrogen-cooled CCD detector in a single chamber [Dan94]. The electron gun was prone to arc if the background pressure rose much above lxl0-4 torr, and on at least one occasion an electrical arc was strong enough to destroy a CCD. Keeping the electron gun clean and free from arcing was the motivation for introducing differential pumping in the second-generation apparatus. One design goal was to keep the electron-gun-chamber pressure PEc at 10-6 torr or below even while running sample gas through the scattering chamber. The aperture linking the two chambers had to be big enough such that the electron beam was not obstructed during a streaking experiment (where the deflection angles are large), and the pumping speed of the electron-gunchamber diffusion pump had to be fast enough to keep PEC low. The selection of the diffusion pump was based on pressure estimates using molecular flow calculations [Moo89], [Ley90]. The pressure in the scattering chamber, Psc, reached 10-4 torr during a diffraction experiment, so a target of 100 was set for the Chapter Three: Lasers. Vacuums. and the Computer 149 ratio PscfPEc- Using gas flow equations it can be shown that: 1 + (3.1) where SEff is the effective pumping velocity at the top of the 6" CFF half-nipple (see Figure 3-8), Cr is the conductance of the T-tube, and CA is the conductance of the aperture linking the two chambers. The effective pumping velocity SEff was estimated from network equations: (3.2) where So is the diffusion pump speed (285 £/s), CWB is the conductance of the water baffle (300 ,f,/s), and CAF, Ccv, and CHN are the conductances of the adapter flange, gate valve, and half-nipple, respectively. For a straight tube of length L (cm) and diameter d (cm), the molecular-flow conductance is: (3 .3) so CAF = 2800 £/s, Ccv = 1670 ,f,/s, and CHN = 1670 £/s, and SEJJ is estimated to be 120 £/s. The T-tube contained a bend, and the tube's effective length was estimated as [Ley90]: LE!f = 34 + 1.33d (3.4) where Lr is the length of one arm of the tube (-6.5"). Applying Leff to Eq. 3.3 yielded a value of 610 ,f,/s for Cr. The conductance of the aperture was estimated from: C = 3.7 A,JT/ MW £/ s (3.5) where A is the aperture area (cm2), Tis the temperature (set at 300 K), and MW is the molecular weight of the sample gas in amu (set at 100 amu). Chapter Three: Lasers. Vacuums. and the Computer Figure 3-9 plots the 150 0 0 mm 0 ,.. 10 mm 2 calculated pressure ratio as a ,/' 1rl function of SEff for four different aperture areas. The theoretical 0.. V oo C/)0 0.. ,.. , 0 ~ 100 should be possible if the ~ 0 ::::, ,.. a: of PsclPEc were then measured ,. 7 I V Cl) A ,.,, 1.. ,J,r ~ "' - 1 1000 mm "' 17 I/ ,.. •• ,,. :i.. C. 100 mm r:. A Ar,, I/ u, u, of 10 mm2 . Experimental values ,,.. A'J' I" ._..I,<" V A data showed that a PsclPEc of aperture size were on the order I I ,. LI' / ~ l,,,ol,,, " 10 ~"" - r.- • ... l,v i.,. ... i..- I I 100 1000 __ Pumping Speed: S Eff (Us) using nitrogen gas for three 2 different-size apertures: 14 mm , 50 mm2 , and 170 mm2 (no aperture; butterfly valve Figure 3-9: Differential pumping pressure ratio between the scattering chamber and the electron gun chamber as a function of the effective pumping speed SEff at the base of the electron gun chamber. The dashed line is the calculated value of SEff (120 R/s). Curves are shown for four different aperture areas. The circles are experimentally measur~d pressure ratios for different sizes of apertures (14, 50, and 170 mm\ completely open). The average effective pump velocity obtained from these measurements was 105 f/s, in good agreement with the estimate. The 14 mm2 aperture (2 mm x 7 mm) was used routinely for diffraction and other experiments; the aperture's long dimension was oriented vertically, along the streaking axis. 3.2.2 The Scattering Chamber Ultrafast gas-phase electron diffraction took place within the scattering chamber, an 8" -CFF cube with flange connections on all faces (Figure 3-10 and Figure 3-11). Each axis of the cube paralleled the trajectory of one of the three interacting beams in the Chapter Three: Lasers, Vacuums, and the Computer CCD Camera Head Input ~ 151 Electrical Feedthrough ___ Viewing Window ''*~ Excitation Laser XYZ-Positioner Stage Figure 3-10: Overhead view of the scattering chamber. The electron beam would travel from top to bottom in the figure. The camera head input on the scattering chamber connects to the small , inexpensive CCD with wh_ich direct bombardment electron images were recorded. experiment. The electron beam passed from back to front, through the 14 mm2 aperture at the end of the electron gun chamber and towards the phosphor detector screen (Figure 311 ). The molecular sample flowed into the scattering chamber through the top flange, effusing from the nozzle just above the electron beam, and the sample was evacuated from the chamber by the pumping apparatus below. The molecular sample was excited by an ultrafast laser pulse which passed in and out of the cube through window ports on the two side flanges. The cube rested on a 4"-long nipple with an 0.5"-OD SS tube and valve assembly through which the scattering chamber was roughed out (Figure 3-11). Beneath the nipple was a pneumatic gate valve (Huntington; GV AP-600-C) and a home made liquid nitrogen baffle. The LN 2 baffle consisted of a loosely-spaced coil of 0.25" SS tubing wound within an 8" CFF ring. Weld connections and Swagelok fittings linked the tubing to an external, insulated 2-R reservoir, which had to be refilled with LN 2 every few hours. A 700-R/s oil Chapter Three: Lasers. Vacuums, and the Computer 152 diffusion pump (Edwards; Diffstak MK2 160) filled with Santovac-5 oil was connected to the baffle, ~ 1 - --'-------'----------'----'----l-- and the diffusion pump was backed with Molecular Bea m Nozzle an Alcatel 2012 mechanical cfm; (11.0 pump Laser Baffles recommended backing for Electron Beam Aperture the MK2 160 is 7.1 cfm). with As the :::::~---·.......... l: Gate electron gun chamber, the Va Ive ~LN2 Baff le vacuum line between the diffusion and mechanical pumps contained a rightangle pneumatic and a Edwards D iffstak M K2 160 Diffusion Pump valve thermocouple gauge (Duniway; DTS06M) for measuring the foreline pressure. The foreline was pressure continuously monitored To Alcatel 2012 Mechanical Pump Figure 3-11: End-on view of the scattering chamber, looking from the detector towards the electron gun chamber. The excitation laser, molecular beam, and electron beam all intersect directly underneath the nozzle tip. Scattered electrons travel out of the page. TCG : thermocouple gauge. Chapter Three: Lasers, Vacuums, and the Computer 110 V 153 Proteus Flow Switch Granville-Phillips Gauge Controller Foreline Pressure Limit Switch . Switch To Electron Gun Chamber Interlocks 220V Edwards Diffusion Pump Power Restart Button Manual Override Switch ' ~ ~ Edwards Diffusion Pump On/Off Lm,..I- ~;;;;;;tt' To ThermoElectric Cooler Power Supply To Edwards Diffusion Pump To Gate Valve Gate Valve Open/Close Figure 3-12: Electrical schematic of the scattering chamber interlock system. The Edwards diffusion pump shuts off and the Huntington gate valve closes if the cooling water flow is interrupted, or if the foreline pressure of either the scattering chamber or electron gun chamber exceeds a preset value. These faults also shut down the electron gun chamber and the thermoelectric cooler in the detector chamber. on the Granville-Phillips pressure gauge controller, and the scattering chamber had the same assortment of water, power, and pressure interlocks as the electron gun chamber. The circuitry for these interlocks is shown in Figure 3-12. The back face of the cube was connected to the electron gun chamber's 8" CF Chapter Three: Lasers, Vacuums, and the Computer 154 butterfly-valve flange, and the front face (the detector side) was connected to a homemade flange assembly with a sliding cover to protect the phosphor screen (see 3.2.3 below). The top of the cube was capped with a customized 8" CFF containing one 2.75" CFF attachment near the center of the flange and four 1.33" CFF attachments (Figure 310). A high-precision XfZ translation stage (see 3.3.1 below) was connected to the 2.75" port and used to position the molecular beam assembly just above the electron beam. Some parts of the translation stage were magnetized, so the inner face of the top flange was lined with µ-metal. The 1.33" ports were connected to a Bayard-Alpert ionization gauge (Duniway; I-CFF-133), the vent valve for the scattering chamber, and electrical or motion feedthroughs. The sides of the cube were sealed with 8" rotatable CFFs, each containing two home made 2" -OD ports. The excitation laser entered and exited through the two openings nearest the detector screen. The entrance port contained a 1"-OD window, AR-coated for either 620 nm or 310 nm (CVI); the exit port was connected to a 12-cm long baffle tube with Brewster-angle output window and Wood's horn to minimize back-reflections into the scattering chamber. (Baffle tubes were also installed within the scattering chamber on either side of the nozzle.) A viewing window was placed in the third port on the laser-input side, and the fourth port on the laser-output side contained a male, 26-pin Bendix feedthrough (Welco; PTIH-16-26P) for connecting the scattering chamber's charge-coupled device to the SpectraSource camera head (see Chapter Six). One of the 8" rotatable CFFs also had four electrically-insulated copper wire feedthroughs which were used to thermoelectrically cool the CCD and monitor its temperature. In a GED experiment, the pressure of the molecular sample at the point of intersection with the electron beam is recommended to be 1 to 10 torr. The expected Chapter Three: Lasers, Vacuums, and the Computer 155 sample pressure in the Zewail laboratory's UGED vacuum system can be estimated from the equation for chemical throughput [Moo89], [Ley90]: Q = (3.6) SP From conservation principles, the sample pressure at the nozzle, PNoz, is related to the scattering chamber background pressure P by: pNoz = (3.7) SEff P/SNoz where SEJJ is the effective pumping velocity and SNoz is the flow rate of sample through the interaction region. The distance from the mouth of the diffusion pump to the bottom of the cube was ~8", so according to Eqs. 3.2 and 3.3, SEJJ was 524 f/s. Since the background pressure was actually measured at the top of the cube, SEJJ should be corrected for an additional eight inches of 6" ID tubing, yielding SEJJ = 419 f/s. The sample flow rate through the interaction region is equal to: SNoz = VA (3.8) where A is the cross section of the interaction region and v is the molecular translational velocity given by: v = PNoz ,J3RT/ MW (3.9) was calculated for typical UGED experimental conditions: background chamber pressure of 2xl04 torr, a molecular beam diameter of ~300 µm (A = 7.lxl0- 8 m2), and a CH2Ii sample gas (MW= 267.8 g/mol) heated to 160 °C (433 K). Under these conditions PNoz was found to be in the desired range for GED, about 6 torr, and the throughput Q in the scattering chamber was 1.1x104 f-atm/s, or 3.1 x 10-6 molls. During an actual UGED experiment, 8 g of CH2h were used over the course of 5.5 hours, so the Chapter Three: Lasers, Vacuums, and the Computer 156 experimentally measured throughput was 1.5x 10-6 molls. 3.2.3 The Detector Chamber The second-generation UGED apparatus had two CCD detectors, a commercialgrade chip installed in the scattering chamber to characterize the electron beam by direct bombardment, and a scientific-grade CCD located in a separate chamber and linked to the scattering chamber by fiber-optic components and an image intensifier. The detector chamber was an 8" CFF nipple, 5" long, with two half-nipple connections on opposite sides of the tube (Figure 3-13). One half-nipple ended with a Detector Mount And Cover Flange Tl CCD )? 2.75" CFF containing four BNC feedthroughs for the lffiage intensifier bias voltages. The second half-nipple ended with a 2.25" ASA flange containing a male, 26-pin Bendix connector which linked the SpectraSource camera head to the scientific- 0 -Rin g > -~:. :. •.==::~- • • 'I' Large Phosphor 0 n ~ FiberFiber-Optic ~=== === /Optic Clamping Ring~ ¥ Taper :-r: CCD Camera Head Input Image Intensifier Input grade CCD. On the scattering chamber To Alcatel 2010 Roughing Pump side, the 8" CFF nipple was capped by a home made, threeflange assembly which supported Figure 3-13: Exploded overhead view of the detector chamber. (Only a few of the detection components are shown.) Scattered electrons would enter from the top of the figure. Chapter Three: Lasers. Vacuums. and the Computer 157 and protected the phosphor-coated fiber-optic detection window (Figure 3-13). The assembly was made by stacking two 8" CFF rings on top of an 8" -to-4.5" CFF reducing flange (Duniway) and welding the flanges together. The 2"-OD, 0.25"-thick fiber-optic window with phosphor coating sat in a machined 4.5" CFF, pressed against a viton O-ring with a 2.5"-OD Teflon clamping ring. The 4.5" CFF was attached to the reducing flange. The clamping ring had a 40-mm ID so that the large fiber-optic taper could be coupled to the window (6.1). An 0.5"-OD SS tube welded to the outer ring of the three-flange assembly was connected by a 2.75" CFF to a rotational- and translational-motion feedthrough (MDC; CRPP-1). With this feedthrough, an aluminum cover could be moved in front of the phosphor screen and locked in place. Small vent holes linking the space behind the cover to the main scattering chamber were added after one unfortunate incident in which the phosphor coating was sucked off by a severe pressure differential. The commercial-grade CCD used in direct-bombardment studies of the electron beam was mounted on the aluminum cover (6.8.2). The side of the three-flange assembly facing the detector chamber contained nine tapped holes (3/8"-40) evenly spaced around a 4.5"diameter circle. Nuts for SO-threads-per-inch screws (Thor Labs; FAS300) were put in the tapped holes; the image intensifier, fiber-optic tapers, and CCD were supported on these high-precision screws (6.2). The back end of the detector nipple was sealed with an 8" CFF containing an assortment of vacuum, electrical, and water feedthroughs (Figure 3-14). The detector chamber was continuously roughed out to 10-2 torr with the electron gun chamber's mechanical pump to prevent condensation from forming on the thermoelectrically-cooled CCD. Thermocouple connections and power for the TEC were fed through the back Chapter Three: Lasers. Vacuums. and the Computer Detector Mounting Nuts 158 Electrical Feedthroughs Phosphor Screen Protective Cover Feedthrough To Alcatel 2010 Roughing Pump Figure 3-14: End-on view of the detector chamber, looking towards the scattering chamber. The phosphor screen protection cover is half open. flange, as was the cooling water needed to remove heat from the TEC. The TEC's power supply was interlocked to the flow meter, just like the oil diffusion pumps, to avoid overheating the CCD in the event the flow of cooling water stopped. A venting valve was also added to the back flange. 3.3 The Sample Inlet System Tremmel and Hargittai have reviewed the design of nozzle systems for GED [Tre88], and they comment that once a diffraction instrument has been constructed and is operating reliably, it is still often necessary to tailor the nozzle to the physical properties of each molecular sample. Two nozzles systems were built for the Zewail laboratory's ultrafast diffraction apparatus: (1) a continuously-flowing free-jet expansion from a needle tip which could be heated up to 200 °C, and (2) a piezoelectric pulsed nozzle which could be heated up to 75 °C. These nozzles and the input manifold are described in the following paragraphs. Chapter Three: Lasers, Vacuums, and the Computer 159 3.3.1 The Input Manifold 0 The same input manifold was used for the CW and pulsed nozzles. tel 2012 chanical Pump The manifold was a T-shaped system consisting '--... ---------- --------, ,-- - -' ' of 0.25" -OD SS tubing welded to SS joints Sam pie Bulb and valves (Figure 3-15). The neck of the '' ,, ',' ,', -::' \- XYZ -/ \ Positioner :i T was welded into a 2.75" CFF and '' ,, : ~: Stage :·· , / ------- -~------- ',, --, --------- -----------., extended down through the bellows of the :·------------ --------- XfZ-positioner ---- ---- ---- -------------- -------- -- ----- --- -------------- -----------· Top Flange i.. into the scattering chamber. The 0.25"-OD SS tubing of the neck ended in a Swagelok fitting to which either nozzle was attached. Gas flow Nozzle Connection Figure 3-15: The sample input manifold for the UGED apparatus. With gaseous samples, the bulb would be replaced by a needle valve leading to a gas regulator. through the neck was adjusted with a bellows valve (Nupro; SS-4H-TW) ; this valve was left shut while degassing a liquid sample or waiting for the temperature of the sample and manifold to equilibrate. One side of the manifold's crossbar ended in a second bellows valve and a female 0.25"-NPT fitting . Aluminum tubing linked this arm to the scattering chamber's mechanical pump such that the manifold could be evacuated and liquid samples degassed. The sample reservoir was attached to the other side of the manifold's crossbar, which ended in a right-angle female 1/4"-NPT fitting. Liquid samples were stored in a 30-mf glass bulb with a Pyrex-to-Kovar stem joint which ended in a male 1/4"-NPT fitting . For gaseous samples, a right-angle fine metering valve (Nupro; SS-4MA) was added on instead to regulate flow from the sample cylinder tank. Chapter Three: Lasers, Vacuums, and the Computer 160 Liquid samples with low vapor pressures were warmed up with heating tapes and an insulating layer of glass wool and aluminum foil. Three heating tapes were used: one around the sample bulb, one around the external portion of the T, and a third around the neck in vacuo. Temperatures were controlled with V ariacs. To avoid condensation and clogging, the sample bulb was always coolest and the neck and nozzle always hottest. Temperatures were measured with Type E thermocouples (Omega; #TT-E-30) prepared by spot-welding the two leads together using ~4 Watt-sec of power. The temperatures were displayed on a calibrated monitor (Omega; CN76000). The positions of the electron gun and the detection system in the UGED apparatus were not adjustable, and at the beginning of an experiment the path of the electron beam had to be shifted onto the beam stop by setting the deflection plate voltages. Since the electron beam trajectory was fixed after this correction, the nozzle had to be moved into position immediately above the electron beam. This would have been very difficult without the high-precision XY2-positioning stage (Thermionics; EC-1275-1-1-2). The stage had one inch of travel along the x- and y-axes, two inches of travel along the z-axis, and a precision of ~0.0002" (5 µm) on all three axes. 3.3.2 The CW Free-Jet Expansion Nozzle The continuous free-jet expansion nozzle in the UGED apparatus was simply a hypodermic needle tip from Hamilton, either size 26S (130-µm ID; 470-µm OD) or size 22S (150-µm ID; 710-µm OD). The Caltech Chemistry Machine Shop shortened the tips to a length of ~5 mm and added a 60° degree taper to the ends. Sometimes the needles became magnetized after the machining process and had to be degaussed. Evidence for Chapter Three: Lasers. Vacuums, and the Computer 161 magnetization problems included sudden jumps in the electron beam position as the needle was moved horizontally or vertically. The end of a hypodermic-needle mount was machined into a 1/8"-OD tube such that the mount could be connected to the neck of the input manifold with a 1/8" -to-1/4" Swagelok reducing joint. The heating tape for the manifold neck could only reach within ~2 centimeters of the needle tip, so to keep the tip hot and avoid clogging, copper braid was wrapped from the needle mount down to the needle tip and soldered in place. The copper braid (actually just Soder-Wick) transmitted heat very well and was insulated with a few layers of aluminum foil. Temperature at the base of the needle tip was measured with a thermocouple. 3.3.3 The Piezoelectric Pulsed Nozzle All diffraction data reported in this thesis were recorded using the CW-nozzle source, but a pulsed Sample Input \ V J\_ nozzle system was also constructed and tested with scattering from ground-state CF3I. Voltage Pulses Most GED experiments use CW sources [Tre88] because of the large, fluctuating electromagnetic fields associated with solenoid pulsers, although Bartell and French have □ :: ia' Bimorph Piezo ~~ t 1=~; tli 0-Ring Nozzle Figure 3-16: The UGED piezoelectric pulsed nozzle. shown that distortions due to EMF can be avoided with sufficient magnetic shielding [Bar89]. For the UGED apparatus, a home made pulsed nozzle based on a piezoelectric wafer was built. The 2.3-cm diameter, round piezo (Motorola; 40-1383, found inside Radio Shack 2" piezo tweeters) was a bimorph - two Chapter Three: Lasers, Vacuums, and the Computer reverse-polarized ceramic plates separated by a central electrode. -- 20 > 10 162 Piezo Voltage Pulse Cl) A potential difference between the ceramic plates and the central - g> O- 1 - - - - - + - - - - - - - - - - \ - - - - - - - - 0 > -1 O electrode caused the birnorph to -20 - - , ~ - - 8 0 0 µ 5 - - ~ - - - - - - - make a concave or convex bend. Photo diode Signal In the UGED pulsed nozzle, one end of the birnorph was clamped in Figure 3-17: Example of the voltage signal going to one lead of the bimorph piezo in the pulsed nozzle. place, forcing the opposite side to either bend up or down (Figure 3-16). Electrical connections were made with silver paint, and the two ceramic plates were connected with a small segment of a copper spring. A 1/8" -OD viton poppet was superglued onto the moving end of the piezo and covered the orifice leading to the needle when the piezo was bent down. Proper adjustment of the poppet and needle assembly to ensure a tight seal required a great deal of care and practice. A home-made electronic controller provided the positive and negative voltage pulses which bent the piezo up and allowed sample gas to flow through the 2-cm needle stem into the scattering chamber. Voltage levels and pulse widths could all be varied; the controller was triggered using the rising edge of the oscillator synchronization signal from the Nd:YAG laser. Figure 3-17 shows a qualitative voltage trace for one of the two leads to the piezo. The pulse had an 800-µs-wide base and a 140-µs-wide flat top, and extended from - 19 V to +20 V. The start of the pulse preceded the signal from a photodiode (setup on the laser table) by a time !::.t. The temporal shape of the molecular Chapter Three: Lasers, Vacuums, and the Computer beam was estimated by measuring the multi- 163 <( 6 C. photon ionization signal of CF3I excited with :::- 5 ultrafast 620-nm laser pulses. The backing lo., C: ~ 4 pressure of CF3l gas into the input manifold was 12 psi. The pulsed nozzle emitted CF3I 83 C: 0 .:; ca 1 .!:::! C: 0 between two copper plates, one biased at 2 0 0.6 0.8 1 1.2 1.4 Time Delay Lit (ms) +240 V and the other, the collector, set at ground. Current on the collector was measured as a function of time with an Figure 3-18: Temporal shape of the pulsed molecular beam emitting from the piezoelectric nozzle relative to the start of the voltage signal in Figure 3-17. The delay reflects the time required for the sample to t_ravel down the nozzle stem before emitting. electrometer (Keithley; 610B). The graph of /(lit) plotted in Figure 3-18 shows that the gas density was greatest 1 ms after the start of the piezo voltage pulse using the pulse conditions shown in Figure 3-17. 3.4 The Metal-Evaporation Vacuum Chamber UGED experiments frequently required the preparation of metal coatings with thicknesses on the order of a few hundred Angstr¢ms. The electron gun photocathode, for example, was a thin metal film deposited on a quartz substrate, and the components in the detection system sometimes needed aluminum overcoats to block or reduce stray light. An unused metal evaporation chamber was recovered from the Caltech Chemistry Machine Shop and refurbished for the UGED laboratory. The chamber consisted of a 100-f glass bell jar, an aluminum base containing various ports sealed with viton gaskets, a leaky mechanical gate valve (Consolidated Vacuum Corp.; VCS-2), a water baffle (CVC; Chapter Three: Lasers, Vacuums, and the Computer 164 BC-41) filled instead with liquid nitrogen, and a Bell Jar water-cooled oil diffusion pump (Unknown) - Thickness Monitor see Figure 3-19. Roughing pressures of 10-2 torr were obtained with a mechanical pump (Welch). After evacuating the chamber with the diffusion pump for several hours, the pressure registered 2x 10-6 torr as measured on a SchulzPhelps ionization gauge (Electron Technologies) connected to a pressure gauge LN2 controller (Granville-Phillips; Model 224). The Baffle pressure tended to rise as high as 10-5 torr Diffusion during the course of an evaporation. Unlike the Pump electron gun and scattering chambers, the metal evaporation chamber had no pressure interlock and the gate valve was not pneumatic. The The evaporation chamber used to coat thin metal films. Figure 3-19: diffusion pump would shut off if the flow of cooling water was interrupted, and the pump required a manual restart if the power failed. Pure metal samples were placed on tungsten or molybdenum boats (R. D. Mathis; e.g., S3-.005W) and evaporated through resistive heating. Special boats with aluminumoxide coatings (S35B-A0-W) were used when evaporating aluminum because of the metal's tendency to creep when melted. Currents of 100 to 150 A were sufficient for aluminum, silver, and gold, and coating rates were from 1 to 10 A!s. Targets were Chapter Three: Lasers, Vacuums, and the Computer 165 mounted 20 to 40 cm above the sample boats with the side-to-be-coated facing down, and the distance d from boat to target was measured to within a few mm using string and ruler. A vibrating crystal (Phelps Electronics; 110-01) was mounted near the target inside the chamber, and a thickness monitor (Granville-Phillips) measured the change of frequency as metal deposited on the crystal. The depth of the coating was reported in A, calibrated for aluminum. The value displayed by the thickness monitor had to be corrected for deposition distances and metal densities: (3.10) .. where trM is the thickness reported by the monitor, dvc is the distance to the vibrating crystal, and PA1 is the density of aluminum. Table 3-2 lists -the densities of the most common metals deposited in the UGED evaporation chamber. The experimental uncertainty of Metal p (g/cm 3) P / PAI Al Cr Ag Au 2.70 7.19 10.5 19.3 1.00 2.66 3.89 7.15 Table 3-2: List of densities and correction factors for several metals commonly evaporated . a coating thickness was on the order of 4%. 3.5 The Computer System Data collection and computations were conducted with a 486DX / 33 MHz IBM compatible computer. Each CCD diffraction image required as much as 2 Mb of memory (typical values were 0.5 Mb), so the computer was equipped with a SCSI interface to speed data transfer. Two hard drives provided a total of 1.5 Gb of storage space, and a 100 Mb Zip drive (Iomega) made the transfer of images to other terminals easy. The Chapter Three: Lasers. Vacuums. and the Computer PC Computer 166 Translation Stage Camera Head Figure 3-20: Hardware and software connections between the UGED laboratory computer, the charge-coupled device, and the translation stage during a time-resolved diffraction experiment. laboratory computer also had a 500 Mb tape backup system (Colorado; PT-25) for archiving data. Several computer programs were written in Borland C to interact with laboratory instruments and analyze CCD images and diffraction data (see Appendix D). The program CIRC (D.12) controlled the optical delay line's translation stage (Aerotech; ATS 100200NN20) and the monochromator (Instruments SA; H20), and read data from the A➔D converter (Stanford Research Systems; SR245). Images were downloaded from chargecoupled devices using SpectraSource's Windows-based program, HPC-1. In order to automate CCD image data collection and adjust the translation stage in between exposures, macro programs were written for Microsoft's EXCEL 4.0 (Appendix E). As shown in Figure 3-20, during an experiment an EXCEL macro was initiated on the computer. The macro in turn began HPC-1 and passed keystroke commands such that CCD images were taken and stored on the hard drive. HPC-1 opened and closed a 1"-ID shutter (Uniblitz; VSR25) placed in the path of the laser beam. After recording a preset Chapter Three: Lasers, Vacuums, and the Computer 167 number of images, the EXCEL macro changed the translation stage position by executing either AUTOHOME or AUTOSCAN (D.13), and then resumed control of HPC-1. 168 Chapter Four Ultrafast Electron Pulse Generation The electron is not as simple as it looks. Sir W. L. Bragg The source for ultrafast electron pulses in the UGED laboratory was a photoemission electron gun. Photoemission is a complex process, full of surprising variation and subtlety. Other methods of electron emission, such as thermionic emission and field emission, can intertwine with photoemission on the ultrafast time scale, and all three processes are briefly reviewed in 4.1. The discussion shows that field emission assists in electron generation, but thermionic emission is deleterious to UGED and must be avoided. Five criteria for selection of the photocathode material are identified in 4.2. In accordance with these criteria, a 450-A silver film was installed as the photocathode for the UGED electron gun, and pertinent physical characteristics of the film are summarized. 4.3 describes the construction and performance of the UGED electron gun. Trajectory simulations are compared with the true experimental response, and the electron beam's Chapter Four: Ultrafast Electron Pulse Generation 169 temporal and spatial coherence at the nozzle tip are estimated. The temporal characteristics of the UGED electron gun were measured in situ with streaking experiments. 4.4 describes the streak experiment and presents a graph of the electron pulse width as a function of the number of electrons per pulse. 4. 1 Methods of Generating Free Electrons From Metals In a metal solid, the outer valence Metal electrons are relatively free to travel from Vacuum 0 atom to atom across the lattice structure. > -s E Cl) To first approximation, the electrons in this iii Cl) conduction band behave like particles in a well, trapped by the potential boundary at 0 a. •r ....,...,..._ _ _~---r-,----,----,---r--.---,--,-r-+ 1 the metal-vacuum interface [Eis85] . The potential well has a depth eVo on the order of 5 to 12 eV, and the well boundary is not perfectly sharp (Figure 4-1) because free <E--- n(E) 0 ~ -10 1 x-axis (nm) Figure 4-1: Electron emission from a metal. At O K all states in the potential well are fully populated up until the Fermi energy, EFEnergy exceeding the work function qi must be deposited in a conduction band electron for it to escape into the vacuum. electrons in the vacuum are attracted to the metal surface by their image charges. The potential energy function outside the metal due to an image charge is: (4.1) where xis the axis normal to the metal surface and the units of x in the right-hand side of Eq. 4.1 are nanometers. In the limit of x➔O, Eq. 4.1 unrealistically predicts that eV1c(x) Chapter Four: Ultrafast Electron Pulse Generation 170 goes to -00 ; however, by the time eVic(x) falls to -eV0 , xis on the order of 0.5 A which is less than the covalent atomic radius of metal atoms, and the simple image-charge model is no longer valid. The conduction band can be treated like an ideal electron gas which obeys fermion statistics. The population distribution of energy levels within the well is then: (4.2) where EF is called the Fermi energy. At absolute zero, all energy levels below EF are fully occupied and all energy levels above EF are empty. The work function cp is defined as the minimum energy required to move an electron from the metal to the vacuum at O K: (4.3) In order to generate free electrons from a metal cathode, either an electron in the metal must be given energy greater than or equal to cp, or the potential barrier must be lowered below EF, Three common methods for freeing electrons from metals include thermal emission (electron energies are increased by heating the metal), field emission (the potential barrier is lowered by applying a strong electric field), and the photoelectric effect (an electron absorbs energy from incident photons) [Gom61], [Not56], [CaM78]. As discussed in the next few sections, these methods can be combined, and all play a role in the creation of ultrafast electron pulses. 4.1.1 Thermionic Emission According to Eq. 4.2, conduction band energy levels above EF become populated as the temperature rises. For sufficiently high temperatures, some electrons reach thermal Chapter Four: Ultrafast Electron Pulse Generation energies greater than <j> and are 171 Metal Vacuum e spontaneously emitted from the vacuum. -ca -s E 0 >Cl) Figure 4-2 shows the population distribution function for silver at two different Cl) 0 a. temperatures; thermionic emission becomes significant once the temperature is greater than at least 1,000 K. Thermionic electron beam sources are more commonly known as -10 1 <E---- n(E) 0 ------3,> 1 x-axis (nm) Figure 4-2: Thermionic emission. Higher states in the potential well are populated as the temperature increases. If T is large enough, then the thermal energy of some electrons will be greater than <j>. cathode ray tubes, which of course pervade the modern world both in laboratories and homes (e.g., the television set). The hotcathode filament is also the most common electron beam source in GED instruments [Tre88] . Thermionic properties have been researched extensively [HeC49], [Fom66] but because heated cathodes emit continuously, thermionic emission by itself is not suitable as a source of ultrafast electron pulses. Thermionic effects are important in conjunction with photoemission (discussed below in 4.1.3), and depend strongly on the time scale of excitation [Rif93]. When ultraviolet, visible, or infra-red radiation is incident on a metal, photonic energy is absorbed first by the electrons, which rapidly thermalize due to scattering and collisions. Transfer of this energy to the atomic lattice takes place via electron-phonon coupling, which has a much slower time constant. On the ns time scale, this equilibration is still instantaneous. Thermionic emission (TE) begins dominating multi-photon photoemission (MPPE) once the laser fluence is greater than 50 to 100 rnJ/cm2 [Log69], and surface temperature response curves of solids have been calculated as a function of the temporal Chapter Four: Ultrafast Electron Pulse Generation 172 profile of ns laser pulses [Lin81]. On the ps time scale, electron-phonon coupling still occurs faster than the laser pulse duration, but pure thermionic emission is no longer observed because the surface damage threshold of the solid is reached before TE exceeds MPPE. Femtosecond laser pulses, however, excite the conduction band electrons faster than energy can be channeled to the atomic lattice. On the fs time scale, the electron gas is decoupled from the lattice and superheats because the electron heat capacity is small. Thermal emission dominates MPPE at much lower fluences on the fs time scale, typically around 0.1 to 1.0 mJ/cm2 [Rif93], [Fuj84], [Gir95a]. Time-of-flight studies of photoelectron kinetic energies show clearly that the single KE peak due to photoemission gradually gives way to a spread of kinetic energies as the fluence increases from 1 to 40 mJ/cm2 [Rif93]. Fann and co- workers used time-resolved photoemission spectroscopy to follow the superheating process in a gold film, and determined that the thermalization process was complete within 1 ps [FaW92a], [FaW92b]. The electron temperature reached a peak value of 1,680 K by 400 fs using 109 W/cm2 (0.3 mJ/cm2 ) of laser power. Power-dependent estimates of electron and lattice temperatures in copper following fs-laser excitation yielded similar time constants [Tsa92]. According to Tsang et al. 's calculations, the electrons reached peak temperatures of 10,000 K and cooled down within 3 ps following illumination with 10 12 W/cm2 (625 nm; 200 fs) of power; the lattice temperature equilibrated to ~1,000 K. At 10 11 W/cm2 (20 mJ/cm2 ) of power, the peak electron temperature was 2,000 Kand the thermalization time constant was less than 1 ps. Chapter Four: Ultrafast Electron Pulse Generation 4.1.2 Field Emission The potential barrier at the metal- 173 Metal Vacuum - - - - - - - - - - -" - - - - - - - - ' ' ,,,,,----' 'V eV,c 0 > i I"- Cl) •--=-'~? vacuum interface can be lowered by the -s E E Jg 0 ll. presence of an electromagnetic field [Not56], """"'....._ [Gom61], [Hol79]. If the electromagnetic 1 ....._ _ _.,__,_-;-.-,-,---r-,----,--r-+ -10 <E--- n(e) 0 Xo --'7 x-axis (nm) 1 field is strong enough or the lattice electrons are already thermally hot, then this effect (known as the Schottky effect [ScW23]) can Figure 4-3: Field emission. The presence of a strong electric field near the cathode reduces the barrier. Less thermal energy is required for an electron to escape to the vacuum. be an excellent electron beam source. The potential outside the metal surface gains an additional term due to the electric field of strength E. (Eis directed towards the surface.): eV(x) = - eEx (4.4) As shown in Figure 4-3, this function has a maximum at a distance x 0 from the surface: (4.5) and the effective work function of the metal is lowered by: 11¢ = -e✓ eE = -0.03795./E eV (4.6) 47r£o where Eon the right-hand side of Eq. 4.6 has units of kV/mm. Even if ~<I> does not pull the barrier below the highest thermally-populated energy levels, free electrons can still be formed by tunneling through the barrier. Electric field effects can also assist photoemission processes by lowering the work function and increasing the quantum efficiency of the cathode. Srinivasan-Rao and co- Chapter Four: Ultrafast Electron Pulse Generation 174 workers have shown that the current emitted in a one-photon process increased linearly with the applied electric field (up to 24 kV /cm) when the incident laser intensity remained constant [Sri91]. This observation may be related to space-charge effects; the high density of free electrons immediately above the metal surface is repulsive, and pushes other nascent free electrons back into the cathode unless the extraction field is sufficiently large [Cla89]. An "optical Schottky effect" is also possible: the transient field strength of short, intense laser pulses can be strong enough to "rip" electrons from a metal cathode without absorption of photons. This topic is discussed in 4.1.3.5. 4.1.3 Photoemission Light incident on a metal surface is absorbed by conduction-band electrons, and Metal the photon energy hv is usually transferred hv Vacuum 0 -E> Cl) hv to the lattice in the form of heat. If hv is iij -s Cl) 0 greater than the metallic work function <j> , though, then the absorbing electron has C. i-.-.........................+a-,--.--,---,--.----,-.--,---.-+ -10 1 <E-- n(e) 0 ------:7 1 x-axis (nm) sufficient energy to escape to the vacuum. Einstein used the photoelectric effect as Figure 4-4: Photoemission. Electrons can obtain escape energies by absorbing one or more photons. evidence of energy quantization: in his experiments, no photoelectrons were emitted when hv was less than <j>, regardless of the incident light intensity [Eis85]. However, modern pulsed lasers provide orders-of- magnitude-more photon flux per unit time than the continuous lamps Einstein used, and higher-order effects become observable: two or more photons of energy hv < <I> can be Chapter Four: Ultrafast Electron Pulse Generation 175 simultaneously absorbed by an electron, freeing it to the vacuum (Figure 4-4). The quantum efficiency of multiphoton photoemission (MPPE) can exceed single-photon (linear) emission if incident light intensities are high enough [Ani77]; for metal photocathodes, this transition occurs at power densities on the order of 10 10 W/cm2 [Tsa92]. The physics of photoemission can be quite complex, involving several different processes such as bulk emission, surface emission, thermally-assisted emission, surfaceplasmon emission, and optical tunneling [Far93], [Far78], [Ani77]. These topics and their relationship to ultrafast electron pulse generation are discussed below: 4.1.3.1 Bulk Emission Conduction-band electrons within the optical skin depth of a metal have a relatively free range of motion along directions parallel to the surface, and the electrons can therefore absorb photons incident at almost any angle. Photoelectrons from the bulk of the metal must then make their way to the surface to escape. The emitted current 2 depends on the absorbed light intensity, 1£1 , and for an MPPE process requiring n photons, the emitted current is: where l1n is the quantum efficiency. If interference effects are ignored, the current emanating from a metal cathode is a linear sum of all processes [Bec75], [Tsa91]: (4.8) According to Fowler-DuBridge theory [DuB33], [DuB32], [Fow31], In can be written as: Chapter Four: Ultrafast Electron Pulse Generation J = n a (_!_)n Ar(I- Rf T 2 F(nhv - </>) n hv kT 176 (4.9) where A is the Richardson constant (120 A/cm2/K2), Tis the temperature, R is the optical reflectivity of the metal surface, / is the incident light intensity, and an is an experimentallymeasured constant. Fis known as the Fowler function: F(x) (4.10) 1C2 - 6 X2 + - 2 ~( + L.. -1 m=l )"' e-mx 2- , - m x>O The very first term of Eq. 4.9 (n = 0) corresponds to thermionic emission: (4.11) lln can be estimated from Eqs. 4.9 and 4.10 (see 4.2.1.5 for some measured values of lln)- 4.1.3.2 Surface Emission When a component of the incident electric field is normal to the metallic surface, a surface electron can be ejected directly into the vacuum. The photocurrent from surface 2 emission is proportional to IE..1.l n. Several research groups have measured the ratio between surface and volume emission as a function of incidence angle (see, e.g., [Yen79], [Gir93]) but the distinction between the two processes remains hazy because the method of cathode preparation, particularly the surface roughness, is very important [Far93], [End71]. Farkas et al. measured the angular distributions and power dependence of gold photoelectrons as a function of laser wavelength (248, 343, and 1060 nm) and polarization vector [Far93], [Cha89], [Far87]. Incident 20-ns laser pulses struck a gold target at a grazing angle of 85° to the normal, so photoelectrons from the bulk were expected when Chapter Four: Ultrafast Electron Pulse Generation 177 the laser polarization was s, and surface emission was expected when the laser polarization wasp. The authors found that the emission ratio Jp/ls increased from a value of 3 for a one-photon process (248 nm) to 100 for a five-photon process (1060 nm). The angular distribution of ejected electrons was narrower for p-polarization, and also was observed to narrow as n increased. A similar study conducted with 450-fs pulses (248 nm) also found that more photoelectrons were generated using p- rather than s-polarization [Gir93]. In order to create an ultrafast pulse of photoelectrons from a fs-laser pulse, the time scale of photoemission must also be ultrafast. Generally, the ejection of electrons from a metal photocathode is thought to be constrained only by the transmission time from the bulk to the vacuum, and perhaps by coupling to surface states [Tsa91]. For a volumeemitted electron with 0.5 eV of kinetic energy, the transmission time to the surface is on the order offs barring any collisions; in contrast, the response of surface emission should be instantaneous. But the temporal width of electron pulses generated by surface emission is limited for geometrical reasons - the incident radiation grazes the cathode and is therefore approximately normal to the direction the photoelectrons take. In this geometry, the minimum pulse width of electrons coming from a tiny, 100-µm-diameter photocathode would be 300 fs, the time required for the laser pulse to pass across the active area. Geometrical temporal broadening is insignificant when the laser radiation is normal to the cathode surface because the light only penetrates a few hundred Angstr¢ms into the metal. Tsang compared the autocorrelation traces of an ultrafast laser with the photoelectron pulse created under normal incidence on a 450-A-thick photocathode, and the two curves were identical to within ~25 fs [Tsa93]. One interpretation of this datum is that the timeconstant for volume emission is very fast, although another possibility is that the surface of Chapter Four: Ultrafast Electron Pulse Generation 178 the photocathode was sufficiently rough to permit surface emission even at normal incidence. 4.1.3.3 Thermally-Assisted Photoemission Although incident radiation intensities may be low enough to prevent thermionic electron emission, the electron and lattice temperatures of the metal are still elevated. This heating can assist MPPE if the thermal energies of cathode electrons increase to the point that one fewer photon is required for ejection. Yen and co-workers showed that if the intensity of 30-ps, 1060-nm laser pulses exceeds 109 W/cm2 , then only three photons were required to generate tungsten photoelectrons. instead of the usual four [Yen80]. Vodopyanov et al. found evidence for thermally-assisted MPPE in the photocurrent emitted from a train oflR pulses (100 ps; 2.8-µm; separated by 7 ns) [Vod89]. Electron emission increased from successive laser pulses in the train even after the intensity of the pulses decreased, and the authors ascribed this observation to a gradual increase in surface temperature which made more thermally-excited electrons available to later pulses in the train. Femtosecond thermionic emission studies have already been discussed in 4.1.1; thermally-assisted MPPE is very important on the fs-time scale since the electron gas is decoupled from the lattice and the electron temperature rises within the pulse width of the laser [Tsa92]. 4.1.3.4 Surface-Plasmon-Assisted Photoemission Tsang and co-workers have shown that MPPE can be enhanced by surfaceplasmon excitation [Tsa91] . Using thin-film metal photocathodes (silver, gold, aluminum, or copper) and an attenuated-total-reflection geometry, the authors measured the Chapter Four: Ultrafast Electron Pulse Generation 179 transmission photocurrent generated with 90-fs, 625-nrn laser pulses, focused down to a diameter of 80 µm. At a critical angle of incidence near 42°, the quantum efficiencies of the two- or three-photon processes increased by up to three orders of magnitude of standard values. Laser intensities (5xl07 W/cm2 ; ~0.2 nJ per pulse) were well below the threshold for thermionic emission. Autocorrelation traces of the electron pulses, made by sending two laser pulses to the photocathode separated by a varying delay /it, showed negligible temporal broadening. This measurement method would not account for geometrical temporal broadening of the electron pulse, however, which is estimated to be ~ 180 fs based on the incidence angle and beam waist. 4.1.3.5 Optical Tunneling If a component of the incident laser's electric field is normal to the surface, then the possibility exists for electron emission without photon absorption. The process is similar to field emission: the transient E.1_ must be strong enough to lower the potential well barrier such that an electron can tunnel through it, into the vacuum. Very-high laser intensities are required, on the order of 10 11 to 10 13 W/cm2 [Far93], [Far78]; the feasibility of optical tunneling is often estimated by calculating the Keldysh parameter [Kel65]: r = (4.12) where v is the optical frequency. MPPE occurs when y >> 1, and optical tunneling is expected to be the predominant channel when y << 1. Several attempts have been made to observe optical tunneling experimentally using IR lasers to simultaneously lower y and keep the total intensity below the damage threshold of the cathode material [Far85], Chapter Four: Ultrafast Electron Pulse Generation 180 [Far84], [Far83]. In recent work, T6th et al. irradiated a gold target with 2.94-µm, 110ps laser pulses at grazing angles with the polarization vector oriented normal to the cathode surface [T6t91]. As the laser intensity increased towards 10 11 W/cm2 (and y fell to 1), the measured power-dependence of photoelectron current dropped from the expected value of n = 12 down as low as n = 6. The authors calculated that such a large change could not be due to thermally-assisted photoemission alone and concluded that the results were evidence of optical tunneling. The temporal resolution of an ultrafast electron source based on optical tunneling would be limited by geometrical broadening. 4.2 The Photocathode The photocathode in commercial streak cameras is most often an air-sensitive alkali or multialkali semiconductor, usually either the S-1 (AgOCs) or the S-20 (Na2 KSb[Cs]). Laboratory electron guns with ns or ps resolution, however, are more likely to use a metal photocathode, such as aluminum [Mou82], gold [WiS84], [Els90], titanium [Ewb90], or tantalum [Ewb92]. 4.2.1 lists several important criteria which must be considered when choosing a photocathode material for ultrafast electron pulse generation. Based on these criteria and recent research by Tsang [Tsa93], a 450-A thick silver photocathode was selected for the UGED electron gun. Preparation and characterization techniques for this photocathode are described in 4.2.2. 4.2.1 Photocathode Selection Criteria Candidate materials for the UGED electron gun photocathode were evaluated in Chapter Four: Ultrafast Electron Pulse Generation 181 terms of five factors: durability, light transmission, work function, energy distribution of photoelectrons, and quantum efficiency. These factors are interrelated in a complex way within the constraints of ultrafast photoemission, as discussed below: 4.2.1.1 Durability Development of UGED required frequent tinkering with the electron gun at atmospheric pressure, and during diffraction experiments the photocathode was potentially exposed to small amounts of reactive chemicals, even though the electron gun chamber was differentially-pumped. The photocathode had to be hardy and able to withstand a few hours exposure to air. Multialkali photocathodes were therefore out of the question, without even considering the difficulties of their preparation. The lifetime of multialkali photocathodes is short unless they are kept under high vacuum; even at pressures of only 10-5 torr, the quantum efficiency of a Cs 3Sb photocathode drops by three orders of magnitude [KaY84]. Metal photocathodes are much more resistant to chemical attack, although most form surface oxide layers in the presence of air, and metals also have high damage thresholds, on the order of 0.2 J/cm2 for ultrafast lasers [PrS95]. With a laser focal spot 150 µm in diameter, pulse energies of 35 µJ would be required to reach this damage threshold. 4.2.1.2 Light Transmission Unless the excitation laser strikes the photocathode normal to the surface, the ejected electron pulse will be temporally broadened by the geometry of the interaction. At non-normal incidence angles, the laser pulse generates electrons progressively across the active region of the photocathode, introducing a temporal spread f}.tg equal to: Chapter Four: Ultrafast Electron Pulse Generation /it 8 = (w/c)sin0 182 (4.13) where 0 is relative to the normal and w is the width of the active region. Geometrical broadening is on the order of 200 fs for a 100-µm active region and a 45° angle of incidence. To keep /it8 at 0 while simultaneously avoiding the experimental difficulties associated with a counterpropagating arrangement (i.e., sending the laser backwards through the electron gun), the UGED electron gun was built with a back-illuminated, thinfilm photocathode. In this arrangement, if the photocathode is too thick, then the input light intensity may approach damage thresholds before the output light intensity is sufficient for electron emission. Photocathode selection is further complicated by the fact that the work function of thin-films also has a thickness dependence. Estimates for the transmission of light through various photocathodes were calculated from [Wea81], [ChK69]: T = (1 - R)exp ( -4nkt) ~ (4.14) where R is the reflectivity, t is the film thickness, and k is the optical extinction coefficient. Values for R, k, and the refractive index n are tabulated as a function of 'A in the CRC Handbook [Lid92]. Note that R also has a thickness dependence for small t. Figure 4-5 compares calculated and experimental transmission curves for a 712-A silver film using optical parameters from [ScL54] and [Ha175] . Agreement between theory and experiment is fairly good, given that the thin film was exposed to air in order to record the transmission curve. Chapter Four: Ultrafast Electron Pulse Generation 183 100 C: 0 'iii .!!! E u, --Experimental - -+- -HGK c Schulz 10 1 + C: ca + :i.. t0.1 -;!?., 0 +. • ·+- ... 0.01 200 300 400 500 600 700 800 Wavelength (nm) Figure 4-5: Experimental and theoretical transmission curves for a 712-A silver film. The film was exposed to air. Theoretical optical constants are from [Scl54] and [Haj75]. 4.2.1.3 The Work Function Although the creation of other wavelengths from the CPM / PDA femtosecond laser system is straightforward (3.1.4), continuum generation output is less stable and requires extra laser power from the Nd: YAG - power better allocated to increasing the pump laser intensity. Photoemission using the CPM's fundamental wavelength of 620 nm (2.0 eV) or its second harmonic would be preferable. In order to keep the electron flux high, though, the photoemission process should require as few photons as possible, so the initial upper limit on the photocathode work function was set at 4.0 eV. Actually there was some leeway in <j>, on the order of ~0.1 eV, because: ( 1) the field strength at the photocathode of the UGED electron gun was 2.7 kV/mm, which reduces the work function by 0.06 eV according to Eq. 4.6, and (2) the energy bandwidth of the femtosecond laser could span an additional 0.01 to 0.02 eV (see Eq. D.47 in D.9.1.9). Tabulated values of work functions for bulk materials were consulted at first, Chapter Four: Ultrafast Electron Pulse Generation 184 Gold Silver Aluminum Indium (1064 °C) PE(al 5.1 PE(b) 4.7 (961 °C) PE(a) 4.0 (660 °C) PE<9> 4.28 PE(b) 4.2 (157 °C) PE(h) 4.08 PE<il 4.09 5.1 5.37 cpo<c> FERP(d) 4.26 4.41 4.46 4.35 PE<e> CPD<c> FERP(d) PE<!) 4.17 4.26 Zirconium (1852 °C) PE<a> 4.05 CPD<c> FERP(dl Table 4-1: Melting temperatures and work functions (in eV) for selected bulk metals (polycrystalline forms). Method of determining <I> is indicated - PE: photoemission; CPD: contact potential difference; FERP: field emission retarding potential. References: (a) [Eas70]; (b) [Lei73]; (c) [Tha75]; (d) [BaS77]; (e) [Dwe75]; (f) [ScE83]; (g) [EaR73]; (h) [Laa60]; (i) [Hol79]. including [Fom66], [Som68], [Riv69], and [Eas70], and <j> was found to be greater than 4.3 eV for most metals. Zirconium and indium are two metals with polycrystalline bulk work functions which were within the target range (Table 4-1 ). Work functions are slippery numbers, though, dependent on sample purity, crystal structure, and the method of measurement. The most common approaches for determining <j> are to construct Fowler plots from photoemission data [Fow31], [Lea69], measure contact potential differences [Hop64], or to use the field-emission retarding potential method [Hol66], [BaS77]. Table 4-1 summarizes several work function measurements for gold, silver, and aluminum, showing that the variation in reported <j> is sometimes larger than 0.4 eV. The work functions for thin metal films (<5,000 A) can be different from that of bulk samples, particularly as the film's character becomes less metallic and more like a semiconductor. Although polycrystalline aluminum films deposited on a quartz substrate showed no variation in <j> with t, the work function of aluminum deposited on bulk single crystals dropped below expected values by several tenths of an eV, unless the coating was annealed [EaR73]. Silver exhibited similar behavior [Dwe75], except polycrystalline films deposited on quartz had work functions greater than the bulk when the thickness was less Chapter Four: Ultrafast Electron Pulse Generation 185 Gold Silver Aluminum Copper Thickness (A) Film <j> (eV) n@ 620 nm 455 3.8 3 475 110 3.9 3 430 3.65 2 Bulk <I> (eV) 5.1 4.26 4.28 4.65 4.2 3 Table 4-2: Comparison of work functions tor thin metal films [Tsa91] and bulk solids [Lid92]. The films were exposed to air for several hours before qi was measured by photoemission. The number of photons n tor emission at 620 nm (2.0 eV) are also shown and exhibit some inconsistency with measured qi. than 1,500 A, and less than the bulk out to 2,000 A. The bulk value was reached by a thickness of ~2,200 A. Thin film work functions are highly influenced by surface contamination, such as exposure to air, and values of <j> can shift eithe.r up or down depending on the material [Ren45], [Dwe75]. Tsang and co-workers used the photoernission method to measure the work functions of thin metal films which had been exposed to air for several hours [Tsa91]. As shown in Table 4-2, the measured work functions were several tenths of an eV lower than the bulk values, although detailed explanations for the observed decrease were not provided. The authors also measured the slope of power dependence curves at 620 nm (2.0 eV) and found n = 2 for silver and n = 3 for aluminum, gold, and copper. According to their values of <j>, n should have been 2 for aluminum and gold. 4.2.1.4 Photoelectron Energy Distribution The narrower the initial energy distribution of photoelectrons, .!1£, the shorter the temporal width of the electron pulse. For example, the arrival time of 18 ke V electrons after 0.3 m of travel varies over 100 fs if the width of the electrons' initial energy distribution is 1 eV. The FWHM of the energy distribution increases with the amount of excess energy in the photoernission process, nhv - <j> , where n is the number of photons: Chapter Four: Ultrafast Electron Pulse Generation 186 Tests of the S-20 photocathode (<I> < 2 eV [Den86]) show a ~E of 0.3 eV at "A = 600 run (2.1 eV) and a ~E of 0.6 eV at "A= 400 nm (3.1 eV) [Kin87], [Kin90]. Photoemission from gold films exhibits a similar trend, with a ~E of 0.6 eV at 250 run (5.0 eV) and a ~E of 1.1 eV at 210 run (5.9 eV) [Ran80]. At 347 run (3.6 eV) two photons are required for photoemission from thick gold films, and the energy distribution has a ~E of 1.2 eV [Log69], broader than the value at 250 nm because the excess energy is greater. To keep the energy distribution small, laser fluences on the cathode must be below 1 rnJ/cm2 in order to prevent thermally-assisted photoemission (4.1.1 and 4.1.3.3). Riffe et al.' s photoelectron kinetic energy studies showed that the distribution from Ag( 111) was 0.4-eV wide when the 620-nm, 90-fs laser intensity was 0.9 rnJ/cm2 , but the ~E increased to -3 eV for fluences of 13.7 rnJ/cm2 [Rrl93]. With 8-ps, 1.06-µm laser pulses and a gold photocathode, Farkas and Toth observed energy distributions spread over several hundred eV for fluences of 80 rnJ/cm2 [Far90]. 4.2.1.5 Quantum Efficiency The quantum efficiency (and transmission) of the photocathode material must be high enough to keep the incident laser intensity below the threshold for thermally-assisted photoemission or damage. The multialkali photocathodes have QE's greater than 0.01 [Gho82], [Den86], but are not durable enough for UGED. Most metals have QE's between 104 and 10-5 for single-photon emission processes in the UV [KaY84], [Sri91], [ChE94]. The QE of two-photon processes depends on the power density, but is between 10-7 and 10-8 at 50 MW/cm2 (50 µJ/cm 2 with 100-fs laser pulses) for metals like silver, gold, and aluminum [Tsa91] . For ultrafast photoemission, the quantum efficiency is Chapter Four: Ultrafast Electron Pulse Generation 187 reduced by space-charge near the photocathode if the electron density is too high or the extraction field is too small [Cla89], [Sri91]. The surface-plasmon effect (4.1.3.4) is one approach for increasing the QE of metals [Tsa91], but the electron pulse widths broaden due to geometrical effects. Lowering the work function by implanting ions in the metal can also increase the quantum efficiency, perhaps at the expense of a wider initial kinetic energy distribution [Gir95b]. Bryukhnevich et al. have recommended using an air-resistant metal-oxide, (AlMgCu)Ox, for UGED electron guns [Bry92]. The quantum efficiency was 10-3 at 353 nm. The photoelectron energy distributions and work function of the material, which would be useful for further evaluation of the temporal properties, were not reported. 4.2.2 Choosing and Testing the 450-.A Silver Photocathode A 250-A gold photocathode was selected for the first generation UGED apparatus based on Elsayed-Ali and Herman's design of a picosecond electron gun [Els90]. Those authors generated their electron pulses with a 266-nm (4.66-eV), 100-ps laser, noting that gold's work function was 4.68 eV. In order to create electrons in the UGED laboratory with a one-photon process, femtosecond pulses at 258 nm (4.81 eV) were formed using the continuum method [Dan94]. Several factors motivated the search for a different photocathode in the second-generation apparatus. Most importantly, power dependence studies of the UGED photocathode actually showed a two-photon dependence at 258 nm. Comparable electron fluxes were created when 310-nm laser pulses were used instead, which made the effort spent on continuum generation somewhat pointless. The gold photocathode may have been coated without correcting the thickness monitor reading for Chapter Four: Ultrafast Electron Pulse Generation metal density (3.4), so t may have been ~40 A instead of 250 A. However, the work function which Elsayed-Ali and Herman referenced was based on photoemission from a bulk gold sample, Thickness 100 A 300A 45oA 712 A 188 Percent Transmission 310 nm 620 nm 84.7 45.4 56.7 9.8 39.0 2.1 22.7 0.2 Table 4-3: Substrate-corrected percent transmission of silver films at 310 and 620 nm as a function of film thickness. not a thin film, in which the laser was incident at glancing angles, not normal to the surface [Lom78]. The value of 4.68 eV was therefore not necessarily correct for the experimental conditions of UGED. The decision was made to investigate materials with work functions near to 4.0 eV, so that continuum generation could be avoided, and to examine the literature for other photoemission experiments closer in design to the UGED electron gun. Zirconium and indium were identified as possible candidates because their bulk work functions are in the neighborhood of 4.0 to 4.1 eV (see Table 4-1). As an added plus, the work function of zirconium drops when exposed to air due to oxygen contamination [Ren45], but the melting point of zirconium was too high to create thin-film coatings in the UGED laboratory's metal evaporation chamber. Indium coatings were not attempted because the material agglomerates when deposited at room temperature; to create electrically-continuous coatings with thicknesses of only a few hundred Angstqzsms, the substrate must be cooled to at least 150 K [MuD79]. Tsang and co-workers' report of work functions below 4.0 eV for air-exposed thin films of gold, aluminum, and silver were reconsidered [Tsa91]. The gold and aluminum results were perplexing given that the authors had observed three-photon emission processes from both metals using a 620-nm (2.0-eV) laser, and cast doubt on their Chapter Four: Ultrafast Electron Pulse Generation 189 100 --100A - - - 300A c: 80 --4soA 0 u, - - - - - -112 A .!!? 60 E u, C: ~ 40 120 300 400 500 600 700 800 Wavelength (nm) Figure 4-6: Experimental transmission curves for silver films exposed to air. transmission curves have been corrected for the substrate. The observations of silver. In a second study, Tsang measured <I>= 3.5 eV for a 450-A silver film and again observed n = 2 for the CPM fundamental (1.98 eV) [Tsa93]. The laser was a 90-fs, 625-nm CPM system with energy densities on the photocathode no greater than 10 µJ/cm2 (below the threshold for thermally-assisted photoernission), and electrons were emitted from the front-illuminated photocathode with no temporal lag. These results were worth testing in the UGED laboratory - silver films were durable, and the quantum efficiency of silver was not abnormally low [Tsa91], [Sri91]. Barring thermal effects, the photoelectron energy distribution should be narrow under these conditions, with a ~£ of at most 0.4 eV, and probably less. Tsang's photoernission results were confirmed in the UGED laboratory, although <I> was not explicitly measured. High purity silver (99.999%, Aldrich) was deposited on photocathode mounts (see 4.3.2 below) in varying thicknesses using the metal evaporation chamber. Photocathodes were exposed to air for no more than an hour, and if several Chapter Four: Ultrafast Electron Pulse Generation 190 IJ\___ . I E: PDA Oscilloscope CCD Output Figure 4-7: Experimental scheme for measuring the power dependence of photoemission. Laser intensity was detected with a photodiode and integrated on an oscilloscope. Electron counts were recorded by direct bombardment on a CCD chip. PDA: pulsed dye amplifier; WG: wavelength generation; BS: beam splitter; F: filter; PD: photodiode. photocathodes were prepared at once, then the spares were stored under vacuum in the electron gun chamber. Transmission curves were recorded on a UV-VIS spectrometer and corrected for the photocathode substrate window (Figure 4-6). The data agreed well with theoretical predictions (Figure 4-5 in 4.2.1.2). Table 4-3 summarizes values of Tat wavelengths of 310 and 620 nm; transmission remained high at 310 nm even for the thicker films, so there would be less risk of damaging the input side of the photocathode. Power dependence curves for electron emission from silver photocathodes were recorded as a function of film thickness and wavelength. The incident laser was focused to a diameter of ~ 150 µm (A = l.8x104 cm2) and had a pulse width of 300 fs. These experiments were performed in the first-generation UGED apparatus, where photoelectrons were detected by direct bombardment on a CCD chip. The total intensity of the electron beam in the CCD images was measured with the program HPC-1, background-corrected, and converted from ADUs to number of electrons. A portion of the incident laser was monitored with a blue-enhanced photodiode (UDT) and an oscilloscope (Figure 4-7) to guarantee that each electron image corresponded to a single laser pulse. The photodiode signal was integrated using a mathematical package built in to Chapter Four: Ultrafast Electron Pulse Generation Thickness 100A 300A 45oA 191 Wavelength Energy Range Slope n 258 nm (4.8 eV) 310 nm (4.0 eV) 258 nm (4.8 eV) 620 nm (2.0 eV) 620 nm (2.0 eV) 0.8 to 8 nJ 0.3 to 8 nJ 0.2 to 6 nJ 60 to 600 nJ 30 to 400 nJ 2.0 2.0 2.3 3.0 2.0 Range of <I> 4.8 to 8.0 eV 4.8 to 6.0 eV 2.0 to 4.0 eV Table 4-4: Slope of power dependence electron emission curves from silver for various wavelengths and film thicknesses. the oscilloscope, and then converted to units of joules based on the transmission curves of the beam splitters and filters, and the response curve of the photodiode. In general, the measured power dependence curves were linear with moderate-to-little noise, and the slopes were analyzed by least-squares. .. Table 4-4 summarizes the results of the study, and Figure 4-8 shows the power dependence curve for the 450-A photocathode illuminated with 620-nm light. Based on the measured values of n, the 100-A and 300-A silver films had work functions above 4.0 eV. The results for the 100-A film were tenuous because the photocathode may have been damaged right at the start by too much laser intensity; the other films were studied with more care. The 450-A film showed a two-photon electron emission dependence at nm, 620 rn agreement with Tsang's work -- 4 s::: ::::, 0 () 3 s::: 0 - 0 0 0 Cl) w 2 Slope= 2.04 0 en 0 .J 1 1.5 1.8 2.1 2.4 2.7 Log( Pulse Energy; nJ ) [Tsa91], [Tsa93]. The quantum 9 efficiency was estimated to be 10- 2 for 100-nJ pulses (0.6 rnJ/cm ), Figure 4-8: Power dependence curve for a 450-A silver photocathode illuminated at 620 nm. The slope indicates that electron emission is a two-photon process. Chapter Four: Ultrafast Electron Pulse Generation 192 although not every electron generated at the photocathode was expected to pass through the extraction pinhole into the remainder of the electron gun. Based on the power dependence experiments and the other selection criteria, the 450-A silver photocathode was chosen for the UGED electron gun. Elsayed-Ali and co-workers have also reported switching from the 250-A gold photocathode to a 400-A silver photocathode [Aes95a]; they observed a one-photon power dependence curve using 295-nm (4.2 eV) laser pulses. 4.3 The UGED Electron Gun .. The purpose of an electron gun, be it in a streak camera, television, or diffraction apparatus, is to transfer electrons from one point in space to another. Beyond this definition, the performance objectives required of the UGED electron gun included: 1. Offering picosecond or subpicosecond temporal resolution while maximizing the number of electrons per pulse. One consequence of this was avoiding cross-over points in electron trajectories which might exacerbate space-charge. 2. Accelerating the electrons to GED kinetic energies, -20 keV or greater. 3. Providing a focal point with a diameter of a few hundred microns at a position external to the gun by -0.3 m (the location of the detector). 4. Providing a well-collimated electron beam such that the beam diameter at the sample was also on the order of a few hundred microns. At the start of the Zewail laboratory's UGED project, Dr. Hani Elsayed-Ali graciously provided electron gun design plans which he had helped develop for picosecond RHEED studies (1.5) [Els95]. An electron gun was constructed in the Caltech Chemistry Machine Shop based on these schematics. The UGED electron gun consisted of a back-illuminated Chapter Four: Ultrafast Electron Pulse Generation Ph otocath ode 193 Butterfly Valve Nozzle ~ p~~~:~.°' --,_J ___ \ Final Pinhole /1 Direct Bombardment CCD Figure 4-9: Flight path of the electron beam in the UGED electron apparatus. Photoelectrons were extracted from the photocathode through a pinhole, and collimated and focused with electrostatic optics in the electron gun. The electron beam traveled through a final pinhole, deflection plates, and exited the electron gun chamber via a butterfly valve and differential-pumping aperture. In the scattering chamber, electrons passed under the molecular beam nozzle tip and were detected either by direct bombardment on a CCD, or by emission from a phosphor scintillator. photocathode, an extraction pinhole, and a series of electrostatic lenses which focused the electron beam 20- to 30-cm downstream (Figure 4-9). A final pinhole capped the end of the electron gun and blocked off-axis aberrations of the electron beam, and the pinhole was followed by three pairs of deflection plates for positioning or streaking the electron beam. Table 4-5 summarizes the distances between the electron gun mounting flange and various landmarks along the electron beam trajectory. Elsayed-Ali's design served the UGED laboratory well. The 18 keV electron beam could be focused to diameters with FWHM as small as 200 µm and an angular divergence of 1.8 mrad. According to streaking measurements (4.4), pulses containing 1,000 electrons were only 1 to 2 ps in duration, and an order of magnitude more electrons could be obtained with 10-ps pulses. Aeschlimann et al. have discussed the design principles and electro-optical characteristics for this type of electron gun extensively, and Chapter Four: Ultrafast Electron Pulse Generation the reader is referred to their publication [Aes95a]. This section provides a more general discussion of electron gun, including construction and operational details. the UGED A cursory theoretical evaluation of the temporal response and coherence lengths 194 Component L(mm) Time (ns) Photocathode Extraction Pinhole End of Electron Gun Body Final Pinhole Center of Streak Plates Center of Y-Axis Deflectors Center of X-Axis Deflectors Butterflv Valve Differential Pumoinq Aperture Molecular Beam Nozzle Direct Bombardment CCD Phosohor Scintillator 35.4 38.0 201 213 238 263 282 343 368 491 542 591 0.0 2.4 2.6 2.9 3.2 3.4 4.2 4.6 6.1 6.8 7.4 Table 4-5: Length L between the electron gun mounting flange and components within the UGED apparatus. The precision of most measurements was ±2 mm. The gap between photocathode and extraction pinhole was measured to within 0.1 mm. Arrival times are calculated for relativistic 18 keV electrons. The transit time through the electron gun body was estimated with SIMION. is also included. 4.3.1 The High-Voltage Power Supply Electron gun power supplies in gas-phase electron diffraction experiments have voltage stabilities on the order of 1 part in 104 [Tre88]. This stability is necessary to maintain chromatic resolution; voltage stability is equally important in ultrafast diffraction experiments in order to maintain temporal resolution, because any fluctuation in accelerating voltage corresponds to a fluctuation in electron velocity and arrival time of the electron pulse at the nozzle tip. The UGED electron gun was biased with a variable 40-kV, 2.5-mA high voltage power supply (Glassman High Voltage; PS/EH40R02.5) rated at 0.005%. The standard operating voltage was -18 kV, applied to the photocathode. Intermediate voltages were needed for four more electrodes within the gun: the extraction pinhole (EPH) and three lensing elements (Ll, L2, and L3). The fifth electrode (L4) and the final pinhole were grounded. Chapter Four: Ultrafast Electron Pulse Generation 195 The voltages for EPH, Ll, L2, and L3 were Glass man High Voltage Power Supply obtained with a home-built high-voltage divider (Figure 4-10). Each of the four arms in the divider contained a series of 3- or 6-MQ, 2-W resistors, ending in a 5-, 7.5-, or 10-MQ variable resistor pot. The variable resistor pots were connected to front panel knobs by several inches of plastic rod, and each arm of the divider was mounted on widely-spaced pegboard within a Plexiglas shell to prevent arcing. Despite these precautions, the voltage divider began arcing if the input voltage approached -19 kV. This was the primary reason for limiting the photocathode voltage to -18 kV - not because of arcing within the electron gun. PC EPH L1 L2 L3 Figure 4-10: Home-built divider for generating the different electron gun voltages. Each output arm consisted of a series of 3- or 6-Mn resistors and a variable resistor pot. The Glassman power supply had both voltage- and current-limiting control knobs with position locks. To ensure that the photocathode was biased at the same value from day to day, the setting of the voltagelimiting knob was locked in place and the power supply was brought up with the currentlimiting knob. The total current flowing through the voltage divider was estimated to be 1.57 mA, and the value displayed on the Glassman power supply panel meter read 1.52 mA. The maximum thermal energy emanating from 6-MQ resistors was calculated as 1 W, and the voltage divider unit was cooled with a fan. Chapter Four: Ultrafast Electron Pulse Generation The resistor pots provided a 1 to 2 kV range for each arm, with the offset determined by which resistor the lead was connected to (Table 4-6). Electron gun voltages were measured with a PC EPH L1 L2 L3 L4 196 Theoretical Ran~e (kV) Experimental Range (kV) Operating Values (kV) - - -10.5 to -11.8 -1.4 to -4.8 -2.6 to -5.5 -10.5 to -11.4 -10.3 to -11 .3 -1.2 to -3.5 -2.0 to -4.1 -9 .8 to -10.7 - - -18.00 -10.92 -2.01 -4.07 -10.51 0.00 Table 4-6: Theoretical and experimental voltage ranges for electrodes within the UGED electron gun. The ranges can be adjusted by changing attachment points within the high voltage divider unit (Figure 4-10). Standard operating voltages are also shown. high voltage probe (Keithley; Model 1600A) and a Fluke multimeter. With these instruments, the highest voltages showed no variance to within ±5 V (the limit of the multimeter's precision) over many hours. According to the manufacturer, however, the high voltage probe's accuracy is rated at only ±2.5%, or ±450 V at -18 kV. The Glassman power supply has a back panel voltage monitor rated at ±1 % over 40 kV; when the PC voltage was measured to be -18.00 kV with the probe, the back panel monitor read -18.1 ± 0.2 kV. In the future, more precise methods for determining the electron's kinetic energy (and Ae) should be sought, especially since measurements of the GED camera constant LAe have proven to be problematic (7.3). 4.3.2 The Photocathode and Extraction Pinhole The aluminum photocathode mount was a hollow cylinder with an OD of 0.938" (slightly less than 24 mm), where the extraction pinhole side was machined down to an 0.793"-OD, inset for 0.160" (Figure 4-11). Earlier mounts had total lengths of 0.34", but the length was increased to -1" in later versions to limit tilting. A 1/2" -OD, 1/16"-thick Chapter Four: Ultrafast Electron Pulse Generation Photocathode Mount\ Silver Paint Photocathode nd0 o.Hso~i W 0 283 \ • " -===,=-r f __ __ • __ •, ~ ~ i1 : 1 lo : 450~::~~v-er Vent Holes j;'j -i - JJ! ~ 11a".0.i: ,: " ~ j····•· ·;; \),,,. Film 197 Extraction Pinhole ~T. --~l-rn •• i~!!~ : o :: o ] ! II :i 111 en LJJi o. 35 o· ~ ;·1f ~ ;JJ -~~~':i},~ it. ::__L Extraction Pinhole Ceramic Base --;~ I I Extraction Pinhole Mount Figure 4-11: Schematics of the photocathode and extraction pinhole mounts for the UGED electron gun. Most components were aluminum; the base for the EPH mount was machined from Macor, an electrical insulator, and the extraction pinhole itself was stainless steel. The gap between the PC and EPH was 2.6 mm. quartz window (Heraeus-Amersil; 1899) fit snugly in an aperture in the narrow end and was held in place with silver paint. Silver paint was also applied around the outer millimeter of the window in order to guarantee an electrical connection between the as yet unapplied photocathode (PC) and the mount. The window-face of the mount was coated with a 450-A silver film in the metal evaporation chamber. When backlit by room lights, the photocathode window looked dark blue because of the silver transmission peak extending to 320 nm (Figure 4-6). A white card with a 1.8"-diameter hole cut out from the center was placed in the input side of the photocathode mount to assist in alignment of the UV input laser. The extraction pinhole mount was a thin aluminum disk with a chamfered central aperture and a slight, 0.005"-deep, 9.5-mm-wide inset on the back side (Figure 4-11). The extraction pinhole, a 13-µm-thick stainless steel foil with 9.5-mm OD (Melles-Griot; e.g., 04 PIP 017) slipped into this inset. The aperture of the EPH was 200 µm, although Chapter Four: Ultrafast Electron Pulse Generation 400-µm apertures were tested too. 198 To join the EPH and its mount together, the extraction pinhole was placed on top of a 12-mm-wide aluminum cylinder, ~2-cm tall, and the mount was carefully and firmly pressed down on the cylinder, making sure that the extraction pinhole remained centered and flat. Silver paint was applied around the chamfered edge to secure the EPH in place. The mount was then spun on a lathe to confirm that the extraction pinhole aperture was perfectly centered within the mount. The extraction pinhole mount fit snugly within the central aperture of a ceramic base with 0.938" OD (Figure 4-11). The ceramic base capped the window-side of the photocathode mount, electrically isolating the photocathode and the extraction pinhole, and the gap between the PC and EPH was measured as 2.6 mm. Venting holes were drilled through the edges of the photocathode mount so that the region between the PC and EPH was properly evacuated. The coupled unit slid into the rear of the electron gun (Figure 4-12) and was held in place by clamping screws which also provided electrical connections. The angular distribution of electrons emitted from a photocathode is Lambertian (Eq. 4.15) [Kin87], [Fry28], [lvH28], and the kinetic energy tends to decrease with angle. p(0, r) oc cos0/r 2 (4.15) The 200-µm EPH aperture matched the estimated diameter of the laser at the photocathode, about 150 µm, so only the central region of the distribution passed through the aperture into the main body of the electron gun. Although nearly 40% of 310-nrn light transmits through a 450-A silver film (Table 4-3), photoemission from the extraction pinhole was insignificant; this was tested by setting the photocathode voltage equal to the extraction pinhole voltage and observing that no electrons were detected. Chapter Four: Ultrafast Electron Pulse Generation 199 4.3.3 The Electron Gun Body and Focusing Electrodes The main body of the electron gun was formed from a hollowed 1.5" (38.1-mm) diameter rod of Macor, a machinable ceramic (Figure 4-12). The photocathode-side of the tube was screwed onto a 2.75" CFF, which in turn was attached (without gasket) to the electron gun chamber's high voltage feedthrough flange. Channels were machined into the 2.75" CFF base for pumping out the rear of the electron gun. The photocathode-side of the Macor tube had a 24-mm ID with a depth of 31 mm, and the lensing-side had a 21mm ID with a depth of 158 mm; the two hollow regions were separated by a 3-mm wall with a 6-mm-ID aperture. The extraction pinhole mount nestled up against this wall on the rear side, and the back of Ll was on the front side. The four lensing electrodes, Ll through L4, were 21-mm-OD stainless steel tubes, separated from each other by 2 mm with Macor spacers. The lengths of the electrodes were 17, 74, 15, and 45 mm, respectively. LI had an 18-mm ID, and L2, L3, and L4 had a 15-mm ID. LI and L2 both had back walls, ~2-mm thick, with 3-mm-ID apertures. Electrical connections to each electrode were made through the main body wall with spring-loaded screws. Together, EPH, LI, and L2 acted as a long focal-length zoom lens; the design was actually a Riddle lens intended for minimizing chromatic aberrations [Rid78], [Aes95a]. Secondary focusing was provided by L2, L3, and L4, an Einzel lens. The two lenses were used in combination so that the electron beam was well-collimated and only one image was formed, about 30 cm from the end of L4. The formation of additional images within the gun might cause space-charge broadening because each image coincides to a plane where the angular distribution of electrons, emitted from a single point on the photocathode, rejoin in space and their trajectories cross over. Chapter Four: Ultrafast Electron Pulse Generation 200 :ti I 38.1 m In order to understand the properties ; 21 m and dynamics of the electron gun a bit better, --1 15 mm single electron trajectories were simulated L4 E E l!) "<I' with the program SIMION (Idaho National Engineering Laboratory). __ l SIMION calculates only one trajectory at a time, so space-charge effects are L3 ignored; furthermore, SIMION does not correct for -~~f E E relativistic effects on electron CX) velocity (Appendix A). At the time of the simulation, l!) E E N 0, a slightly different set of electron gun L2 E E "<I' r-- voltages were used: PC= -18.00 kV, EPH = -10.94 kV, Ll = -1.85 kV, L2 = -3.78 kV, L3 = -10.56 kV, and L4 = 0 V instead of the values listed in Table 4-6. None of these caveats interfere with the general conclusions of the simulation, however. The PES for the electron gun is shown in Figure 4-13; SIMION predicted that the time-of-flight of an electron through this potential was 2.4 ns. 9mm Cross-over points cannot be completely eliminated from the electron gun - _L - Figure 4-12: Schematic for the UGED electron gun. The Macer main body was inset in a 2.75" CFF. The electrodes were stainless steel. Chapter Four: Ultrafast Electron Pulse Generation 201 0 L4 L1 L2 G> L3 en o - ca "":- EPH 0 > ~I Li l~c~□==c==========================c:=:::=~==========~ 0 C\J ---L-..,.----,,-----.--....--..------,.---,--....-----,----.--.....--.-------,---.--..,........----,--~ I 0 50 100 150 Distance (mm) Figure 4-13: The potential energy surface as a function of longitudinal distance inside the UGED electron gun. because there are, in fact, two different kinds. As shown in Figure 4-14, the image plane of the lens is one type of cross-over point because it corresponds to the focal point of the photoelectrons' angular distribution (f0 ). A second cross-over point occurs at fs, though, where the paths of photoelectrons with parallel trajectories but different points of origin intersect. The beam diameter as a function of position along the electron gun is determined by a combination of spatial and angular distribution trajectories. The locations offs andfa, and their dependence on electrode voltages, were tested with SIMION. In the following paragraphs, increasing an electrode's voltage refers to magnitude, not sign; under this parlance, changing L2 from -3.78 kV to -4.07 kV is an increase in voltage. The focal point of the image was located inside the gun, just at the end of L2 and approximately 65 mm before the exit. This location changed by ~ 1 mm / 35 V if PC, Chapter Four: Ultrafast Electron Pulse Generation I◄ ~>.~ fa ✓ 202 fs I-◄--✓---►I ►I ------->4 Angular Distribution Focal Point (Image Plane) Image Focal Point Figure 4-14: Two types of cross-over points in the electron gun optics. One corresponds to the intersection of the angular distribution trajectories and one corresponds to the intersection of the spatial distribution (image) trajectories. The focal point under the nozzle tip is atfa, EPH, or Ll were individually adjusted. Increasing PC or Ll moved ls out, towards the end of the electron gun, and increasing EPH moved fs in. If PC, EPH, and Ll were changed simultaneously, keeping the ratio of voltages the same, thenfs did not move. L2 and L3 did not affect the position offs. According to SIMION, electron trajectories beyondfs diverged by 0.04° (0.7 mrad) for every 100-µm of displacement along the face of the photocathode. The focal point of the angular distribution was located 257 mm from the end of L4, near the molecular beam nozzle tip. (Comparison with experimental measurements of fa showed a difference of several centimeters). Increasing the photocathode or L2 voltage moved fa out by either 1 mm/ 5 V or 1 mm/ 15 V. Decreasing L3 moved fa out at a rate of 1 PC (-18.00) EPH (-10.94) L1 (-1.85) L2 (-3.78) L3(-10.56) Is la +0.027 -0.035 +0.194 -0.003 -0.003 +0.066 -0.2 to -0.4 +0.022 - Table 4-7: Change of electron beam spatial and angular distribution focal points as a function of electrode voltage. Units are mmN. Values were calculated with SIMION. A positive sign means the focal point moves out, away from the photocathode, as the voltage magnitude increases (becomes more negative). The values are for perturbations of a few percent relative to the indicated starting voltages; the values do not necessarily change linearly with voltage. Chapter Four: Ultrafast Electron Pulse Generation 203 mm for every 3 to 5 V, depending on L3; if L3 was reduced as low as -9 kV, the angular distribution trajectories were essentially parallel and fa was located at =. Adjustment of EPH or Ll had minimal effects onfa• After the focal point, SIMION predicted that the electron beam would diverge by 0.003° (0.05 mrad) per degree of angular emission from the photocathode. Variations of fs and fa as a function of electrode voltage are summarized in Table 4-7. 4.3.4 The Final Pinhole and Deflection Plates A 1.75"-OD, 1.125"-long, electrically grounded aluminum cylinder capped the last half-inch of the electron gun's ceramic body (Figure 4-15). Four 0.25"-square, 3.25"-long Delrin struts were attached to the end cap with set screws. The struts supported three pairs of aluminum deflection plates. The first pair, 1"-long with an interstice of 4 mm, were streak plates, normally grounded except when measuring the duration of electron pulses in a streaking experiment (see 4.4 below). The streak plates deflected the electron beam along the y-axis at a rate of 150 µm/V (~2 pix/V) as measured at the phosphor screen. The remaining two pairs of deflection plates were used to position the electron beam along they- and x-axes. Each pair of plates were 0.5"-long with an interstice of 6 mm. The y-axis plates deflected the electron beam 27 µm/V (~0.35 pix/V), and the x-axis plates deflected at a rate of 22 µmN (~0.29 pix/V), as measured at the phosphor screen. The bottom y-deflector and left x-deflector (from the detector's perspective) were connected to MHV feedthroughs on the three-port side flange of the electron gun chamber; the top y-deflector and right x-deflector were grounded. A thin aluminum plate with an 0.375" aperture supported the free ends of the four Delrin struts. This plate was Chapter Four: Ultrafast Electron Pulse Generation Final Pinhole 204 X- and Y-Axis End Panel Deflection Plates End Cap Cl) .c ::J ti.. 0 (.) cu :l: I I i.-o.s".J I I i.-o.s·.j 4mm Final Pinhole Streak Plates Y-Axis Deflection Plates X-Axis Deflection Plates End Panel Figure 4-15: Schematic for the deflection plate assembly mounted on the end of the UGED electron gun Macer body. The end cap, final pinhole, deflection plates, and end panel were aluminum; the support struts were Delrin. The separation between successive deflection plate pairs was 0.25". also at O V; the ground-line connection led from the plate to the grounded deflection plates, the end cap, electrode IA, and on back to the Macor tube's 2.75" CFF mounting flange. Aberrations within the electron optics, most likely coma [Aes95a], caused winglike patterns to extend outward from the central electron beam. A final aluminum pinhole was set into the end cap (Figure 4-15) to "clean up" the electron beam by blocking these wings. After experimenting with different-size apertures, the diameter of the electron Chapter Four: Ultrafast Electron Pulse Generation 205 beam at the aperture was found to be large, 1.5 mm when generated with a 310-nm laser. These results were not in agreement with the SIMION simulation, which predicted that the maximum electron diameter at the end cap would be ~300 µm. As a confirmatory test, the final pinhole was removed and electron gun voltages were adjusted to move fa out to infinity (L3 was minimized and L2 was maximized within their set ranges - see 4.3.3). The electron beam on the phosphor screen then had a diameter of 3 mm. Space-charge could not be blamed for the electron beam cross section because the same spot size was observed for low and high electron fluxes. (Note that at relativistic velocities, self-field focusing counteracts space-charge broadening along the transverse axis [Kat92]; self-field focusing is the reason high-energy particle beams remain collimated for long times within accelerators.) The off-axis trajectories were estimated to have a total path length only 5 to 10 µm longer than an on-axis trajectory, so the difference in arrival times at the nozzle tip would be no more than 150 fs. Further investigations into the electron beam trajectory were deemed unnecessary, and the 1.5-mm diameter final pinhole was reinstalled. 4.3.5 The Electron-Generating Laser Five percent of the total output from the PDA was devoted to electron generation (see Figure 4-21 below). The laser path included filters, lenses, an 0.5-mm KD*P doubling crystal for converting 620-nm light to 310 nm, and a Michelson interferometer of which one arm was normally blocked; the second arm was only required during streaking experiments. The output was directed onto the photocathode with a mirror in a highprecision mount (Klinger; SL 51, 133-011), and the laser was focused through a 150-mm focal length lens set on an orthogonal pair of translation stages. The size of the laser beam Chapter Four: Ultrafast Electron Pulse Generation 206 at the photocathode did not appear to affect the electron beam diameter, but shifting the focal point longitudinally 3 mm from the PC surface reduced the electron intensity by two orders of magnitude. With a 100-rnrn focal length lens, the electron intensity was too sensitive to the longitudinal lens position and laser intensity, and the photocathode was easily damaged. The positioning knobs on the high-precision mirror mount were marked with fifty divisions per turn, and one division corresponded to a transverse displacement of the laser beam at the photocathode of ~5 µrn. The diameter of the laser at the PC was 150 µm, as estimated from changes in the laser intensity transmitted through the extraction pinhole while scanning the beam position with the mirror mount. Transverse displacements of the laser beam on the PC affected both the electron beam intensity and its position on the phosphor screen, shifting the beam spot by a few pixels. As described in the next two sections, basic electron beam characteristics including its diameter, angular convergence, and degree of collimation showed a surpnsmg dependence on the number of photons required for electron generation. The general conclusion was that with 620-nrn light (n = 2), electrons were emitted only from distinct point sources on the photocathode, while when using 310-nm light (n = 1) electrons from the photocathode represented a more complete, spatial image of the laser beam spot. 4.3.5.1 Electron Beam Generated With 620 nm The electron beam generated with 620-nm light had an elliptical cross section. Three pieces of evidence supported the conclusion that the electrons came from only point sources scattered across the photocathode. First, the electron beam could be tightly Chapter Four: Ultrafast Electron Pulse Generation focused in the image plane (at fa) down to diameters as small as 30 µm. 207 Figure 4-16 shows the change in x- and y-axis widths of the electron beam as a function of L3 voltage; the electron beam was not well-collimated at all, changing diameter by ~ 100 µrn/cm as the focal point was approached. (A 100 V adjustment to L3 changed the focal point by ~2 cm - Table 4-7). Collimation of the electron beam was lost beyond Ja because the electron beam self-dispersed, presumably due to the strong space-charge effects originating at such a tight focal spot. Second, the electron beam intensity was very sensitive to the position of the laser on the photocathode, varying by an order of magnitude following input mirror adjustments of just one division. Third, multiple electron beam images could sometimes be observed, particularly if the laser spot size was large. Adjustment of the input mirror would bring different, slightly displaced electron beams in and out of existence. The electron beam was large at the final pinhole, ~2.5 mm, and the angular convergence leading up to the focal point was estimated to be 3.8 mrad. Although ground-state diffraction and streaking experiments were completed using electrons photoernitted from 620-nm light, attempts at determining time zero with photoionizationinduced lensing (9.3.2) were frustratingly unsuccessful. The reasons for this can be found in Figure 4-16. Matching the electron beam diameter to the width of the interaction region (~300 µm) places the focal point right at the direct bombardment CCD (5-cm away), where the beam spans at most 3 or 4 pixels. Any perturbations in the electron trajectories due to the ionized gas sample were unresolvable, either completely masked by the electron beam's strong convergence and poor collimation, or else requiring a spatial resolution greater than 14 µm. Moving the electron beam focal point before the needle and using the subsequent divergence to amplify plasma lensing effects was not viable Chapter Four: Ultrafast Electron Pulse Generation -~ -.c: "C Cl) ID C: - L2 = -2.00 kV - - • - - 620 nm; X-Axis; L2 = -3.20 kV - - -~ - -620 nm; Y-Axis; L2 = -3.20 kV 600 500 ')( I .■ I I 300 0 200 ( .) Cl) 100 I , ,, ■-,, X I ,X X • I I Dispersed Due To Space-Charge '- w ,x --o- 310 nm; X-Axis; 700 i 400 E ('CS 208 ,II' -• 0 +-.--------.-----,---,---t---.----.--.----.--+--.---.-----.------,---+~~~~-~~~~,------1 -10.6 -10.5 -10.4 -10.3 -10.2 -10.1 L3 Voltage (kV) Figure 4-16: Change in electron beam spot size as a function of L3 voltage and the wavelength of the photoemission laser. A 100-V decrease in the magnitude of L3 moves the fa focal point towards the phosphor screen by ~2 cm. The 310-nm electron beam cross section was round and the 620-nm cross section was elliptical. The 310-nm curve was measured with a knife edge at the nozzle tip. The 620-nm curves were measured from images recorded on the direct bombardment CCD, 5-cm further downstream. The 620-nm electron beam self-dispersed rapidly after fa; at -10.56 kV, the beam had a small central core of electrons surrounded by a diffuse, uncollimated cloud. because of the space-charge-induced self-dispersion. 4.3.5.2 Electron Beam Generated With 310 nm The electron beam's cross section before the focal point became round when 310nm light was used. The electron beam was smaller at the final pinhole (~ 1.5 mm) and could be focused down to a FWHM of 200 µm, as measured at the nozzle tip with a knife edge (Figure 4-16). The angular convergence was estimated to be 1.8 mrad. The electron beam intensity was much less sensitive to the position of the laser on the photocathode, passing gradually through a maximum as the input mirror knobs were rotated more than a full turn. Beyond the focal point, the electron beam cross section became splotchy (Figure 4-17), indicating that the photocathode had a patchwork of active regions rather than Chapter Four: Ultrafast Electron Pulse Generation complete photoactivity. 209 As with 620-nm 16 electron generation, different patches would -·x 26 -~ a. come into and out of existence as the laser u, was displaced transversely across the 36 ctI ),. photocathode, but the change was much more gradual. The conclusion reached from this set of observations was that the 450-A silver photocathode was active across twodimensions when illuminated with the 310nm laser, perhaps because the quantum X -Axis (pix) Figure 4-17: Suriace contour image of the 310-nm electron beam on the direct bombardment CCD. L2 was -2.00 kV and L3 was -10.20 kV. The beam spot was round at L3 = -10.10 kV, but in this image the beam appears patchy, as if only selected regions of the photocathode generated electrons. efficiency was less sensitive to laser intensity than in a two-photon process. The 310-nm-based electron beam remained collimated and did not self-disperse after fa, despite its patchwork appearance. As seen in Figure 4-16, the electron beam diameter was smaller than 300 µmover a 300+ V range of L3; the electron beam diameter could be matched to the size of the interaction region under the nozzle tip, and still remain sufficiently small 10-cm away on the phosphor screen. Figure 4-18 shows that the patchwork effects were not noticeable in images of the electron beam recorded from the phosphor screen. Photoionization-induced lensing was finally observed in the secondgeneration UGED apparatus after switching to 310-nm light, and time zero was found within a few days. Typical intensities of the 310-nm laser on the photocathode were 400 nJ per pulse or lower, although values as high as 1-2 µJ could be reached if the entire 5% of the 620- Chapter Four: Ultrafast Electron Pulse Generation -5 - 210 7200 6200 <( ~ 5200 ·;; C J!:? 4200 C 3200 + - r - m ~ ~ . . . + - , - ~ ~ ~ - - r - 1 229 239 249 X -Axis (pix) X -Axis (pix) Figure 4-18: The electron beam as detected on the phosphor screen (L2 = -4.07 kV; L3 = -10.50 kV) . (Right) X-axis average profile. At these voltages the FWHM was 5 pixels, or 380 µm . After correcting for the detector's point spread function, the actual FWHM was -300 µm. (Left) Three-dimensional surface plot of the beam spot. The low intensity region surrounding the electron beam is the aluminum-coated beam stop; scattered electrons are detected outside the beam stop. nm laser was incident on the doubling crystal. 400 nJ, however, corresponded to an energy density of 1 rnJ/cm2 , the starting point for thermally-assisted photoemission and broadening of the electron energy distribution curve (4.1.3.3 and 4.2.1.4). The quantum efficiency was not known because a power dependence curve for photoemission at 310 nm was not recorded. 4.3.6 Estimations of Temporal Coherence Photoemission from thin metal films is instantaneous, but subpicosecond electron pulses are difficult to deliver from the photocathode to a target because the temporal coherence of the electron pulse deteriorates rapidly during transit. Temporal broadening occurs through two main processes. Firstly, electrons are ejected from the photocathode with a distribution of kinetic energies (4.2.1.4); the further the electron pulse travels to reach the target, the greater the temporal lag between high velocity and low velocity Chapter Four: Ultrafast Electron Pulse Generation 211 electrons within the pulse. This is equivalent to the broadening femtosecond laser pulses experience when they pass through solids and liquids (group velocity dispersion). Secondly, an electron pulse self-disperses due to Coulombic interactions (the space-charge effect). Electrons at the leading edge of the pulse are accelerated forward by the negative charge behind them, and electrons at the trailing edge are similarly decelerated. This results in a time and charge-density dependent increase of the electron pulse's velocity distribution. These two process are discussed in further detail below: 4.3.6.1 Temporal Broadening Due to the Initial Photoelectron Energy Distribution In the absence of space-charge, the temporal width of an ultrafast electron source is limited by the initial photoelectron energy distribution, dE, and the electron optics. The response can be written as a sum of two contributions: (4.16) dtpc is the broadening which occurs during the initial acceleration of the electrons away from the photocathode. dtpc depends on dE and the strength of the extraction electric field E [Men92a], [ScM71], [Kor69]: (4.17) dtpc The second contribution to dt1-,E is the temporal broadening which occurs as the electron pulse travels with a constant distribution of velocities. derived - An equation for dtT is easily ignoring relativistic corrections, the kinetic energy and electron velocity are related by: KE eV .l.m v 2 e 2 (4.18) Chapter Four: Ultrafast Electron Pulse Generation 212 so the width of the velocity distribution is approximately proportional to the initial energy distribution: (4.19) The transit time of an electron in a constant velocity region of length L is: t (4.20) L/v = and therefore the difference in transit times is equal to: Ll1v = L/1£ mev 3 L 11£ = -2v KE (4.21) using Eqs. 4.18 and 4.19. Removing the electron velocity from Eq. 4.21 gives: 11tT r:::::-io z Lvme/0 11£ (eV) 3/2 (4.22) Contributions to 11tt:.E for the UGED electron gun were calculated for a 11£ of 0.4 eV (an upper limit) and are summarized in Table 4-8. The temporal response is estimated to be just under a picosecond, with the majority of the temporal broadening occurring during the extraction of the electrons from the photocathode. Clearly the strength of the electric field in this region should be higher, if possible. The electrical breakdown limit in vacuum is 30 kV/mm [Aes95a], but values of E in streak cameras tend to be between 5 and 10 kV/mm [Kin87], [Niu88a], [Bab92]. Higher field strengths lead to problems with field emission and arcing from defects or blemishes. The second method for improving the temporal response is to decrease 11£. Developers of state-of-the-art streak cameras have tested an unidentified photocathode material which yields energy distributions of only 0.1 eV for A = 620 nm (2.0 eV) [Niu88b], [FiA88]. Their applied electric field was 4 kV/mm, and the authors observed Chapter Four: Ultrafast Electron Pulse Generation e· Gun Segment Photocathode e· Gun Segment Extraction Pinhole L1 L2 L3 L4 to Nozzle 213 Voltage (kV) Length (mm) E(kV/mm) l!..tpc (fs) -18.00 to -10.92 2.6 2.72 783 Voltage (kV) Length (mm) KE(keV) l!..tr(fs) -10.92 4 7.08 2 -2.01 19 15.99 3 -4.07 76 13.93 16 -10.51 17 7.49 9 0.00 336 18.00 47 Total Transit Time Broadening 77 fs Table 4-8: Estimates for temporal broadening of the electron pulse width in the UGED electron gun due to the initial photoelectron velocity distribution 11£ (taken as 0.4 eV). Mr is an order of magnitude less than Mpc. streaked electron pulses as fast as 300 fs. According to Eq. 4.17, the expected value of l!..tpc was 267 fs. By increasing E and making a few other modifications, theoretical calculations show that l!..te,.E could be reduced to 50 fs [Niu88a], [Kin90]. 4.3.6.2 Temporal Broadening Due to Space-Charge Effects Space-charge broadening is the exchange of energy between electrons within an electron pulse; this exchange increases the electron energy distribution !!..£ continuously as a function of time. Since the Coulombic force is inversely dependent on the square of the separation distance, space-charge is most significant when the electron density is high, such as at cross-over points in the electron optics or low-velocity regions (e.g., near the photocathode). The fastest electron pulse widths measured with streak cameras have had low charge densities, less than 100 electrons per pulse, but UGED demands higher fluxes. A general observation is that the electron pulse width increases linearly with the number of electrons per pulse [Suy88], [Sib82], [Niu81], but unfortunately the contribution of spacecharge effects to the total temporal response cannot be estimated with simple equations. Chapter Four: Ultrafast Electron Pulse Generation 214 Simulations are necessary, involving hundreds or thousands of mutually interacting electrons and their trajectories. Such simulations have not been done for the UGED gun, but some general expectations about space-charge broadening can be gleaned from the work of others. High extraction electric fields at the photocathode are necessary to accelerate nascent electrons as quickly as possible, spreading them out longitudinally across space and weakening Coulombic interactions. (A 1-ps electron pulse with 10 eV of kinetic energy spans 2 µm of space, while a 1-ps, 18-keV electron pulse spans 80 µm). If electron densities are high and E is small, space-charge effects near the photocathode can force later-born electrons back into the cathode [Cla89]. Aside from the impact on QE, this observation means that the initial energy distribution broadens immediately upon emission, spreading both towards 0 eV and towards higher energies. The size and duration of the photoernission laser pulse determine the initial charge density near the photocathode, affecting the electron pulse width [Suy88] . Space-charge broadening increases as the size of the focal spot decreases because electrons are emitted from a smaller cross-sectional area. Reducing the laser pulse width will also increase the charge density (more electrons are ejected per unit time), as Liu and Sibbett observed in streak camera electron trajectory calculations [Liu90]. Suyama and Kinoshita, however, measured identical streak response curves regardless of whether the input laser pulse was 55, 100, or 385 fs [Suy88]. Space-charge is important during the constant velocity segments of electron transit as well. Simulations by Kinoshita et al. predicted that a 1,000-electron pulse at 10 keV broadens by 1 ps during 1.7 ns of travel [Kin88]. In the UGED electron gun, the transit Chapter Four: Ultrafast Electron Pulse Generation 215 time from photocathode to streak plates was 2.9 ns, and the transit time from streak plates to nozzle tip was another 3.3 ns (Table 4-5). Space-charge broadening should not be as severe in the UGED system, however, because the electron beam cross section is larger and the acceleration voltage is higher. Suyama and Kinoshita have shown that increasing the total accelerating voltage decreases space-charge broadening [Suy88]; a change from 3.6 kV to 10 kV increased the number of possible electrons in a 2-ps pulse by a factor of seven. At present, electron pulse widths in the UGED gun have only been measured at the streaking plates (4.4). Pulses with 1,000 electrons were less than 3-ps in duration (Figure 4-23) and an additional 3 ns of transit time to the nozzle tip would not be expected to increase the electron pulse width by more than 1 or 2 ps. 4.3. 7 Estimations of Spatial Coherence Since the primary purpose of the UGED electron gun was to record diffraction images, not streak images, the electron beam had to maintain spatial coherence as well as temporal coherence. Spatial coherence describes the phase correlation between different points in the electron beam; if phase correlation is lost over a distance X, then two atoms separated by X will not contribute interference terms to the scattered intensity. Estimates of coherence are reported for transverse (lateral) dimensions and longitudinal (chromatic) dimensions [Cow90], [Ton93]. The lateral coherence length, XL, for a circular, uniform, and monochromatic source is calculated from: (4.23) where a is the angular divergence of the beam. Using a = 1.8 mrad and the relativistic wavelength for 18 keV electrons, 0.0906 A, the lateral coherence length of the UGED Chapter Four: Ultrafast Electron Pulse Generation 216 electron beam is estimated to be 50 A. Non-monochromaticity corrections are not included in this value. The chromatic coherence length, Xe, is estimated from the energy bandwidth !iv of the electron beam according to: (4.24) Note that !iv is not simply l:iflh because space-charge broadening increases the electron energy distribution. If the laser pulse duration is negligible compared with the actual electron pulse width !it, then Xe can be written in terms of l:ite using equations similar to 4.19 and 4.21: X e -- vh ntill = h nme !iv = Lh (4.25) In the UGED apparatus, L = 456 mm and KE= 18 keV. The chromatic coherence length for a 5-ps electron pulse would be 33 A. (The spread in electron energies bloomed from 0.4 eV to 30 eV due to space-charge effects!) These estimates for XL and Xe confirm that internuclear separations of gas-phase molecules should be resolvable with the UGED electron beam. Note that the coherence lengths can be improved by choosing laser pulse widths which avoid space-charge broadening. For example, assume a 300-fs and an 8-ps laser pulse create identical electron pulses A and B, respectively, each 10-ps long and containing 10,000 electrons. The monochromaticity of pulse A should be inferior because the pulse's temporal width is due almost entirely to space-charge-induced broadening of the electron energy distribution. The duration of pulse B instead reflects the original laser pulse width, and space-charge is less severe. Chapter Four: Ultrafast Electron Pulse Generation 217 4.4 Measurement of the Electron Pulse Width The sensitivity requirements for detection of ultrafast GED patterns depend upon the total scattered electron flux, and the electron flux is constrained by the desired temporal resolution and space-charge effects. Single-shot measurements of the electron pulse width, l:!,,.te, as a function of the number of electrons per pulse are therefore necessary to establish the limits of detectability and temporal resolution. Auto- or cross-correlation methods for measuring ultrafast electron pulse widths are not well-established (Chapter Nine discusses some possible approaches), so true determination of l:!,,.te at the UGED interaction region is unfortunately not yet possible. Instead, l:!,,.te was determined in situ by incorporating components of a streak camera directly into the UGED electron gun [Men92b], [RoP92]. In a streak camera, the ultrafast electron pulse travels between a pair of deflection plates. A fast, high voltage ramp with dV/dt on the order of 1 kV/ns is passed across these plates, causing the front part of the electron pulse to deflect along a different trajectory than the rear part of the pulse. In effect, the electron pulse's temporal coordinate is linearly transformed into a transverse spatial coordinate (see 4.4.1), and l:!,,.te can be measured if the streaked pulse is detected with single-electron sensitivity along one dimension. The latest UGED streaking experiments, described below in 4.4.2, showed that there must be fewer than 1,000 electrons per pulse to keep l:!,,.te on the order of 1-2 ps. 4.4.1 A Theoretical Model of Streaking Experiments The experimental requirements for streak measurements can be estimated with a simple model. Two separate electrons travel with velocity Ve along the z-axis towards a Chapter Four: Ultrafast Electron Pulse Generation 1 d i- . 218 Detector L , ., , ' -e - - e - ~---I·-···---------------- -- --.::::::::::::::-·-·-·- ----- --------- ---- --------- -- ------- 1. v -6.t ~1 ····------------------ Streak Plates e ------- -- ______ _ -6.y I Figure 4-19: A simple diagram of the streaking experiment. Two electrons separated in time by Menter a pair of streak plates of length l. The gap between the plates is d, and the streak plates are a distance L from the detector. A fast voltage gradient across the streak plates causes the electrons to be separated by a distance 11y at the detector. detector (Figure 4-19). Ideal streak plates with length l and separation d are located a distance L from the detector, and the potential differences between the two plates changes linearly with time according to: V(t) = (4.26) V0 + k,t where ks is the sweep rate. The first electron reaches the midpoint of the streak plates at time t 1, the second at time t2 , and the temporal delay between the electrons is ~t. Ignoring any electron-electron interactions and image-charge potentials, the force acting on one electron is given by: F = m,a = -eE dV(t) dy = e-- = eV(t) d (4.27) so the temporal dependencies of the electron's acceleration, velocity, and position along the y-axis are: a(t) = e -(v0 + k,t) (4.28) m,d (4.29) v(t) y(t) 3 (v: k,t- ) + +2m,d 3 -e- of Vot + Yo (4.30) Chapter Four: Ultrafast Electron Pulse Generation 219 Before passing between the streak plates, y = 0 and Vy = 0 for each electron. Thus, v(t; - l/2v x) = 0. If the deflection voltage is assumed to be 0 at time t = 0, then each electron exits the streak plates with a transverse velocity of: (4.31) and a y-axis displacement of: (4.32) The spatial separation of the two electrons at the detector is therefore linearly dependent on their temporal separation: (4.33) where Vs, the streak velocity, is: (4.34) The temporal resolution of a streaking experiment (the shortest resolvable pulse width) is equal to Rlvs, where R is the spatial resolution of the detector along the y-axis. According to Eq. 4.34, the streak velocity increases when the plate separation is reduced because the electric field is inversely proportional to d. If dis too small, however, then the possibility exists that the electron will strike a streak plate instead of continuing on towards the detector. In the UGED electron gun, v "'" c/4, l = 25 mm, d = 4 mm, and the sweep rate ks was approximately 1 kV/ns. If t1 = +50 ps and t2 = -50 ps, then the maximum deflection along the y-axis by the end of the streak plates would be no more than 0.26 mm, a safe distance even if the electron beam diameter was ~2 mm (4.3.5.2). Chapter Four: Ultrafast Electron Pulse Generation 220 - - -A- - - Sweep Traces 5Mn ·····r ·····~\ I I ~ I: I \ T500 pF > LO PCS V+ 5MQ 1--~--' Streak Plates I I \ \ I I - 0 -'---jf--'-------0 0 - .' T500 pF LO ----A----- H 3 ns Figure 4-20: (Left) Photoconductive switch circuit diagram for the streak plates. (Right) Typical voltage traces at the streak plates. The combined gradient was estimated to be at least 1 kV/ns. The relative delay between the two laser pulses incident on the PCSs was adjusted to start both voltage pulses within 0.1 ns of each other. Input voltages V+ and Vwere fine tuned so that the central regions of the fast rises crossed at O V. Since L = 339 mm, the predicted streak velocity for the UGED electron gun was 0.7x108 mis (Eq. 4.34). 4.4.2 The UGED Streaking Experiment As shown in Figure 4-15, closely-spaced deflection plates designed specifically for streaking experiments were installed at the end of the electron gun. A method then had to be developed for generating the synchronized high-voltage sweep across the plates. Commercial streak cameras often use dual-sweep circuits based on avalanche transistors [JaM86], [ThS90] or power MOSFETs [Bak94]; the sweep can be triggered with a single, low-intensity optical pulse. In the first-generation UGED apparatus [Dan94], streak velocities of 0.5x108 mis were obtained with a simple, single-sweep circuit based on an iron-doped, indium Chapter Four: Ultrafast Electron Pulse Generation 221 phosphide photoconductive switch [Foy84], [lvA87], [Jos89]. In the second-generation apparatus, the streak velocity was increased threefold with a dual-sweep circuit using two Fe:InP switches and two laser pulses (Figure 4-20). The Fe:InP switch maintains a resistance of 105 to 108 Q cm in ambient room light. When exposed to intense light, however, the switch conducts with a response time as short as picoseconds. The Fe:InP switches used in the UGED sweep circuits were small disks, 1-mm thick and 6.4-mm in diameter. To create good electrical contacts, 100-A of chromium and 300-A of gold were deposited on either side of the disk face using the metal evaporation chamber (3.4), and leads were connected to the coated regions with silver paint. The sweep pulses reached the streak plates via MHV feedthroughs and solid copper leads, 1/8" in diameter and insulated with plastic tubing. Traces of the voltage sweeps were measured at the streak plates by opening the electron gun chamber and using 100: 1 oscilloscope probes with bandwidths of 300 MHz (Figure 4-20). Starting values for the bias voltages were ±1.5 kV, but these would be individually adjusted up or down until the two sweeps crossed at 0 V. Typically both the positive and the negative sweeps showed a 1,000 V change over 2 to 3 ns, so the lower limit of the sweep rate was 1 kV/ns. The actual sweep rate was probably faster but could not be resolved because of the probe bandwidth. The arrangement of optics for the streaking experiment is shown in Figure 4-21. The portion of the laser normally used for exciting the molecular beam (95% of the total PDA output) was redirected through a rail-mounted optical delay line and split into two arms, one per photoconductive switch. The laser beam waist was reduced with a lens to match the diameters of the PCSs, and the path lengths of each arm were adjusted so that Chapter Four: Ultrafast Electron Pulse Generation 222 ~1 4- /-\---/-\-0-,-- Electron Gun I◄ Oscilloscope ,. M ,. ! ./ ,_ .,, '- F - :- =i SHG c;:, > PDA A i -~~-i"/--t----->;:,,..--Httt Output Translation Stage PhotoConductive Switches Figure 4-21: Optical table arrangement for streaking experiments, 5% of the PDA output went towards the electron gun, where two optical pulses with a well-defined temporal separation M were created with a Michelson interferometer. The remaining 95% of the PDA output triggered the two photoconductive switches, An optical delay line was adjusted to synchronize the fast rise of the voltage gradient with the arrival of the electron pulses at the streak plates, The streaked electron pulses were detected on the phosphor screen, A fraction of the input laser was monitored with a photodiode to guarantee that only one pair of electron pulses were streaked per detected image, BS: beam splitter; PD: photodiode; F: filter; SHG: second harmonic generation crystal (KD*P), the positive and negative sweeps started within 0, 1 ns of each other, as measured on the oscilloscope, Any jitter between the two voltage sweeps and electron pulse generation was less than a few picoseconds, although the amplitudes of the voltage sweeps were strongly dependent on the incident laser intensity, Because of this amplitude-dependence, the streak velocity varied from shot to shot and had to be measured for each data point The streak velocity was calibrated by sending two electron pulses, separated in time by a well-defined delay 11t, through the gun during each streak measurement. For this reason, the laser path leading up to the photocathode included a Michelson interferometer, The photodiode signal from a stray laser beam was observed on an oscilloscope to ensure that every streak trace corresponded to only one electron pulse pair, Chapter Four: Ultrafast Electron Pulse Generation 223 The voltage sweep at the streak plates had to be synchronized with the arrival of the electron pulses. An initial value for the length of the optical delay line leading to the PCSs was estimated assuming that the transit time of electrons from the photocathode to the middle of the streak plates was 2.9 ns (Table 4-5). The delay line length was finetuned by noting the position of the unstreaked electron beam on the phosphor-screen detector, and then adjusting the delay until the two streaked electron beam profiles were centered about this position. The time delay M between electron pulse pairs had to be large enough such that temporally long, streaked electron pulse pairs did not overlap, but short enough that neither pulse was clipped by the aperture separating the electron gun chamber from the scattering chamber. A value of M = 66.7 ps was used in the experiments reported here. Streaked pulse pairs were recorded as a function of the number of electrons per pulse by varying the laser intensity incident on the photocathode with filters. The images were analyzed using a combination of software, including SpectraSource's HPC-1, and the UGED laboratory's RADAR2 (D.3), PROFILE (D.6), and STREAK (D.7) programs. Typically a pulse's ADU intensity was found with HPC-1 and corrected for the background. The ADU value was then converted to number of electrons based on the II gain setting and a calibration factor, whose derivation is discussed in 6.9.3. Average profiles of the streaked images along the streaking axis were computed with either PROFILE or STREAK. The streak velocity was then calculated according to: vs = (76.8_µmJ!1y/!1t pix (4.35) where !1y is the separation of the two streaked profile's centers in pixels. The average Chapter Four: Ultrafast Electron Pulse Generation 7400 e· 6.6 ps 224 3790 e· 4.3 ps ~- - / \ , - - ~ ~ k 66.7 ps 295 e· 0.5 ps H-!-1-+++-H- 150 e· 0.5 ps Figure 4-22: Surface contour plots of low- and high-intensity streaked electron pulse pairs. Each pair comes from two incident light pulses, one of which is delayed by 66.7 ps. The horizontal coordinate is the streaking axis. The temporal durations of pulses with high electron numbers (top trace) were broadened by space-charge effects. For low electron numbers (bottom trace), accuracy in the measurement of the pulse width was limited by the detector spatial resolution. Pulse widths were corrected for the unstreaked length of the electron beam profile. streaking velocity was found to be l.6xl08 mis, more than twice as large as the theoretical estimate calculated in 4.4.1. This discrepancy is most likely due to an underestimation of the sweep rate. Since one pixel corresponds to a distance of 76.8 µm at the phosphor screen, the streak velocity can also be written as 2.1 pix / ps. The temporal pulse width Me for each pulse was found using: (4.36) where Wsrr is the FWHM (in pixels) of the streaked pulse's profile. The shapes of the streaked profiles were Lorentzian, and Eq. 4.36 corrects for the FWHM of unstreaked Lorentzian pulses, Wun • A series of single-shot images of unstreaked electron pulses were recorded at the same time as the streak data, and Wun was found to be 3.9 ± 0.5 pix with no significant dependence on the electron count. Figure 4-22 compares surface contour Chapter Four: Ultrafast Electron Pulse Generation 225 20 ~ - - - - - - - - - - - - - - - - - - - - - Streak Velocity 2.1 pixels/ ps 1.6 X 108 m/s en 15 a. -.c: "C ·- 10 3: Cl) ~ ::s a. 5 0 1 10 100 1000 10000 100000 Number Of Electrons Figure 4-23: Electron pulse widths as a function of the number of electrons per pulse as measured by streaking experiments using the UGED electron gun. Uncertainty in the pulse width measurements was on the order of 1 ps. plots from images of low- and high-intensity streaked electron pulse pairs. The horizontal coordinate is the streaking axis, and the high-intensity pulses are clearly broadened along this axis (longer in time), presumably due to space-charge effects. The low-intensity pulses are only slightly wider than their unstreaked counterparts; because of the size of Wun and the detector's pixel dimensions, the temporal resolution of the streaking experiment was ~1 ps. The streaked electron pulse width as a function of the number of electrons per pulse are presented in Figure 4-23 and Figure 4-24 with linear and logarithmic time axes. The linear plot in Figure 4-23 is similar to streak camera calibrations [Suy88], [Sib82] and match calculations of space-charge effects in streak tubes [Niu81]. The logarithmic plot, Figure 4-24, shows that the relationship between lite and the number of electrons per pulse is linear over more than an order of magnitude of electron intensity: lite increases by 1 ps Chapter Four: Ultrafast Electron Pulse Generation 226 100 - : i - - - - - . - - - - - - - , - - - - - - - - - , - - - - - - Streak Velocit 2.1 pi els / ps 1.6 X 08 m/s u, .8: 10 - : ! - - - - - - - + - - - - - - - + - - - - - - - - - , - .c "C i ~ ::::, D. ♦ 1 ♦ 10 100 1000 10000 100000 Number Of Electrons Figure 4-24: The streaking data from Figure 4-23 replotted with a logarithmic temporal axis. There is a linear relationship between thef number of electrons per pulse and Me above count values of 1,000 electrons. Noise in the streaking experiment dominates the Me measurement for pulses with fewer than 1,000 electrons. for every 1,000 electrons in the pulse. If a l},.te of 10 ps is acceptable, then the number limit is on the order of 10,000 electrons per pulse. Note that the streaking experiment measures l},.te at the streak plates, not at the needle tip, and space-charge effects will broaden the pulse width during the additional travel time from the streak plates to the needle (a distance of ~240 mm, or a travel time of 3.1 ns for 18 keV electrons). The effects of space-charge in this segment could be tested by temporarily inserting a 9" nipple into the electron gun chamber, moving the electron gun back, while keeping the streak electrodes at their current position. The streak velocity attained with the UGED electron gun was comparable to that found in commercial streak cameras [Pro91], [Yan94], and not far from the values of ~4x108 mis reported for state-of-the-art instruments [Bab92], [Niu92]. The temporal resolution of the streak experiment, however, was not as good because the spatial Chapter Four: Ultrafast Electron Pulse Generation 227 resolution at the detector was optimized for diffraction, not streaking. Figure 4-24 shows that the duration of pulses with fewer than 1,000 electrons was less than or equal to the noise limit of the streaking experiment (~ 1 ps), and could not be resolved. Without making major modifications to the apparatus, the temporal resolution can only be improved by increasing Vs, which, according to Eq. 4.34, requires either increasing l or ks, or decreasing d. One method for increasing ks is to install traveling wave deflection plates which match the changing potential gradient down the longitudinal axis of the streak plates to the electron beam velocity [Niu92], [Niu88b], [FiA88]. Sweep rates as high as 1 kV/ps have been reported for millimeter-scale electrodes [MoT91], so a second option might be to install the photoconductive switches right at the streak plates, inside the electron gun chamber. As a final comment, Guidi and Novokhatsky have streaked electron pulses using a radiofrequency cavity with a rotating magnetic field [Gui95]. In this instrument the streaked electron pulses map out a circle (rather than a line) whose diameter depends on the strength of the magnetic field. 228 Chapter Five Real-Time, Single-Electron Detection Across Two Dimensions 5. 1 Evaluation of Electron Flux The response curve of the electron gun (Figures 4-23 and 4-24) showed that a trade off had to be made between the UGED experimental temporal resolution and the total number of incident electrons. Choosing a value of Me set an upper limit on the total electron flux; the question was then whether or not that flux was sufficient for extracting structural parameters from the diffraction data. This problem can be evaluated in two different ways: (1) by making an order of magnitude (OM) comparison between the UGED electron flux and the flux typically used in steady-state diffraction experiments, and (2) by estimating the total number of incident electrons required to resolve a diffraction feature at a particular value of s. Both analyses concur that the UGED electron flux should be sufficient provided that the detector system Chapter Five: Single-Electron Detection Across Two Dimensions 229 is sensitive to single electrons across two dimensions, i.e., that every scattered electron is detected. The analyses also predict, however, that the structural resolution attained by the instrument described in this thesis will be poorer than in steady-state GED. 5.1.1 Comparison With Standard GED Electron Flux With number densities between 1,000 and 10,000 electrons per pulse (4.4) and a 30-Hz repetition rate, the total incident beam current in the UGED laboratory was~ 10 fA. The beam current in traditional GED experiments is 0.1 to 1.0 µA [Har88a], seven orders of magnitude greater. For UGED to succeed, this flux deficit must be corrected. Aside from speeding up the laser repetition rate or improving the temporal-flux response of the ultrafast electron gun, the only method of overcoming the deficit is to increase the effective exposure time, either by taking longer exposures, or by improving the detection system such that the information present in the scattered electrons is transferred to the detector more efficiently. Traditional GED images are exposed for a few seconds or less; the total exposure time for a single data point in a UGED transient (a diffraction image at time t) was one hour or more, accounting for 3 OM of the missing electron flux. Although the instrument could run continuously for about 24 hours, diffraction patterns had to be recorded from several different data points during one session in order to obtain the complete transient. One to two hours of exposure time per data point was a practical upper limit. Further compensation for the electron flux deficit had to be made by altering the detection system. Aside from the real-time detectors described below in 5.2, most GED instruments record the scattered electron signal by direct bombardment on photographic Chapter Five: Single-Electron Detection Across Two Dimensions 230 plates [Har88a]. Photographic plates are excellent detectors for 10 to 100 keV electrons because the electrons have sufficient energy to penetrate a few microns into the emulsion, activating several silver halide grains along the way [Val66], [Bea78] . The efficiency is therefore greater than one. The spatial resolution of photographic plates is high (~30 µm [Nit63], [Dow82], [Rui92]), the dynamic range spans between two and three orders of magnitude [Sch76], [Her82], [Rui92], and single electron events can be detected with proper film development. Consequently, the sensitivity of photographic plates is difficult to beat, and electronic detection schemes can improve the degree of information transfer by at most a factor of two (see 5.3.10 and 5.5.5). The UGED electron flux deficit therefore could not be erased with a better detector. Diffractionists, however, intentionally "throw away" scattering data by blocking the photographic plate with a rotating sector [TrF33], [Sch76], [Tre88]. A rotating sector is a carefully-machined, thin metal shield mounted in front of the detector and spun about the central axis (the ko axis) at several thousand rpm. The open area of the sector increases like sX, where xis usually between 2 and 3. The reasons for installing a rotating sector are made clear in Figure 5-1, which plots an effective differential scattering cross section into solid angle dQ as a function of s for molecular scattering from homonuclear diatomics. (5.1) According to Eq. 5.1, the DSCS dcrM/dQ corresponds to the peak-to-peak amplitude envelope of the interference terms if vibrational damping is ignored, and Figure 5-1 shows that dcrM/dQ spans six orders of magnitude over a range of 2 to 40 A- 1. The rotating Chapter Five: Single-Electron Detection Across Two Dimensions 231 1E+2 \ - - - Carbon -. ,._ 1E+1 +---->........->c----+-------+--1 \. (/) --Iodine \ ';;, 1E+0 - - - Carbon After Rotating Sector C ,._ 1E-1 cu -a '' ..0 "0 ::if: 1E-2 1E-3 t, "0 1E-4 --- --- 1E-5 0 10 20 30 40 50 Figure 5-1: Coefficient of the differential molecular scattering cross section for homonuclear diatomics C-C (r = 1.4 A) and 1-1 (r = 2.7 A). The sin(sl) term and vibrational damping term are neglected. The carbon data is also shown after rescaling with an x = 2.5 rotating sector. sector rescales dcrM/dQ. as a function of s such that the span of the data matches the dynamic range of the photographic plate, and the entire pattern can be recorded in a single exposure. Removing the rotating sector, and then recording many short exposures instead of one long exposure, would recover up to 3 OM of scattering data. This alternative is possible with real-time detection schemes because image processing and analysis can be automated with a computer; it would not be practical with photographic plates. After increasing the total exposure time to an hour and removing the rotating sector from the diffraction instrument, the UGED experiment still would have at least one OM less electron flux than traditional GED. This difference would be devastating if not for the fact that the molecular scattering intensity falls off like s4. The total scattering signal as a function of s is found by integrating Eq. 5.1 about the cylindrical scattering angle <j> (see Eq. 2.55c in 2.1.4). The cross section for molecular scattering into the cone- Chapter Five: Single-Electron Detection Across Two Dimensions 232 1E+0 1E-1 - - + - < - - - - - - + - - - - - - - + - - - - - - - + - - - - - < -Cl) 1E-2 '' 1E-3 :: - - - Carbon I - - - , --Iodine ' b 1E-4 <l 1E-5 1E-6 --- --- 1E-7 0 10 20 30 40 50 Figure 5-2: Coefficient of the molecular scattering cross section into differential angle .6.0 for homonuclear diatomics C-C (r = 1.4 A) arid 1-1 (r = 2.7 A). The sin(sr) term and vibrational damping term are neglected. like differential volume .tl8 is then: (5.2) [l(jM and Figure 5-2 plots ilaM as a function of s. Standard GED patterns are recorded out to s values between 30 and 40 A- 1; Figure 5-2 shows that the loss of 1+ OM of electron flux would simply cut down the available range of scattering data to 15 to 20 A- 1. This range is sufficient for detecting at least two full interference oscillations from even the shortest internuclear separation. The structural resolution obtained with such data would be poorer than standard values of ±0.005 A [Har88a], but a loss of even 1 OM in structural resolution would still be acceptable in terms of observing chemical dynamics. The underlying assumption in this analysis is that the sensitivity and collection efficiency (detection over area) of the UGED detection system is comparable to photographic plates. If the detection system is less effective, the available range of s is Chapter Five: Single-Electron Detection Across Two Dimensions 233 shortened further as per Figure 5-2. 5.1.2 Estimation of the Signal-to-Noise Ratio A second method for evaluating whether the UGED electron flux is sufficient for determining molecular structure is to calculate the number of electrons required to resolve a feature of the interference pattern, and then confirm that the corresponding exposure time is within practical limits. This method requires an estimate of the signal-to-noise ratio SNR in the diffraction image as a function of s: (5.3) where g is the mean scattering intensity at position s and CTg is the standard deviation in the distribution of measured intensities. If the detection system is perfect (meaning that no information is lost), then the noise in the image is due entirely to statistical variations of the measured signal. Electron diffraction is a measurement of the occurrence of discrete events. For each incident single electron, a small area A of the peifect detector screen observes only one of two possible outcomes: either the electron lands in A or it does not. If there are N total electrons and a probability p that a single electron reaches A, then the probability of n electrons reaching A follows a binomial distribution [BaW8 la], [Roe92]: p ( N,n ) = N! n(l )N-n n!(N-n)!p -p (5.4) The mean number of electrons n reaching A is: N n 2.,nP(N,n) = pN n=O and the variance about n is found to be: (5.5) Chapter Five: Single-Electron Detection Across Two Dimensions 234 N var(n) = a~ = I(n-nf P(N,n) = n(l- p) (5.6) n=O Both equations require re-indexing the summations and grinding through the algebra to simplify the result. In the limit of p << 1 and N >> 1, the detection of electrons in A obeys the Poisson distribution and: var(n) = a~ ➔ n (5.7) Thus the SNR at a particular value of sis given by: SNR = pN fan = n/✓ n = ✓ n (5.8) The molecular scattering intensity is an oscillating function which rides on top of the atomic scattering intensity (Eq. 2.42). A crude description of the total scattering is that a fraction of the n electrons which reach A are both atomically and molecularly scattered, while the remainder are only atomically scattered. The ratio between molecular and atomic intensities can be estimated from the differential cross sections for scattering into an angle ~0. An equation for ~<:JM was given in Eq. 5.2; recall that ~<:JM represents the probability of molecular scattering into a differential ring region A,.,8 on the detector. The corresponding equation for elastic and inelastic atomic scattering into ~0 is: The fraction JM is defined as ~a M / ~a A , the fraction of all scattered electrons which contribute to the signal of interest, ~<:JM. Figure 5-3 shows that JM decreases continuously withs because of the additional 1/s term in ~<:JM. Using Eq. 5.8, the number of electrons which must be detected in ring A,.,8 to give a signal-to-noise ratio SNR(s) in the molecular scattering intensity is: Chapter Five: Single-Electron Detection Across Two Dimensions 235 (5.10) n(s) The total number of scattered electrons N is equal to n(s) 0.6 0.5 divided by the fraction ft:.e of all electrons that are scattered into At:.e• actually Since the - - - Carbon --Iodine \ 0.4 \ \ ~ 0.3 \ ' ' ..... ......... 0.2 0.1 0.0 molecular scattering intensity is a modulation on the 0 5 ... __ --- ----- ----25 30 atomic scattering intensity, ft:.e can be Figure 5-3: -· Fraction of molecular scattering in the total electron scattering for two homonuclear diatomics. estimated as the ratio between the differential atomic cross section ~O'A and the total atomic cross section O'A . N becomes: (5.11) Now the total exposure time required to obtain a particular SNR at s can be determined from the electron beam current I and the fraction of scattered electrons f: = N~ fl (5.12) Figure 5-4 shows SNR(s) calculated from Eqs. 5.11 and 5.12 for one hour of exposure with 1-ps electron pulses (/ = 5 fA) and 2% scattering probability. The signal-to-noise ratio decreases by 2 OM over a range of 1 to 30 A- 1. The Rose relation is used to set a lower limit on the signal-to-noise ratio required to detect a signal in an image. Rose found that an imaged pattern was resolvable once the Chapter Five: Single-Electron Detection Across Two Dimensions 236 1000 : i - - - - - - , - - - - -- - , -- - - , - - - - , - - - - . - - - - - - - - , -- -1 -t-----,----.---,---,--+---.-----,---.----,----t-,---,-----.---.---+--.---,--,----,--+----.~---,--~-+-,----,---,-~----l 0 5 10 15 20 25 30 s cA- ) 1 Figure 5-4: Estimated signal-to-noise ratio of molecular scattering into differential angle Ll0 for two homonuclear diatomics. Theoretical conditions are one hour of exposure with a 5 fA electron beam and 2% scattering. signal-to-noise ratio reached a value of at least five [Ros48], [Her82]. The exposure time necessary to obtain an SNR of 5 is plotted as a function of s in Figure 5-5. As in the order-of-magnitude analysis (5.1.1), the range of molecular scattering intensity available under ultrafast experimental conditions described in this thesis is between 15 and 20 A- 1 if there is no loss of information during the detection process. No attempt has been made to quantify the structural resolution expected from the available range of s and the signal-to-noise ratio. Extraction of internuclear distances and mean amplitudes of vibration from scattering intensities is a computationally-demanding process which typically requires iterative fitting of the background scattering curve (see Chapter Seven). Although Rose's relation can be used to say whether or not a maximum in the molecular intensity curve definitely exists at a position s, there is a substantial difference between identifying a maximum and analyzing the scattering intensity curve for molecular structure. Chapter Five: Single-Electron Detection Across Two Dimensions 237 1E+5 -F1 Day 0 1E+4 .. 1 Hour Cl) E 1E+3 i= ~ Cl) I. ~ 1E+2 0 a. ~ /f' ~1 Min~ ~ >< W 1E+1 ..../4"' ---~ ~ - ~ --- --= L.-- - ,____ - - - Carbon --Iodine Time Markers ,____ 1E+0 0 5 10 20 25 30 Figure 5-5: Estimated exposure times necessary for the signal-to-noise ratio of molecular scattering into differential angle ~0 to reach the Rose relation (SNR = 5). Theoretical conditions are a 5 fA electron beam and 2% scattering. 5.2 Real-Time Electronic Methods of GED Detection An underlying assumption in 5.1 was that the photographic plate detector found in standard GED instruments would be replaced with newer technology in the UGED apparatus, i.e. , some type of electronic imager with single-electron sensitivity. Three factors motivate this decision. First of all, computers have aided the analysis of GED data to some extent for at least fifty years [ShP46]. Typically the average scattering intensity is extracted from a photographic plate by spinning the plate about the center of the diffraction pattern [Deg35], [Kar47] and recording optical density as a function of distance from the center with a microdensitometer [MoR80], [Tre88]. The optical densities are then converted from analog to digital and transferred to a computer, either point-by-point or along radial cross sections [Ewb81], [Loo83], [PaD83], [Ben84]. With Chapter Five: Single-Electron Detection Across Two Dimensions 238 an electronic detector, however, analog scattering intensities are downloaded directly in a digital format,• and the photographic intermediate is eliminated - along with any noise introduced by the development and microdensitometry processes. Furthermore, scattering data is available immediately for computer analysis, and, with sufficient computational power, signal averaging of the molecular scattering intensities can be observed as the data is recorded. A second motivation for electronic detection is the possibility of standardizing the correction for background scattering intensities. In traditional GED, ls(s) is determined iteratively while extracting structural parameters from the diffraction data (7.2). A new ls(s) must be found for each experiment because the optical densities of electronbombarded films vary widely, depend on exposure times, and also on the method of development [Val64], [FoH70], [Dow82]. "Real-time" electronic detectors enable the direct measurement of relative scattering cross sections, including a simple calibration for shot-to-shot variations in electron flux. The same background scattering intensity would be expected from different studies on a particular molecule assuming that the gas pressure and beam overlap within the interaction region were unchanged. Finally, with the labor-intensive task of photographic processing removed from GED analysis, there is virtually no limit to the number of diffraction images that can be recorded during an experiment. This encourages removal of the rotating sector because the detector's dynamic range now extends beyond saturation levels: ten short-exposure images can be recorded instead of one overexposed image. Multiple exposures are very • At the single-electron counting level of detection, one could argue that the input signal is already digital. Chapter Five: Single-Electron Detection Across Two Dimensions 239 important to time-resolved diffraction studies because the preferred method of data collection is to record single, short-exposure images from successive time steps, and then repeat the cycle many times. In this way, long-term changes in experimental parameters (like laser intensity or beam alignment) are averaged over time for each data point. The introduction of electronic detectors into GED experiments has been gradual, with major modifications occurring about once each decade. Fink and Bonham developed an electron-counting instrument containing a single-point, solid angle detector: a scintillator coupled by light-pipe to a cooled photomultiplier tube [Fin70b]. To scan the diffraction pattern, the detector position was stepped along an arc having the nozzle as its center, and the integration time was adjusted for changes in scattering intensity. The signal was continuously calibrated using a second, identical detector located at a fixed position. Several research groups have built instruments based on this approach [Kon72], [KiS82], [Gol83]. Recording the diffraction pattern point-by-point yielded the background-corrected scattering cross sections Fink and Bonham sought, but required hours of exposure time. A linear electronic detector which sampled an entire radial slice of the diffraction pattern was first incorporated into a GED instrument in the mid-eighties by Ewbank and coworkers [Ewb84], [Ewb86], [Ewb89]. Fluorescence from a P20 phosphor scintillator was imaged onto a linear diode array with either lenses or fused fiber optics, and the 1,024pixel array intensities were digitized and transferred to a computer. A "butterfly slit" was placed in front of the detector array to mimic the effects of a rotating sector, and a ratiometric background-correction technique was established [Ewb86]. Exposure times were substantially reduced by introducing an image intensifier into the optical chain Chapter Five: Single-Electron Detection Across Two Dimensions 240 [Ewb93], and the instrument has been used for time-resolved studies with ns resolution (1.6.3). Hall et al. constructed an electron diffraction apparatus which detected the scattering pattern on linear charge-coupled devices (CCDs) through direct bombardment [HaB91a], [HaB91b] . There was no scintillator in their instrument; instead the highenergy scattered electrons penetrated the upper layers of individual pixels and activated them through various physical processes. A completely different approach to one- dimensional sampling of GED intensities was developed by Geiser and Weber [Gei95]. The scattered electrons were directed into an angle analyzer, where electrons emitted in a narrow range of s were focused through an aperture and onto a microchannel plate (MCP). Signal from the MCP was gated to remove background and unscattered intensities, and then digitized and stored in the computer. Although the angle analyzer had to be scanned as a function of time to record a complete diffraction pattern, the scans were conducted much more quickly than in single-point instruments because all electrons within a range of /:is were collected, and the scan was stepped electronically rather than physically. A two-dimensional charge-coupled device was installed as a detector in RHEED instruments by Spence and Zuo [Spe88] and by Barlett et al. [BaD91]. Both groups optically coupled scintillator fluorescence to the CCD without further amplification. The Zewail laboratory was the first to use a two-dimensional electronic detector for GED [Wil92], [Dan94] . Electrons directly bombarded a CCD composed of an array of one million active pixels, and the unscattered electron beam intensity was attenuated with a few microns of deposited aluminum. A 700-A.-thick aluminum coating was applied to the entire CCD to block scattered laser light. This detection scheme provided the single- Chapter Five: Single-Electron Detection Across Two Dimensions 241 electron sensitivity across two-dimensions necessary for ultrafast GED, but it was too fragile, and alternatives were sought that still used a 2-D CCD as a computer interface. The next section, 5.3, lists the criteria which were considered when evaluating proposed detector systems. 5.4 describes the properties of individual electro-optical components, and estimates are made in 5.5 of the detective quantum efficiency (defined in 5.3.10) for several arrangements of these components. Chapter Six contains a complete discussion of the actual detector system built for the second-generation UGED apparatus. 5.3 Characterizing Two-Dimensional Imaging Systems The purpose of an imaging system is twofold. First, the system must trans/er an input signal from the experimental apparatus into a temporary storage device. Second, the imaging system must translate for the human operator, converting the data from its raw physical form, often undetectable by humans, into pictures or numbers that the brain can process. The imaging system must be carefully designed such that the transfer and translation devices introduce as little noise as possible: all dimensions of information present in the input signal must be retained. With the advent of CCD cameras, two-dimensional imaging systems have found greater prominence in chemical investigations [MoM93], [Hra93]. Two-dimensional imagers collect three dimensions of data: the x-y spatial coordinates and the corresponding values of the input signal. For gas-phase electron diffraction, the x- and y-coordinates are related to the momentum transfers, and the third dimension of data is the total scattered electron intensity. This section presents eleven criteria with which the efficacy of two- Chapter Five: Single-Electron Detection Across Two Dimensions dimensional electron imaging systems were evaluated. 242 (Many of these criteria are reviewed in a textbook on the related topic of photographic imaging [Dai74].) Electron imaging components will be described in terms of these parameters in 5.4. 5.3.1 Gain A component's gain, g, changes the intensity coordinate of the image from /(x, y) to gl(x, y) . For some particle-to-particle conversions, such as the transformation of photons into electrons at a photocathode, the gain is referred to as the quantum efficiency: the ratio of the number of output particles to the number of input particles. For electronto-photon conversions at a scintillator, where· many photons are created from one electron, the gain is called the radiant efficiency, the efficiency of energy conversion. With "heads/tails" components such as lenses or windows (the particle is either stopped or transmitted), the "gain" might be a percent transmission or a similar throughput estimate. The total gain g101 of the UGED imaging system had to be large enough such that the signal from a single incident electron registered above the background noise in the CCD storage device. Individual pixels in a CCD record signal as electron-hole pairs (EHP), so g101 is expressed in units of electron-hole pairs per incident electron (EHP/e-). 5.3.2 Pulse-Height Distribution The gain provides only an average description of how the intensity coordinate is altered by an imaging component; statistical fluctuations are ignored. As an example, if sets of ten photons pass through a window with gain 0.4, the average output signal will be four photons, but a particular set of ten photons could yield an output signal anywhere between zero and ten photons. As discussed in 5.1.2, the standard deviation about the Chapter Five: Single-Electron Detection Across Two Dimensions 243 mean for the occurrence of discrete events is equal to .JgN(l - g) , or 1.5 photons in this example. A more complete picture Q) CJ s:: Q) of the amplification process within ...... ::I an imaging component is obtained - CJ CJ 0 0 by plotting distribution the pulse-height (PHD). The x- >, CJ s:: Q) ::I O" ... 0.20 0.15 0.10 0.05 Q) LL coordinate of a PHD is a list of all 0.25 0.00 0 which each possible 2 3 4 5 6 7 8 9 10 Possible Outcomes (Number of Detected Photons) possible outcomes, and the ycoordinate is the frequency with 1 Figure 5-6: Pulse-height distribution for the detection of ten incident photons when the probability of detecting a single photon is 40%. outcome occurs. Figure 5-6 shows the PHD for the example discussed here, where the possible outcomes are the detection of between zero and ten photons. The graph shows that for ten incident photons and a detection probability of 40%, six photons will be detected on average 11 % of the time. In this case the pulse-height distribution is just the binomial distribution, but PHDs are not limited to the detection of discrete events. Values for g and var(g) can be calculated from experimental pulse-height distributions using Eqs. 5.5 and 5.6. The PHD of a noiseless component would be a delta function. 5.3.3 Response Time, Readout Time, and Gating The response time of an imaging system is the time required to move signal from the detector, down the chain of intermediate components, and into the internal storage device (e.g., the CCD). The readout time is the time required to transfer data from the Chapter Five: Single-Electron Detection Across Two Dimensions 244 internal storage device out to an external memory such as a computer hard drive. For applications like high-speed photography, the response and readout times of the imaging system limit the temporal resolution of the measurement. This was not true for UGED because the experimental design was pump-probe, and data at a particular time step could be continuously collected on the CCD until the exposure was complete. Nevertheless, the readout time had to be small compared to the integration time because the lasers continued to fire even though no data was collected during readout. The UGED detector had to remove scattered laser light from the background signal and collect only incident electrons. This was accomplished with aluminum coatings in the first-generation apparatus [Dan94], but alternatives such as gating the detector were considered for the second-generation instrument. When gating the imaging system, the response time of all components preceding the gate must be fast in order to maximize the desired signal and minimize noise. 5.3.4 Dynamic Range The last element in the chain of imager components, the storage device, has a limit to the amount of information it can record. For example, there is a finite (albeit very large) number of active silver halide particles per unit area of film, and if all are activated then the region is no longer sensitive to signal; similarly, an individual CCD pixel can only collect so many electron-hole pairs before excess charge spills over to neighboring pixels. The dynamic range of the storage device is equal to W /g 1 , where Wis the "depth" of the storage device per unit area (e.g., 300,000 EHP/pixel) and g1 is the average signal caused by the detection of one event in the first stage of the imager. g1 has the same units as W. Chapter Five: Single-Electron Detection Across Two Dimensions 245 The total system gain must be adjusted such that g1 is above the background noise but not too large, since the number of unsaturated exposures required to collect a given set of images is inversely proportional to the dynamic range. Recall that rotating sectors were installed in GED instruments because the dynamic range of photographic plates was 102 to 103, and the scattered intensity spanned six orders of magnitude (5.1.1). 5.3.5 Linearity and Uniformity The gain of imaging components should be linear with respect to the intensity coordinate: on average, one hundred events should provide 100 times the signal as one event. The useful dynamic range of electron-bombarded photographic plates is limited to 1/4 the saturation density because the gain decreases as the likelihood of an electron interacting with unactivated silver halide particles decreases [Val66] . The gain should also be constant across the spatial dimensions of the detector, although non-uniform gain can be corrected in post-processing of the image (nonlinear gain cannot be corrected!). 5.3.6 Distortion Imaging components which corrupt the spatial integrity of the image, such as with astigmatism or pincushion distortion [Hec87], should be avoided. Accounting for linear stretching is easily handled in post-processing, but nonlinear distortions require complicated calibration and correction routines. 5.3. 7 Point Spread Function and the Limit of Spatial Resolution Information is transferred through the imaging system as photons or electrons, particles whose trajectories can diverge or scatter. When this happens, the spatial Chapter Five: Single-Electron Detection Across Two Dimensions 246 resolution degrades because the intensity at a given point is distributed amongst neighboring regions. This distribution is characterized by the point spread function h(r), the output spatial profile generated from a point-like input signal (the PSF is assumed to be circularly symmetric here). Usually the PSF is treated as exponential or gaussian, and only the FWHM is reported for a particular imaging component. The PSF is related to the line spread function l(x) and the edge spread function e(x) by integral transforms [Dai74]. The total point spread function for an imaging system is calculated by convoluting the PSFs of individual components and the input signal beam shape; the spatial resolution of the imaging system is then limited by the total PSF and the interpixel spacing of the storage device (the CCD pixel dimension a). Standard values for a are between 5 and 30 µm [Fos94] . Choosing a CCD in which a is much less than the total PSF does not increase the spatial resolution, and instead wastes time, computer memory, and money: for a fixed area detector, readout times and data files are proportional to a2 , and the cost of a CCD increases with pixel density. Note that if a must be much less than the total PSF, time and computer memory can be saved by binning pixels during readout - collecting the signal from four pixels and outputting the sum as if they were one pixel [HoG96]. Binning also increases the dynamic range. 5.3.8 Detector Area Maximizing the area of the first stage detector can improve the total PSF if the input signal beam waist is a limiting factor in spatial resolution. Demagnification components within the imaging system are generally required because the cost of CCD detectors and other electro-optical devices increases dramatically with the diameter of Chapter Five: Single-Electron Detection Across Two Dimensions 247 their active areas. 5.3.9 Modulation Transfer Function Information in the spatial coordinates of the input signal degrades as the data passes through the imaging system because of the unavoidable transverse smoothing process. The decay depends on the imager' s spread function, but Figure 5-7 shows that the loss of contrast is not uniform. Spatial signals whose oscillation periods are long compared with the PSF are less damped than higher frequency signals. Using the parameters shown in Figure 5-8, the fractional loss in amplitude can be summarized by a frequency-dependent function M(m): M(co) = (CO) - / min (CO) f ma) CO) + / min (CO) / max (5.13) M(m) is known as the modulation transfer function (MTF), the magnitude of the complex Line Spread Function l (x) 0 10 20 30 FWHM = 8.3 40 50 60 70 80 90 100 x-Axis Figure 5-7: Convolutions of two signals having different spatial frequencies with a line spread function l(x). The amplitude of the higher-frequency signal is damped more than the amplitude of the lower-frequency signal. Chapter Five: Single-Electron Detection Across Two Dimensions Input Signal 248 Output Signal Figure 5-8: A representation of the damping of spatial oscillations. The total input signal intensity (the area) is conserved, but the oscillations of the output signal span Imax - lm;n rather than I max+ I min• transfer function [ChW64], [Dai74]. The optical optical 1 --:s 8 transfer function is the Fourier transform of the line spread 0.8 0.6 0.4 0.2 0 function l(x), which means that 0 0.1 0.05 0.15 Oscillations Per Division M(m) can be determined for an imaging system if any of the spread functions (h(r), l(x), e(x)) are known. Table 5-1 Figure 5-9: Modulation transfer function for a gaussian line spread function with FWHM = 8.3. The open circles correspond to the spatial frequencies of the two signals in Figure 5-7. lists functional forms of M(m) for various PSF shapes, and Figure 5-9 shows the MTF for the line spread function used in the example of Figure 5-7. For a chain of imaging components, the total MTF is a product of the MTF of each component: (5.14) Understanding the modulation transfer function is particularly important for imaging GED data because the input signal intensities are a mixture of different spatial frequencies. In fact, initial attempts at fitting experimental molecular scattering intensities for diiodotetrafluoroethane (C2F4 h) were unsuccessful because the effects of the MTF Chapter Five: Single-Electron Detection Across Two Dimensions 249 were not appreciated. In the first generation UGED apparatus, the size of the electron 1 beam waist (300 µm ➔ 0.4 A- ) approached the period of interference oscillations due to the I·• •I internuclear separation (~5 A; T = 1.4 A- 1), and the theoretical sM(s) oscillations could not be duplicated until the point spread function was included in the analysis. The MTF of an imaging system can be measured in several ways [Dai74]. The edge spread function is obtained from images of a knife edge, and differentiating e(x) yields the line spread function. Images of sinusoid or bar targets can also be converted to M(ro) with varying degrees of difficulty [Col54], [KeD65], [Pos71]; the 1951 U. S. Air Force Test Target is a common choice [Fan93b], [Bor95] and commercially available. Analyzing the power spectrum of a white noise image is a third approach [Kri93], [Rui92]. Calculating the MTF for devices with discrete Point Spread Function Line Spread Function Modulation Transfer Function more h(r) l(x) M(ro) 1 - K0 (r/k) 1 -exp(-lxl/k) 1 because storage elements, such as a CCD, complicated is 2nk M(ro) depends on the angular rotation of the oscillatory spatial signal relative to the device's axes (the MTF is two dimensional) [MiP95]. [Rei91], 2k 1 + (2nkm)2 1 - 2 exp(-r/k) J4 1 1 1 1 2nk nk K1 3/2 (lxl/ k) (1 1 exp(-2nklrol) 2nk (1+(rjk)2t2 nk l+(xjk)2 1 - - 2 exp(-(r/2k ✓-iexp(-(x/2k) ) 2k n 4nk )2) 1 + (2nkm)2 ) 2 exp(-(2nkro )2) Table 5-1: Different forms of the point spread function h(r) and the corresponding line spread functions /(x) and modulation transfer function M(oo). K; are Bessel functions of the third kind. Adapted from [Dai74]. Chapter Five: Single-Electron Detection Across Two Dimensions 250 5.3.10 Detective Quantum Efficiency The total gain is actually an incomplete description of how well the input signal intensity coordinate is recorded in an imaging system. For example, two imagers might both have a gain g of 10 EHP per incident electron, but the quality of the output signal will be superior for the imager with the narrower pulse height distribution. The gain also does not indicate how imaging systems with different storage devices compare: the electron-hole pairs activated in a CCD do not resemble undeveloped silver halide particles in a photographic plate. Albert Rose was faced with this problem while evaluating the relative light detection abilities of film, televisi?n tubes, and the human eye [Ros46], [Ros48]. He characterized an imaging system's perfonnance by comparing the output signal-to-noise ratio with the input signal-to-noise ratio, and Jones later extrapolated from this work by defining the detective quantum efficiency (DQE) as [Jon59]: DQE SNR~ 111 SNRJ,, = ( s Jvar(N) 2 N2 var(S) (5.15) where N and S are the average input and output signals. In an ideal detector, the output noise is equivalent to the input noise and DQE = 1. For real detectors, the quality of the input signal always deteriorates and DQE < 1. The DQE represents the quality of the information in the input signal's intensity coordinate after it has been transferred through the imaging system. If the input signal obeys Poisson statistics and var(N) = N (5.1.2), then Eq. 5.15 simplifies to: Chapter Five: Single-Electron Detection Across Two Dimensions DQE = 251 (5.16) N var(S) With Poisson input statistics, the DQE can be related to exposure times. In order to obtain the same amount of information from the input signal, an 0.2-DQE imaging system requires exposures three times as long as an 0.6-DQE imaging system. For visible photons, the best optoelectronic detection systems have a DQE of 0.1, and photographic film can reach a DQE as high as 0.01, but only over a limited set of exposure conditions [Nit63]. The human eye has the remarkable ability of providing an 0.01 DQE over more than seven OM of exposure intensities [Jon68]. .. DQEs approaching unity are possible when the incident particles are mediumenergy electrons. This is true for both photographic [Ham67], [Dai74] and optoelectronic imaging systems [Her84], so a high DQE was an important design parameter for the second-generation UGED electron detection system. According to Eq. 5.16, predicting the DQE for an imaging system requires an estimate of the variance in the output signal. This can be a complicated calculation, since the output signal comes from a cascade of transformations through the chain of components in the imager, each transformation having its own gain and variance. The derivations which appear in the next few sections are an adaptation of work by Breitenberger [Bre55], who employed probability generating functions to greatly simplify the mathematics. Other authors have chosen different approaches [Sho38], [MaL59]. 5.3.10.1 Probability Generating Functions Suppose that an event has n+ l possible integral outcomes, g = 0, l, 2, ... , n, and each outcome has a corresponding probability po, p1, pz, ... , Pn with: Chapter Five: Single-Electron Detection Across Two Dimensions 252 n "'P L.,; g = 1 (5.17) g=O The probability generating function (PGF) for this event is defined to be [Jor48]: n G(x) = 2,.Pg xg (5.18) g=O where x is an auxiliary variable without any physical meaning. Note that G(l) = 1 according to Eq. 5.17. The mean value and variance of an event can be calculated directly from its probability generating function. Taking the derivative of G(x) with respect to x and then evaluating at x = l gives: (5.19) In a similar way it can be shown that: var(g) = G"(l) + G'(l) - [G'(l)J2 (5.20) As will be demonstrated in the next two sections, the importance of probability generating functions for calculating the DQE is not in finding Pn coefficients to describe a specific process; instead PGFs are a tool through which the DQE can be written in terms of known mean values and variances for each step in the detector chain. 5.3.10.2 Application of Probability Generating Functions to Simultaneous Events If two independent events described by PGFs G 1(x) and Gi(x) occur at the same time, then the distribution of possible outcomes is the product of their PGFs: (5.21) Using Eqs. 5.19 and 5.20, the mean and variance for simultaneous events is: Chapter Five: Single-Electron Detection Across Two Dimensions g and: = var(g) 253 "l1 + "l2 (5.22) = var(g1) + var(gi) (5.23) To demonstrate how probability generating functions simplify the calculation of mean values and variances, the problem involving N incident electrons is reconsidered (5.1.2). A single electron has a probability p of reaching area A on the detector (or else nothing happens), so the PGF for detecting one electron has only two terms: (5.24) where the mean and variance of the event are: (5.25) All electrons have the same PGF, so extension of Eqs. 5.22 and 5.23 to ten independent, simultaneous events gives: g = pN; var(g) = pN(l-p) (5.26) which are the same results that were found m 5.1.2 after much more cumbersome mathematical manipulations. 5.3.10.3 Application of Probability Generating Functions to Cascade Events When the outcome of an event is contingent on what has happened in a preceding event, the combined probability generating function is: (5.27) Again, the mean outcome g is found by taking the derivative of G(x): (5 .28) Chapter Five: Single-Electron Detection Across Two Dimensions 254 (5.29) (5.30) and then evaluating at x = 1: (5.31) (5.32) As might be expected for a cascaded pair of everits, the average outcome is the product of the gains for each individual event. Using Eq. 5.20, the variance about the mean is found: (5.33) For a sequence of N cascaded events, induction leads to the following equations for the cumulative mean and variance [Sho38], [Bre55], [MaL59]: g = var(g) g1g2·•• gN (5.34) = gf;~g,) + :, var/t) + ••• + g,g,-\N_, varif")) (5.35) The ratio var(g)/g 2 is called the relative variance. Eq. 5.35 reveals that the lower limit on var(g) for cascaded components is determined by the first stage: if g1 is large, then only the first term in Eq. 5.35 is significant and the relative variance is equal to var(g 1)/g12 . When the first-stage gain is small, then contributions from the second and subsequent stages increase var(g). As shown in the next section, this decreases the DQE. Chapter Five: Single-Electron Detection Across Two Dimensions 255 5.3.10.4 Application of Probability Generating Functions to the DQE Output from an imaging system is a combination of cascaded and simultaneous events. The signal of interest reaches the storage device after a cascade of transformation through each step in the chain of imaging components; background noise collects as a simultaneous event in the storage device, assuming that the background signal is independent of the input signal. The probability generating function for an imager is thus: (5.36) where G(x) is the cascaded PGF of all components in the imaging system and G8 (x) is the composite background PGF. According to Eqs. 5.22 and 5.23, the mean outcome S is: (5.37) g 8 is a constant offset which can be removed from the output image by subtraction in post-processing unless the dynamic range is exceeded and the image has been saturated. Using Eqs. 5.22 and 5.23, the variance of the output signal is: var(S) var(S) ;g2var(N) + Nvar(g) + var(g 8 ) = N(g 2 + var(g)) + var(g 8) (5.38) (5.39) where the final equality is made assuming that the input signal obeys Poisson statistics. Combining these results with Eq. 5.16, the DQE of an imaging system is: DQE DQE Processed = [1 + ) (5.40) var(g) -2 g + var(g 8)]-I - Ng 2 (5.41) Eq. 5.41 is applied in 5.5 to four different single-electron detection schemes. Detailed Chapter Five: Single-Electron Detection Across Two Dimensions 256 discussions of the DQE in photographic and electronic imaging are found in [Dai74] and [Her84] respectively. 5.3.11 Durability The major reason for revamping the UGED detection system was the susceptibility of the charge-coupled device to damage, caused either by the high-energy incident electrons, arcing within the electron gun, or corrosive sample molecules. With the new imaging system, the first stage detector and any other components mounted within the scattering chamber had to be much more resistant to electrical and chemical attacks, and the CCD had to be isolated in a separate chamber; 5.4 Electron Imaging Components The generic imager is a chain of one or more electro-optical components, each of which alters the image in some way. Usually the first stage of the chain is the actual detector which converts the input signal into a form of information that is easily manipulated, like photons or electrons. 5.4.1 describes physical characteristics of three possible electron detectors: the charge-coupled device, scintillators, and microchannel plates. The new data particles created with each of these detectors are electron-hole pairs (EHP), photons, and electrons, respectively. The last stage of the chain collects and stores the results, either chemically (film) or electronically (CCD). From the outset, the second-generation UGED detection system was to be based on a two-dimensional CCD storage device (5.4.4). Chapter Five: Single-Electron Detection Across Two Dimensions 257 Intermediate components in the chain amplify, transform, or physically displace the image. Ideally the physical form of the input signal changes only once, into the memory elements of the storage device. This is the case for direct-bombardment CCD detection of GED data, where the transformation is: cco ➔ EHPs (5.42) Different types of intermediate components operate only on certain particles, and more transformations may be necessary depending on the experimental requirements. For example, in order to remove the CCD detector from the scattering chamber, the diffraction signal must pass through a vacuum-tight feedthrough in the chamber wall while still maintaining all three dimensions of information. This is simple to do with photon data particles, and the transformation of the input signal would be: Scintillator ) hV cco ➔ EHPs (5.43) 5.4.2 describes two types of optical imaging components. Amplification of an image, however, can only be done on electron data particles with present technology (5.4.3). An amplifier introduces one extra transformation step into the detector chain: Detector / Amplifier ➔ e Scintillator ) hv CCD ) EHPs (5.44) assuming, of course, that the amplifier can be mounted within the scattering chamber. If not, then more conversions must occur. An excellent review of imaging components can be found in [BaM95]. 5.4.1 Two-Dimensional Electron Detectors The focus of 5.2 was on the evolution of electronic imaging storage devices in Chapter Five: Single-Electron Detection Across Two Dimensions 258 GED, but the instruments described in that section also exhibited a variety of methods for the first-stage of detection. Scintillators are by far the most common first-stage detectors for ke V electrons, as they are found in every cathode-ray tube. In recent years, though, diffractionists have also detected scattered electrons by direct bombardment on chargecoupled devices [HaB91b], [Wil92] or microchannel plates [Aes95a], [Gei95]. This section characterizes scintillators, CCDs, and MCP detectors in terms of the criteria outlined in 5.3; some parameters are dependent on the kinetic energy of the incident electrons and a default value of 20 ke V is used. 5.4.1.1 Charge-Coupled Devices A keV electron which strikes silicon creates secondary electrons and their corresponding holes through the electron-bombarded semiconductor cascade process (EBS). The conversion rate is one electron-hole pair for every 3.64 eV of kinetic energy [Fie72], so semiconductors-based detectors such as charge-coupled devices have high gains on the order of 1,000. This is a desirable feature in the first stage of an imaging system (5.3.10.3). The first-generation UGED apparatus attained single-electron sensitivity by direct bombardment on a front-illuminated CCD [Wil92], [Dan94], and the spatial resolution was limited only by the CCD's MTF and the size of the electron beam because one electron struck only one pixel. With front-illuminated CCDs, however, the incident electrons collide with delicate features of the CCD architecture and over time can cause permanent damage, including possibly a complete failure of the device. This was observed in the first-generation UGED apparatus. Although the total electron flux was low, the front-illuminated CCDs were clearly damaged after several diffraction Chapter Five: Single-Electron Detection Across Two Dimensions 259 experiments- rates of dark current production increased in regions near the center of the diffraction pattern, where the detected flux was greatest. Specialized CCD designs are more resistant to this type of damage. Hall and coworkers used a virtual phase CCD in their diffractometer [HaB91b]; this type of CCD was front-illuminated but had a protective 1.6-µm layer of SiO2 on top. Another option is to thin the rear face of a CCD down to 10 µm or less, allowing backside illumination with either photons or electrons [Tek91a]. The electron penetration depth d as a function of kinetic energy KE in keV is given by [Eve71], [Ste89]: d = 0.0174 (KE)1' 75 µm (5.45) so for 20 ke V electrons the EBS process occurs within the first three microns of the backilluminated device and there is no risk of damage. Nascent electron-hole pairs then diffuse to the front of the CCD, collecting in the potential energy wells of individual pixels. The information represented by incident electrons is transformed into EHP data particles in a two-step cascade process. First of all, there is a probability that some incident electrons will backscatter with reduced kinetic energy from the semiconductor surface. This is a "heads/tails"-type process; either energy is lost to backscattering or it is not, so the gain and variance for this stage of detection follow from Eq. 5.25: (5.46) In Eq. 5.46, llss is the backscattering probability and f "i is the mean fraction of energy with which the backscattered electron departs. For 20 ke V electrons, 17 8 s is -0.17 [Dar72], [Dar75], [New86], and f "i is 0.5 [StE54], [Dau87]. The second step is the conversion of available electron kinetic energy into Chapter Five: Single-Electron Detection Across Two Dimensions 260 electron-hole pairs through the EBS process, and the subsequent collection of the EHPs. The gain of this step is: KE - VDR (5.47) 3.64 eV where VvR is the effective potential of a depletion region at the surface of the back side, in which EHPs can be trapped and lost. Typically VvR is on the order of 4 kV or higher, [Hie79], [Sav85], [BeL88], but VvR can be reduced to ~500 V by doping the back side to raise the potential [Ste89], [WiG95]. During the migration process from the back side to the pixel potential wells, the EHPs will diffuse with a final point spread function on the order of 5 µm [Ste89]. Unlike with front-illuminated detection, the signal from one incident electron can be distributed across more than one pixel (see 5.4.4) which complicates analysis of the pulse-height distribution [Hie79], [BeL88]. Proper reconstruction of the PHD yields a near-gaussian peak, well displaced from the background signal, and the relative variance of a gaussian PHD is: var(g) g2 2 = (a_! J = _1 (FW1!MJ g 8ln2 2 g Using the PHD shown in Hier et al.'s 20 keV data and Eq. 5.48, the relative variance of the EBS process is 0.03. Williams et al. and also Howard chose a theoretical approach for calculating the relative variance of the EBS process [WiG95], [How95], making use of the Fano factor F where [FaU47]: F = var(g)/g (5.49) The gain has units of EHP. F = 1 for a Poissonian process, and F < 1 when the noise of Chapter Five: Single-Electron Detection Across Two Dimensions 261 the process is better than Poisson; F for electron-hole pair generation in silicon is reported to be 0.12 [RoW65], and Williams et al. and Howard used that value for estimating CCD performance. This estimate is not supported by experiments, however, because direct measurements of the PHD for electron-bombarded CCDs are found to be much noisier (broader) than a Poisson distribution [Hie79], [BeL88] . For example, the value of F calculated from Hier and co-workers' data is 129. According to the theory for cascaded events developed in 5.3.10, the total gain for a back-illuminated CCD is a product of Eqs. 5.46 and 5.47: = (1 - 11ssfe )(KE - VvR) 3.64 eV -· (5.50) and the relative variance is: var(g) -2 g = (5.51) The detective quantum efficiency for direct bombardment electron detection, including CCD background noise, is treated in 5.5.1. The advantages to direct bombardment CCD detection include a small PSF (5 µm), no distortion, linear response, and high uniformity (pixel-to-pixel gain variation is easily corrected in post-processing). The disadvantages, even ignoring the durability criterion, are troublesome. The small, fixed size of the detector (~ 1 cm2) means that the total spatial resolution is limited by the width of the electron beam, which is an order of magnitude larger than most CCD pixel dimensions. The gain cannot be varied, and the dynamic range is limited to 102 since the typical well depth of a pixel is 500,000 EHPs. The response time is of course instantaneous but the CCD cannot be gated, and scattered Chapter Five: Single-Electron Detection Across Two Dimensions 262 laser light would have to be blocked with aluminum overcoats, as was done in the firstgeneration UGED apparatus. 5.4.1.2 Scintillators With a first-stage scintillator detector, the kinetic energy of the incident electrons is converted to photons with emission wavelengths centered about some Amax• The photons emit from the scintillator isotropically so an aluminum overcoat is applied to reflect light back towards collection optics. With a thickness of several hundred Angstr¢ms, the overcoat does not impede incident electrons and also grounds the scintillator surface, preventing charge buildup. The gain of the scintillator is equal to: (5.52) where £ is the radiant efficiency, E,._ is the energy of the emitted photons, R is the reflectivity of the aluminum overcoat, and M is the amount of energy actually transferred into the scintillator after loss mechanisms such as backscattering. Some authors simply assume that all energy is transferred and M = KE, but Herrmann and Sikeler found that the bracketed portion in Eq. 5.52 was limited to 0.74 for 5-keV electrons and 0.8 for 20keV electrons, and their results will be used here [Her95]. The collection efficiency of scintillator emission increases as the scintillator's refractive index n0 decreases (see Eq. 5.61). Scintillators take several different forms (powders, single crystals, and doped fiber optics) and their individual properties are discussed in the next few sections. In general, scintillators can have diameters of several centimeters, their response is linear, and they are Chapter Five: Single-Electron Detection Across Two Dimensions Amax E,., e 'td (nm) (eV) % (us) P20 (ZnCdS) P46 (YAG:Ce) P47 (Y2SbO7:Ce) Crystal YAG:Ce Crystal CaF2:Eu 560 540 400 560 435 2.21 2.30 3.10 2.21 2.85 14 to 20 5 6 to 9 5 to 10 5 -500 0.16 0.05 0.05 1.0 Terbium Fiber 550 2.25 0.85(a) 5,000 Scintillator no 1.2 1.2 1.2 1.83 1.44 1.58 (Core) 1.49 (Clad) 263 PSF var(g) (u.m) "T 10 10 10 20 20 0.43 0.43 0.43 0.11 0.11(b) 6 0.11(b) Table 5-2: Physical characteristics of common scintillators. Point spread function FWHM are based on the thickness of the scintillator layer, except for terbium-doped fiber optics. (a) Product of radiant efficiency (1 %) and the open area ratio. (b) Estimate based on results for cerium-doped YAG single crystal. much more resistant to chemical attack than electro-optical components (single crystal and doped fiber optic scintillators can actually be cleaned). The decay time 'tJ of most scintillators varies between ms and ns and the emission cannot be gated without external components, although the aluminum overcoat will reflect away unwanted scattered light. The PSF of emission is approximately equal to the thickness of the scintillator (except for doped fiber optics) [Spe88], [Her92] . 5.4.1.2.1 Powder Phosphors Powder phosphors are frequently chosen for first-stage detection because their refractive index is low (-1.2), so the collection efficiency is high [Her84]. A wide selection of powder phosphors are available with different values for e, E,.,, and 'tJ [Bri62], [Gal90a], [Hmt92]; Table 5-2 summarizes the properties of three of the more common phosphors (P20, P46, and P47). The recommended mass-thickness parameter pt for detection of 20 keV electrons is 2 to 5 mg/cm2 [BaW81b], so the typical PSF from a powder phosphor is -10 µm. The PSF can be reduced further (at substantial expense) by depositing the scintillator on a fiber optic window in which the upper few microns of core Chapter Five: Single-Electron Detection Across Two Dimensions 264 material in the fiber have been etched away, leaving holes for the powder granules [Ost85]. The dominant negative characteristic of powder scintillators is their granularity. Since each granule has a diameter of a few microns, powder phosphors are not very uniform on the 10-µm scale, and show fluctuations in emitted intensity on the order of 25% [Dab91] , [Hib92]. Light scattering, and to a lesser extent absorption, cause the pulse-height distribution to be more exponential than peaked, and several experimental and theoretical studies of P20 and P47 powders concur that the relative variance of emission is about 0.43 [BaW8 la], [Oat85], [Kuj92]. Earlier measurements of the relative variance for various scintillators gave higher values [Paw74], [Aut83], but experiments such as Pawley's were not based on direct measurements of the pulse-height distribution. 5.4.1.2.2 YAG Single Crystals A number of electron microscopy groups• have compared the performance of powder phosphors with solid cerium-doped YAG, a scintillator with the same chemical composition as P46 but recently grown as a single crystal [Aut78] , [Aut83]. Although the radiant efficiency of single-crystal YAG:Ce3+ is less than P20 (Table 5-2), the uniformity is superior with intensity variations of only 5% on the 10-µm scale [Rui92], [Hib92]. The relative variance of emission is also significantly better, with reported values on the order of 0.11 [Dab91], [Her95]. The primary disadvantages of single-crystal YAG:Ce3+ are the high refractive index and the difficulty of evenly grinding the crystal down to micron • See, for example, [Dab91], [Kuj92], [Kri93], and [Fan94] . Chapter Five: Single-Electron Detection Across Two Dimensions 265 thicknesses. The smallest reported thickness is 20 µm [Spe88], so the PSF is generally worse than for powder phosphors. Other possible choices for single-crystal scintillators include europium-doped calcium fluoride, which has a radiant efficiency comparable to YAG:Ce3+, a lower refractive index, and emission in the blue [Kno79], [Her84]. The relative variance of emission and the PSF are expected to be similar to YAG:Ce3+. 5.4.1.2.3 Doped Fiber Optics Fused fiber optics containing core glass doped either with terbium [Ruc83], [Ruc84] or cerium [Ruc85], [Ruc86], [Pus88] have been developed for tracking decay particle trajectories in high energy physics experiments. The radiant efficiency of these glasses are low - 1% for terbium doping and 0.2% for cerium doping (Table 5-2) - but the point-spread function is determined only by the core glass diameter, which can be as small as 6 µm with an open area ratio (OAR) of 85% for hexagonal fibers [CoH89], [Fan93b] . The open area ratio is the active area (the area of the core glass) divided by the total area. Fan et al. report that a 10-mm thick terbium-doped fiber optic has an 80% transmission. A slightly-peaked pulse-height distribution has been reported for cerium-doped fibers, but the test particles were 550 ke V electrons from the radioactive decay of 90 Sr [Ruc86]. Since the penetration depth of 20 keV electrons is orders of magnitude less (see Eq. 5.45), the relative variance of emission at GED energies is more likely to be similar to single-crystal scintillators. Chapter Five: Single-Electron Detection Across Two Dimensions 266 5.4.1.3 Microchannel Plates Microchannel plates are two-dimensional signal amplifiers responsive to x-rays, VUV photons, and low energy electrons. The MCP is a thin glass plate, up to several centimeters in diameter, which contains millions of parallel, open channels with diameters on the order of 10 µm. (MCPs are made by etching the core glass from fused fiber optics). The two faces are coated with Nichrome and application of a potential difference between the two MCP faces (up to 1,000 V) causes each channel to act as an electron multiplier with a voltage-dependent gain gMCP ranging from 102 to 104 [MaB69], [Wiz79], [Gal90b]. In imaging applications, the electron output from an MCP is then drawn towards a scintillator by a 5 kV potential difference. The OAR for MCPs can be as high as 69% [Gal90b] and the PSF is determined by the channel-to-channel spacing, as with fused fiber optics (5.4.2) . Several authors have studied the efficiency Tl of a microchannel plate undergoing electron bombardment, where Tl is the probability that an output signal is generated by a single incident electron [Mac76], [Wij80], [Fra83]. Since Tl includes the open area ratio TloAR, the total gain is 7J gMCP. Tl depends on the electron kinetic energy and the angle between the electron trajectory and the interior channel wall. At an optimum bombardment angle of a few degrees, Tl approaches 0.40 for 20 keV electrons [Wij80]. The pulse-height distribution of a microchannel plate is a negative exponential proportional to e- g/lMcP [GaM71], [Wiz79], [Her87], and this function has a relative variance of 1. A more complete model of electron multiplication statistics in an MCP was Chapter Five: Single-Electron Detection Across Two Dimensions 267 developed by Herrmann and Korn [Her87], who broke the process down into a threeevent cascade: 1. The primary electron successfully enters an open channel. 2. The primary electron generates 01 secondary electrons. 3. The secondary electrons multiply within the channel. According to Eq. 5.34, the gain for this process is: (5.53) where 8 1 is the mean number of secondary electrons generated by the primary electron and g~CP is a correction of the reported MCP gain: g MCP / 8 max • The relative variance is: (5.54) In Eq. 5.54, b 1 and b2 are related to the mean and variance of the primary-to-secondary and secondary multiplication processes, respectively. For a Poisson PHD, bi = 0 and for an exponential PHD, b; = 1. Herrmann and Korn treated the primary-to-secondary conversion as Poissonian and the secondary multiplication as exponential, and after noting that g~cP >> 1, the relative variance simplified to: (5.55) Using data from Hill [Hil7 6], the authors found that 81 = 1. 1 for 20 ke V electrons, significantly less than the maximum value of 8 max = ~3. 7 reported for 300 eV electrons [AuA76]. The MCP gain for 20 keV electron bombardment is therefore: (5.56) When the output from one microchannel plate goes into a second MCP m a Chapter Five: Single-Electron Detection Across Two Dimensions 268 chevron arrangement, the electron multiplication gain spans from 104 to 107 [Wiz79], [Gal90b]. At the upper end of this gain, the pulse-height distribution becomes peaked due to saturation within the channel and b2 ➔ 0 [Her87] . Then the relative variance becomes: (5.57) Microchannel plates offer no image distortion and are linear at low incident fluxes. The dynamic range is limited by channel saturation, as described above, but this was not expected to be a problem for UGED because the MCP response time is fast (ns), the channels are small, and the estimated number of scattered electrons per shot was only 1O to 103 . The MCP can be gated in conjunction with a photocathode, but not under direct bombardment; however, MCPs with tilted or curved channels are nearly opaque and would not transmit much scattered laser light. There are two primary difficulties associated with an MCP detector. First, the background pressure must be below 10-6 torr to prevent ion feedback [Gal90b], and the MCP must be isolated from the UGED scattering chamber as Geiser and Weber have done [Gei95]. Chemical contamination may also degrade the MCP response. Second, the MCP gain is strongly dependent on the incidence angle of the incoming ke V electrons. This makes the issue of gain uniformity extremely complicated for two-dimensional imaging of diffraction patterns, where the incidence angle varies both as a function of s and <p. The gain and DQE estimates made here have been for the optimum incidence angle. 5.4.2 Photon Imaging Optics Photon data particles can be transferred from the scintillator to the storage device Chapter Five: Single-Electron Detection Across Two Dimensions 269 with either a lens assembly or fused fiber optics. Both systems can image diameters of 4 cm or more, and both would be durable enough to mount inside the UGED scattering chamber. An optical lens assembly was not seriously considered for the second-generation UGED detector, however, because of several drawbacks: (1) light transmission through a lens assembly is generally an order of magnitude less than through fused fiber optics [Her84], [Her92], [Kri93], [Fan93a], (2) a lens assembly would be less compact and more difficult to install and align, and (3) a lens assembly is more prone to monochromatic optical aberrations [Hec87] and the transmission of stray reflections. Electron microscopists favor lens assemblies only when the incident electron energy is above 100 keV and secondary x-ray radiation can affect the CCD [Her92], [Fan93a]. A single fiber optic is a glass cylinder (the core) surrounded by an outer shell of a glass with a lower refractive index (the cladding) [Hec87], [ScF95]. The numerical aperture of an optical fiber is given by: (5.58) Light which enters the fiber is totally internally reflected and transmits out the opposite end. By bundling together fibers, heating, and drawing them, the internal core diameter of individual fibers can be as small as a few microns. Often tiny black glass threads, called extramural absorption (EMA) are inserted between fibers to absorb stray or scattered light. Bundles are fused together into a vacuum-tight boule which can be cut and polished to form a fiber optic window, or redrawn and cut to form a magnifying taper. The gain through a fused fiber optic window or taper is given by [ScF95]: (5.59) Chapter Five: Single-Electron Detection Across Two Dimensions 270 where µ is the absorption coefficient, l is the length, To corrects for reflections, T1 accounts for Fresnel reflection losses, and lloAR is the open area ratio. If an optical coupling compound is applied between components, then T1 equals 1, and To equals 1 for all except the first fiber optic. NAE!f is the effective numerical aperture, defined as: = NA dmin (5.60) dmax dmax and dmin are the maximum and minimum diameters of the taper and NA is the numerical aperture at the narrow end. Values for all these parameters are available from the manufacturers (see Table 5-4). When a scintillator coats the input surface of a fused fiber optic, the collection efficiency llcou depends on the scintillator's refractive index no [Her84]: 2 T/ Coll = l - J NAEJt 1 - (no (5.61) Since fused fiber optics are "heads/tails" devices (the photon is either transmitted or it is not), the relative variance of emission is gFO(l - gFO). The optics exhibit minimal distortion and high uniformity, although the transmission of a taper can fall off towards the edges where the fibers are bent the most. The transmission is also lower at the bundle-to-bundle boundaries where bundles are joined together to form the boule; this creates a "chickenwire" pattern in the output image that can be corrected in post-processing. The point-spread function is approximately equal to the center-to-center spacing dc-c of fibers (also called the pitch). With circular fibers, dc-c is related to the core diameter d and the OAR lloAR by: Chapter Five: Single-Electron Detection Across Two Dimensions 271 (5.62) The modulation transfer function for a fused fiber optic with circular fibers is given by: (5.63) where ffi is the spatial frequency in line pairs / mm [WiG95]. 5.4.3 Two-Dimensional Amplifiers image Two-dimensional intensifiers are components which self-contained amplify input photons into output photons using stages intermediate of Microchannel Plate electron Input Fiber 0 ptic 0 u tp u t Fiber Optic acceleration and multiplication [Her84]. A "first-generation" accelerates photocathode intensifier emission Photocathode Scintillator Figure 5-10: Schematic of a proximity-focused image intensifier. towards a scintillator, inverting the image and providing a gain of up to 102 . A "second-generation" intensifier contains a microchannel plate in front of the scintillator, and the gain reaches 104 . Both methods distort the input image by as much as 5% at the edges because of the electron optics. Distortion is avoided in an alternative design, the proximity-focused image intensifier (PFII), where photoemission ejects directly into one or more MCPs (Figure 510) [GaM71], [Hmt92]. The proximity-focused image intensifier is a five-stage, cascaded imaging system: Chapter Five: Single-Electron Detection Across Two Dimensions 272 Stage Gain Symbol Formula Value Input Fiber Optic gFOI NA 211 Fo T,e-µ1, 0.47 S20 Photocathode OAR 0 - 0.10 gpc 11PC Microchannel Plate gMCP MCP11oAR gsc 6500 P20 Phosphor gSci KE(M l+R) KE_2_ 5 keV 335 Output Fiber Optic gF0 2 (1 - @JNA'11~J, T,,-µ; 0.18 £ Eil Table 5-3: Gain formulas and values for the five stages in a proximity-focused image intensifier. The fused fiber optic material is assumed to be Schott's 32AS-HT (Table 5-4). The quantum efficiency for the S20 photocathode is from [Hmt92]. 1. An incident photon is transmitted through the 8-mm input fiber optic (Eq. 5.59). 2. The photon creates an electron at the photocathode with probability T\Pc3. The electron is multiplied within the microchannel plate (Eq. 5.53). 4. The MCP electron output strikes the scintillator with 5 keV of kinetic energy and generates photons (Eq. 5.52). 5. Scintillator emission is collected (Eq. 5.61) and transmitted (Eq. 5.59} through the 20-mm output fiber optic window. This intensifier can be gated to within a few nanoseconds by switching the photocathode voltage positive relative to the front-face voltage of the MCP. Table 5-3 summarizes the gain formulas for the five stages and provides numeric values for each stage assuming that the photocathode is S20, the scintillator is P20, the MCP has a 12-µm pitch (dc-c), and the fiber optic material is Schott' s 32AS-HT (Table 54). Spectral matching factors are ignored since the source of the incident photons is unknown [Ebe68], [Her84]. The total gain is: Chapter Five: Single-Electron Detection Across Two Dimensions 273 (5.64) and according to the data in Table 5-3, g11 = 1.8xl04 • Values of g11 reported by Hamamatsu for their gated, proximity-focused image intensifiers are similar, 6.8x103 [Hmt92], and can be matched in this estimate by using a lower grade fused fiber optic material such as 32AS [ScF95]. Since the gain calculation agrees with reported values, a reasonable estimate of the relative variance for this type of intensifier can be expected by assembling the relative variances of each stage according to Eq. 5.35: = (5.65) The relative variance of the image intensifier is very high, 49, because the first two stages have low gain. Using Eq. 5.41 with no background noise, the detective quantum efficiency is estimated to be 0.02, so an image intensifier will not aid the basic sensitivity of an imaging system: components preceding the PFII must have high gain. The utility of the PFII is in amplifying the input signal above the storage device's background noise. The proximity-focused image intensifier is also a source of background noise due to spontaneous electron emission from the photocathode. The gain of the background noise per CCD pixel is equal to: (5.66) (5.67) where t is the exposure time, r is the laser repetition rate, t8 is the length of the gate window (typically -100 µs), a is the CCD pixel width, including any magnification between the PFII and CCD, and Du is the rate of spontaneous emission. According to Chapter Five: Single-Electron Detection Across Two Dimensions 274 data from Hamamatsu, the maximum value of Du is a product of the photocathode sensitivity and the equivalent background input [Hmt92]: = (150 µA)(4xl0- 13 ~ 2) = 374 e- 2 lm mm s·mm (5.68) Du decreases with cooling, and in practice is found to be an order of magnitude less than the value shown in Eq. 5.68. The variance of the background emission is: var ( g Bil ) = (8 MCP+ 82 + var(gsci)J _ ( _ ) -=+ g Bil 1- g F02 gSE gMCPgSci g;ll 1 (5.69) -2 11oAR , and the signal from a spontaneous event will have a PSF due to the MCP, scintillator, output fiber optic, and subsequent components. •• Theoretically, the modulation transfer function for the proximity-focused image intensifier should be the product of the MTFs for all five stages: (5.70) The photocathode has a submicron thickness and makes a 1.0 negligible 0.8 contribution to the MTF; the remaining terms follow Eq. 5.63 except for MP2o(ro) -8 --Hamamatsu MTF .... 0.6 • - - - - • Calculated MTF .... . •, :lE 0.4 ... .. . 0.2 which corresponds to a gaussian 0.0 PSF (see Table 5-1). In Figure 511, the product Mu( ffi) 0 10 20 30 40 50 Spatial Frequency (Ip/mm) 60 1s compared to the MTF curve reported by Hamamatsu [Hmt92] Figure 5-11: Modulation transfer functions for the proximity-focused image intensifier. A curve calculated by multiplying M(ro) of individual components is much more optimistic than manufacturers' data [Hmt92]. Chapter Five: Single-Electron Detection Across Two Dimensions 275 which fits approximately to: k = 0.012 mm (5.71) This function has a FWHM of 16.6 µm (Table 5-1). The MTF calculated in Eq. 5.70 greatly underestimates the actual curve, perhaps because the spatial spread of electrons, traveling from photocathode to MCP and from MCP to scintillator, is not included. 5.4.4 The CCD Storage Device The charge-coupled device is an array of photoactive picture elements ("pixels") each of which can individually retain a finite amount of electric charge. As discussed in Chapter Six, the pixel charge is read out sequentially, row by row and pixel by pixel, and passed through amplification stages, an analog-to-digital converter, and into a computer. The interaction of keV electrons with the CCD was described in 5.4.1.1; CCD pixels respond to visible photons with a wavelength-dependent quantum efficiency T\ccv for generating a single electron-hole pair, and the relative variance of conversion is T\ccv(l T\cco). In addition, the CCD introduces at least two sources of background noise into the imaged signal at each pixel [Kuj92], [lsh93], [Dab96]. Dark current accrues continuously within the potential well of each pixel and obeys Poisson statistics: var(gvc) = Nvc = Dt where D is the temperature-dependent rate for dark current. (5.72) There is also noise associated with the readout of pixel charge, primarily due to noise in the on-chip output amplifier or off-chip electronics. CCD manufacturers report the standard deviation of the Chapter Five: Single-Electron Detection Across Two Dimensions 276 output noise, crR, Dark current and readout noise occur independently so the variance in background signal is: (5.73) where np;x is the average number of pixels over which the input signal is spread. One method of estimating np;x is to imagine randomly dropping a circle of diameter d onto a grid of squares with sides of length a. It can be shown that the average number of squares which are overlapped by some part of the circle is given by: n = (d) 2 d + n 1 + 2a 4 a (5.74) Ninety percent of the signal contained under a gaussian point spread function is found within a circle of diameter l.8xFWHM, so using this value ford in Eq. 5.74 and setting a equal to the CCD pixel width yields an estimate for np;x . For example, single-electron signal from direct bombardment of a back-illuminated CCD (PSF = 5 µm; d = 9 µm; a= 25 µm) is distributed over 1.8 pixels on average. The modulation transfer function of the imaging system is ultimately limited by the pixel dimensions of the CCD storage device. To first approximation, the MTF is: = lsin(nam )I nam (5.75) where a is the pixel width [How95], [WiG95]. Recall that the MTF of a CCD is actually a two-dimensional surface dependent on the angle of the input signal relative to the CCD axes [Rui92], [MiP95]. Chapter Five: Single-Electron Detection Across Two Dimensions 277 5.5 Design Examples and Detective Quantum Efficiency The detective quantum efficiencies of several low-signal imaging systems have been evaluated in the literature.• Using similar models, the DQEs of four possible detector schemes culminating in charge-coupled devices are calculated here for detection of a single, 20-keV electron. The signal from the electron may be distributed across several pixels. All fused fiber optics were assumed to be Schott's 32AS-HT glass with physical parameters summarized in Table 5-4. The CCD was assumed to be a 512x512 array with physical parameters summarized in Table 5-4. The CCD was back-illuminated for direct electron bombardment, and front-illuminated through a mounted, fused fiber optic window (dc-c = 6 µm) for photons. When possible, the diameter at the input of the imaging system (in the scattering chamber) was 4 cm, and a fiber optic taper reduced the image to 1.8 cm, the distance of the CCD's diagonal. Fused Fiber Optic first The scheme NA TloAR described in this section is direct bombardment of a backilluminated Although CCD this (5.5.1). method was never going to be implemented lll the a 0.70 Tlcco µ 0.76 0.144 cm- 1 dc-c 6µm To CCD 1.0 (a) (JR 24µm 0.25 10; 100 EHP (b) D 2 EHP /pix/ s (cl t 60 s Table 5-4: Physical parameters of fiber optic components and the CCD storage device. Fiber optic data is based on Schott's 32AS-HT material [ScF95]. (a) NA on small side of fused fiber optic. (b) Manufacturers report crR of 10 EHP, but typical laboratory value is 100 EHP. (c) Typical value for device cooled to -50 °c [Tek92] . second-generation • See, for example, [BaW8la], [Her84], [Her87], [Dab91], [Her92], [Kuj92], [Rui92], [Dab93], [Fan93a], [Ish93] , [Kri93], [Fan94] , [Her95], and [Dab96]. Chapter Five: Single-Electron Detection Across Two Dimensions 278 UGED apparatus, the results provided a means of comparing other proposed methods with the detection conditions similar to the first-generation UGED apparatus. 5.5.3 discusses direct bombardment of a microchannel plate used in conjunction with a terbiumdoped fused fiber optic window. First-stage scintillation detectors, with and without amplification, are described in 5.5.2 and 5.5.4. All of these systems are compared in 5.5.5 using the criteria listed in 5.3; the conclusion reached is that an amplified, P20 phosphor imager would be the best choice for the second-generation UGED detector. 5.5.1 Direct Bombardment of Charge-Coupled Device A physical description of direct electron bombardment of a back-illuminated charge- Back-Illuminated CCD coupled device has already been presented in 5.4.1.1. Briefly, an incident electron penetrates e the rear side of the CCD (Figure 5-12) and generates electron-hole electron-bombarded process. parrs through semiconductor the cascade Figure 5-12: Electron detection by direct bombardment on a backilluminated charge-coupled device. The point spread function during migration of the EHPs to the pixel potential wells is ~5 µm. The modulation transfer function of this imaging system is a product of the EHPs' spatial diffusion and the CCD pixel spacing: (5.76) According to Eq. 5.50, the gain for direct bombardment is 4,900 BHP (Tlss = 0.17; f E = Chapter Five: Single-Electron Detection Across Two Dimensions 279 0.5; VDR = 500 V). An equation for the detective quantum efficiency, including CCD background noise, can be derived from Eqs. 5.41, 5.51, and 5.73: DQE _ - [ ( 1 ( var(ge8s)J np;x(Dt+a~)]-t ) 1+ _ + 2 2 1- 17BsfK 8eBs Ng (5.77) Using parameters in Table 5-4 and a value of 0.03 for the relative variance of the EBS process [Hie79], the DQE for direct bombardment is near-ideal, 0.89. 5.5.2 Scintillators With this scheme, the incident electron strikes a scintillating material and emitted photons are passed through a e fused fiber optic window and taper to a front-illuminated charge-coupled device (Figure 513). S C i n t i 11 a t O r • Fiber Optic Window Three scintillators were compared: P20 powder Figure 5-13: Electron detection with a scintillator. Emitted light is collected and brought to the chargecoupled device through a fiber optic taper. phosphor, single-crystal ceriumdoped YAG, and terbium-doped fiber optics. The total modulation transfer function is a product of M(ro) for the scintillator, window, taper, and CCD window and pixel spacing (Eqs. 5.63 and 5.75): (5.78) All of the primed terms in Eq. 5.78 must include corrections for image reduction by the Chapter Five: Single-Electron Detection Across Two Dimensions 280 taper, which improves the spatial resolution by reducing the point spread function. The PSFs for each scintillator (listed in Table 5-6) were estimated by fitting a gaussian MTF curve to Mro1(w)/Mp;x(W). The total gain for this imaging system is given by: g = (5.79) gSci Tlcol/ gFOI gF02 gCCD and the estimated values for each term are listed in Table 5-5. The detective quantum efficiency, including CCD background noise, is: (5.80) Table 5-6 shows that the presence of P20 YAG:Ce Tb FO 1,448 724 60 gFOI 0.45 0.49 0.16 0.49 0.06 0.80 - gF02 0.08 0.08 0.08 - gCCD 0.25 0.25 0.25 g 6.3 1.1 0.06 background noise reduces the DQE to gSci undesirably low levels (below 0.1) because the total gain from 20-keV electrons was too small. Note that Kujawa and Krahl considered a nearly identical imaging system for 100-keV T\Coll Table 5-5: Individual gain terms of scintillator/ fiber optic / CCD imaging system for 20-keV electrons. Total gain is in CCD electron-hole pairs per incident electron. electrons and predicted single-electron DQEs, with CCD noise, of 0.7 for P20 phosphor and 0.6 for single-crystal YAG [Kuj92]. Their superior values reflect a fivefold increase in gain due to the electron kinetic energy, and an estimate of 32% transmission for the fiber optic window and taper. According to equations from Schott, gF01 gF02 should be only 4%. Chapter Five: Single-Electron Detection Across Two Dimensions 281 5.5.3 Direct Bombardment of Microchannel Plate Figure 5-14 shows an imaging system where Fiber Optic Taper the incident electrons are detected with two rnicrochannel plates in a chevron configuration. e The amplified electron output from the MCPs accelerates / Chevron across a 5 kV potential to a MCPs Terbium-Doped Fiber Optic Window terbium-doped fused fiber optic window, and scintillation the resulting passes through Figure 5-14: Electron detection by direct bombardment on a pair of microchannel plates. Electron output from the MCPs strikes the terbium-doped fused fiber optic window with 5 keV of kinetic energy. Scintillation is collected and brought to the CCD through a fiber optic taper. fiber optics to the chargecoupled device. Since the angular distribution of electrons ejected from the MCP should be important to the overall spatial resolution (5.4.3), the modulation transfer function of the MCP stage is estimated to be one-half of the MTF for an image intensifier, and the total MTF builds from Eq. 5.78 for the terbium scintillator: (5.81) The composite point spread function is then 12 µm. The single-channel gain gsc for an MCP pair can be adjusted between 104 and 107 , and the total gain of this imaging system ranges from 25 to 25,000 EHP per incident 20 ke V electron. The DQE is given by: Chapter Five: Single-Electron Detection Across Two Dimensions 282 Note the dependence on the parameter b2 , which was defined in 5.4.1.3. At low gain (104) b2 = 1 and the DQE is ~0.2 with a minimum amount of CCD noise. At high gain (107) single-channel saturation occurs within the MCP and b2 ➔ 0, which improves the DQE to 0.34, independent of background noise. The rate of change of b2 between these two limits is not known. The angle-dependence of electron bombardment on the MCP has not been taken into account. 5.5.4 Scintillators With Amplification Introducing an image intensifier into the scintillator / fiber optic / CCD chain (Figure 5-15) can raise the gain above CCD background noise levels, although additional gain-dependent noise is introduced due to spontaneous emission from the PFII' s e / Scintillator !!·~ ~ - Fiber Optic Window Figure 5-15: Electron detection with a scintillator. Emitted light is collected and brought to a proximity-focused image intensifier through a fiber optic taper. The amplified photon output is detected on the charge-coupled device. Chapter Five: Single-Electron Detection Across Two Dimensions 283 photocathode. The detective quantum efficiency is: -1 1 + DQE = var(gsci) 1 -2 gSci gSci + l (1 + gSci g FOi g F02 1- gCCD g var(gu )) -2 + gll (5.83) npix (Dt + a~ + var(g Bll ) ) + Ng2 where the variance in PFII spontaneous emission is approximately (Eq. 5.69): (5.84) since gMcP is large. Under conditions where t = 60 s, r = 30 Hz, t8 = 100 µs, a = 24 µm, and Du= 30 e- / s / mm2 , the likelihood gsE of one spontaneous event occurring per pixel is 0.003, and the average gain g8 u ranges from 1.6 to 160 EHP per pixel (as gu varies from 102 to 104 ). The signal from one spontaneous event is gBil /gsE . Table 5-6 summarizes the total gain and DQE for three possible scintillators as a function of the image intensifier gain. Because of the amplification, the DQE remains almost constant despite the addition of CCD background noise and spontaneous emission. The modulation transfer function for this imaging system is a multiplication of Eq. 5.78 by M 1~"'1(m), which dominates. The estimated point spread function, 17 µm, is independent of scintillator type. 5.5.5 Conclusions The modulation transfer functions for the four basic imaging systems discussed in this section are compared in Figure 5-16. The amplified scintillator system has the poorest resolution because of the image intensifier's MTF; all other systems are limited by the Chapter Five: Single-Electron Detection Across Two Dimensions 284 1.0 - - Direct Bombardment CCD - - Scintillator (P20) 0.8 - - - Chevron MCPs and Tb FO _o.6 • • • • • • Intensified Scintillator (P20) 8 '' :S 0.4 ... 0.2 ... 0.0 0 10 ----- . 40 30 Spatial Frequency (Ip/mm) 20 50 60 Figure 5-16: Estimated modulation transfer functions for the proposed imaging systems. The spatial resolution of the CCD limits the MTF;- except for the detector systems with an image intensifier. M(ro) for single-crystal YAG:Ce and terbium-doped fiber optics differ only slightly from P20 (Tb FO are better and YAG is worse). pixel spacing of the charge-coupled device. In a UGED experiment, however, the actual limit to spatial resolution in the diffraction image is set by the 300-µm width of the electron beam waist. Figure 5-17 compares the MTFs for the imaging systems once the electron beam waist has been included in the calculation. In this case, direct bombardment of a CCD has the worst spatial resolution because the ratio between the diameter of the first stage and the CCD is one. This ratio is 0.45 in all other imaging systems due to the 40-mm to 18-mm fiber optic reducing taper, but still the electron beam limits resolution, as is shown by the nearly identical MTF curves. This is not a desirable condition for the imaging system as was explained earlier in 5.3.7; introducing another fiber optic taper which reduces the PFII output image diameter to the horizontal width of the CCD (12.3 mm) would be worthwhile. The other detection characteristics of the four imaging systems are summarized in Chapter Five: Single-Electron Detection Across Two Dimensions Table 5-6. Direct electron bombardment on a CCD has the highest detective quantum efficiency, 0.89, superior even to film under ideal exposure and 285 1.0 - - - Direct Bombardment CCD 0.8 - - Scintillator (P20) - 80.6 - - - Chevron MCPs and Tb FO :E 0.4 • • • • • • Intensified Scintillator (P20) 0.2 development conditions [Ham67] , 0 [Dai74]. choice would be an unamplified 10 15 Spatial Frequency (Ip/mm) In the absence of background noise, the next best 5 Figure 5-17: Estimated modulation transfer functions for proposed imaging systems after inclusion of the electron beam cross section (300 µm). Now the direct bombardment CCD method has the most unfavorable M(co) because there are no reducing optics. P20 (0.63) or YAG:Ce scintillator (0.51). The gain of these systems for 20 keV electrons, however, is just too low to avoid losing the image's information content within the dark current and readout noise of the CCD: the DQE drops precipitously. Table 5-6 shows that inserting an image intensifier reduces the DQE (relative to zero-noise values without an intensifier) because the PFII itself has such a high relative variance. However, the expected background noise levels are no longer fatal to image detection, and there is only a small dependence of the DQE on the PFII gain setting. Scattered laser light can also be removed since the PFII is gated. Although the uniformity and durability of single-crystal YAG:Ce3+ is attractive, the lower radiant efficiency and higher refractive index of the material result in a lower gain and DQE than a P20 powder scintillator. Furthermore, the uniformity of the YAG is somewhat moot given that the image intensifier already has a powder scintillator. Chapter Five: Single-Electron Detection Across Two Dimensions Detection Gain Dy. Rg. Unif. Dur. PSF Method (EHP) (OM) (µm) Direct Bombard. CCD 4,900 2 E p 5 P20 YAG Tb 6.3 s 0.06 5 6 7 G G G E E Direct Bombard. 104 MCP and Tb FO 107 25 25,000 4 p{a) 102 P20 104 Scintillator 102 With YAG 104 Image 830 83,000 3 1 150 15,000 102 Tb 104 5.5 550 Scintillators: Intensifier: 1.1 - 286 DQE npix No Bek CTR= 10 100 1.9 0.89 0.89 0.89 6 10 4 2.0 2.9 1.7 0.63 0.51 0.05 0.08 2x10·3 8x10"6 2x10" 4x10"5 2x10"7 p 12 3.4 0.23 0.34 0.18 0.34 0.02 0.34 s G 17 4.7 0.34 0.34 0.34 0.34 0.33 0.34 3 1 s E 17 4.7 0.11 0.11 0.10 0.10 0.08 0.10 5 3 s E 17 4.7 4x10"3 4x10·3 2x10"3 2x10·3 5x10·4 2x10·3 1 3 Table 5-6: Characteristics of proposed single-electron detection imaging systems. For each method and its variants, the table reports (1) the gain in EHPs per incident 20 keV electron; (2) the dynamic range in orders of magnitude; (3) the overall uniformity (Rating Code: P - Poor; S - Satisfactory; G - Good; E - Excellent); (4) the durability; (5) the estimated point spread function; (6) the average number of CCD pixels over which 90% of the signal is distributed; and (7) the detective quantum efficiency with and without background noise. Background noise includes CCD dark current, CCD readout noise (tor crR equal to either 10 or 100 EHPs), and spontaneous emission from an image intensifier, if present. Entries for imaging systems with microchannel plates are subdivided into maximum and minimum gains. (a) The angle-dependence of MCP gain might possibly be an advantage under the proper experimental conditions. The direct bombardment MCP system has gain and DQE values comparable to an amplified P20 scintillator. However, an MCP system would require an additional differential-pumping vacuum system, which would be very difficult to construct given the two-dimensional expansion of the scattered electrons over a short distance. Geiser and Weber were able to use MCPs because their system refocused the scattered electrons, allowing only a certain angular segment /).s of the pattern to pass through a small, circular aperture into the MCP chamber [Gei95]. The angle-dependence of the MCP gain is potentially an even bigger problem, although a scattering geometry could be envisioned in Chapter Five: Single-Electron Detection Across Two Dimensions 287 which the channel direction parallels ko and the gain increases with s, functioning like an electronic rotating sector. Based on this comprehensive analysis of imaging systems, the best choice for the second-generation UGED apparatus was an intensified, P20 scintillator imaging system. The gain is high enough to register single electron events above background noise levels, but the information content reaching the storage device is expected to be noisier than for photographic plates (DQE of 0.5 or greater). This noise would shorten the available range of s by a few A- 1 relative to the estimates made in 5.1. 288 Chapter Six The UGED Imaging System Based on the comprehensive companson of two-dimensional single electron imaging systems presented in the previous chapter, the primary detector for the secondgeneration UGED instrument was chosen to be a 4-cm-diameter, P20 phosphor scintillator optically coupled through fused fiber optic tapers to a proximity-focused image intensifier (PFII) and a scientific-grade charge-coupled device (Figure 6-1). In addition, a second fiber optic taper was inserted between the image intensifier and the CCD. This taper reduced the imaging area from the PFII window's diameter down to the length of one side of the CCD, as opposed to the length of the diagonal of the CCD. In this way, the entire circular active area of the phosphor scintillator was imaged onto the square CCD; the unexposed corner regions of the CCD could be used for measuring the background offset correction of each image (see 7.1.3 and Figure 7-2). Furthermore, the extra Chapter Six: The UGED Imaging System 289 Thermoelectric Cooler SI Te CCD Tl CCD P20 Fiber Optic Taper Figure 6-1: The second-generation UGED imaging system. Incident electrons could be detected with direct bombardment on the TI CCD, or with the scintillator / fiber optic / image intensifier / SITe CCD chain of components. Both CCDs were cooled with thermoelectric devices. demagnification of the small taper made more efficient use of the charge-coupled device's spatial resolution by increasing the effective CCD pixel size relative to the electron beam width. Although the second taper actually reduced the spatial resolution of the imaging system (by making the pixel size larger at the scintillator), the taper improved the imaging system's ability to resolve the diffraction pattern because the electron beam was effectively smaller (demagnified) on the CCD (see 5.5.5). The detection system also had to record other two-dimensional electron images besides diffraction patterns. In order to establish the zero of time during the preparatory phase of a UGED experiment, high-resolution images of the unscattered electron beam were needed. The intensity distribution of the electron beam shifted with time due to photoionization-induced lensing, but the intensity shift was small and could only be Chapter Six: The UGED Imaging System 290 observed if the detector's spatial resolution was about 20 µm (9.3). Thus the UGED imaging system had to meet two contradictory goals: for diffraction patterns, the optimum spatial resolution had to be comparable to the electron beam waist (5.3.7), but for time zero measurements, the spatial resolution had to be an order of magnitude better. A second detector system was required to solve this problem. Direct electron bombardment of a charge-coupled device provides high gain, high DQE, and excellent spatial resolution, exactly what was needed for electron beam imaging, so a small, inexpensive ($30) commercial-grade CCD was installed inside the scattering chamber. This CCD was easily replaced if corrosive chemicals or electrical arcing damaged it. The characteristics of the fused fiber optic components purchased for the secondgeneration UGED imaging system are described in 6.1, and a synopsis of the assembly procedure for the scintillator detector is presented in 6.2. 6.3 discusses the thicknessdependence of light transmission for thin aluminum films: fluorescence signal from the unscattered electron beam was attenuated by aluminum-coating a small beam stop on the center of the large fiber optic taper. Then 6.4 discusses the thickness-dependence of ke V electron transmission for thin aluminum films with respect to the preparation of the P20 phosphor scintillator and its aluminum overcoat. The proximity-focused image intensifier and its controller and power supply are described in 6.5, and 6.6 outlines the basic principles of charge-coupled devices and the differences between the scientific- and commercial-grade CCDs used in the imaging system. 6.7 provides a detailed description of the customized camera head electronics which downloaded the analog data from both CCDs, converted the signals to a digital format, and transferred the data to the computer. Both CCDs were thermoelectrically-cooled to reduce dark current (6.8). A summary of Chapter Six: The UGED Imaging System 291 experimentally-measured characteristics of the imaging system comprise 6.9, including pulse-height distributions, noise levels, modulation transfer functions, and detective quantum efficiencies. 6.1 The Fused Fiber Optic Components The properties of fused fiber optic windows and tapers have already been described in 5.4.2. Three fiber optic components were purchased from Schott Fiber Optics for the scintillator-based imaging system in the UGED instrument. The first component was a vacuum-tight window, 0.25" thick, which isolated the scattering chamber from the detector chamber through an O-ring seal (Figure 6-1). The scintillator detector was designed to have an active area 4 cm in diameter inside the scattering chamber, so the diameter of the fiber optic window was 2", leaving ~5 mm of clearance around the window's edge for making the O-ring seal. The second fiber optic component was a 40: 18 mm reducing taper which demagnified the primary fluorescence images down to the active area of the proximity-focused image intensifier. This taper was glued with torr-seal into a 40-mm-OD aluminum shell, making more or less a single cylindrical piece about 40 mm long. (As a general rule, the length of a taper is equal to its maximum diameter.) The aluminum shell contained tapped holes for ease of mounting. The third fiber optic component was an 18: 12.5 mm reducing taper which demagnified the PFII output image down to the width of the scientific-grade charge-coupled device. This taper was small and light enough that an aluminum mounting shell was not necessary. The total demagnification of the imaging system was 3.2x. Table 6-1 summarizes Chapter Six: The UGED Imaging System 292 the physical properties of the three fiber optic components according to data published by Schott [ScF95]. The gain of each component was calculated according to Eqs. 5.59 and 5.60, although the To term was only included for the first window since the optical coupling compound virtually Phosphor Window 40:18 Taper 18:12.5 Taper Glass 47A 32A 32AS 'TlOAR 0.75 0.50 0.50 To 0.66 0.68 0.68 1 µ (cm· ) 0.284 0.163 0.163 l (cm) 0.64 4.0 1.8 d c-c (µm) 6 10 4 NAEff 1.0 0.45 0.69 gFO 0.41 0.053 0.18 Table 6-1: Physical parameters for the three fiber optic components used in the scintillator-based imaging system. Values taken from [ScF95]. eliminated reflections at subsequent fiber optic interfaces. In retrospect, choosing higher quality glasses (e. g., 32A-HT) for the window and large taper would have increased the pre-MCP gain by a factor of two (compare with Tables 5-4 and 5-5). The actual transmission of each component was not measured, and examination of the tapers showed that the transmission was not uniform, decreasing as a function of distance from the center. This non-uniform gain was unavoidable and complicated data analysis (7.1.4). 6.2 Assembly of the Scintillator-Based Imaging System The scintillator-based UGED imaging system was housed within its own vacuum chamber, a 5"-long, 8"-CFF nipple which was evacuated to 10·2 torr (3.2.3). The system was assembled starting with the phosphor-coated fiber optic window and working backwards to the scientific-grade CCD and its thermoelectric cooler. To begin with, the fiber optic window and the large fiber optic taper were joined together using an optical Chapter Six: The UGED Imaging System coupling compound (Dow Corning; 293 Detector Mount And Cover Flange TI CCD j? Q2-3067), and this had to be done carefully, without touching the I I phosphor coating on the window. An aluminum baseplate was machined with an inset hole equal in diameter to the window (2"), and as deep as the Large !ape~ ~ ~~~ Mounting Ring T I I 1 Image Intensifier~ Mounting Ring , , I I I I window's thickness (0.25"). A 2"-OD Small Taper _ _ _....;>•' Mount 1 • O-ring with 1/16" cross section was SIT e CC D Mounting Ring inserted into the hole; the window fit snugly in the hole, phosphor-side down, leaving the back window face exposed but the phosphor coating I Figure 6-2: Mounting system for the UGED imaging system. Each of the three mounting rings are supported (independently) by three screws. The SITe CCD thermoelectric cooling system is not shown. completely protected and untouched. After cleaning the fiber optic faces, a dollop of optical coupling compound was applied to the center of the window and the taper was slowly pressed down making large, circular sliding motions to work out bubbles and excess compound. This procedure took some practice, but fortunately any trapped bubbles could be seen through the narrow end of the taper. Once the window and large taper were coupled, the two components were inserted into the 4.5"-CF mounting flange, already installed (with copper gasket) on the scatteringchamber side of the three-flange detector cover assembly (Figure 6-2). Using a Teflon clamping ring with an ID greater than the large taper' s OD, the phosphor window was Chapter Six: The UGED Imaging System 294 squeezed against a viton O-ring to make a vacuum-tight seal, thus isolating the scattering chamber from the detector chamber. The top of Figure 6-3 shows the three-flange assembly at this stage of construction. The aluminum-coated beam stop on the wide face of the large fiber optic taper (6.3) can be seen on the narrow face. The detector-chamber side of the three-flange assembly contained nine inset nuts, regularly spaced about a 4.5" -diameter circle, for three sets of three 80-threads-per-inch screws (Thor Labs; FAS300). Once inserted into the nuts, each set of three screws held an aluminum mounting ring, and the three mounting rings in turn held aluminum support pieces which secured in place the large fiber optic taper, the image intensifier, and the CCD. Depending on their lengths, the screws were encircled by a steel spring and a Teflon tubing spacer. By tightening or loosening the screws, the tilt of each mounting ring could be individually adjusted for proper positioning of its respective imaging component. The bottom of Figure 6-3 shows the first mounting ring and its aluminum support piece in place for the large fiber optic taper. In this particular case the screws were not adjusted much because an unevenly-applied force would slightly separate the large taper from the window, creating bubbles. Sometimes these bubbles could be removed just by squeezing the two fiber optics back together; other times the components had to be removed, cleaned, and recoupled. Next the input window of the proximity-focused image intensifier was optically coupled to the narrow end of the large taper (top of Figure 6-4). It was impossible to tell whether or not all bubbles were worked out of the joint because the phosphor window was opaque, so this particular stage was practiced "blind" several times in advance using just the large taper and the PFII. The results could be checked by looking through the Chapter Six: The UGED Imaging System 295 Figure 6-3: Construction of the UGED imaging system. (Top) The phosphor-coated fiber optic window and large fiber optic taper are installed through the three-flange detector cover assembly into a 4.5" CFF. (Bottom) Installation of the mounting ring and support piece for the large fiber optic taper. Chapter Six: The UGED Imaging System 296 Figure 6-4: Construction of the UGED imaging system . (Top) The proximity-focused image intensifier is optically coupled to the narrow end of the large fiber optic taper. (Bottom) Installation of the mounting ring and support piece for the image intensifier. Chapter Six: The UGED Imaging System 297 Figure 6-5: Construction of the UGED imaging system. (Top) The small fiber optic taper is optically coupled to the output window of the image intensifier. (Bottom) Installation of the support piece for the small fiber optic taper. Chapter Six: The UGED Imaging System 298 Figure 6-6: The inside of the detector chamber after installation of the CCD. The CCD pre-amp circuit board was screwed onto the third mounting ring, and voltage leads extended upward to the left where the Bendix half-nipple feedthrough was located. The image intensifier voltage leads extended to the lower right to a BNC feedthrough flange. The square copper block cold sink in the center of the Zip socket and circuit board was coated with a thermal coupling compound . wide end of the taper. The bottom of Figure 6-4 shows the mounting ring and aluminum support piece in place for the PFII. The small fiber optic taper was coupled to the output window of the PFII (top of Figure 6-5). The aluminum support piece for the small taper did not have its own mounting ring; the Thor Labs screws attached to nuts mounted in the back of the PFII' s support piece (bottom of Figure 6-5). Finally, the screws and mounting ring for the CCD were installed, but the CCD was not. At this point the detector chamber nipple was brought down onto the three flange assembly and held in place by encircling the connecting flanges with duct tape. The image intensifier's four voltage leads were Chapter Six: The UGED Imaging System 299 soldered into the electrical feedthroughs on one of the attached half-nipples (Figure 3-13) and carefully insulated to prevent arcing. The entire unit was then moved to the scattering chamber and bolted into place, simultaneously pinching two copper gasket seals (between the scattering chamber and the three-flange assembly, and the three-flange assembly and the detector chamber nipple). The CCD pre-amp board and Zip socket were temporarily installed on the third mounting ring so the twenty-three camera head voltage leads could be soldered to the Bendix connector on the detector chamber nipple. After disconnecting the pre-amp board from the mounting ring, all voltages and timing signals were tested at the Zip socket with a multimeter and an oscilloscope. The CCD was inserted and sample images were recorded to confirm everything was functioning properly. Finally, the CCD was optically coupled to the small fiber optic taper and held in place by screwing the pre-amp board onto the third mounting ring (Figure 6-6). At this stage of construction, the fine tilt adjustment provided by the high-precision support screws was found to be very important in making a good connection between the CCD and the taper, since their areas were small. In order to check for bubbles and the transverse alignment of the CCD and taper, a light-emitting diode was placed beside the small taper and images were recorded. Bubbles were easily seen by light passing sideways through the coupling compound joint; often these bubbles could be eliminated simply by adjusting the support screws. The detector chamber was sealed with an 8" CFF which contained water and electrical feedthroughs for thermocouples and the thermoelectric cooler (Figures 3-13 and 3-14). As the flange was brought into place, the socket of the TEC cold sink (Figure 6-7) had to fit snugly into the copper block inset of the CCD Zip socket (Figure 6-6). A poor Chapter Six: The UGED Imaging System 300 Figure 6-7: The detector chamber back flange showing the TEC copper cold sink and the two-stage thermoelectric cooler mounted in a plastic support. The aluminum "wing" pieces helped align the cold sink to the CCD copper block in the Zip socket (Figure 6~7) . thermal connection limited the temperature to which the CCD could be cooled. 6.3 The Aluminum Beam Stop In the UGED instrument, about ten percent of the incident electron beam was scattered across the detector by the gaseous sample. The unscattered electron beam struck the detector within a 300-µm circle (the electron beam width), so 90% of the total electron signal intensity was concentrated in less than 0.01 % of the active area of the detector. This intense signal would quickly saturate the central CCD pixels and cause prominent blooming problems in the raw diffraction images. One simple solution to this Chapter Six: The UGED Imaging System 301 problem would be to block the unscattered beam with a Faraday cup, as is done in traditional GED instruments where the imaging system (a photographic plate) is replaced in every experiment. This method, however, complicates the determination of the diffraction pattern's center [MoR80], and since the UGED imaging system is both static and real-time, a more logical solution would be to filter the unscattered electron beam signal. This section describes how the electron beam intensity was attenuated by applying a localized, thin aluminum film to the imaging optics. 6.3.1 Aluminum Transmission Characteristics In order to make the unscattered electron beam signal comparable to the scattering intensity at smalls, the beam signal had to be attenuated by a factor of approximately 103. The transmission of a thin film depends on its thickness t according to [Wea81], [ChK69] : T 4n kt) = (1 - R)exp ( --A- (6.1) 10 0 9 8 7 0 6 ■ ■ ~ 5 ■ ■ 4 3 oo • •ooo ■ ooo o ■ ■ oO OOO O o 0 □ □ oo 0 D □ D D □ D ■ D [Scl54] ■ [Has61] • [FaR61], [Nea70] ■ 2 0 [Mat71] -[ShE80] 1 0 200 □ 0 B 300 400 500 600 700 800 900 1000 Wavelength (nm) Figure 6-8: Optical extinction coefficients for aluminum films in the visible region. Chapter Six: The UGED Imaging System 302 where k is the optical extinction 77A 100 coefficient, 'A, is the wavelength of .... R is the (.) 169 A (1) incident light, and C 10 241 A (U reflectance. Figure 6-8 shows the ~ E II) C dependence of k upon 'A, for aluminum films as reported by ... 301 A 1 510A (U I- 0.1 1 several different authors. In the region of 200 to 700 nm, the relationship 1s linear (k/'A, : .-: 10 100 Exposure To Air (Days) Figure 6-9: Transmittance of aluminum films at 550 nm as a function of exposure time to air. The film thicknesses are indicated in the graph. 1.2x10-3 A- 1), meaning that the percent transmittance is independent of wavelength. Assuming R = 0.9, Eq. 6.1 predicts that a 300-A film should attenuate the scintillator emission by 103 . However, R also has a dependence upon t for thin films, and the transmittance of aluminum films increases with time upon exposure to air because of oxidation effects [Ade92]. To test these effects, aluminum films of varying thickness were coated on microscope slides and the percent transmission was monitored as a function of time. (The films were exposed to air for about an hour before the first spectral measurements were made.) Figure 6-9 shows that the measured transmittance was about one order of magnitude greater than the values predicted by Eq. 6.1, and that over the course of a few months the transmittance gradually increased by a factor of about 1.4. These observations were similar to Adegboyega's results [Ade92] . Chapter Six: The UGED Imaging System 303 6.3.2 Preparation of the Beam Stop The aluminum coating was applied to the wide end of the large fiber optic taper using the laboratory's metal evaporation chamber (3.4). An end cap with a small aperture was machined so that only the central region of the taper would be coated. The beam stop radius had to be larger than the electron beam waist, but less than the distance equivalent to s"" 0.8 A- 1 so that scattering data surrounding the first zero in the sM(s) curve would not be cut off. An aperture diameter of 1.5 mm was chosen. No problems occurred when coupling the large fiber optic taper to the scintillator window: the aluminum coating did not wipe off. Initially, the beam stop thickness was 500 A, and after several months the transmittance was 0.13%, right on target for UGED, but an order of magnitude less than what was expected from the microscope slide experiments. After working with this beam stop, it was clear that more attenuation was desirable, perhaps 104 , because saturation still occurred in the central region. When the imaging system was assembled a second time, a new, 725-A-thick center spot was coated, but this time the transmittance was 1% and blooming was a problem. Diffraction data was recorded anyway, but a new center spot should be prepared at some point in the future, perhaps while simultaneously coating a microscope slide to double-check the percent transmittance before reassembling the imaging system. 6.4 The P20 Phosphor Scintillator A layer of P20 phosphor powder with an aluminum overcoat was deposited on the 2" fiber optic window by CRT Scientific Corporation. The diameter of the phosphor Chapter Six: The UGED Imaging System 304 coating was 40 mm and its mass-thickness was 4 mg/cm2 , or 10-µm thick. The diameter of the aluminum overcoat was larger, -45 mm, with a thickness of 3,000 A. The value for the aluminum overcoat thickness was based on a compromise between three criteria: ( 1) high reflectivity, (2) low light transmission, and (3) efficient ke V electron transmission. Increasing the overcoat's thickness increases its reflectivity of visible light (up to a maximum of -90% ), which would keep more scattered laser light out of the imaging system and more scintillator fluorescence in the imaging system. Increasing the overcoat thickness would also reduce the transmission of unreflected scattered light according to Eq. 6.1. A 3,000-A film should block every scattered photon in the pump laser pulse. Unfortunately, the aluminum overcoat will reduce the kinetic energy of incident electrons due to inelastic collisions, and should therefore not be too thick. According to data presented by Reimer, 17-keV electrons passing through a 3,000-A aluminum film (pt= 81 µg/cm 2 ) still retained 95% of their kinetic energy [ReL85]. The fraction of retained energy increased nonlinearly with the initial kinetic energy: 25-keV electrons lost 5% of their kinetic energy when passing through a 6,000-A aluminum film. CRT Scientific prepared the aluminum overcoat by metal evaporation, and small, unavoidable pinholes could be seen in the coating when the fiber optic window was held up to light. In addition, the coating transmitted far more scattered light than would be expected from Eq. 6.1. Either that equation is an inappropriate model for the particular experimental conditions, or CRT did not actually apply 3,000 A of aluminum. If higher ke V electrons are used in the future, then a better alternative might be to glue down a very thin aluminum foil (< 1-µm thick), if the foil can be prepared and applied without disturbing the phosphor. Chapter Six: The UGED Imaging System 305 The temporal response of the P20 scintillator is described in 6.5.5. 6.5 The Proximity-Focused Image Intensifier A gated, single-MCP, proximity-focused image intensifier with fiber optic input and output windows was purchased from Hamamatsu Corporation (Model V3063U-04). The design principles of this type of image intensifier were discussed in 3.4.3. The PFII photocathode was S20 with a peak quantum efficiency of 14% at 430 nm and a QE of 10% in the neighborhood of the P20 emission wavelengths. The scintillator at the output of the microchannel plate was also P20. According to a test data sheet provided with the PFII, the device's spatial resolution was 28.5 lp/mm, corresponding to the 5% position in the modulation transfer function. The manufacturer's measured rate of spontaneous emission from this intensifier (called the equivalent background input) was 4.lxl0- 12 lumens per cm2 (see 6.9.3 for more details). 6.5.1 The Power Supply The image intensifier had four input voltages: (1) a low, negative bias at the photocathode, (2) ground at the microchannel plate input, (3) up to +900 V at the microchannel plate output, and (4) +6,000 Vat the scintillator. In addition, the outer face of the output fiber optic window was coated with indium tin oxide which could be connected to experimental ground. This coating was recommended due to the high bias voltage on the inner face of the window, which could cause static buildup on the outer face, and perhaps damage the CCD downstream. The PFII gain was controlled by varying Chapter Six: The UGED Imaging System the voltage at the microchannel plate output; the PFII could be gated by swinging the photocathode voltage to a positive low bias voltage, thus preventing 306 PFII Component PFII Wire Color Voltage (V) Photocathode MCP In MCP Out Scintillator Outer Face Green Violet Black Red Gray +35 (Off); -200 (On) 0 +200 to +900 +6,000 Chamber Ground Table 6-2: Voltage connections for the proximityfocused image intensifier. photoelectrons from escaping to the MCP. Spontaneous emission was also stopped when the gate was off. A summary of the input signals for the PFII is shown in Table 6-2. A power supply for the image intensifier was purchased from GBS Micro Power Supply (Model HVPS 20059600-001). This supply required four input signals: (1) E+, a +10 Vdc, 50 mA power line, (2) Vconr, a Oto +10 Vdc signal for controlling the MCP Out voltage, (3) Vcare, a TTL signal which activated the photocathode (to -200 V) when Vcare fell low, and (4) ground. The fall and rise times of the photocathode voltage pulse 10000 - = , - - - - - , - - - , - - - , - - - , - - - , - - - - - , - - - - ~ C ca c., 1000 - : : ! - - - - + - - - - + - - - - + - - - - - t - - - - - - - - - - : : , { Y C - - - - + - - - - - l :i.. Cl) ..:: 'iii C Cl) 100 - d - - - - - - - - + - - - - + - - - r . " " " " ' - - - - - - l - - - + - - - + - - - - - - - j C 8, ca 10 -=f-------------j,,~--+-----+-~---_-_-_➔~---_-_-_-_-_➔~---_-_-_-_-_➔~--------i Log(g) = 0.505 V cont - 1.072 E 1 3 4 5 6 7 8 9 10 VCont (V) Figure 6-10: Gain calibration cuNe for the proximity-focused image intensifier relative to the voltage Vconr supplied by the controller unit. Gain units are ft-Uft-c. Chapter Six: The UGED Imaging System 307 Main Power Switch 1/2-A Fuse 11 O Vac 0 I GND -=-A +15 Vdc Power Supply l -=-s +15 +SA Gain Digital Display ~ 1 Image Intensifier Power LED -s ~ 0 -=-A -=-A -=-s 250 n LM317L 0 +Se -=-A Image lntens ifier Power Switch LM7805 +5 Vdc Power Supply Controller Unit TTL Triggering Circuit +10.0V Gain Adjust Pot E+ C C -"' -"' a, C\J 10 kn Gnd -st -=-A -=-A Cathode Vaate GBS Micro Power Supply Vcont MCP In ... Q) rJ) C: Q) C: MCP Out Screen Q) en ca E 0 I- Figure 6-11: Electronics inside the image intensifier controller unit for powering and driving the GBS Micro Power Supply. The TTL circuit diagram is shown in Figure 6-12. emitting from the power supply were 60 ns with a 100-ns lag time. 6.5.2 The Controller Unit A controller circuit was constructed to drive the PFII power supply (Figure 6-11 and Figure 6-12). The controller contained two transformers to convert the 110 Vac power from the wall into separate +15 Vdc and +5 Vdc sources. The +15 Vdc line Chapter Six: The UGED Imaging System Input Impedance Switch External Trigger Input 308 i Gate Window Delay Generation Circuit a I SN74LS123N l---'l" '-------11 A 1C 'i':: 0 m 1B 1R/ C1----~----'------l I I +Sso--'-1_1_C_L_R__1'!-0_ +Ss +Ss 5 .3 kn IL C 11) ~ Gate Window Delay Pot Trigger Active LED 1 g ~ +Ss 1R/C I I I VGate ~ Output 1 ti tl I rl I Continuous I Edge Triggering Switch 10 n 2N3904 npn Trigger 0 u t put o - - - - - - - ' f..1 11,1 I I Gate Window Width :;; Pot 18 9 1C 1CLR ~--10 1A SN74LS123N ----- Ii ii +Ss 0--...-----<12 CL R 2 A 28 2R/ C _ ____, 20 +Ss ~ 2C 1----0---- Ii 1 oo nF ~-n~ _ _ _ __. I Gate Window Width Generation Circuit L °j~ ___ ii ~ I t! _j fl Gate Window Range Switch ~ rro Figure 6-12: The TTL circuitry in the image intensifier controller unit. This circuit generates Vaate, the photocathode activation pulse for the GBS Micro Power Supply. In continuous-mode, Vaate, is equal to the external trigger. In edge-mode, a gate pulse is generated after each falling edge in the external trigger. The delay and width of the gate pulse are controlled by the user with potentiometers. A second pulse is generated to turn on the "Trigger Active" LED. powered an LM317L voltage regulation circuit adjusted to output+ 10.0 V, which fed into the E+ and Vcont inputs of the PFII power supply. Both E+ and Vcont remained grounded until a secondary power switch on the front panel was turned on. Vcont was further regulated by a simple voltage divider circuit connected to an external potentiometer, which allowed the user to vary Vcont between +3.5 and +10.0 V. Chapter Six: The UGED Imaging System 309 SpectraSource Camera Head TTL Trigger Signal Shutter Only Mode +5 0 - - 0 Shutter Plus YAG Lamp Mode ....r:----° _ Inverted Trigger Output I ~-~-o I Trigger Mode Switch Logic Table-~ ; Shutte_r Only Nd:YAG -· • Laser Lamp Synch Signal *~;i:; cm lr ' Sht.i'tter , L L iH _Trigger . H H' H Figure 6-13: TTL circuitry added to the SpectraSource camera head power supply for generating the image intensifier trigger signal from the external shutter signal and the Nd:YAG laser lamp signal. The circuit used SN74LS01 NAND and SN74LS04 NOT chips. The trigger mode switch was mounted on the camera head power supply. The value of Vconr was displayed continuously on a digital LED monitor. By measuring the voltage at MCP Out and referring to the PFII test data sheet provided by Hamamatsu, a gain calibration curve was created based on the value of V cont (Figure 6-10). The gain has units of foot-Lamberts per foot-candles. * The +5 Vdc line powered the TTL logic which prepared Vaare based upon an external triggering source (Figure 6-12). The controller unit could be switched between two different triggering modes: (1) continuous, where the PFII photocathode was active (at -200 V) as long as the trigger was low, and (2) edge, where the PFII photocathode was activated for a preset gate window whenever the trigger fell from high to low. The delay and width of the gate window were set by the user with two external • See [HoG96] for a brief review of illuminance units in photometry. Chapter Six: The UGED Imaging System 310 potentiometers which were part of retriggerable monostable multivibrator circuits (SN74LS 123N chips). A BNC output was added so that the gate window could be observed on an oscilloscope. The delay between the trigger's falling edge and the rise of the gate window could be varied over a few microseconds; the width could be varied either over microseconds or a few milliseconds, depending upon the position of a switch. 6.5.3 Triggering the Image Intensifier The external trigger signal for the image intensifier came from the power supply for the CCD camera head (6.5.3). Whenever an image was exposed, SpectraSource's HPC-1 program a opened shutter mechanism placed in Shutter Active SpectraSource Camera Head TTL Shutter Signal ►I the laser beam path. The TTL signal for Nd:YAG Laser Lamp Synch Signal driving the shutter was identified camera within head 33 ms the Image Intensifier Trigger Signals power Shutter Only supply and split off to trigger image the Shutter+ Y AG intensifier. A small logic circuit and switch (Figure 6-13) were added to the power (Top) Input pulse traces for generating the external image intensifier trigger signal. The camera head shutter signal occurs whenever an exposure was taken with the HPC-1 software. The 30-Hz Nd:YAG laser lamp signal pulsed continuously when the laser was on. (Bottom) The external image intensifier trigger signal for "Shutter Only" mode and "Shutter + YAG" mode. Figure 6-14: Chapter Six: The UGED Imaging System 311 supply in conjunction with the two different triggering modes established in the PFII controller unit. On the "Shutter Only" mode of this circuit, the controller unit was set to the continuous-triggering mode and the image intensifier remained on for the duration of the exposure. On the "Shutter + YAG" setting, however, the controller unit was set to the edge-triggering mode. The shutter signal was mixed with the Nd:YAG laser's lamp 200-µs synchronization pulse so that the trigger signal fell low repeatedly, a few microseconds before each laser shot, for the duration of the exposure (Figure 6-14 ). With each falling edge, the controller unit then activated the image intensifier according to the gate window settings. 6.5.4 Setting the Image Intensifier Gate Delay The criterion for selecting the start time of the gate window was to collect as much fluorescence from electron bombardment of the scintillator as possible, while cutting out scattered laser light. Earlier, CCD images recorded under the continuous-triggering mode had been found to contain patterns which could only be due to residual transmitted light from the electron-generation laser. (This was evidence of the inadequacy of the aluminum overcoat.) The residual light signal was used to identify the gate delay. The gate width was set to 1 µs and images were recorded as a function of the gate delay; the residual light pattern appeared only when the window position overlapped with the delay time between the falling edge of the Nd: YAG lamp pulse and the firing of the laser. This delay time was found to be 5.94 µs . During diffraction experiments, the actual gate delay time was set to between 6.2 and 6.5 µs to ensure that no scattered light from either the pump or the electron- Chag_ter Six: The UGED Imaging_ S'i_stem - J, "t, (I) • • 0 0 0 0 • ~ E > en ~ r:: en m r:: t- (I) (I) r:: .::: lo., ~ • oe 312 • 0 X ,~~ m ~ ~ X ~~* X XXX (I) a: 0.001 0 1 0.01 0.1 1 2 3 Gate Width (ms) 10 4 5 Figure 6-15: Fluorescence signal through the imaging system as a function of the image intensifier gate width. Emission from the P20 scintillator decreased exponentially with a 10% time constant of 440 µs. The vertical bar indicates the 210-µs gate width used in UGED experiments. generation lasers remained in the scattering chamber when the PFII was activated. Unwanted background light signal could still occur, however, if the excited sample molecules fluoresced strongly and the time scale of emission was longer than 250 ns. 6.5.5 Setting the Image Intensifier Gate Width The width of the PFII gate window was chosen to maximize the electronbombardment scintillator emission while minimizing the amount of spontaneous emission from within the PFII. The time constant of P20 fluorescence depends on the amount of incident electron beam current [Gal90a], [Hmt92], so the response of the UGED scintillator was measured experimentally by varying the gate width and integrating the electron beam signal. The gate delay was set at 5.94 µs, permitting the transmission of residual light from the electron-generation laser which was used as an intensity calibration reference. Figure 6-15 shows the scintillator's temporal response from two separate Chapter Six: The UGED Imaging System 313 200 µS Shutter + Y AG Image Intensifier Trigger Signal 210 µS ►I Edge-Triggered Gate Window Figure 6-16: (Top) Segment of the "Shutter + YAG" mode external image intensifier trigger signal containing one 200-µs Nd:YAG laser lamp pulse (see Figure 6-14). (Bottom) The edge-triggered gate window created by the controller unit. The window delay was 6.2 µs relative to the falling edge of the external trigger, and the window's width was 21 O µs. experiments; the decay time to 10% of the initial emission intensity was 440 µs. Based on Figure 6-15, the gate window width was chosen to be 210 µs, corresponding to a collection of 67% of the total fluorescence emission signal. An example of the gate window pulse timing is shown in Figure 6-16. 6.6 The Charge-Coupled Device The storage components of the second-generation UGED imaging system were charge-coupled devices, two-dimensional arrays of tiny, photoactive sensors. As discussed in the introduction of this chapter, the imaging system employed two types of CCDs to satisfy different imaging needs: (1) high resolution images of the electron beam were recorded by direct bombardment on a commercial-grade CCD purchased from Texas Instruments (Tl), and (2) complete electron diffraction patterns detected on the P20 scintillator and amplified with the image intensifier were recorded on a scientific-grade CCD purchased from Scientific Imaging Technologies, Inc. (SITe). Although both the TI Chapter Six: The UGED Imaging System 314 Element -----Picture or Pixel 11 :a.. 11 Q) u, C co :a.. I- co 0 A----0 :a.. Q) Conversion > Amplifier Computer Horizontal Transfer Figure 6-17: Operation of a full-frame transfer charge-coupled device. Electrons collect in a pixel during an integration period and are then transferred to an amplifier, first vertically (down the column) and then horizontally (across the serial register). The amplifier converts electric charge to a voltage, which is in turn converted to a binary signal. This signal is sent to the computer. and SITe CCDs operate under the same basic principles (both were read out using the same camera head), the two are markedly different. This is evident in their prices ($2,200 for the SITe SIC502AF versus $30 for the TI TC211) and in the number of pin connections (44 for the SITe versus 6 for the Tl). This section outlines the fundamentals of image collection with charge-coupled devices, and compares the operation of the SITe and TI CCDs. 6.6.1 Basic Principles Excellent discussions of CCD technology can be found in various books, journal articles, and commercial product literature.• Several CCD architectures - • See, for example, [JaJ87], [Blo87], [Tek91b], [Tek92], [SIT94], and Holst's book [HoG96]. full-frame Chapter Six: The UGED Imaging System 315 transfer, sub-array transfer, interline transfer - are available for different applications, and only the full-frame transfer imager will be reviewed here. The entire 2D array of these imagers is active, and there is one readout channel. During a user-defined integration time, charge collects in the individual picture elements (pixels) as a result of photon, electron, or atomic bombardment. The charge "image" is then downloaded as shown in Figure 6-17: distinct pockets of charge corresponding to the pixels are transferred down the columns, across the last row, and out through an on-chip preamplifier which converts electric charge to voltage. This voltage is amplified further in off-chip electronics, eventually converted to a digital signal, and stored in computer memory. With a fullframe transfer device, the imaging area remains active during readout, so the input signal must be shuttered to avoid smearing. 6.6.1.1 Collection of Charge The pixels in a charge-coupled device are metal-oxide-semiconductor (MOS) capacitors with dimensions on the order of 20x20 µm 2 . The CCD substrate, a p-type silicon wafer, is covered with a thin insulating layer of silicon dioxide, and column edges are defined by doping to make channel stops. Charge cannot be transferred over the channel stops (along rows), only up or down the columns. Above the silicon dioxide layer are repeating rows of polysilicon, known as gates. The horizontal boundaries of a single pixel are defined by the channel stops, and the vertical boundaries are defined by between one and four gates, depending on the CCD design and additional doping of the substrate. An incident visible photon creates an electron-hole pair within the substrate via the photoelectric effect. The quantum efficiency is wavelength-dependent but can approach Chapter Six: The UGED Imaging System 316 90% by the application of anti-reflection coatings to back-illuminated devices [SIT94]. Two or more electron-hole pairs can be created by ultraviolet photons, and many EHPs are formed following direct bombardment of ke V electrons (5.4.1.1). If a positive voltage is applied to one of the polysilicon gates, then a potential energy well is formed under the gate within the pixel, and photoelectrons are trapped there while their positive-hole partners are repelled into the substrate. The negative charge collects at the substrate / silicon dioxide interface and can be stored indefinitely. (In buried channel devices, dark current is reduced by collecting the charge near an n-type region implanted just below the silicon dioxide interface.) The amount of charge which can be stored within a pixel's potential well is of course limited; this well depth is defined in terms of number of electrons (EHP). The dynamic range of the imager is therefore equal to the well depth divided by the number of collected electrons necessary to observe an event. If too much charge accumulates in a pixel (saturation), the charge will spill over into neighboring pixels up and down the column. This is known as blooming. Charge-collection efficiency (CCE) refers to the likelihood a particular pixel will collect the electrons initially formed within the pixel's boundaries [JaJ85]. For visible photons which create at most one EHP, the CCE is nearly the ideal value of one. An example of when CCE is less than one is direct electron bombardment of a backilluminated device (5.4.1.1), where the migration of the EHPs to the pixel potential wells can result in diffusion to adjacent pixels. 6.6.1.2 Transfer of Charge For the CCD to function as an imager, the charge stored within the potential well Chapter Six: The UGED Imaging System 317 of each pixel must be individually measured. The full-frame transfer CCD has one readout device, and all pixel charge must be moved through this device while maintaining the integrity of the charge' s initial location. The image is read out one row at a time. First the entire image is cycled down one row (vertical transfer), moving the last row into a shielded (inactive) structure known as the serial registers (Figure 6-17). The well depth of these registers is generally twice that of pixels within the active area. Then, only the charge in the serial register is moved, along the row and out through the on-chip amplifier. Once all the serial registers have been cleared, another vertical transfer talces place. Thus, the linear stream of CCD pixel data reaches the computer organized first by column and then by row. Pixel-to-pixel transfer along the columns or across the serial register is controlled by varying the potentials of the overlying gates. Figure 6-18 shows the clocking sequence for a three-phase device which has three distinct polysilicon gates over each pixel. During integration, Gate A is kept high and Gates B and C are kept low, so that charge collects only under A. This charge is transferred to the next pixel down the column, say from Y to Z, after a sequence of six clocking events: 1. Gate B goes high, so the charge is under both A and B. 2. Gate A falls low, so the charge is under just Gate B. 3. Gate C goes high, so the charge is under both Band C. 4. Gate B falls low, so the charge is under just Gate C. 5. Gate A goes high again, so the charge is now under Gate C of Pixel Y and Gate A of Pixel Z. 6. Gate C falls low, and the charge is now located in the Pixel Z. Chapter Six: The UGED Imaging System Pixel Y Pixel z ~----- 318 Clocking Voltages Ii i C - I A B C 1 A B C B i- - -i- - -i (') Time . . - - - - -m I I e. e· e· I - -B e• e• e • ~ e • e'· - -! . . - - - - - ff g Figure 6-18: Three-phase transfer of charge along a column of CCD pixels. As the three gates A, B, and C, alternate between the high and low rails, the transient potential energy surfaces force charge from Pixel X to Y, Y to Z, and Z onward. At the same time, charge from the preceding pixel, X, has been transferred into Pixel Y, and the charge in the pixels at the end of the column have been transferred into the serial registers. Gate A remains high as the gates over the serial register pixels are cycled in a similar manner to transfer the charge out through the amplifier. The charge-transfer efficiency (CTE), the likelihood of moving all charge frorri one gate to the next, must be kept very high to preserve the image's integrity. For example, the outermost pixel in a three-phase 512x512 CCD undergoes 3,072 transfers: 3 gates Chapter Six: The UGED Imaging System 319 multiplied by 1,024 pixels (512 rows plus 512 serial registers). To move 99% of this pixel's charge through the amplifier, the CTE must be at least 0.9999967. In contrast, a virtual-phase device (one gate) with the same number of pixels would require a CTE of 0.9999900 to move 99% of the charge in the outermost pixel through the amplifier. 6.6.1.3 On-Chip Preamplification The on-chip amplifier has formidable job converting as small as a few electrons per pixel of charge into a detectable, distinct output signal. This conversion is done with a floating diffusion capacitor coupled to an output amplifying MOSFET (metal-oxide-semiconductor field-effect transistor) [SIT94], [Hol96]. As shown in Figure 6-19, charge in the last pixel in the serial register is transferred into a summing well. Reset Drain a (The summing well Reset Gate y Reset Switch MOSFET S SW LG Floating Diffusion Capacitor T 7 Amplifier Drain Output Amplifier MOSFET Video Output Typical structure of on-chip preamplifier. At the start of a single-pixel readout cycle, the floating diffusion capacitor is charged by activation of the reset drain MOSFET switch. This sets a reference level on Video Output through the amplifier MOSFET. Charge is then transferred from the summing well, through the last gate, and onto the capacitor, which changes the Video Output voltage. Figure 6-19: usually has a depth four times as great as the active-area pixels, so that four-pixel binning can be carried out without loss of dynamic range.) Next, a reset gate pulse activates a switching MOSFET, and the floating diffusion capacitor is biased to the reset drain voltage. When the reset gate pulse falls low, the capacitor is isolated and the output MOSFET registers an initial reference voltage. The summing well then falls low, and the charge is moved through a last gate onto the floating Chapter Six: The UGED Imaging System 320 diffusion capacitor, causing a change in the output MOSFET voltage. The voltage differential is linearly proportional to the amount of charge added to the capacitor, and the gain is typically between 0.1 and 10.0 µV per electron. 6.6.1.4 Off-Chip Preamplification The small voltage differential at the CCD output is best resolved if an additional amplification stage is located as close as possible to the CCD output [Tek92]. Usually the connection between the CCD output and amplifier input is made across a capacitor through AC-coupling, which simultaneously protects the static-sensitive CCD from accidental shorts, limits feedback, and removes the 10+ V offset on which the small voltage differential rides. Figure 6-21 and Figure 6-22 show the preamplification circuits used for the SITe and TI CCDs in the UGED instrument. These were inverting operational amplifier circuits and provided roughly an order of magnitude of gain. 6.6.1.5 Noise To keep the dynamic range of the charge-coupled device high, the noise level of the voltage differential must be minimized. There are numerous noise sources during the movement of collected pixel charge and its conversion to a digital signal [HoG96], [Tek92], but only two types will be mentioned here: dark current and readout noise. Electron-hole pair production occurs randomly in the CCD substrate, and some of these electrons accumulate within the potential well of the pixels. This dark current flows continuously and the rate, reported in e· / pix / s, is proportional to pixel area. At room temperatures, dark current can quickly overwhelm any imaged signal. In fact, a CCD image read out at 25 °C has a baseline which increases linearly as a function of row Chapter Six: The UGED Imaging System 321 position up to the saturation limit; this baseline is the accumulation of dark current which occurs during readout of the image. Dark current is strongly dependent on temperature, however, which is why thermoelectric coolers were placed behind both the TI and SITe CCDs. Reducing the CCD temperature by 70 °C cuts the production of dark current by four orders of magnitude, and longer integration times are possible. With buried channel devices, the dark current can be reduced further by clocking the pixel gates in a multipinned phase mode, but the dynamic range suffers [Tek91c]. The dark current is negligible in short exposures at cold temperatures, and the dynamic range is determined by readout noise. This limit is set by 1/f and white noise in the on-chip MOSFET amplifier. For scientific-grade CCDs, the readout noise can be reduced to just a few e- RMS [JaJ87], and in commercial-grade devices the readout noise is on the order of 100 e- RMS. 6.6.2 The SITe CCD The scientific-grade charge-coupled device purchased from SITe (a Grade I SIC502AF), was front-illuminated and had a 6-µm pitch fiber optic window attached to the active area of the front face [SIT95]. The quantum efficiency of the device was -30% in the neighborhood of P20 emission wavelengths. The active area of the CCD was composed of 512x512 square pixels, each pixel 24 µm on a side, and the polysilicon gate structure overlying the pixels was three-phase and MPP. Serial registers A and C were located at the top and the bottom of the CCD (Figure 6-20), but only one particular output could be used at a time. Each serial register had fifteen pre-pixels between the first column of the active area and the summing well; Chapter Six: The UGED Imaging System PrePixel 1 Pixel 1 I ~G ~wl s21 s1 s31 OUTPUT A Pixel 511 Pixel 2 I I S3 S2 S1 S3 S2 S1 tG P2 P2 P1 P1 Row 1 P3 P3 P2 P2 P1 P1 Row 2 ''p3 R~ [ [ Row511 [ P2 P1 P3 P2 P1 P3 P2 P1 P2 P1 Row 512 [ TG TG ID SG S1 S2 S3 S1 S2 S3 Pixel 512 322 Pixel 511 Pixel 512 I S3 S2 S1 S3 S2 1 SG ID G T~ P2 P2 P1 P1 P3 PB P2 P2 P1 P1 P$ (P,3 P2 P1 P2 P1 P3 pj P2 P1 OUTPUT C ••• 1s31s11s2rw~G I Pixel 2 Pixel 1 PrePixel 1 Figure 6-20: Gate structure of the SITe SI502A charge-coupled device. The CCD has two serial registers, A and C, as a fail-safe in case one output is inadvertently damaged. The active area has 512 rows and 512 columns, and the serial registers have fifteen additional pre-pixels between the first column and the last gate. these pre-pixels could be used as a dark reference. Other properties of this CCD are summarized in Table 6-3. 6.6.2.1 Pin Connections Two SITe CCD circuit boards were prepared, one for the A output and one for the C output. Figure 6-21 shows the pin-out diagram and preamplification circuit for downloading the CCD data through the C output. This CCD had forty-four input and output pins and their connections to the SpectraSource camera head are summarized in Table 6-4. Ten pins were devoted to vertical transfer of the image: five clocking signals, each entering through two pins on opposite sides of the chip to accelerate transfer. P1, Chapter Six: The UGED Imaging System P2, and P3 were the three vertical gates for cycling the image either up or down the active area, and TGa and TGc were the transfer gates separating the active area from the serial registers. When reading through the C output, TGa was kept 323 Property SITe 502A TI TC211 On-Chip Pre-amp Gain (µV/e") Off-Chip Pre-amp Gain Charge-Transfer Efficiency Readout Noise (RMS e·) Pixel Well Depth (e") 2 Dark Current @ 20 °c (pA/cm ) Number of Pixels 1.53 4 20.2 6.0 0.999998 0.99998 7.3 150 5 5 3.5x10 1.5x10 40 (MPP) 27 512x512 192x165 24.00x24.00 13.75x16.00 12.29x12.29 2.64x2.64 15 6 2 Pixel Area (µm ) 2 lmager Area (mm ) Number of Pre-Pixels Table 6-3: Characteristics of the charge-coupled devices. Data for the SITe 502A was obtained from a test sheet on the Grade I fiber-optically coupled chip used in the UGED imaging system. The well depth is for MPP readout; well depth during non-MPP readout should be greater. Data for the TI TC211 was obtained from [Tex94]. constant at a low potential to prevent charge from entering the active area through serial register A, and TGc was clocked like P3. The P3, TGa, and TGc gates were specially doped for multi-pinned phase (MPP) readout and required a different high rail voltage than P 1 and P2, although the MPP method of clocking was not used in the UGED lab. Twelve pins were connected to each of the serial registers: eleven input pins and the video output VO . Five of the input signals reaching the active serial register (in this case, C) were clocked and the remaining six were static. The five clocked signals included the three serial transfer gates (SJ c, S2c, S3c), the summing well gate (SWc), and the reset gate (RGc). Static voltages connecting to the on-chip preamplification circuit included the last gate (LGc), the reset drain supply for the floating diffusion capacitor (RDc), the output MOSFET drain supply (VDDc), and analog ground (GNDc). At the opposite end of the serial registers, an input diode (/De) and sampling gate (SGc) were biased low. The unused serial registers (A) were connected according to SITe' s recommendations: VDDa, Chapter Six: The UGED Imaging System RGa, and VOa 324 were allowed to fl.oat, and the remaining nine pins were biased as shown in Table 6-4. All clocking and H3 0----1 S2c Ohm Meter )> H 1 0----1 S3c bias voltages matched the values used by SITe as t (') Q) 3 ,_ -0 LGa a,-.~+VHOR 0.. 5GB 0----ISWc VOTG o--"'LGc E SWa <t: Sia RGB O---fRGc S2a VRD 0----IRDc S3a-o-L-~ reported in their test data A sheet except for the high 23 rail of P1 and P2. SITe used +4 V for this rail, VS/Te 0.1 µF but +3 V was used in the UGED instrument as a comprorruse with the 3570 5.0kn needs of the TI CCD. Of the ten pins Figure 6-21: Pin-out diagram for the SITe S1502A chargecoupled device. The C output was used. The off-chip preamplification circuit is also shown. remaining out of fortyfour, six had no connections and two were connected to substrate ground. The last two pins were linked to an on-chip thermistor which could be calibrated and used as a temperature reference. In similar CCDs, the thermistor's resistance dropped 1.8 Q for each 1-°C loss of temperature, starting from a 2,000-Q resistance at room temperature. Chapter Six: The UGED Imaging System 325 6.6.2.2 Off-Chip Preamplification The design of the off-chip preamplification circuit (Figure 6-21) was provided by electrical engineers at SITe, although one modification was made. The resistor located between the AC-coupling capacitor and the non-inverting input of the operational amplifier was originally 218 kQ, giving a relaxation time constant of 22 ms. With this preamplifier circuit however, intense illumination over a small pixel region (such as the electron beam stop) caused up to a 30-ADU drop in the base line signal intensity for subsequent pixels in that row, and even in the next row. This happened with both the SITe and TI charge-coupled devices, which had nearly identical pre-amp circuits, so the intensity drop was not due to the CCDs. The readout time for a single row was 27 ms regardless of the row length (the SpectraSource camera head always read the serial registers as if they were 1,024 pixels long), and this time was very close to the relaxation time of the AC-coupling circuit. After replacing the 218 kQ resistor with smaller values, the lingering intensity drop spanned fewer and fewer pixels; a 1.0 kQ resistor was finally installed, giving a relaxation time constant of 100 µs, so only the next four pixels or so were affected by the intensity drop. The gain of the pre-amp circuit decreased after this change and was boosted back up by adding a 357-Q resistor in parallel with the 1.0-kQ resistor at the inverting input. The total gain of the preamplification circuit was calculated to be 20.2. 6.6.3 The TI CCD The TC211 was a commercial-grade, front-illuminated charge-coupled device purchased from Texas Instruments [Tex94] . This CCD was a virtual phase device (one Chapter Six: The UGED Imaging System 326 ABG +15 V VT/ 6 0) 2 5 3 4 0 0 SRG ::, 0.1 µF OUT ADB Texas Instruments TC211 CCD -15 V 5.0kn Figure 6-22: Pin-out diagram for the TI TC211 CCD. The off-chip amplification circuit is also shown. clocked gate) and had an active area of 192x165 rectangular pixels; the pixel dimensions were 13.75 µm by 16.00 µm so the active area was square, 2.64 mm on a side. In addition, twelve columns of shielded pixels were located at the end of the image and could serve as a dark image reference. The CCD had one serial register output with six prepixels preceding the summing well and on-chip amplifier. 6.6.3.1 Pin Connections In contrast with the SITe CCD, the TI TC211 had only six pin connections. Vertical transfer was clocked with a single gate, JAG, and the device had an anti-blooming gate ABG which could be clocked but was not needed for UGED applications. The transfer gate, serial registers, summing well, and reset gate were all controlled by a single input, SRG, which required a three-level clocking signal instead of the standard pair of high and low voltage rails. The three other pins were ground (Vss), the amplifier drain (ADB), and video out (OUT). The voltage levels for these connections and their source signals from the camera head are summarized in Table 6-4, and the pin-out diagram and off-chip preamplification circuit is shown in Figure 6-22. Chapter Six: The UGED Imaging System X I Pixel Y Pixel z - - - - i !i· ~ - - - - - m /AG I Virtual Phase I /AG 327 I Virtual Phase Clocking Voltage /AG : I Time i:; C') i I+ - J I I I Figure 6-23: Virtual-phase transfer of charge along a column of CCD pixels. Charge collects within the virtual-phase potential well and is forced to the next pixel downstream when the /AG gate voltage goes high and then back low. 6.6.3.2 Virtual-Phase Transfer Charge can be transferred between CCD pixels with a single clocking gate by doping the substrate. Figure 6-23 shows an example of the potential energy surface underneath a few pixels in the TI TC211 [Tex94] . During integration, JAG is normally low and charge collects in the virtual-phase potential well present under each pixel. To transfer the charge to the next pixel, JAG is cycled to the high rail which temporarily lowers a multi-level segment of the PES below the virtual-phase well. Charge Chapter Six: The UGED Imaging System 328 shifts to the new well. When JAG cycles low again, this well lifts back up, but a potential barrier created by doping prevents the charge from reverting to its original well: the charge is transferred to the next pixel. 6.6.3.3 CCD Preparation The TI TC211 housing had a thin window inset into the top surface to protect the electronic structures of the charge-coupled device. This window had to be removed since the CCD's purpose in the UGED instrument was to detect electrons by direct bombardment. To remove the window, an aluminum block was coupled to the top of a hot plate using heat sink compound. After heating the block to 350 °C (the temperature was monitored with a thermocouple and a multimeter), the TC211 was placed face down on it (pins up) to melt the window's resin. Five minutes later, the CCD was picked up with tweezers and the window could be carefully pried off using a knife edge. 2,000-A of aluminum in a 2.4-mm diameter circle were then deposited on the center of the CCD face using the metal evaporation chamber. This coating was applied to block scattered laser light. An aluminum frontispiece with a 2.2-mm aperture was glued onto the front of the CCD housing to keep light from the uncoated regions of the CCD; this frontispiece also shielded sensitive CCD components along the serial register from possible damage due to errant ke V electrons. 6.7 The SpectraSource Camera Head A CCD controller unit was purchased from SpectraSource Instruments. The Chapter Six: The UGED Imaging System 329 controller consisted of three separate devices: (1) an interface card installed inside the laboratory computer, (2) a power supply, and (3) the camera head. All three devices interacted with each other (Figure 3-20), and only the camera head was connected to the CCD. The interface card sent master timing signals to the camera head and received a stream of binary pixel data in return. The card also commanded the power supply to open or close an external shutter and to µtitiate a cooling unit, which the UGED camera head did not actually have. The power supply activated the external shutter and provided the camera head with +27, +15, and-15 Vdc voltages, transformed from 110 Vac. The purpose of the camera head was threefold: (1) it created well-synchronized clocking pulses necessary for CCD image readout and correlated double sampling, (2) it created high and low voltage rails for the clocking pulses, and (3) it carried out amplification and A➔D conversion of individual pixel intensities. Each of these functions had a corresponding circuit board within the camera head, and their operation is discussed in greater detail in 6.7.1, 6.7.2, and 6.7.3. In addition, several extra circuit boards were fabricated in the UGED laboratory and installed in the camera head, including an optical isolator board to limit noise feedback between the camera head and the computer (6.7.4), and a special timing circuit for the TI TC211 CCD (6.7.5) . The electrical connections between the camera head and the SITe CCD were made through a 26-pin female Bendix connector mounted on the top of the camera head. The entire camera head was plugged into a male receptacle located on a half-nipple extending from the UGED detector chamber (3.2.3) . A cable terminating in a second female Bendix plug was added to the camera head; this cable mated with a male Bendix receptacle on the scattering chamber and connected to the TI CCD inside. Table 6-4 summarizes the input Chapter Six: The UGED Imaging System Signal 330 SITe SI502A (Front) SS Camera C Output Head Bendix A Output TICCD TC211 Voltage Symbol Pin Parallel Gate Parallel Gate Parallel Gate (MPP) Parallel Gate Parallel Gate Parallel Gate (MPP) Transfer Gate Transfer Gate Vt3 Vtt 1 3 B T P2 Pt 30 29 Pt P2 29 30 -9 to +3 -9 to +3 Vt2 2 C P3 28 P3 28 -9 to +7 V23 V2t 18 17 H w P2 Pt 7 6 Pt P2 6 7 Vt2 16 G P3 5 P3 5 -9 to +7 A J TGa TGa 4 31 TGe TGe 27 8 -9 to +7 -9 to +7 Serial Gate Serial Gate Serial Gate 11 10 12 E F D Sta S2a S3a 38 37 36 Ste S2e S3e 11 14 17 -4 to +8 -4 to +8 -4 to +8 Summing Well Reset Gate H2 H3 Ht V22 SGB H3 SGB RGB Last Gate Reset Drain Output Drain Output Drain VOTG VRD VDD +12 6 8 4 Serial Gate V22 V22 Symbol Pin Symbol Pin Symbol Pin V LGa RDa VDDa 40 42 43 LGe RDe VDDe 19 21 24 GNDa SUB SUB OUTa 3 1 12 2 GNDe SUB SUB OUTe 26 1 12 25 TGe TGe /Da /De 27 8 32 9 TGa TGa /Da /De 4 31 32 9 K SGa 33 SGe 10 -4 X Ste S2e S3e SWe LGe SGe 11 14 17 18 19 10 Sta S2a S3a SWa LGa SGa 38 37 36 39 40 33 +8 a p CCDOUT2 M Transfer Gate (unused) -5 R Input Diode +15 Input Sample Gate -4 + 15 V (Preamp) -15 V (Preamp) +15 -15 Thermistor 15 .5 -9 18 20 Video Out +8 R +3 SWe RGe ..&-A 15 5 -9 to +3 -9 to +3 39 41 b 14 6 SWa RGa u z Analog Ground Unused Serial Gates SRG £ 5 7 /AG N y y -4 to +8 Oto +12 ABG 1 ADB 3 -2 +16 +25 +12 Vss 2 0 OUT 4 -5 +15 +15 -15 s TRt TR2 15 16 TRt TR2 15 16 Table 6-4: Composite pin-out diagram for the second-generation UGED imaging system. Signals were transferred between the SpectraSource camera head and either the frontilluminated SITe 502A or the TI TC211 CCDs through a 26-pin Bendix feedthrough. Chapter Six: The UGED Imaging System and output signals 331 passing A between the camera head, the and TI CCDs, and Figure 6-24 0 0 TG V13 C Bendix connectors, and the SITe B 0 -5 V u 0 RGB D 0 s0 V11 -15 V connectors. (Only Bendix eight connections were made through see 6.7.5.) N a 0 0 VRD 0 +12 V E V 0 0 H2 SGB .!<. SRG 0 H3 z M 0 0 y L 0 X V21 0 ?'A VOTG 0 w F 0 +15 V 0 +8 V G K 0 V22 the Tl's Bendix - VDD b shows the composite pin-out two p 0 0 T V12 H1 diagram of the R 0 0 H J 0 0 V23 TG -4 V Selection of the CCD source was made with a toggle switch added Figure 6-24: Pin-out diagram for the Bendix connectors linking the SpectraSource camera head to the vacuum chamber CCD electrical feedthroughs. to the camera head shell; the toggle swapped the camera head's CCDOUT2 between the two off-chip preamplification outputs, VS/Te and VT/, and also switched V23 between P 1 and JAG. The camera head originally controlled a CCD with a slightly different gate structure than the SITe SI502A, so some of the timing signals and voltage rails had to be altered. Furthermore, the camera head itself contained numerous design flaws and also cheap electronic components which needed replacement. In effect, the camera head was completely rebuilt in the UGED laboratory without any assistance from SpectraSource, who were found less than willing to acknowledge and repair their own mistakes. A summary of the UGED laboratory's modifications is provided in 6.7.6. The effort spent overhauling the camera head was fruitful on several levels. Without a detailed understanding of the camera head's operation, the addition of the TI CCD to the UGED Chapter Six: The UGED Imaging System instrument would have 332 Output PAL Logic Sequence H3* /R23 = /12 * 13 * /14 * /16 * 17 + /12 * 13 * /15 * /16 * 17 + /12 * /13 * /14 * 15 * 16 + /12 * /13 * /15 * 16 * /17 Serial Clear Serial Clear Serial Transfer Serial Transfer H2* /R22 = /12 * /14 * /16 * /17 + /12 * 13 * /15 * /17 + /12 * 13 * /16 * /17 + /12 * 13 * /14 * /15 * /16 + 12 * 13 * 15 * 16 * /17 + /12 * /13 * /14 * /15 * 16 + /12 * /13 * 14 * 15 * /16 Serial Transfer Parallel Clear Parallel Clear Serial Clear Serial Clear Serial Transfer Serial Transfer orders of magnitude, from V23* /R21 = /12 * 13 * /14 * /16 * /17 + /12 * 13 * /15 * /16 * /17 Parallel Transfer Parallel Transfer an initial RMS level of V22* /R20 = 13 * 15 * /16 * /17 + 13 * /14 * /15 * 16 * /17 + 12 * 13 * 14 * /16 * /17 Parallel Transfer Parallel Transfer Always Low V21* R19 = 13 * 15 * /16 * /17 + /12 * 13 * 14 * /16 * /17 Parallel Transfer Parallel Transfer V13* /R18 = /12 * 13 * /14 * /16 * /17 + /12 * 13 * /15 * /16 * /17 Parallel Transfer Parallel Transfer V12* /R17 = 13 * 15 * /16 * /17 + 13 * /14 * /15 * 16 * /17 + 12 * 13 * 14 * /16 * /17 Parallel Transfer Parallel Transfer Always Low V11* R16 = 13 * 15 * /16 * /17 + /12 * 13 * 14 * /16 * /17 Parallel Transfer Parallel Transfer H1* R15 = /12 * /13 * /15 * 16 * /17 + /12 * /13 * 14 * 15 * /16 + /12 * 13 * /15 * /16 * 17 + 12 * 13 * 14 Serial Transfer Serial Transfer Serial Clear Serial Clear RGB* /R 14 = /12 * /13 * 14 * 15 * /16 + 12 * 13 * /14 Serial Transfer Serial Clear been considerably more problematic. In addition, the readout noise in SITe was images CCD improved by almost two ~550 ADU down to just 7 ADU. This value was still one order of magnitude greater than the noise level intrinsic to the CCD itself. 6.7.1 The Timing Board A complex sequence of voltage pulses was required to transfer Table 6-5: Logic programmed into the DC1 PAL chip for generating vertical and horizontal pulse sequences and the reset gate. Logic is Boolean: "f' = NOT; "*" = AND; "+" = OR. Output signals identified by an asterisk were inverted one more time before reaching the CCD. charge through the SITe CCD, amplify and correct the signal with correlated double sampling, and carry out the A➔D conversion. The timing circuit board of the camera head received six master timing signals (identified here as C/2 through C/7) from the interface card in the computer. Chapter Six: The UGED Imaging System These signals ran the CCD clearing sequence, parallel transfer, and initiated serial transfer and 333 Output PAL Logic Sequence RST /R22 = /18 + /19 + /12 * /13 * 15 * 17 + /12 * /13 * 16 * 17 Always Low Always Low Always Low CRS/ FIN R21 = 12 * /13 * /14 * 15 * /16 * 17 + /12 * /13 * 14 * /15 * /16 * 17 Serial Transfer Serial Transfer INT RESET R20 = 12 * /13 + 17 * /13 + /12 * /13 * 14 * /15 * /16 */17 Serial Transfer Serial Transfer Serial Transfer clocking. INT- /R19 = 12 * /13 * 14 * /16 * /17 + 12 * /13 * 15 * /16 * /17 Serial Transfer Serial Transfer Computer clocks vary INT+ /R18 = /12 * /13 * 14 * /15 * /16 * 17 + /13 * 15 * /16 * 17 Serial Transfer Serial Transfer in speed and are not HOLD /R17 = /12 * /13 * /14 * 15 * /16 * 17 + /12 * /13 * 14 * /15 * /16 * /17 Serial Transfer Serial Transfer /R16 = 12 * /13 * /16 * /17 + 12 * /13 * /14 * /15 * /16 + /12 * /13 * 14 * 15 * 16 + /12 * /13 * 15 * 16 * /17 + 13 * 15 * /16 * 17 + 12 * 13 * /14 Serial Transfer Serial Transfer Serial Transfer Serial Transfer Serial Clear Serial Clear readout stable enough for SGB* correlated double sampling corrections, (Summing Well) so the actual pulses AMP OFF* /R 15 = 12 * 13 * /15 * /17 + 12 * 13 * /16 * /17 Always Low Always Low sent to the CCD and MPP /R14 = /12 * /13 * 14 * /15 * /16 * /17 Always Low conversion board were generated within the Table 6-6: Logic programmed into the DC2 PAL chip for generating horizontal and correlated double sampling pulse sequences. Logic is Boolean: "f' = NOT; "*" = AND; "+" = OR. Output signals identified by an asterisk were inverted one more time before reaching their destination. camera head, synchronized together by an 8-MHz clock stepped down to 2 MHz through a flipflop chip. Pulse sequences were generated with programmable logic chips (often called PALs) of type GAL22V10B-25 (Lattice) or equivalent. These 24-pin CMOS chips have twelve inputs, including the clock, and up to ten outputs. The output signals are formed by mixing the input signals using AND, OR, and NOT functions of Boolean logic. The camera head originally had five PAL chips located on the timing board, SN 1, SN2, DCl, DC2, and DC3. (The interface card also had a PAL.) SNl and SN2 received Chapter Six: The UGED Imaging System 334 the master timing signals from the interface card and generated an intermediate set of timing signals synchronized with the 2-MHz clock. These two PALs were registered, meaning that the output depended on both the input signals and the output signals from the previous clock cycle. SNl and SN2 were not modified in the UGED laboratory. Their output, identified here as /2 through 17, went to the inputs of P ALs DC 1, DC2, and DC3. These PALs created the parallel and serial transfer pulses and other clocking sequences, and were not registered. DC3 was actually removed from the camera head because its output was not used. DCl and DC2 were reprogrammed to fix problems and meet the needs of the SITe CCD, and the final logic sequences are shown in Table 6-5 and Table 6-6. The PALs were altered in Caltech's Electrical Engineering Department using the software PALASM and BP. The overall timing sequence within the camera head is discussed in 6.7.1.1. The CCD clearing and image readout sequences are shown in more detail in 6.7.1.2 and 6.7.1.3, respectively. 6.7.1.1 Overview of the Timing Sequence The PAL SNl used just C/2, C/4, C/5, and C/6 of the six master timing signals sent by the interface card, and SN2 used those four and C/3 as well. C/7 fed into the 8~2 MHz flip-flop circuitry. The outputs /2 through 17 (the inputs for DCl and DC2) came from both chips: SN2 generated the serial readout sequences and SN 1 handled everything else. Figure 6-25 divides the general timing sequence for recording a CCD image into eight regions. When an exposure was initiated with SpectraSource's HPC-1 program, parallel transfer occurred repeatedly for 95.4 ms CD, which was followed by 68.4 Chapter Six: The UGED Imaging System I Clearing Sequence ~ 95.4ms : sa.4ms ~10.7+ms 1 10 • , i I 1 Parallel I i (D • {) I Serial I @ 335 Readout Sequence I 1 1 4aµs ~27.Gms i ms m i i !]Parallel l PreRegular I I Row 1 I Pixels Pixels i @) ; ([) ~ JI I I I I I I I I I I I I I I.______________I ~ _ J :~ I @ I 1 c_ I I ti I B (j) I 0.9 I I ms 1 i I ; ! 1 ® 1 I I I I I I I I I I I I I I LJ__ rul----------..1 : I i i I c~~JIIIIIII I I IIIIIIIIIIIIIIIIILJU74-i ~--4-------j n: 1 c _~ § ,- - - ~ - - - ~ - -: ' J11111111i11111111111111111 '--=1-------,,---......,,....-----, Cl_~Jlllllllllllllllllllllllllllll~..___.__,J I: 6 CI _ _ _ _ : -----J~l l l l l l l l l l li I l-- C/7 111111111111111111111111111111 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111r Figure 6-25: Overall timing of CCD image exposure sequence for the master signals sent by the computer interface board to the camera head. The readout sequence ~ through ® was repeated for each row in the active area. ms of inactivity (2). Next, the horizontal registers were flushed during a serial clear sequence for a length of time equal to 10.7 ms plus the exposure time G)_ 10-ms of inactivity ® followed the integration of the CCD image, and if a subframe was requested in HPC-1, then the image was transferred down a number of rows equal to the y-offset of the subframe coordinates. The serial registers were not recleared after this, so the first few rows of a subframe were often saturated with leftover charge. The image was then transferred down by one row G:l and serial readout commenced. The first eight values were treated as "pre-pixels" and ignored by the Chapter Six: The UGED Imaging System 1 . 1 Clearing Sequence f • 68.4 ms • I 1 Parallel I i (D I 12 __ : I : I O Readout Sequence i § I 95.4 ms 1 i 336 . I I 10 I I , 10.7+ ms , 48 µs , ~27.6 ms , , ms 1 • I . I 1Parallel l Prel Regular l Serial i l Row 1 I Pixels I Pixels I ® 1 @) 1 ~1111111111111111111111111111 I I l , I ,. I I I I I I i I i I I '- ij '~ !- - - : ~ / ~ "' _~1111111111111111111111111111 11111111111111111111111111111 / _JIIIIIIIIIIIIIIIIIIIIIIIIII ~ 111111111111111111111111111111 I~_ ~1111111111111111111111111111 1111111111111111111111111111 1 ~ _ : lfillJ : i 1 © 1 l11111111111111111111111l1111111111111111111111111111lJ __ I •• -If ~ l (!) ([) J3 i,} @ I O9 I • 1 ms i I I ! I ,~1111111111111111111111~1111111111111111111111111111~-- n JIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIILi __ ~111111111111111111111~1111111111111111111111111111LJ __ : : 11111111111111111111111111111 : lllllllllllllllllllllllllllllllllllllllllllllllllllllLL I i l n ! l l I I Figure 6-26: Overall timing of CCD image exposure sequence for the intermediate signals generated by the PALs SN1 and SN2 within the camera head. software ®. The SITe CCD actually had fifteen pre-pixels, so seven columns of dark reference appeared on the left side of those images, but the TI CCD had only six prepixels, and the first two columns from the active area were lost. If a subframe exposure was requested, the pre-pixel sequence continued for a number of pixels equal to the xoffset of the subframe coordinates. Once the pre-pixel sequence was complete, regular pixel readout took place with about 27 µs required per pixel, giving a readout rate of 37 kHz 0. The program always read 1,024 pixels, regardless of the image size specified by the user, so the readout time Chapter Six: The UGED Imaging System for a CCD with 512 rows was ~ 14 s. 337 Row 1 Row 2 I 48µs ~ This unchangeable "feature" within the SpectraSource software was unfortunate; the seven seconds of unnecessary readout I I time ~-I~ corresponded to a loss of 45 ! C/6 1 minutes or more of exposure time during a typical UGED experiment. An 0.9 ms period of inactivity ® 12 -~------~------- u-- lJ followed readout of the serial registers, and then (3), (6), (J), and ----~ ® repeated for as many rows as /5 1 specified by the user. I6 Figure 6-26 shows the same ~~--~ /7 -=----------,-----------:c overall timing sequence for the I intermediate signals /2 through 17. I During inactive periods where all of V"f2* these signals were low (~, ®, and ®), the parallel gates V11 and V21 and serial gate H2 were on the high voltage rail (collecting charge) and the other gates were on the low Figure 6-27: Master, intermediate, and vertical gate timing pulses during the parallel clear sequence CD. The pulses were the same for the transfer of a single row during image readout @ . The second set of vertical gates ( V21 *, V22*, V23j were the same as the first set. Chapter Six: The UGED Imaging System 338 rail. During parallel clear and transfer sequences (CD and ~), serial gates HJ and H2 were both high and HJ was low. Note from Figure 6-20 and Table 6-4 that charge in the SITe CCD transferred from the active region to H2. 6.7.1.2 The Clearing Sequence Before collecting signal for the length of the exposure time, the CCD had to be cleared of all dark 10.7 ms+ Exposure Time 1 current and other charge accrued since the last i exposure. Ideally the CCD would be cleared by simultaneously conducting both vertical and horizontal transfers so that the active region and the serial registers were both completely flushed . In the SpectraSource camera head, however, 2,000-rows (IL! L __ I (UJ • 1--- CI4 CIS I _ ________ CI6 __,__ CI7 worth of active area were cycled into the serial registers first while the serial registers remained static, and then after 68.4 ms of inactivity, the serial registers were flushed (Figure 6-25). Figure 6-28: Master timing pulses during the serial clear sequence ai. The serial registers were cleared continuously during the exposure of the active area. Not only does dark current accumulate in the active region during this time, but the potential wells of the serial registers can be overwhelmed during the parallel clearing sequence and charge can spread back up into the first few rows of the active area. These rows are then useless for that particular exposure. Figure 6-27 shows the master, intermediate, and vertical gate timing pulses during the parallel clearing sequence, and Figure 6-28 shows the master timing pulses during the Chapter Six: The UGED Imaging System serial clearing sequence. During serial clear, charge was eliminated 339 1 Pixel 1 I 1 Pixel 2 k-3µs~ by I I transferring it to the floating diffusion capacitor and activating the reset gate. Figure 6-29 presents the intermediate timing pulses and also HI*, H2*, H3*, SGB* • (summing well), and RGB* (reset gate) during this time. (The asterisks indicate that these are the actual CMOS outputs from DCI and DC2, but that the signals will be inverted on the voltage amplifier ,,<c»o/;;,. i 17 I ,,.J:•. w "'''~,<,ii I ~,J--- i--J ; j{JTL__j ,- :- l:j. n a H2* I i I L __ H3* SGB7l_j '>; ·, ,I r--:--. •1 .J ,-- circuit board before reaching the CCD.) In SpectraSource's original design, the summing well and reset Figure 6-29: Intermediate timing pulses and serial, summing well, and reset gate pulses during the serial clear sequence Ql. gate remained static on the low rail, and all the serial clearing sequence did was accumulate charge on the serial registers. As a result, the first few rows of every image were always saturated. 6.7.1.3 The Readout Sequence During the readout sequence, the active imaging area was cycled down one row, moving the last row into the serial registers G>. The serial registers were then cycled through the on-chip preamplification stage and into the camera head CB, CV. The timing Chapter Six: The UGED Imaging System 340 pulses during parallel transfer were identical to a single 48-µs segment of the parallel clear sequence (Figure 6-27). Serial readout was initiated by C/6 rising high, and the eight prepixels were demarcated by C/6 temporarily sinking low for a few microseconds (Figure 630, left). C/6 remained high during regular pixel readout and serial transfer of the next pixel was initiated by C/2 falling low (Figure 6-30, right). The camera head carried out two actions simultaneously. While the charge from one pixel was transferred to the floating diffusion capacitor and its output voltage was analyzed by correlated double sampling (CDS), the voltage from the previous pixel was converted to binary by the A➔D chip and received by the interface card on the computer. Figure 6-31 shows the intermediate timing sequence during serial readout, with C/2 also shown as a reference. The arrival time and width of the C/2 pulse sometimes fluctuated by a few microseconds but this did not affect the image quality. Most output pulses Pre-Pixel Readout I 1 Pre-Pixel 2 1 I I i I I I Pre-Pixel 1 '~~19 µs ~ C/2 CI3 C/4 CIS Regular Pixel Readout I 1 i Pixel 1 l i~_ _ _ µs - - ~ l I Pixel 2 27 ~ I 11 - - - - - ~ n i - - - 1 • I I I i - - - - - - - - - - - - - -- ' --i-- l'' ----------1 I i - ' - - - - - - - - - - - - - -! I ! I !_ _ _ _ _ _ _ _ _ _ __ i I I I - ~ - - - - - - - - - - - - - - - - - .. - , - - - - - - - - - - - - - ; ; - - - - - C/6 __ _j C/7 Figure 6-30: Master timing pulses during the pre-pixel and regular pixel readout sequences@, 0. Chapter Six: The UGED Imaging System 341 ... 27 µs 10 µs 13 i iz.7 ,- - - - - - - ~I, R RGB~ · I HJ_*~ I - - - - - - - - . , , . . . - - - - - - - - - - - - - - - - - - - - - - ,1 H~~*D _ j , , ·«((:fh , .. ~ u . , .r~L SGJJ,, *, Figure 6-31: Intermediate timing pulses during the readout sequence of a single pixel 0. The new pixel starts with the falling edge of C/2. Most pulse mixing occurs within the first ten microseconds. The reset gate, serial gate, and summing well pulses are also shown. occurred within the first 10 µs of the sequence, where the intermediate timing was active; the remaining 17 µs provided time for the integrated output from within the CDS circuit to equilibrate. Figure 6-31 shows the serial transfer pulses, the reset gate, and the summing well pulse sequence which started 0.5 µs after C/2 fell low. The summing well remained high Chapter Six: The UGED Imaging System 342 ~ - - - - - - - - - -27 µs 10 µS lr{TI.___ _ _ _ _ _ _ _ _ _ _ ____.I >,. I i L_ i R Gf t ~ :h.;D,, Ll I VS/Te 1 or VT/ 1r Transfer of qharge To Floating Diffusion Capacitor '----- )? : -· I u Reference Signal 1 Integr-a~t~o-r---,L__J~---,u ·- ~-;m - - - - - - - - - - - - - - - -Input1 • I I I I Integrator 0 utp mt • ! I I r -r - - - - - - - - - - - - - -, Figure 6-32: Correlated double sampling pulse sequence during regular pixel readout. The amplified CCD output spiked during the reset gate and dropped to a reference level. Pixel charge was transferred to the floating diffusion capacitor a short time later. for an extended period of time so that camera head could sample the reference output voltage level after the reset gate. Figure 6-32 shows the correlated double sampling pulse sequence during the same interval. After zeroing the integrator output with the INT RESET signal, the reference Chapter Six: The UGED Imaging System 343 10 µs - - - - ~ ------- J_ Current Pixel Next Pixel VREF Final Gain Output i ! ~ Delayed - n __ ! HOLD TRK2 SCLK SDATA . ~'-----'----- i 1100100010101110 =51374ADU Figure 6-33: A➔ D conversion pulse sequence during pixel readout. The CRSIFIN pulse created by the timing board was delayed several microseconds with a small extra circuit so that the pulse started after TRK2 fell (for the previous pixel). TRK2, SCLK, and SDATA were all outputs from the A➔ D chip. voltage level was sampled and inverted by INT- falling low. The output from the integrator responded by changing in voltage. After the summing well dropped and charge was transferred to the floating diffusion capacitor, the output voltage was sampled again (this time noninverted) during INT+, and the integrator output changed a second time, reaching its final value. Finally, Figure 6-33 shows the A➔D conversion pulse sequence which follows CDS. As the integrator output equilibrated, a delayed CRS/FIN pulse (see 6.7.3) went Chapter Six: The UGED Imaging System 344 high for several microseconds and allowed the A➔D chip to make a coarse estimate of the conversion. The fine estimate was made when the CRS/FIN pulse fell low, and the final value was locked in by the falling edge of the HOLD pulse. Once locked in, the A➔D chip ignored further input and the integrator could be zeroed again. The A➔D chip set its TRK2 output signal high while conversion took place, and also transmitted a bit-clocking sequence (SCLK) and the binary form of the data (SDATA). SDATA was sent to the computer beginning with the most significant bit and ending with the least significant bit. As this took place, the next pixel in the serial registers underwent correlated double sampling and the integrator began equilibration again. 6. 7.2 The Voltage Generation Board The +27, +15, and -15 Vdc lines from the +15 V In LM31 7 _ou_t_o__.1:~µF external power supply provided input biases to Adj R6 243 n several voltage regulator and divider circuits within - the camera head. The original SpectraSource board created a total of eight voltages: the parallel register rails ( + WER, -WER), the serial register rails - 1.3 kn +VHOR Figure 6-34: Voltage regulation circuit within the camera head for generating the upper rail +VHOR of the serial gate pulses. ( + VHOR, -VHOR), the upper reset gate rail (VRG), the reset drain (VRD), the output amplifier drain (VDD), and the last gate rail (VOTG). Only VOTG was created with a simple voltage divider; the other seven were formed with voltage regulator circuits based on LM317 or LM337 chips. The source for + VHOR is shown in Figure 6-34 as an example. The SITe CCD needed an additional voltage level, the high rail of the transfer gate + TG, so an extra board with two voltage regulator Chapter Six: The UGED Imaging System 345 circuits was added to the camera head (in early spec sheets, the low rail of the SITe transfer gate was different from -WER and a second source was needed). Table 6-7 summarizes the camera head's voltage rails, their values, and the identity of the resistors which determined the output level. Rail Resistor Voltage R6 R24 R10 R19 R26 R14 R3 VR1 +VHOR -VHOR +VVER -VVER +VRD +VDD +VRG +VOTG +TG -TG +8 -4 +3 -9 +16 +25 +12 -2 +7 -5 Table 6-7: The voltage generation board also created the output gate signals for the CCDs by projecting the List of voltage rails, levels, and adjustment resistor on the voltage generation board of the SpectraSource camera head. CMOS timing signals between a pair of the voltage rails. An example of the circuit is shown in Figure 6-35. The DS0026 chip (National) put the negative amplification input onto the high CMOS rail and the positive amplification input onto the low CMOS rail, effectively inverting the original signal. The switching time I From ~ Timing ! Board Voltage Generation Board +VHOR ! ffl H1* I I H2* D50026 - ~ ~ I ; Iii! To CCD Ii MMPQ2907 ""' ti I I i I -{>-{>- I I 47 n I ~ 47 n I H1 H2 I - ~ -VHOR m Figure 6-35: Circuit on the voltage generation board of the SpectraSource camera head which converted CMOS signals (sent by PALs on the timing board) into pulses between high and low voltage rails, in this case +VHOR and -VHOR. The signals were inverted by the D80026 chip. Chapter Six: The UGED Imaging System 346 between the new amplified rails was ~ 100 ns. A similar circuit was also added on to the extra voltage regulator board to create the transfer gate pulses. Note that SpectraSource did not use the DS0026 according to the manufacturer's recommendations: the input timing signals should have been AC-coupled if both positive and negative amplification rails were used. This was not fixed, however. 6.7.3 The A➔D Conversion Board The third original circuit board within the SpectraSource camera head carried out correlated double sampling (CDS) on the preamplified CCD output signal and then converted the analog voltage to a 16-bit binary pulse sequence. Correlated double sampling is an electronic method of reducing readout noise caused by fluctuations in the offset voltage of the floating diffusion capacitor following the actions of the reset gate. If these fluctuations are assumed to be constant for an individual pixel cycle, then the reset noise (or kTC noise [HoG96]) can be eliminated by sampling the CCD output signal before and after the transfer of charge, and then taking the difference. Figure 6-36 and Figure 6-37 show the CDS circuit within the camera head. Signal from the off-chip preamplification circuit (either VS/Te or VT!) was split into two unitgain followers, one inverting and one noninverting (Figure 6-36). Their outputs passed through switches triggered by the INT- and INT+ CMOS signals before recombining and entering an integrator. As shown in Figure 6-32, INT- was active after the reset gate cleared the floating diffusion capacitor, and INT+ was active after the summing well transferred charge to the capacitor. Thus, the integrator input consisted of two rectangular pulses obtained by sampling the AC-coupled, preamplified CCD output Chapter Six: The UGED Imaging System i:;,s I g - - --- -- rm n:w !&':m Inverting FQIIQwer I I R29 WI I External Toggle Switch ~ ~ 'Tl ~ ~100 cm Cable R39 I Iii41 n U134 1.0 kn m m :@ill tf;.'l Wi.l! {&_'1\1 Non inverting Follower I I To Integrator I U15-3 I I I I m I ~ mm [J I INT+ I I VT/ I ------ -- 1.0 kn a soon 0 'O INT- I ~25 cm Cable I I I I VS/Te 347 ---- - - 1.0 kn il,llil I'${ li!lll lmf.l &r&I I dB Figure 6-36: First half of the correlated-double sampling circuit. Amplified output from the CCD was sampled for 1.5 µs first with an inverting follower and then with a noninverting follower circuit. relative to ground at two different times. The total area under these pulses was proportional to the amount of charge in the pixel. This area was converted to a voltage with the integrator, and passed through a final noninverting gain circuit before reaching the input of the A➔D chip (Figure 6-37). In addition to reset noise, CDS also corrected for fluctuations in the baseline of the AC-coupled output signal. The noise contribution from correlated double sampling is most sensitive to the timing and width of the INT- and INT+ pulses, which is why carefully synchronized signals were generated within the camera head instead of being sent from the computer. After the final gain stage, the pixel signal entered the second input of a twochannel, 16-bit A➔D conversion chip (Crystal Semiconductor; CS5101A-JP8). A detailed description of this chip's operation can be found in [CrS92]; only eight of the Chapter Six: The UGED Imaging System 348 Ol:l-mi!.1!!!!111:llt!-ll!!ll!Zlb Integrator C33 4.72 nF From Followers I I I R47 U154 200n /NTEGRA TION RESET Final Gain ffi I I I !'a 1: 1 I I I ll R69 R67 i I i To A D Converter: I I Ill VA1N2 Figure 6-37: Second half of the correlated-double sampling circuit. Output from the followers was integrated to correct for baseline fluctuations. The integrated output was amplified a second time and then registered at the A~D converter input. twenty-eight pins will be discussed here: four inputs (AIN2, HOLD, CRS/FIN, and VREF) and four outputs (TRKJ, TRK2, SCLK, and SDATA). The tracking channel outputs TRKJ and TRK2 were high whenever a conversion was in progress or when the other channel was engaged (so TRKJ was always high). Once a conversion was complete and the chip was ready for the next pixel signal, TRK2 fell low and the internal buffering circuits began following the voltage level present at the input AIN2. When the CRS/FIN input was high, the input voltage was followed quickly by a coarse adjustment method. The A➔D chip began fine adjustments once CRS/FIN fell low. The falling edge of the HOLD input pulse froze the voltage level at the AIN2 input and initiated an A➔D conversion, and TRK2 responded by going high (Figure 6-33). A stable and consistent 4.5 V reference signal was required at the VREF input to establish the upper limit of the A➔D conversion range (i.e., 0 V = 0 ADU, 4.500 V = Chapter Six: The UGED Imaging System 349 +15 V .i,. '-I :><" ::, VAIN2 ~ +15 V 01 ~ LM 385 1.2 V 0 ::, .i,. '-I :><" ::, ~ VREF 22n ~p -15 V ~ ~ 0 @ ~0 A .i,. -..J :><" ::, ij 10~ 0.1 µF R73 ~ 1.1 kn 0.01 µF A R61 3.9 kn Figure 6-38: SpectraSource's original voltage reference circuit for the A➔ D conversion. 65,535 ADU). The original VREF generation circuit in the SpectraSource camera head (Figure 6-38) was poorly designed on at least two counts: (1) VREF was 5.2 V, outside of the range set by Crystal Semiconductor's specification sheet, and (2) VREF was created by amplification of a 1.2 V reference source, which also amplified the noise level by more than a factor of four. This circuit was replaced according to Crystal's recommendations using a 4.5 V reference chip from Linear Technologies (Figure 6-39). The CRS/FIN pulse was also the source of problems. Originally, the pulse started when TRK2 was still high from the previous pixel, and as a result the last few output bits in SDATA were corrupted. In addition, the integrator output was not equilibrated by the time that CRS/FIN pulse fell low, into fine adjustment mode. Unfortunately, the pulse could not be shifted out of the TRK2 window simply by reprogramming the DC2 PAL logic, so a small board was added containing a monostable multivibrator circuit similar to the pulse generators found in the image intensifier (6.5.2). The CRS/FIN timing signal from DC2 was redirected to this circuit and triggered a new, delayed pulse which then went to the CRS/FIN input of the A➔D chip. Chapter Six: The UGED Imaging System 350 +15 V I\) +15 V b 7'" ::, R63 VREF LT1019 CN8-4.5 4.5 VREF 22n ~p ~ -15 V ~ 0 A .i,. -.J 7'" ::, :0 ~ 10~ 0.1 µF A O.Q1 µF A R61 1.0 kn Figure 6-39: The modified voltage reference circuit for the A➔ D conversion. After the HOLD pulse fell low and TRK2 went high, the A➔D chip sent out the binary form of the input signal through SDATA as a stream of bits, starting with the most significant (Figure 6-33). The SCLK output cycled simultaneously, with SCLK falling low each time a new bit emerged from the chip, so that the interface card would know when to latch on to each bit. TRK2 went low again after the least significant bit emerged, and the A➔D chip was ready to convert signal from the next pixel. If the A➔D chip was removed from its socket (or the entire board was removed from the camera head), the HPC-1 software would lock up during an exposure because the TRKJ and TRK2 signals were not at the correct voltages. To test the operation of the camera head without the A➔D chip present, a software crash could be circumvented by temporarily wiring the TRKJ output high and the TRK2 output low (ground). 6.7 .4 The Optical Isolator Board Computers are the source of a great deal of electronic noise, some of which can creep into the analog camera head signals along ground lines and the input and output Chapter Six: The UGED Imaging System Bl Computer 1 Interface 1 Cable 0 utput Signals 74ALS642 I i I ::) ~ HCPL-2430 fl I ~ (X) I\) -=-c --{>- I I -<]- R 0, ~ 74HC04 ti To Timing Board m +SH .. I I I +Sc Q I i'I I I I Optical Isolator Board I Input Signals 351 I To SN1 and SN2 PALs From 74ALS05 Chip 0 ::) -=-c -::-H +SH ~ I Figure 6-40: The optical isolator circuit added to the SpectraSource camera head to reduce the effect of computer noise on the analog CCD output signals. C: Computer; H: Camera Head. connections. To remove this contribution to readout noise, a circuit board containing ten optocouplers (Hewlett-Packard; HCPL-2430) was constructed as an interface between the camera head and the cable from the computer. This cable had six input signals (CI2 through C/7) and four output signals (TRKI, TRK2, SCLK, and SDATA), and was rewired to include a +5 V line from the computer. The optical isolation circuits for input and output signals are shown in Figure 6-40. Since the optocouplers passed their signals as photons, a direct electronic connection between the computer and the camera head no longer existed. The two were still linked indirectly, however, through the camera head power supply, although an optocoupler circuit could eventually be added to the power supply / computer cable connection too. Chapter Six: The UGED Imaging System 352 Vertical Gate Pulse IA G SRG Transfer Gate Pulse Readout Pixel 1 Readout Pixel 2 Figure 6-41: /AG and SRG pulses during readout sequence for TI TC211 CCD. The pulse widths are not to scale. 6.7.5 Generation of the TI CCD's SRG Signal An extra circuit board was added to the camera head to adapt its three-phase pulse sequences to the TI CCD's virtual phase readout requirements. The tirning sequence for the parallel and serial gates of the TI CCD is shown in Figure 6-41. IA G cycled up to the high 11::r.@ ~ W'zl il.\TI il.\TI 1lm1! £D ffi!1 !e lli\U! mm SRG Middle Rail Voltage i In -15 V LM 337 Out Adj 0.1~µF : 10 I voltage rail and back down to shift the active A I area by one row (Figure 6-23), and the SRG voltage had to cycle like a transfer gate pulse in order for the last row of charge to be accepted -VVER < > - . - - - , A 15 into the serial registers. clocked out through the on-chip amplifier by sending a series of three-level pulses in through SRG [Tex94]. These pulses began with a short 7 Out 6 4 C~4051 C Then the serial register pixels were 4H1 B A 13 O 1 2 V22* +5 V H3* S GB*.,__~ +VVER Figure 6-42: Circuit diagram for generating the TI CCD serial transfer voltage rail SRG. Chapter Six: The UGED Imaging System spike up to the high rail (equivalent to the reset gate), followed by a shift to a middle rail voltage, 353 Logic Inputs Output C B A Voltage (V22") (H3") (SGB") Rail 0 0 0 0 1 1 1 1 during which time the reference output level could be measured for correlated double sampling. Charge was transferred to the floating diffusion capacitor when the pulse voltage dropped down to the low rail, and the output 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 High High High High Middle High Middle Low Table 6-8: Logic table for creation of th e 11 CCD's SRG pulse. voltage level was sampled again. The JAG pulse was equivalent to V13 or V23, but generation of SRG required mixing several input pulses through an analog multiplexer (National; CD4051) to form a three-level signal. Figure 6-42 shows the circuit used to create SRG. An LM337 voltage regulator circuit with a variable resistor was the source for the middle voltage rail, and the high and low rails were + WER and -WER. These three voltages supplied the eight analog multiplexer inputs, and the output was determined by timing signals which entered the chip's three logic inputs. The transfer gate portion of the pulse was the same as V22*, and the middle rail region of the serial sequence had to be formed from the summing well pulse SGB * in order to keep the CDS timing correct. The reset gate pulse was formed from H3*. The logic table for making SRG with the multiplexer is shown in Table 6-8. Only eight input and output connections TICCD Winch. Bendix Signal Pin SRG +15 V -15 V Ground VT/ A B C D E F H J ABG ADB /AG Pin £ y s N M z b H Table 6-9: Winchester and Bendix plug pin assignments on the cable linking the camera head to the TI CCD. Chapter Six: The UGED Imaging System 354 between the camera head and the TI CCD were necessary, so the cable linking the two had the 26-pin female Bendix connector on one end and a simple 9-pin Winchester plug on the other end. The pin assignments for these connectors is shown in Table 6-9. 6. 7.6 Summary of Modifications Made to the SpectraSource Camera Head The following alterations were made to the SpectraSource camera head to correct major design flaws, and to adapt the camera head's operation to the requirements of the SITe and TI CCDs: 1. Carbon resistors were replaced with less-noisy metal film resistors; resistances on the voltage generation __board were adjusted to produce different voltage rails. 2. The original quad operational amplifier (U12) for the CDS follower circuits had a settling time longer than the INT+ and INT- pulse widths. A faster chip was installed (Analog Devices; OP-467). 3. The serial register clearing sequence was expanded to cycle the summing well and reset gate so that charge would actually be removed from the CCD. 4. The DC-coupled preamplification circuit was changed to AC-coupling and placed immediately adjacent to the CCDs, inside the vacuum chambers. 5. The duration of the INT RESET pulse was increased by 0.5 µs to give the integrator a longer time to reach zero. 6. The order of the INT+ and INT- pulses were swapped since the output signal was no longer inverted in the off-chip preamplification circuit. The sampling pulse (now INT+) was delayed an additional 2.5 µs to let all summing well charge transfer to the floating diffusion capacitor. Chapter Six: The UGED Imaging System 355 7. A small circuit was added to delay the start of the CRS/FIN pulse until after TRK2 had fallen and the integrator output began equilibrating. 8. The voltage reference circuit VREF for the A➔ D chip was replaced to meet the chip manufacturer's recommendations. 9. The pre-pixel timing pulses were changed to prevent image smearing during the readout of subframe exposures. 10. An optical isolator circuit was added to remove direct electrical connections between the camera head and the computer. 11. An extra circuit was added to generate the upper voltage rail for the SITe CCD's transfer gate. 12. An extra circuit was added to generate SRG for the Tl CCD. 13. Unused components such as the DC3 PAL and AMPOFF and MPP circuitry were removed . 14. A small fan was installed to stabilize the camera head temperature. 6.8 Thermoelectric Cooling Systems Charge-coupled devices must be cooled well below room temperature to reduce the level of dark current during exposures. In the first-generation UGED apparatus, the CCD was thermally-coupled to a liquid nitrogen dewar, and the operating temperature of the device was -120 °C. This method was not particularly stable, though: the temperature of the CCD could fluctuate over several degrees, the dewar had to be tended once every two or three hours, and it was impractical to keep the CCD cold for an extended period of time. Furthermore, the minimum recommended operating temperature for the SITe CCD Chapter Six: The UGED Imaging System 356 purchased for the second-generation apparatus was -50 °C because of the attached fiber optic window, and a better alternative to the LN2 dewar was sought. Thermoelectric devices cool according to the Peltier effect. A thermoelectric cooler (TEC) contains an array of small semiconductor blocks sandwiched between thin, ceramic plates. The blocks are linked in series, and their electrical connections are located alternately on the two sandwich faces. In addition, the blocks themselves alternate between p-type and n-type doping. When an electric current is applied through the series of blocks, the ceramic face joined to all p-n connections becomes colder because the electrons must absorb thermal energy to pass from the low potential p-junction to the high potential n-junction. This thermal energy is transferred to the other ceramic face at the next electrical connection, where the electrons pass from an n-junction back to a pjunction. The net effect is the creation of a temperature differential !it between the two ceramic faces. The magnitude of /it increases with the applied current up until resistive heating creates as much heat as the Peltier effect can remove. The temperature of the cold face depends on the temperature of the hot face: some method must exist for efficiently removing heat from the hot face of the TEC. Many different thermoelectric cooler configurations are available. Suitable units for the two UGED CCD detectors were chosen by estimating the heat load from the CCDs and other sources (radiative, convective, and conductive heating), and then using worksheets supplied by TEC manufacturers such as Melcer and Marlow Industries. As discussed in the next two sections, the design of the SITe and TI CCD cooling systems were markedly different. Chapter Six: The UGED Imaging System 357 I 2-Stage TEC WaterCooled Heat Sink \ I•••~ IIMlllllll!iiB I - ' I I I JI I \ ._; I I SI Te CCD • I I I i .I I I I :·---,Zip : Socket I t Hot Plate t Cold ·p 1ate :...._circuit ' Board Figure 6-43: The cooling unit for the SITe CCD. Heat from the CCD was transferred to a water-cooled heat sink through a two-stage thermoelectric cooler and copper blocks. 6.8.1 Cooling the SITe CCD In order to keep dark current noise negligible over exposure times of one minute or more, a thermoelectric cooling system was designed to maintain the SITe CCD at a temperature below -30 °C. The estimated total heat load of the SITe CCD and its associated hardware was 3 W, so given a 10% cooling efficiency and a desired 55 °C temperature differential, a two-stage TEC with a 30 W Qmax was purchased from Melcor (2CP 085-065-71-3 lL). The construction of the cooling system is shown in Figure 6-43. Heat was passed from the CCD to the water-cooled heat sink through a series of copper blocks and the TEC; all interfaces were liberally coated with heat sink compound and worked together to provide a good thermal connection. The CCD sat in a zero-force insertion socket, or Zip socket, which was soldered onto the off-chip preamplification Chapter Six: The UGED Imaging System 358 circuit board. The central portion of the Zip socket was milled out so that a copper block 20 0 10 ~ heat sink could be installed from the CCD side of the socket. These components were 0 Cl) 11., :::s -10 ca ~ -20 C. all mounted on the third support ring in the E -30 Cl) I- -40 detector chamber when the CCD was -50 -+--,---,-r,--,-+-r-,---,---,-,--+-,---,--=,-...,........! 0 coupled to the small fiber optic taper (6.2 and Figure 6-6). The thermoelectric cooler was 3 6 9 Current (A) Figure 6-44: Cold plate temperature as a function of current applied to the thermoelectric cooler for the SITe CCD. sandwiched between two pieces of copper, the cold plate and the hot plate (Figure 6-43). The plates were held together by two screws, and fiber insulator washers limited heat conduction between the two plates along these screws. The hot plate was silver-soldered onto a home-built heat sink which circulated 14-°C water. This heat sink was double-sealed; in the event of a hole in the solder, water would leak into the laboratory through an overflow tube in the back flange of the detector chamber, instead of into the detector chamber. The cold plate / TEC I hot plate / heat sink unit (Figure 6-7) was not connected to the SITe CCD heat sink until the detector chamber was sealed. The cold plate's stem went through the pre-amp circuit board, and the inset in the cold stem fit snugly around the back side of the copper CCD heat sink. The home-built power supply for the thermoelectric cooler was interlocked with the flow switch in the cooling water and shut down if flow stopped to prevent overheating the CCD. Chapter Six: The UGED Imaging System 359 Scintillator Cover I- C 0 ·- -3:: cu = ·- en 1-Stage TEC / - TI I I CCD I I I I I I I I CJ - ■- I., Cl) t .c + I I I I 11 Hot Plate i Cold Plate I I I I I I 3I I I I I I I ::~ Circuit Board Figure 6-45: The cooling unit for the TI CCD. Heat from the CCD was transferred to the scattering chamber wall through a single-stage thermoelectric cooler, copper blocks, and the scintillator gate cover. Figure 6-44 plots the temperature of the cold plate as a function of the current supplied to the TEC. A maximum of -50 °C was reached for 8.5 A of current, and the temperature of the CCD was typically 10 °C warmer. Further cooling could probably be achieved using a three-stage TEC instead of a two-stage TEC, but the dark current at -40 °C was low enough to allow exposures of five minutes or more. The temperature at the image-intensifier-side of the small fiber optic taper remained above 0 °C; specifications for the PFII recommend against cooling the intensifier below -20 °C. 6.8.2 Cooling the TI CCD Unlike the SITe CCD, which had its own separate vacuum chamber, the amount of space available to the TI CCD and its cooling system was limited. The entire unit had to be mounted on the aluminum scintillator gate cover so that it could be moved out of the Chapter Six: The UGED Imaging System 360 way for diffraction experiments, and the charge-coupled device had to be as far from -- 20 ( .) 0 the nozzle tip as possible. A water-cooled heat sink was not an option. Fortunately, the heat load of the TI CCD was much less, and Cl) I., 10 :::, 1a I., Cl) 0 a. E {!!_ -10 the cooling requirements were not as stringent. The single-electron gain under direct bombardment was very high, so exposure times were at most a few seconds 0 0.1 0.2 0.3 0.4 0.5 Current (A) Figure 6-46: Cold plate temperature as a function of current applied to the thermoelectric cooler for the TI CCD. and the acceptable level of dark current noise could be greater than with the SITe CCD. A single-stage thermoelectric cooler with Qmax equal to 3.6 W was purchased from Melcor (FC 0.45-66-05-2L), and the cooling system shown in Figure 6-45 was constructed. The TEC was sandwiched between copper hot and cold plates, as with the SITe CCD's TEC, but here the heat sink for the hot plate was the scintillator cover and the wall of the scattering chamber. Heat sink compound had to be applied carefully around the fiber optic window orifice to provide a good thermal connection. The TI CCD was soldered into the pre-amp circuit board, and the back of the CCD rested on the prong extending from the cold plate. Figure 6-46 shows that the TI CCD could be cooled to a continuously-operating temperature of -18 °C using a 480-mA current under this arrangement. Cooling the CCD down from room temperature took only a few minutes, but the scintillator cover had to be locked securely in place. The TEC power supply was turned off whenever the cover was opened up. Chapter Six: The UGED Imaging System 361 6.9 Characterization of the Detectors This section summarizes a series of characterization tests performed on the second-generation UGED imaging system. With SITe CCD images, 1 ADU is assumed to correspond to ~ 10 electron-hole pairs (EHP). This is based on comparing the expected single-pixel well depth in non-MPP readout mode (~500,000 EHP) with the estimated saturation limit in ADU. 6.9.1 Single-Electron Pulse-Height Distribution and Gain of the TI CCD To measure the single-electron PHD o( the TI TC211 charge-coupled device under direct bombardment, several images of a defocused 18-keV electron beam were exposed. A low flux was used to prevent multiple hits from occurring within one pixel. Examination of the images showed that the charge-collection efficiency was nearly unity (signal from each electron collected in one and only one pixel). The pulse-height distribution for each image was calculated with RADAR2 (D.3.2.10) and the cumulative results are shown in Figure 6-47. The single-hit region of the PHD was assigned to the range of 300 ADU to 1,700 ADU. The gain for a single electron was calculated as 980 ADU with a standard deviation of 360 ADU and a relative variance of 0.14. The lowlying plateau beyond 1,700 ADU in the PHD most likely corresponded to pixels which received two incident electrons. 6.9.2 Single-Electron Detective Quantum Efficiency of the TI CCD A range of possible values for the detective quantum efficiency of the TI CCD under direct bombardment was calculated from the measured pulse-height distribution. Chapter Six: The UGED Imaging System 362 - No Hits u, Cl) --18-keV Electron Hits 0 C Cl) X100 ➔ Iii- :, 0 0 0 0 :it: -500 0 500 1000 1500 2000 2500 3000 ADU Figure 6-47: Pulse-height distribution for direct bombardment of 18-keV electrons on the front-illuminated TI TC211 charge-coupled device. Two-electron events occurred beyond 1,700 ADU. An upper value for the DQE followed from the assumption that the pulse-height distribution represented all incident electrons, including those which had backscattered and transferred only a portion of their kinetic energy to the CCD. This implied that there were no incident electrons which went completely undetected. From Eq. 5.41, the DQE is: (6.2) where readout noise has been neglected since the single-electron gain 1s orders of magnitude greater. Using the relative variance calculated from the PHD in Figure 6-47, Eq. 6.2 predicted a DQE of 0.88. A lower value for the DQE estimate followed from the assumption that the PHD only represented the 18-keV-electron-to-EHP conversion process, and not backscattering effects. Then Eq. 6.2 should be rewritten according to Eq. 5.51: (6.3) Chapter Six: The UGED Imaging System 363 With g85 equal to 0.915 (5.4.1.1), the DQE was calculated to be 0.80. The true DQE was somewhere between these two limits, perhaps -0.85; after all, the tail to the left of the main peak in Figure 6-47 was indicative of some energy loss due to backscattering, if not necessarily all of it. This PHD measurement confirmed that direct bombardment of ke V electrons on a CCD is a near-ideal detection system in terms of information transfer. 6.9.3 Single-Electron PHD and Gain of the Scintillator Detector Much more painstaking analytical methods were required to determine the gain and pulse-height distribution of the scintillator imaging system. The detector's point spread function caused signal from one incident electron to be distributed over several SITe CCD pixels, and PFII spontaneous emission events were also present. Two sets of images were recorded, with and without the molecular beam sample flowing. When the sample was on, part of the electron beam was elastically scattered across the scintillator, - en Cl) Background Emission - - 18-keV Electron Signal 0 C: Cl) I.. I.. :::, 0 0 0 0 :ij: 0 1000 2000 3000 4000 5000 6000 7000 ADU Figure 6-48: Pulse-height distribution curves for 18-keV single electron events and spontaneous emission from the proximity-focused image intensifier. Chapter Six: The UGED Imaging System 364 o Background Emission en Cl) (.) • 18-keV Electron Signal C 0 Cl) :i.. :i.. • ::::, (.) (.) 0 0 - 0 0 • • ••••• ••• © 0 0 :ii: •• 0 .... 7..... • • • • • • • -- .... T 0 1000 2000 3000 4000 5000 6000 7000 ADU Figure 6-49: Pulse-height distribution curves for 18-keV single electron events and spontaneous emission from the proximity-focused image intensifier. allowing the detection of discrete, single-electron events. Without the sample, only spontaneous emission events occurred away from the electron beam stop. Exposures were kept short to prevent multiple events from overlapping. The PFII gate window was 210-µs wide and delayed by 6.2 µs, and the gain setting was at maximum (10 V on the controller unit display). The central region of each image was examined manually, identifying the number of pixels spanned by each event and the event's total signal in ADU. 361 events were observed in the background set of images, and 972 event were observed in the combined scattered electron / spontaneous emission images. Figure 6-48 shows the resulting pulseheight distributions for spontaneous emission and for 18-keV incident electrons. The electron PHD was obtained by subtracting the background PHD (only spontaneous emission) from the combined PHD after normalizing for relative exposure time. Figure 649 shows that both pulse height distributions had exponential decays characteristic of emission from a single microchannel plate. Chapter Six: The UGED Imaging System 365 The single-electron gain - u, was 1,600 ADU with a standard Background Emission Cl) (.) --18-keV Electron Signal C: ...... ::::, Cl) deviation of 1,200 ADU and a (.) (.) relative variance of 0.56. 0 0 Diffraction patterns were typically recorded with a PFII gain setting * 0 2 4 6 8 10 12 14 16 Number of Pixels of 8 V, so the single-electron signal under those conditions Figure 6-50: Average number of SITe CCD pixels activated by 18-keV single electron signals and by spontaneous emission from the image intensifier. would be 160 ADU (see Figure 610). On average, each event was distributed across four CCD pixels (Figure 6-50). This distribution included at least 90% of the total signal intensity. The spontaneous emission gain was 700 ADU with a standard deviation of 620 ADU. Spontaneous events tended to span fewer pixels, about three, which was not surprising since the point spread function from image intensifier to CCD had to be narrower than the PSF from scintillator to CCD. The rate of spontaneous emission Du was 12 events/ mm2 / s, negligible under standard UGED exposure conditions. The rate reported by Hamamatsu in the specification sheet for the image intensifier was 4.lxl0- 14 lumens per mm2 , or 37 events/ mm2 / s (Eq. 5.68). 6.9.4 Single-Electron Detective Quantum Efficiency of the Scintillator Detector A range for the single-electron DQE of the scintillator imaging system was calculated just like with the TI CCD. Using Eq. 6.2 and the results from the pulse-height distribution measurement, the upper value for the DQE was 0.64 regardless of whether the Chapter Six: The UGED Imaging System 366 single-electron gain was 160 or 1,600 ADU. (Since the readout noise level was~ 75 EHP, the theoretical results presented in Table 5-6 for a scintillator with image intensifier show that readout noise would not affect the DQE and could be neglected. Remember that 1 ADU :::: 10 EHP). To assess the lower limit for the DQE, it was assumed that the pulse-height distribution did not represent the fraction of incident electron signal lost either to backscattering or to fluorescence which escaped through the scintillator's aluminum overcoat. In that case, g85 was given by the bracketed portion of Eq. 5.52, and was about 0.8 (5.4.1.2). Using Eq. 6.3, the lower limit for the DQE was found to be 0.50. This DQE range of 0.50 to 0.64 was better than the DQE value predicted by theoretical estimates (5.5.4), and indicated that the image quality from the second-generation UGED imaging system rivaled that of photographic plates. 6.9.5 Readout Noise and Thermal Noise The level of readout noise in SITe CCD images was measured by taking low temperature dark image exposures (0-s exposure time). Dark current production was negligible in these images, and CJR was obtained by calculating the standard deviation of pixel intensities about the mean over several regions on the image using RADAR2 (D.3.6). Typical values were between 7 and 8 ADU, or~ 75 EHP. This was an order of magnitude greater than the CJR specified by SITe (Table 6-3) and most likely reflected noise contributions from off-chip amplification and the camera head circuitry. The rate of dark current accumulation D in the SITe CCD at -45 °C was measured by recording a series images with progressively longer exposures and no input signal (the Chapter Six: The UGED Imaging System image intensifier was oft). Figure 6-51 shows that the background offset value increased linearly as a - 1000 :::::, C ~ 100 C cu Q) :E function of exposure time, as expected, and D was equal to 367 - 10 "'C I Slope: 0.225 ADU/s I Q) () Q) 1 I., I., 0 (.) 0.225 ADU/ s / pixel, consistent 0.1 with data sheet [SIT95]. The statistical noise 10 100 1000 10000 Exposure Time (s) specifications contribution from dark current 1 Figure 6-51: Accumulation of dark current as a function of exposure time for the SITe CCD at -50 °c. Uncertainty in the corrected mean is 1 ADU. would match the readout noise level only after four to five minutes of exposure time, so the thermoelectric cooling system for the SITe CCD was deemed sufficient for the needs of UGED imaging. 6.9.6 The Point Spread Function The edge spread function e(x) of the without the coating was imaging P20 system scintillator measured by coupling a glass plate to the scattering chamber side of the scintillator fiber optic window. A portion of the glass plate was coated with a thin metal pattern, 235 245 255 265 275 Pixel Figure 6-52: Measured edge spread function of the optical imaging system without the P20 scintillator. The line connecting the points is the best fit to Eq. 6.?. Chapter Six: The UGED Imaging System 368 and the plate was rotated to align - - Line Spread Function the sharp edge of the pattern - - Point Spread Function parallel with a SITe CCD pixel row. An average edge profile from images of this pattern is -4 -3 -2 -1 0 1 2 3 4 shown in Figure 6-52. Of the four Pixels sets of spread functions listed in Figure 6-53: Point spread function and line spread function derived from the experimental edge spread function ( Figure 6-52). Table 5-1, the measured edge function fit well with the third formulation: e(x) fl(x)dx = nlk J[1 + (x/k)2r dx (6.4) (6.5) A four-parameter fit (A, C, x 0 , k) of Eq. 6.5 to the measured e(x) was carried out with commercial software and yielded a value of 0.73 pixels for k. The corresponding point spread and line spread functions are shown in Figure 6-53. The PSF had a FWHM of 1.12 pixels (86 µmat the scintillator window) and the LSF had a FWHM of 1.46 pixels (1.12 µmat the scintillator window). 6.9.7 The Modulation Transfer Function The modulation transfer function for the imaging system (without the P20 scintillator) was derived in two ways: (1) by calculating M(m) from the measured edge spread function, and (2) by measuring the changes in amplitude of well-defined spatial Chapter Six: The UGED Imaging System 1.0 - - From Edge Function - - o - - From Bar Target 0.8 - - Hamamatsu PFII 0 -- 369 0.6 8 :5 0.4 0.2 0.0 0 5 10 15 Ip/mm 20 25 30 Figure 6-54: Modulation transfer functions of the··optical imaging system at the SITe CCD and without the P20 scintillator. Curves were derived from the edge spread function and intensity measurements of the USAF 1951 Test Target. The MTF for the Hamamatsu image intensifier is also shown. frequencies using images of the USAF 1951 Test Target (see 5.3.9 for more details). The results from these two methods are compared in Figure 6-54 with Hamamatsu's reported MTF for the proximity-focused image intensifier. This figure shows the MTFs measured at the SITe CCD, with the image demagnified by the reducing tapers, and the Hamamatsu MTF has been rescaled accordingly. The expected M( ro) produced by the demagnified electron beam profile is plotted with the M(ro) from the measured edge spread function in Figure 6-55. Their product should be the total modulation transfer function for UGED diffraction patterns. To see how the amplitudes of interference signals from different internuclear separations are affected by the MTF, the value of r can be converted to a spatial frequency in line pairs per millimeter using: Chapter Six: The UGED Imaging System 1.0 370 ... .. 0.8 -:-: 0.6 8 0.4 - - - - • • Electron Beam MTF - - Measured MTF 0.2 - -Total UGED MTF 0.0 0 1 2 3 Ip/mm 4 5 6 Figure 6-55: Modulation transfer functions of the··optical imaging system at the SITe CCD. The Electron Beam curve corresponds to a gaussian profile with a FWHM of 300 µm at the scintillator. The Measured MTF is the edge function shown in Figure 6-55. The Total MTF is their product. co(lp/mm) = 2n) - r ( 3.2x- 2n L}.,e = 0.36r (6.) Most internuclear distances (r < 5 A) had frequencies less than 2 lp/mm on the SITe CCD. In some ways, the results presented in Figure 6-55 came as a surprise: the FWHM of the electron beam point spread function was 3.5 times larger than the FWHM of the detector's PSF measured with the edge pattern (3.9 vs. 1.1 pix), and yet the MTF curves clearly showed that the detector PSF had more impact in the spatial frequency regime relevant to UGED. This was because the gaussian PSF of the electron beam was highly localized, and had little effect on low-frequency signals. The shape of the detector PSF, however, did not drop to zero rapidly, and affected both high- and low-frequency signals. Note that the UGED diffraction data presented in this thesis were corrected for the electron beam's PSF, but not the detector's PSF. 371 References [Abr72] M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions, Dover Publications, Inc.: New York, 1972. [Ade92] G. A. Adegboyega, J. Phys. III ( Fra.) 2, 1749-1755 (1992). [Aes95a] M. Aeschlimann, E. Hull, J. Cao, C. A. Schmuttenmaer, L. G. Jahn, Y. Gao, H. E. ElsayedAli, D. A. Mantell, and M. R. Scheinfein, Rev. Sci. lnstrum. 66(2), 1000-1009 (1995). [Aes95b] M. Aeschlimann, E. Hull, C. A. Schmuttenmaer, J. Cao, Y. Gao, D. A. Mantell, and H. E. Elsayed-Ali, Proc. SPIE 2521, 103-112 (1995). [Alm61] A. Almenningen, 0. Bastiansen, and M. Tnetteberg, Acta Chem. Scand. 15, 1557-1562 (1961). [Alm59] A. Almenningen, 0 . Bastiansen, and M. Tnetteberg, Acta Chem. Scand. 13, 1699-1702 (1959). [AnA72] A. L. Andreassen and S. H . Bauer, J. Chem. Phys. 56(8), 3802-3811 (1972). [AnB69] B. Andersen, H. M. Seip, T. G. Strand, and R. St~levik, Acta Chem. Scand. 23(9), 3224-3234 (1969). [AnB66a] B. Andersen and P. Andersen, Acta Chem. Scand. 20(10), 2728-2736 (1966). [AnB66b] B. Andersen and P. Andersen, Trans. Am. Cryst. Assoc. 2, 193-196 (1966). [And93] T. Anderson, I. V. Tomov, and P. M. Rentzepis, J. Chem. Phys. 99(2), 869-875 (1993). [Ani77] S. I. Anisimov, V. A. Benderskii, and Gy. Farkas, Sov. Phys. Usp. 20(6), 467-488 (1977). [AnK71] K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns, 2nd. Ed., Plenum Press: New York, 1971. References 372 [AnP65] P. Andersen, Acta Chem. Scand. 19(3), 629-637 (1965). [Aru63] F. R. Arutyunian and V. A. Tumanian, Phys. Lett. 4(3), 176-178 (1963). [Arv79] M. M. Arvedson and D. A. Kohl, Chem. Phys. Lett. 64(1), 119-121 (1979). [AuA76] A. Authinarayanan and R. W. Dudding, Adv. Electr. Electr. Phys. 40A, 167-181 (1976). [Aut83] R. Autrata, P. Schauer, Jo. Kvapil, and J. Kvapil, Scan. Elec. Microsc., II, 489-500 (1983). [Aut78] R. Autrata, P. Schauer, Jo. Kvapil, and J. Kvapil, J. Phys. E 11, 707-708 (1978). [Bab92] A. V. Babushkin, G. I. Bryunkhnevitch, V. P. Degtyareva, S. A. Kaidalov, B. B. Moskalev, V. E. Postovalov, A. M. Prokhorov, E. I. Titkov, V. I. Fedotov, and M. Ya. Schelev, Proc. SPIE 1801, 218-225 (1992). [Bac77] G. E. Bacon, Neutron Scattering in Chemistry, Butterworths: Boston, 1977. [BaD91] D. Barlett, C. W. Snyder, B. G. Orr, and R. Clarke, Rev. Sci. Instrum. 62(5), 1263-1269 (1991). [Bak94] R. J. Baker and B. P. Johnson, Meas. Sci. Technol. 5, 408-411 (1994). [BaL80] S. L. Baughcum and S. R. Leone, J. Chem. Phys. 72(12), 6531-6545 (1980). [BaM95] M. Bass, E.W. Van Stryland, D.R. Williams, ..and W. L. Wolfe, (eds.), Handbook of Optics, 2nd. Ed., McGraw-Hill, Inc. : New York, 1995. [BaO60] 0. Bastiansen and M. Trretteberg, Acta Cryst. 13, 1108 (1960). [Bar90] L. S. Bartell and T. S. Dibble, J. Am. Chem. Soc. 112, 890-891 (1990). [Bar89] L. S. Bartell and R. J. French, Rev. Sci. Instrum. 60(7), 1223-1227 (1989). [Bar84a] L. S. Bartell and M.A. Kacner, J. Phys. Chem. 88(16), 3485-3489 (1984). [Bar84b] L. S. Bartell and M.A. Kacner, J. Chem. Phys. 81(1), 280-287 (1984). [Bar81a] L. S. Bartell, M.A. Kacner, and S. R. Goates, J. Chem. Phys. 75(6), 2730-2735 (1981). [Bar81b] L. S. Bartell, M.A. Kacner, and S. R. Goates, J. Chem. Phys. 75(6), 2736-2741 (1981). [Bar80] L. S. Bartell, S. R. Goates, and M. A. Kacner, Chem. Phys. Lett. 76(2), 245-248 (1980). [Bar78] L. S. Bartell and S. K. Doun, J. Mol. Struct. 43, 245-249 (1978). [Bar72] L. S. Bartell and T. C. Wong, J. Chem. Phys. 56(5), 2364-2367 (1972). [Bar68] L. S. Bartell, Phys. Lett. 27A(4), 236-237 (1968). [Bar65a] L. S. Bartell, D. A. Kohl, B. L. Carroll, and R. M. Gavin, J. Chem. Phys. 42(9), 3079-3084 (1965). [Bar65b] L. S. Bartell, H.B. Thompson, and R.R. Roskos, Phys. Rev. Lett. 14(21), 851-852 (1965). [Bar55a] L. S. Bartell, J. Chem. Phys. 23(7), 1219-1222 (1955). [Bar55b] L. S. Bartell, L. 0. Brockway, and R. H. Schwendeman, J. Chem. Phys. 23(10), 1854-1859 (1955). [BaS77] S. C. Barnes and K. E. Singer, J. Phys. E 10, 737-740 (1977). [Bas94] J. S. Baskin and A.H. Zewail, J. Phys. Chem. 98(13), 3337-3351 (1994). [Bas89] J. S. Baskin and A.H. Zewail, J. Phys. Chem. 93(15), 5701-5717 (1989). [Bas87] J. S. Baskin, P. M. Felker, and A.H. Zewail, J. Chem. Phys. 86(5), 2483-2499 (1987). References [Bas86] J. S. Baskin, P. M. Felker, and A.H. Zewail, J. Chem. Phys. 84(8), 4708-4710 (1986). [Bau50] S. H. Bauer, J. Chem. Phys. 18(1), 27-41 (1950). 373 [BaW81a] W. Baumann and L. Reimer, Scanning 4(3), 141-151 (1981). [BaW81b] W. Baumann, A. Niemietz, L. Reimer, and B. Volbert, J. Microsc. 122(2), 181-186 (1981). [Bea78] B. Beagley, A. Foord, and V. Ulbrecht, J. Phys. E 11, 357-360 (1978). [Bec75] J. H. Bechtel, W. L. Smith, and N. Bloembergen, Opt. Comm. 13(1), 56-59 (1975). [BeL88] L. Bergonzi, M. Lemonier, and M. Petit, Adv. Electr. Electr. Phys. 74, 165-172 (1988). [BeM96] M. Ben-Nun, T. J. Martfnez, P. M. Weber, and K. R. Wilson, Chem. Phys. Lett. 262, 405-414 (1996). [Ben84] 0. J. Benston, J. D. Ewbank, D. W. Paul, V. J. Klimkowski, and L. Schafer, Appl. Spec. 38(2), 204-208 (1984). [BeR89] R. B. Bernstein and A.H. Zewail, J. Chem. Phys. 90(2), 829-842 (1989). [Ber86] J.P. Bergsma, M. H. Coladonato, P. M. Edelsten, J. D. Kahn, K. R. Wilson, and D.R. Fredkin, J. Chem. Phys. 84(11), 6151-6159 (1986). [BeW88] W. Becker, J. K. Mciver, and R.R. Schlicher, Phys. Rev. A 38(9), 4891-4894 (1988). [Bey82] W. H. Beyer (ed.), CRC Standard Mathematical Tables, 26th Ed., CRC Press, Inc.: Boca Raton, 1982. [Bij69] J. M. Bijvoet, W. G. Burgers, and G. Hagg, Early Papers on Diffraction of X-Rays by Crystals, International Union of Crystallography: Utrecht, 1969. [Blo87] M. M. Blouke, B. Corrie, D. L. Heidtmann, F. H. Yang, M. Winzenread, M. L. Lust, H. H. Marsh, and J. R. Janesick, Opt. Eng. 26(9), 837-843 (1987). [Boh67] R. K. Bohn and S. H. Bauer, Inorg. Chem. 6(2), 304-309 (1967). [Bon74] R. A. Bonham and M. Fink, High Energy Electron Scattering, Van Nostrand Reinhold Co.: New York, 1974. [Bon69] R. A. Bonham, M. Fink, and D. A. Kohl, Chem. Phys. Lett. 4(6), 349-351 (1969). [Bon65a] R. A. Bonham and T. Iijima, J. Chem. Phys. 42, 2612-2614 (1965). [Bon65b] R. A. Bonham, J. Chem. Phys. 43(4), 1103-1109 (1965). [Bon65c] R. A. Bonham, J. Chem. Phys. 43(6), 1933-1940 (1965). [Bon63a] R. A. Bonham and J. L. Peacher, J. Chem. Phys. 38(10), 2319-2325 (1963). [Bon63b] R. A. Bonham and T. Iijima, J. Phys. Chem. 67(11), 2266-2272 (1963). [Bon62] R. A. Bonham, J. Chem. Phys. 36(12), 3260-3269 (1962). [Bon59] R. A. Bonham and L. S. Bartell, J. Chem. Phys. 31(3), 702-708 (1959). [Bor95] G.D. Boreman and S. Yang, Optics and Photonics News 6(2), Eng. and Lab. Notes (1995). [Bow89] R. M. Bowman, M. Dantus, and A.H. Zewail, Chem. Phys. Lett. 161(4,5), 297-302 (1989). [Bow95] N. Bowering, M. Volkmer, Ch. Meier, J. Lieschke, R. Dreier, J. Mol. Struct. 348, 49-52 (1995). [Bow94] N. Bowering, M. Volkmer, C. Meier, J. Lieschke, M. Fink, Z. Phys. D 30, 177-182 (1994). References 374 [Boy92] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 5th Ed., John Wiley and Sons: New York, 1992. [Bra75] D. J. Bradley and W. Sibbett, Appl. Phys. Lett. 27(7), 382-384 (1975). [Bra71] D. J. Bradley, B. Liddy, and W. E. Sleat, Opt. Comm. 2(8), 391-395 (1971). [Bre55] E. Breitenberger, Prag. Nucl. Phys. 4, 56-94 (1955). [Bri62] A. Bril in Luminescence of Organic and Inorganic Materials, H.P. Kallmann and G. M. Spruch (eds.), Wiley: New York, pp. 479-493, 1962. [BrL25] L. de Broglie, Ann. d. Phys. 3, 22+ (1925). [Bro36] L. 0. Brockway, Rev. Mod. Phys. 8(3), 231-266 (1936). [BrS64] L. S. Brown and T. W. B. Kibble, Phys. Rev. 133(3A), A705-A719 (1964). [Bru91] A. Brun, P. Georges, G. Le Saux, and F. Salin, J. Phys. D 24, 1225-1233 (1991). [BrW12] W. L. Bragg, Proc. Cambridge Phil. Soc. 17, 43-57 (1912). [Bry92] G. I. Bryukhnevich, S. A. Kaidalov, B. B. Moskalev, V. E. Postovalov, A. M. Prokhorov, A. V. Srnirnov, and M . Ya. Schelev, Proc. SPIE 1801, 115-118 (1992). [Buc88] P.H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, Phys. Rev. Lett. 61(10), 11821185 (1988). •• [Buc87] P.H. Bucksbaum, M. Bashkansky, and T. J. Mcilrath, Phys. Rev. Lett. 58(4), 349-352 (1987). [CaM78] M. Cardona and L. Ley (eds.), Topics In Applied Physics: Photoemission In Solids I, Vol. 26, Springer-Verlag: Berlin, 1978. [Car74] J. L. Carlos, R.R. Karl, and S. H. Bauer, J. Chem. Doc. Far. Trans. 2, 177-187 (1974). [Cha89] D. Charalambidis, E. Hontzopoulos, C. Fotakis, Gy. Farkas, and Cs. Toth, J. Appl. Phys. 65(7), 2843-2846 (1989). [ChE94] E. Chevallay, J. Durand, S. Hutchins, G. Suberlucq, and M. Wurgel, Nucl. Instrum. Meth. A340, 146-156 (1994). [Che96] M. Chergui (ed.), Femtochemistry: Ultrafast Chemical and Physical Processes in Molecular Systems, World Scientific: Singapore, 1996. [ChJ94] J. Chen, K. lmasaki, M. Fujita, C. Yamanaka, M. Asakawa, S. Nakai, and T. Asakuma, Nucl. Instrum. Meth. A341, 346-350 (1994). [ChK69] K. L. Chopra, Thin Film Phenomena, McGraw-Hill Book Co.: New York, 1969. [Cho86] S. E. Choi and R. B. Bernstein, J. Chem. Phys. 85(1), 150-161 (1986). [ChP87] P. Chen, Particle Accelerators 20, 171-182 (1987). [ChW64] W. N. Charman, Photog. Sci. Eng. 8, 253-259 (1964). [ChY79] Y. W . Chan and W. L. Tsui, Phys. Rev. A 20(1), 294-303 (1979). [Cla89] R. Clauberg and A. Blacha, J. Appl. Phys. 65(11), 4095-4106 (1989). [CoD83] D. M. Considine (ed.), Van Nostrand's Scientific Encyclopedia, 6th Ed., Van Nostrand Reinhold Co.: New York, 1983. [CoH89] Collimated Holes, Inc., Fiber Optic Scintillating Screens, (1989). [Col54] J. W. Coltman, J. Opt. Soc. Am. 44(6), 468-471 (1954). References 375 [Con96] P. Cong, G. Roberts, J. L. Herek, A. Mokhtari, and A.H. Zewail, J. Phys. Chem. 100(19), 7832-7848 (1996). [Cos66] C. C. Costain, Trans. Am. Cryst. Assoc. 2, 157-164 (1966). [Cou85] E. A. Coutsias and J. K. Mciver, Phys. Rev. A 31(5), 3155-3168 (1985). [Cow90] J.M. Cowley, Diffraction Physics, 2nd Ed., North-Holland: Amsterdam, 1990. [CrS92] Crystal Semiconductor Corporation, Volume I Data Book: AID Conversion ]C's, (1992). [Dab96] I. Daberkow, K.-H. Herrmann, L. Liu, W. D. Rau, and H. Tietz, Ultramicroscopy 64, 35-48 (1996). [Dab93] I. Daberkow, K.-H. Herrmann, and F. Lenz, Ultramicroscopy 50, 75-82 (1993). [Dab91] I. Daberkow, K.-H. Herrmann, L. Liu, and W. D. Rau, Ultramicroscopy 38, 215-223 (1991). [Dac78] H. Dachs (ed.), Neutron Diffraction, Springer-Verlag: Berlin, 1978. [Dai74] J.C. Dainty and R. Shaw, Image Science: Principles, Analysis, and Evaluation of Photographic-Type Imaging Processes, Academic Press: London, 1974. [DAn71] P. D' Antonio, C. George, A.H. Lowery, and J. Karle, J. Chem. Phys. 55(3), 1071-1075 (1971). [Dan94] M. Dantus, S. B. Kim, J.C. Williamson, and·A. H. Zewail, J. Phys. Chem. 98(11), 27822796 (1994). [Dan9la] M. Dantus, M. H. M. Janssen, and A. H. Zewail, Chem. Phys. Lett. 181(4), 281-287 (1991). [Dan9lb] M. Dantus, Ph.D. Dissertation, California Institute of Technology, 1991. [Dan90] M. Dantus, R. M. Bowman, and A.H. Zewail, Nature 343, 737-739 (1990). [Dan88] M. Dantus, M. J. Rosker, and A.H. Zewail, J. Chem. Phys. 89(10), 6128-6140 (1988). [Dan87] M. Dantus, M. J. Rosker, and A.H. Zewail, J. Chem. Phys. 87(4), 2395-2397 (1987). [Dar75] E. H. Darlington, J. Phys. D 8, 85-93 (1975). [Dar72] E. H. Darlington and V. E. Cosslett, J. Phys. D 5, 1969-1981 (1972). [Dau87] T. Daud, J. R. Janesick, K. Evans, and T. Elliot, Opt. Eng. 26(8), 686-691 (1987). [Dav27] C. Davisson and L. H. Germer, Phys. Rev. 30(6), 705-740 (1927). [Deb88] P. J. W. Debye, The Collected Papers of Peter J. W. Debye, Ox Bow Press: Woodbridge, 1988. [Deb41] P. Debye,J. Chem. Phys. 9, 55-60 (1941). [Deb30] P. Debye, Physik. Zeitschr. 31, 419-428 (1930). [Deb29] P. Debye, L. Bewilogua, and F. Ehrhardt, Physik. Zeitschr. 30, 84-87 (1929). [Debl6] P. Debye and P. Scherrer, Physik. Zeitschr. 17, 277-283 (1916). [Debl5] P. Debye, Ann. d. Phys. 46, 809-823 (1915). [Deg37] Ch. Degard, Bull. Soc. Roy. Sci. Liege 12, 383+ (1937). [Deg35] Ch. Degard, J. Pierard, and W. van der Grinten, Nature 136, 142-143 (1935). [Den86] P. N. J. Dennis, Photodetectors: An Introduction To Current Technology, Plenum Press: New York, 1986. References 376 [Dha94] L. Dhar, J. T. Fourkas, and K. A. Nelson, Opt. Lett. 19(9), 643-645 (1994). [Dib92] T. S. Dibble and L. S. Bartell, J. Phys. Chem. 96(21), 8603-8610 (1992). [Dom92] A. Domenicano and I. Hargittai (eds.), Accurate Molecular Structures: Their Determination and Importance, Oxford University Press: London, 1992. [Dow82] K. H. Downing and D. A. Grano, Ultramicroscopy 7, 381-404 (1982). [DuB33] L.A. DuBridge, Phys. Rev. 43, 727-741 (1933). [DuB32] L.A. DuBridge, Phys. Rev. 39, 108-118 (1932). [Dvo89] M. I. Dvorkin, S. L. Dobychin, S. N. Nekhoroshkov, and A. V. Seryakov, Opt. Spec. (USSR) 67(3), 343-346 (1989). [Dwe75] A. W. Dweydari and C.H. B. Mee, Phys. Stat. Sol. A 27, 223-230 (1975). [EaR73] R. M. Eastment and C.H. B. Mee, J. Phys. F 3, 1738-1745 (1973). [Eas70] D. E. Eastman, Phys. Rev. B 2(1), 1-2 (1970). [Ebe68] E. H. Eberhardt, Appl. Opt. 7(10), 2037-2047 (1968). [Edg92] J.P. Edgecumbe, V. W. Aebi, and G. A. Davis, Proc. SPIE 1655, 204-210 (1992). [Ehl87] F. Ehlotzky, J. Phys. B 20, 2619-2626 (1987): [Eid95] E.-S. Eid, A.G. Dickinson, D. A. Inglis, B. D. Ackland, and E. R. Fossum, Proc. SPIE 2415, 265-275 (1995). [Eis85] R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd Ed., John Wiley and Sons: New York, 1985. [Els95] H. E. Elsayed-Ali, Proc. SPIE 2521, 92-102 (1995). [Els90] H. E. Elsayed-Ali and J. W. Herman, Rev. Sci. Instrum. 61(6), 1636-1647 (1990). [Els88] H. E. Elsayed-Ali and G. A. Mourou, Appl. Phys. Lett. 52(2), 103-104 (1988). [End71] J. G. Endriz and W. E. Spicer, Phys. Rev. B 4(12), 4159-4184 (1971). [Eng83] T. J. Englert and E. A. Rinehart, Phys. Rev. A 28(3), 1539-1545 (1983). [Eps77] J. Epstein and R. F. Stewart, J. Chem. Phys. 66(9), 4057-4064 (1977). [Eve71] T. E. Everhart and P.H. Hoff, J. Appl. Phys. 42(13), 5837-5846 (1971). [Ewb94] J. D. Ewbank, L. Schafer, and A. A. Ischenko, J. Mol. Struct. 321, 265-278 (1994). [Ewb93] J. D. Ewbank, J. Y. Luo, J. T. English, R. Liu, W. L. Faust, and L. Schafer, J. Phys. Chem. 97(34), 8745-8751 (1993). [Ewb92] J. D. Ewbank, W. L. Faust, J. Y. Luo, J. T. English, D. L. Monts, D. W. Paul, Q. Dou, and L. Schafer, Rev. Sci. Instrum. 63(6), 3352-3358 (1992). [Ewb90] J. D. Ewbank, W. L. Faust, D. L. Monts, D. W. Paul, L. Schafer, R. Bakhtiar, and Q. Dou, Mol. Cryst. Liq. Cryst. 187, 351-356 (1990). [Ewb89] J. D. Ewbank, D. W. Paul, L. Schafer, and R. Bakhtiar, Appl. Spec. 43(3), 415-419 (1989). [Ewb86] J. D. Ewbank, L. Schafer, D. W. Paul, D. L. Monts, and W. L. Faust, Rev. Sci. Instrum. 57(5), 967-972 (1986). [Ewb84] J. D. Ewbank, L. Schafer, D. W. Paul, 0. J. Benston, and J. C. Lennox, Rev. Sci. Instrum. 55(10), 1598-1603 (1984). References 377 [Ewb81] J. D. Ewbank, P. Bowers, J. Pinegar, and L. Schafer, Appl. Spec. 35(6), 540-543 (1981). [Fan94] G. Y. Fan, D. G. Dunkelberger, and M. H. Ellisman, Vltramicroscopy 55, 7-14 (1994). [Fan93a] G. Y. Fan and M. H. Ellisman, Vltramicroscopy 52, 21-29 (1993). [Fan93b] G. Y. Fan, C. Bueno, D. Dunkelberger, and M. H. Ellisman, J. Electr. Microsc. 42, 419-423 (1993). [FaR69] R. W. Fane and W. E. J. Neal, J. Opt. Soc. Am. 60(6), 790-793 (1969). [Far93] Gy. Farkas and C. Toth, Opt. Eng. 32(10), 2469-2474 (1993). [Far90] Gy. Farkas and Cs. Toth, Phys. Rev. A 41(7), 4123-4126 (1990). [Far87] Gy. Farkas, Z. Gy. Horvath, Cs. Toth, C. Fotakis, and E. Hontzopoulos, J. Appl. Phys. 62(11), 4545-4547 (1987). [Far85] Gy. Farkas and S. L. Chin, Appl. Phys. B 37, 141-143 (1985). [Far84] Gy. Farkas and S. L. Chin in Multiphoton Processes, P. Lambropoulos and S. J. Smith (eds.), Springer Series On Atoms And Plasmas, Vol. 2, Springer-Verlag: Berlin, pp. 191-199 1984. [Far83] Gy. Farkas, S. L. Chin, P. Galarneau, and F. Yergeau, Opt. Comm. 48(4), 275-278 (1983). [Far78] Gy. Farkas in Multiphoton Processes, J. H. Eberly and P. Lambropoulos (eds.), John Wiley and Sons: New York, pp. 81-100, 1978. [FaU47] U. Fano, Phys. Rev. 72(1), 26-29 (1947). [Fax27] H. Faxen and J. Holtsmark, Z. Physik 45, 307-324 (1927). [FaW92a] W. S. Fann, R. Storz, H . W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68(18), 2834-2837 (1992). [FaW92b] W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46(20), 13592-13595 (1992). [Fed97] M. V. Fedorov, S. P. Goreslavsky, and V. S. Letokhov, Phys. Rev. E 55(1), 1015-1027 (1997). [Fed91] M. V. Fedorov, Interaction of Intense Laser Light with Free Electrons, Harwood Academic Publishers: Chur, 1991. [Fed81] M. V. Fedorov, Prog. Quant. Electr. 7, 73-116 (1981). [Fed67] M. V. Fedorov, Sov. Phys. JETP 25(5), 952-959 (1967). [Fel87] P. M. Felker and A.H. Zewail, J. Chem. Phys. 86(5), 2460-2482 (1987). [FeP92] P. Felder, Chem. Phys. Lett. 197(4,5), 425-432 (1992). [FeP91] P. Felder, Chem. Phys. 155, 435-445 (1991). [FiA88] A. Finch, Y. Liu, H. Niu, W. Sibbett, W. E. Sleat, D.R. Walker, Q. L. Yang, and H. Zhang, Proc. SPIE 1032, 622-626 (1988). [Fie72] J. R. Fiebiger and R. S. Muller, J. Appl. Phys. 43(7), 3202-3207 (1972). [Fin89] M. Fink, A. W. Ross, and R. J. Fink, Z. Phys. D 11, 231-238 (1989). [Fin88] M. Fink and D. A. Kohl in Chapter Five of [Har88a]. [Fin79] M. Fink, P. G. Moore, and D. Gregory, J. Chem. Phys. 71(12), 5227-5237 (1979). References 378 [Fin70a] M. Fink, D. A. Kohl, and R. A. Bonham, J. Chem. Phys. 52, 5487-5489 (1970). [Fin70b] M. Fink and R. A. Bonham, Rev. Sci. lnstrum. 41(3), 389-396 (1970). [Fio63] G. Fiocco and E. Thompson, Phys. Rev. Lett. 10(3), 89-91 (1963). [Fle86] G. R. Fleming, Chemical Applications of Ultrafast Spectroscopy, Oxford University Press: New York, 1986. [FoH70] H. R. Foster, J. Appl. Phys. 41, 5344-5346 (1970). [Fom66] V. S. Fomenko, Handbook Of Thermionic Properties, G. V. Samsonov (ed.), Plenum Press Data Division: New York, 1966. [For84] R. L. Fork, 0. E. Martinez, and J.P. Gordon, Opt. Lett. 9(5), 150-152 (1984). [For83] R. L. Fork, C. V. Shank, R. Yen, and C. A. Hirlimann, IEEE J. Quant. Elec. QE-19(4), 500506 (1983). [For82] R. L. Fork, C. V. Shank, and R. T. Yen, Appl. Phys. Lett. 41(3), 223-225 (1982). [For81] R. L. Fork, B. I. Greene, and C. V. Shank, Appl. Phys. Lett. 38, 671-672 (1981). [Fos94] E. R. Fossum, Proc. SPIE 2172, 1-16 (1994). [Fou95] J. T. Fourkas, L. Dhar, K. A. Nelson, and R. _Trebino, J. Opt. Soc. Am. B 12(1), 155-165 (1995). [Fow31] R.H. Fowler, Phys. Rev. 38, 45-56 (1931). [Foy84] A.G. Foyt and F. J. Leonberger in Picosecond Optoelectronic Devices, C.H. Lee (ed.), Academic Press: Orlando, pp. 271-311, 1984. [Fra83] G. W. Fraser, Nucl. lnstrum. Meth. 206, 445-449 (1983). [Fre86] R.R. Freeman, T. J. Mcilrath, P.H. Bucksbaum, and M. Bashkansky, Phys. Rev. Lett. 57(25), 3156-3159 (1986). [Fri12] W. Friedrich, P. Knipping, and M. von Laue, Ann. Physik 41, 971+ (1912). [Fry28] T. C. Fry and H. E. Ives, Phys. Rev. 32, 44-56 (1928). [Fuj84] J. G. Fujimoto, J.M. Liu, E. P. lppen, and N. Bloembergen, Phys. Rev. Lett. 53(19), 18371840 (1984). [Gal90a] Galileo Electro-Optics Corp., Spectral Response of Typical Photosensitive Devices, (1990). [Gal90b] Galileo Electro-Optics Corp., Detector Assemblies and also About Galileo Long-Life Microchannel Plates, (1990). [GaM71] M. Galanti, R. Gott, and J. F. Renaud, Rev. Sci. Instrum. 42(12), 1818-1822 (1971). [GeA81] A.G. Gershikov, Teor. i Eksper. Khim. 17(4), 463-468 (1981). [Gei95] J. D. Geiser and P. M. Weber, Proc. SPIE 2521, 136-144 (1995). [Ger85] S. Gerstenkorn and P. Luc, J. Physique 46(6), 867-881 (1985). [Gho82] C. Ghosh, Proc. SPIE 346, 62-68 (1982). [Gir95a] J.P. Girardeau-Montaut, C. Girardeau-Montaut, and S. D. Moustaizis, J. Phys. D 28, 212215 (1995). [Gir95b] J.-P. Girardeau-Montaut, M. Afif, A. Perez, C. Girardeau-Montaut, and C. Tomas, Proc. SPIE 2521, 32-43 (1995). References 379 [Gir93] J. P. Girardeau-Montaut, C. Girardeau-Montat, S. D. Moustaizis, and C. Fotakis, Appl. Phys. Lett. 63(5), 699-701 (1993). [Gla58] R. J. Glauber, Lectures in Theoretical Physics 1, 315-414 (1958). [Gla53] R. Glauber and V. Schomaker, Phys. Rev. 89(4), 667-671 (1953). [Glu94] J.P. Glusker, M. Lewis, and M. Rossi, Crystal Structure Analysis for Chemists and Biologists, VCH Publishers: New York, 1994. [Gol83] V. V. Golubkov, A. V. Zgurskii, A. A. Ischenko, and V. I. Petrov, /zv. Akad. Nauk SSSR, Ser. Fiz. 47(6), 1115-1118 (1983). [Gom61] R. Gomer, Field Emission and Field Ionization, Harvard University Press: Cambridge, 1961. [Gra80] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press: New York, 1980. [Gre74] R. C. Greenhow and A. J. Schmidt, Adv. Quant. Elec. 2, 157-286 (1974). [Gru93] M. Gruebele and A.H. Zewail, J. Chem. Phys. 98(2), 883-902 (1993). [Gru90] M. Gruebele, G. Roberts, M. Dantus, R. M. Bowman, and A. H. Zewail, Chem. Phys. Lett. 166(5,6), 459-469 (1990). [GuD96] D.-S. Guo, Phys. Rev. A 53(6), 4311-4319 (1996). [GuD92] D.-S. Guo and G. W. F. Drake, Phys. Rev. A 45(9), 6622-6635 (1992). [Gui95] V. Guidi and A. V. Novokhatsky, Meas. Sci. Technol. 6, 1555-1556 (1995). [Gus71] R. Gush and H.P. Gush, Phys. Rev. D 3(8), 1712-1721 (1971). [Guo94] H. Guo and A.H. Zewail, Can. J. Chem. 72, 947-957 (1994). [Haa70a] J. Haase, Z. Natu,forschung A 25, 1219-1235 (1970). [Haa70b] J. Haase, Z. Natu,forschung A 25, 936-945 (1970). [HaB91a] B. D. Hall, D. Reinhard, J.-P. Borel, and R. Monot, Z. Phys. D 20, 457-459 (1991). [HaB91b] B. D. Hall, M. Fltieli, D. Reinhard, J.-P. Borel, and R. Monot, Rev. Sci. Instrum. 62(6), 14811488 (1991). [HaF95] F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, Phys. Rev. E 51(5), 4833-4843 (1995). [Hag95] T. Hager, Force of Nature: The Life of Linus Pauling, Simon and Schuster: New York, 1995. [HaH36] H. Halban and P. Preiswork, C. R. Acad. Sci. Paris 203, 73+ (1936). [HaJ75] H.-J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65(6), 742-744 (1975). Values of n, k, and R are tabulated in [Wea81]. [Hal78] D. Halliday and R. Resnick, Physics, J. Wiley and Sons: New York (1978). [HaM79] M. D. Harmony, V. W. Laurie, R. L. Kuczkowski, R.H. Schwendeman, D. A. Ramsay, F. J. Lovas, W. J. Lafferty, and A.G. Maki, J. Phys. Chem. Ref Data 8(3), 619-722 (1979). [Ham67] J. F. Hamilton and J.C. Marchant, J. Opt. Soc. Am. 57(2), 232-239 (1967). [Har92] I. Hargittai in Chapter Five of [Dom92]. [Har88a] I. Hargittai and M. Hargittai (eds.), Stereochemical Applications of Gas-Phase Electron Diffraction, VCH Publishers: New York, 1988. References 380 [Har88b] I. Hargittai in Chapter One of [Har88a]. [Has61] G. Hass and J.E. Waylonis, J. Opt. Soc. Am. 51(7), 719-722 (1961). [Hay70] J. G. Hayes (ed.), Numerical Approximation to Functions and Data, Oxford University Press, Inc.: New York, 1970. [HeC49] C. Herring and M. H. Nichols, Rev. Mod. Phys. 21(2), 185-270 (1949). [Hec87] E. Hecht and A. Zajac, Optics, 2nd Ed., Addison-Wesley Publishing Co.: Reading, 1987. [Hel80] T. M. Helliwell, Introduction to Special Relativity, Harvey Mudd College: Claremont, 1980. [Her95] K.-H. Herrmann and R. Sikeler, Optik 98(3), 119-124 (1995). [Her92] K.-H. Herrmann and L. Liu, Optik 92(1), 48-50 (1992). [Her87] K.-H. Herrmann and M. Korn, J. Phys. E 20, 177-181 (1987). [Her84] K.-H. Herrmann and D. Krah!, Adv. Opt. Electr. Microsc. 9, 1-64 (1984). [Her82] K.-H. Herrmann and D. Krah!, J. Microsc. 127(1), 17-28 (1982). [Hib92] M. Hibino, K. Irie, R. Autrata, and P. Schauer, J. Electr. Microsc. 41, 453-457 (1992). [HiE83] E. Hirota, J. Phys. Chem. 87, 3375-3383 (1983). [Hie79] R. G. Hier, E. A. Beaver, G. W. Schmidt, and G. D. Schmidt, Adv. Electr. Electr. Phys. 52, 463-480 (1979). [Hil76] G. E. Hill, Adv. Electr. Electr. Phys. 40A, 153-165 (1976). [Hir77] P. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan, Electron Microscopy of Thin Crystals, 2nd Ed., R. E. Krieger Publishing Co.: Malabar, 1977. [Hmt92] Hamamatsu Photonics K. K., Image Intensifiers, (1992). [Hoe53] J. A. Hoerni and J. A. lbers, Phys. Rev. 91(5), 1182-1185 (1953). [HoG96] G. C. Holst, CCD Arrays, Cameras, and Displays, SPIE Optical Engineering Press: Bellingham, 1996. [Hol66] A. A. Holscher, Surf Sci. 4, 89-102 (1966). [Hol79] J. Holz! and F. K. Schulte, Springer Tracts In Modern Physics 85, 1-150 (1979). [Hop64] B. J. Hopkins and J.C. Riviere, Brit. J. Appl. Phys. 15, 941-946 (1964). [Hor96] H. Hora, W. Scheid, B. W. Boreham, R. Hopf!, P. R. Bolton, and Y.-K. Ho, Opt. Comm. 130, 283-287 (1996). [How95] N. E. Howard, Proc. SPIE 2415, 188-198 (1995). [Hra93] V. P. Hradil, T. Suzuki, S. A. Hewitt, P. L. Houston, and B. J. Whitaker, J. Chem. Phys. 99(6), 4455-4463 (1993). [HuA17] A. W. Hull, Phys. Rev. 9(1), 84-87 (1917). [Hub80] J. H. Hubbell, H. A. Gimm, and I. 0verb0, J. Phys. Chem. Ref Data 9(4), 1023-1147 (1980). [Hub79] J. H. Hubbell and I. 0verb0, J. Phys. Chem. Ref Data 8(1), 69-105 (1979). [Hul61] H. M. Hulburt and J. 0. Hirschfelder, J. Chem. Phys. 35, 1901 (1961). [Hul41] H. M. Hulburt and J. 0. Hirschfelder, J. Chem. Phys. 9, 61-69 (1941). [Hun82] T. F. Hunter and K. S. Kristjansson, Chem. Phys. Lett. 90(1), 35-40 (1982). .. References 381 [Hwa92] H. J. Hwang and M.A. El-Sayed, J. Phys. Chem. 96(22), 8728-8735 (1992). [Ibe74] J. A. Ibers and W. C. Hamilton (eds.), International Tables For X-Ray Crystallography, Vol. 4, Kynoch Press: Birmingham, pp. 176-269, 1974. See corrections in [Sel78]. [Ihe97] H. Ihee, J. Cao, and A. H. Zewail, submitted to Chem. Phys. Lett.. [Ipp75] E. P. Ippen and C. V. Shank, Appl. Phys. Lett. 27(9), 488-490 (1975). [Isc96a] A. A. Ischenko, L. Schafer, and J. D. Ewbank, J. Mol. Struct. 376, 157-171 (1996). [Isc96b] A. A. Ischenko, V. A. Lobastov, L. Schafer, and J. D. Ewbank, J. Mol. Struct. 377, 261-269 (1996). [Isc95] A. A. Ischenko, J. D. Ewbank, and L. Schafer, J. Phys. Chem. 99(43), 15790-15797 (1995). [Isc94a] A. A. Ischenko, J. D. Ewbank, and L. Schafer, J. Mol. Struct. 320, 147-158 (1994). [Isc94b] A. A. Ischenko, J. D. Ewbank, and L. Schafer, J. Phys. Chem. 98(16), 4287-4300 (1994). [Isc94c] A. A. Ischenko, L. Schafer, J. Y. Luo, and J. D. Ewbank, J. Phys. Chem. 98(35), 8673-8678 (1994). [Isc93] A. A. Ischenko, V. P. Spiridonov, L. Schafer, and J. D. Ewbank, J. Mol. Struct. 300, 115-140 (1993). [Isc90] A. A. Ischenko, V. P. Spiridonov, and Yu. I. Tarasov, Sov. J. Chem. Phys. 6(1), 48-59 (1990). [Isc89] A. A. Ischenko, B. G. Sartakov, V. P. Spiridonov, and Yu. I. Tarasov, Sov. J. Chem. Phys. 5(3), 427-443 (1989). [Isc88] A. A. Ischenko, V. P. Spiridonov, Yu. I. Tarasov, and A. A. Stuchebryukhov, J. Mol. Struct. 172, 255-273 (1988). [Isc83] A. A. Ischenko, V. V. Golubkov, V. P. Spiridonov, A. V. Zgurskii, A. S. Akhmanov, M. G. Vabischevich, and V. N. Bagratashvili, Appl. Phys. B 32, 161-163 (1983). [Ish93] K . Ishizuka, Ultramicroscopy 52, 7-20 (1993). [lti90] Y. Itikawa and A. lchimura, J. Phys. Chem. Ref Data 19(3), 637-651 (1990). [IvA87] A. E. Iverson, D. L. Smith, N. G. Paulter, and R. B. Hammond, J. Appl. Phys. 61(1), 234-239 (1987). [Ive74] R. C. Ivey, P. D. Schulze, T. L. Leggett, and D. A. Kohl, J. Chem. Phys. 60(8), 3174-3177 (1974). [IvH28] H . E. Ives, A. R. Olpin, and A. L. Johnsrud, Phys. Rev. 32, 57-80 (1928). [Jac70] E. J. Jacob and L. S. Bartell, J. Chem. Phys. 53(6), 2231-2235 (1970). [Jaf75] M. Jafarpour, Ph.D. Dissertation, University of Wyoming, 1975. [JaJ87] J. R. Janesick, T. Elliot, S. Collins, M. M. Blouke, and J. Freeman, Opt. Eng. 26(8), 692-714 (1987). [JaJ85] J. Janesick, K. Klaasen, and T. Elliot, Proc. SPIE 570, 7-19 (1985). [JaM86] M. C. Jackson, R. D. Long, D. Lee, and N. J. Freeman, Laser and Particle Beams 4(1), 145156 (1986). [Jan93] M. H. M. Janssen, M. Dantus, H. Guo, and A.H. Zewail, Chem. Phys. Lett. 214(3,4), 281289 (1993). .. References 382 [Jon68] R. C. Jones, Sci. Amer. 219(3), 110-117 (1968). [Jor48] T. Jorgensen, Am. J. Phys. 16, 285-289 (1948). [Jos89] N. V. Joshi, J. C. Sanchez, and J.M. Martin, J. Phys. Chem. Sol. 50(6), 629-632 (1989). [KaM75] M. Kawasaki, S. J. Lee, and R. Bersohn, J. Chem. Phys. 63(2), 809-814 (1975). [Kan93] D. J. Kane and R. Trebino, IEEE J. Quant. Electro. 29(2), 571-578 (1993). [Kap33] P. L. Kapitza and P.A. M. Dirac, Proc. Cambridge Phil. Soc. 29, 297-300 (1933). [KaJ50] J. Karle and I. L. Karle, J. Chem. Phys. 18(7), 957-962 (1950). [Kar50] I. L. Karle and J. Karle, J. Chem. Phys. 18(7), 963-971 (1950). [Kar49] I. L. Karle and J. Karle, J. Chem. Phys. 17(11), 1052-1058 (1949). [Kar47] I. L. Karle, D. Hoober, and J. Karle, J. Chem. Phys. 15(10), 765 (1947). [Kat92] T. Katsouleas, Am. J. Phys. 60(6), 568-569 (1992). [Kaw95] H. Kawashima, M. M. Wefers, and K. A. Nelson, Ann. Rev. Phys. Chem. 46, 627-656 (1995). [KaY84] Y. Kawamura, K. Toyoda, and M. Kawai, Appl. Phys. Lett. 45(4), 307-309 (1984). [KeD65] D. H. Kelly, Appl. Opt. 4(4), 435-437 (1965) ... [Kel65] L. V. Keldysh, Sov. Phys. JETP 20(5), 1307-1314 (1965). [Ker88] B. W. Kernighan and D. M. Ritchie, The C Programming Language, 2nd Ed., Prentice Hall PTR: Englewood Cliffs, 1988. [Khu90] L. R. Khundkar and A.H. Zewail, J. Chem. Phys. 92(1), 231-242 (1990). [Kib66a] T. W. B. Kibble, Phys. Rev. Lett. 16(23), 1054-1056 (1966) and erratum in Phys. Rev. Lett. 16(26), 1233 (1966). [Kib66b] T. W. B. Kibble, Phys. Rev. 150(4), 1060-1069 (1966). [KiM67] M. Kimura, S. Konaka, and M. Ogasawara, J. Chem. Phys. 46(7), 2599-2603 (1967). [Kim94] K.-J. Kim, S. Chattopadhyay, and C. V. Shank, Nucl. Instrum. Meth. A341, 351-354 (1994). [Kin90] K. Kinoshita, M. Suyama, Y. Inagaki, Y. Ishihara, and M. Ito, Proc. SPIE 1358, 490-496 (1990). [Kin88] K. Kinoshita, M. Ito, and M. Suyama, Proc. SPIE 1032, 441-447 (1988). [Kin87] K. Kinoshita, M. Ito, and Y. Suzuki, Rev. Sci. /nstrum. 58(6), 932-938 (1987). [KiS82] S.S. Kim and G.D. Stein, Rev. Sci. Instrum. 53(6), 838-844 (1982). [Kit93] D. Kitriotis and Y. Aoyagi, Jpn. J. Appl. Phys. 32, Pt. 2 (3B), L441-L443 (1993). [Kle29] 0. Klein and Y. Nishina, Z. Physik 52, 853-868 (1929). [Klu74] H.P. Klug and L. E. Alexander, X-Ray Diffraction Procedures For Polycrystalline and Amorphous Materials, 2nd Ed., John Wiley and Sons: New York, 1974. [Kne85] J. L. Knee, L. R. Khundkar, and A.H. Zewail, J. Chem. Phys. 83(4), 1996-1998 (1985). [Kno79] G. F. Knoll, Radiation Detection and Measurement, John Wiley and Sons: New York, 1979. [Kof81] J. B. Koffend and S. R. Leone, Chem. Phys. Lett. 81(1), 136-141 (1981). [Koh92a] D. A. Kohl and E. J. Shipsey, Z. Phys. D 24, 33-38 (1992). References 383 [Koh92b] D. A. Kohl and E. J. Shipsey, Z. Phys. D 24, 39-45 (1992). [Koh80] D. A. Kohl and M. M. Arvedson, J. Chem. Phys. 72(3), 1922-1927 (1980). [Koh67] D. A. Kohl and R. A. Bonham, J. Chem. Phys. 47(5), 1634-1646 (1967). [Kon88] S. Konaka in Chapter Three of [Har88a]. [Kon72] S. Konaka, Japan. J. Appl. Phys. 11(8), 1199-1204 (1972). [Kor69] V. V. Korobkin, A. A. Maljutin, and M. Ya. Schelev, J. Photog. Sci. 17, 179-182 (1969). [Kra53] J. Kraitchman, Am. J. Phys. 21(1), 17-24 (1953). [Kri93] 0. L. Krivanek and P. E. Mooney, Ultramicroscopy 49, 95-108 (1993). [Kro76] P. M. Kroger, P. C. Demou, and S. J. Riley, J. Chem. Phys. 65(5), 1823-1834 (1976). [Kub62] R. Kubo, J. Phys. Soc. Japan 17, 110- (1962). [Kuc92] K. Kuchitsu in Chapter Two of [Dom92]. [Kuc88] K. Kuchitsu, M. Nakata, and S. Yamamoto in Chapter Seven of [Har88a]. [Kuc72a] K. Kuchitsu in Molecular Structures and Vibrations, S. J. Cyvin (ed.), Elsevier Publishing Co.: Amsterdam, pp. 148-170, 1972. [Kuc72b] K. Kuchitsu and S. J. Cyvin in Molecular Structures and Vibrations, S. J. Cyvin (ed.), Elsevier Publishing Co.: Amsterdam, pp. 183-211, 1972. [Kuc67] K. Kuchitsu, Bull. Chem. Soc. Japan 40(3), 498-504 (1967). [Kuc65] K. Kuchitsu and Y. Morino, Bull. Chem. Soc. Japan 38(5), 805-813 (1965). [Kuc61] K. Kuchitsu and L. S. Bartell, J, Chem. Phys. 35(6), 1945-1949 (1961). [Kuj92] S. Kujawa and D. Krahl, Ultramicroscopy 46, 395-403 (1992). [Laa60] J. van Laar and J. J. Scheer, Phil. Res. Rep. 15(1), 1-6 (1960). [Lad93] M. F. C. Ladd and R. A. Palmer, Structure Determination by X-Ray Crystallography, Plenum Press: New York, 1993. [Lea69] C. Lea, B. H. Blott, and C.H. B. Mee, Appl. Opt. 8(1), 203-204 (1969). [Leg74] T. L. Leggett, R. E. Kennerly, and D. A. Kohl, J. Chem. Phys. 60(8), 3264-3267 (1974). [Leg73] T. L. Leggett and D. A. Kohl, J. Chem. Phys. 59(2), 611-616 (1973). [Lei73] W. Leiser and K. H. Gankler, Optik 38(2), 177-186 (1973). [Ley90] Leybold Vacuum Products Inc., Product and Vacuum Technology Reference Book, 1990. [Lid92] D.R. Lide (ed.), CRC Handbook of Chemistry and Physics, 73rd Ed., CRC Press, Inc.: Boca Raton, 1992. [Lie93] Ch. Lienau, J.C. Williamson, and A.H. Zewail, Chem. Phys. Lett. 213(3,4), 289-296 (1993). [Lin83] J.-T. Lin and T. F. George, J. Appl. Phys. 54(1), 382-387 (1983). [Liu90] Y. Liu and W. Sibbett, Proc. SPIE 1358, 503-510 (1990). [LiW97] W.-K. Liu and S. H. Lin, Phys. Rev. A 55(1), 641-647 (1997). [Log69] E. M. Logothetis and P. L. Hartman, Phys. Rev. 187(2), 460-474 (1969). [Lom78] L.A. Lompre, G. Mainfray, C. Manus, J. Thebault, Gy. Farkas, and Z. Horvath, Appl. Phys. Lett. 33(2), 124-126 (1978). References 384 [Loo83] J. F. Van Loock, L. Van den Enden, and H.J. Geise, J. Phys. E 16, 255-257 (1983). [Lov84] S. W. Lovesey, Theory of Neutron Scattering From Condensed Matter, Clarendon Press: Oxford, 1984. [Luc80] P. Luc, J. Mol. Spec. 80, 41-55 (1980). [MaB69] B. W. Manley, A. Guest, and R. T. Holmshaw, Adv. Electr. Electr. Phys. 28A, 471-486 (1969). [Mac76] J.P. Macau, J. Jamar, and S. Gardier, IEEE Trans. Nucl. Sci. NS-23(6), 2049-2055 (1976). [MaH32] H. S. W. Massey and C. B. 0. Mohr, Proc. Royal Soc. London A135, 258-275 (1932). [MaL59] L. Mandel, Brit. J. Appl. Phys. 10, 233-234 (1959). [Man95] J. Manz and L. Woste (eds.), Femtosecond Chemistry, VCH Publishers: New York, 1995. [Man93] J. Manz and A. W. Castleman, J. Phys. Chem. 97(48), 12423-12649 (1993). [MaP87] P. J. Martin, P. L. Gould, B. G. Oldaker, A.H. Miklich, and D. E. Pritchard, Phys. Rev. A 36(5), 2495-2498 (1987). [Mar88] H. F. Mark in Introduction of [Har88a]. [Mar30] H. Mark and R. Wier!, Naturwis. 18, 205 (1 ~30). [Mas91] V. S. Mastryukov, Moscow Univ. Chem. Bull. 46(3), 30-33 (1991). [Mat71] A.G. Mathewson and H.P. Myers, Phys. Scripta 4, 291-292 (1971). [MaU96] U. Marvet and M. Dantus, Chem. Phys. Lett. 256, 57-62 (1996). [McC72] G. H. McCall, Rev. Sci. lnstrum. 43(6), 865-866 (1972). [McP94] A. McPherson, B. D. Thompson, A. B. Borisov, K. Boyer, and C. K. Rhodes, Nature 370, 631-634 (1994). [Mei94] C. Meier, M. Volkmer, J. Lieschke, M. Fink, and N. Bowering, Z. Phys. D 30, 183-187 (1994). [Men92a] A. Mens, D. Gontier, J.C. Huilizen, R. Sauneuf, D. Schirmann, R. Verrecchia, P. Audebert, J.C. Gauthier, J.P. Geindre, A. Antonetti, J.P. Chhambaret, G. Hamoniaux, and A. Mysyrowicz, Proc. SPIE 1801, 502-513 (1992). [Men92b] A. Mens, Endeavour, New Series 16(2), 74-79 (1992). [Mih89] A. Mihill and M. Fink, Z. Phys. D 14, 77-83 (1989). [MiJ92] J. D. Miller and M. Fink, J. Chem. Phys. 97(11), 8197-8200 (1992). [Mij75] F. C. Mijlhoff, J. Mol. Struct. 27,447 (1975). [Mil81] B. R. Miller and M. Fink, J. Chem. Phys. 75(11), 5326-5328 (1981). [Mil80] B. R. Miller and L. S. Bartell, J. Chem. Phys. 72(2), 800-807 (1980). [MiP95] P. Millier and M. A. Darizcuren, Proc. SPIE 2415, 160-171 (1995). [Mit36] D. P. Mitchell and P. N. Powers, Phys. Rev. 50, 486-487 (1936). [MoC95] C. I. Moore, J.P. Knauer, and D. D. Meyerhofer, Phys. Rev. Lett. 74(13), 2439-2442 (1995). [Moc86] J. Moc, Z. Latajka, and H. Ratajczak, Chem. Phys. Lett. 130(6), 541-544 (1986). [Mok90] A. Mokhtari, P. Cong, J. L. Herek, and A.H. Zewail, Nature 348, 225-227 (1990). References 385 [MoM93] M. D. Morris, (ed.), Microscopic and Spectroscopic Imaging of the Chemical State, Marcel Dekker, Inc.: New York, 1993. [Mon87] D. L. Monts, J. D. Ewbank, K. Siam, W. L. Faust, D. W. Paul, and L. Schafer, Appl. Spec. 41(4), 631-635 (1987). [Moo89] J. H. Moore, C. C. Davis, and M. A. Coplan, Building Scientific Apparatus, 2nd. Ed., Addison-Wesley Publishing Company: Reading, 1989. [MoR80] R. Moutran, B. Beagley, D. W. J. Cruickshank, A. Foord, and R. G. Pritchard, J. Phys. E 13, 1189-1192 (1980). [Mor65] Y. Morino and Y. Murata, Bull. Chem. Soc. Japan 38(1), 114-119 (1965). [Mor60a] Y. Morino, Y. Nakamura, and T. Iijima, J. Chem. Phys. 32(3), 643-652 (1960). [Mor60b] Y. Morino, Acta Cryst. 13, 1107 (1960). [MoT91] T. Motet, J. Nees, S. Williamson, and G. Mourou, Appl. Phys. Lett. 59(12), 1455-1457 (1991). [Mot65] N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd. Ed., Oxford University Press: London, 1965. [Mou82] G. Mourou and S. Williamson, Appl. Phys. Lett. 41(1), 44-45 (1982). [MuD79] D. K. Murti, J. Vac. Sci. Tech. 16(2), 226-229 (1979). [Mur94] M. M. Murnane, H. C. Kapteyn, S. P. Gordon, and R. W. Falcone, Appl. Phys. B 58(3), 261266 (1994). [Mur89] M. M. Murnane, H. C. Kapteyn, and R. W. Falcone, Phys. Rev. Lett. 62(2), 155-158 (1989). [Nag82] M. Nagashima, S. Konaka, and M. Kimura, Bull. Chem. Soc. Japan 55(1), 28-32 (1982). [Nag73] M. Nagashima, S. Konaka, T. Iijima, and M. Kimura, Bull. Chem. Soc. Japan 46(11), 33483352 (1973). [Nak91] H. Nakanishi, Y. Yoshida, T. Ueda, T. Kozawa, H. Shibata, K. Nakajima, T. Kurihara, N. Yugami, Y. Nishida, T. Kobayashi , A. Enomoto, T. Oogoe, H. Kobayashi, B. S. Newberger, S. Tagawa, K. Miya, and A. Ogata, Phys. Rev. Lett. 66(14), 1870-1873 (1991). [Nea70] W. E. J. Neal, R. W. Fane, and N. W. Grimes, Philos. Mag. 21, 167-175 (1970). [New86] D. E. Newbury, D. C. Joy, P. Echlin, C. E. Fiori, and J. I. Goldstein, Advanced Scanning Electron Microscopy and X-Ray Microanalysis, Plenum Press: New York, 1986. [Nit63] H. F. Nitka, Photog. Sci. Eng. 7, 188-195 (1963). [Niu92] H. Niu, H. Zhang, Q. L. Yang, B. P. Guo, Z. X. Song, J. L. Zhou, Y. A. Ren, and H.J. Zhao, Proc. SPIE 1801, 1035-1041 (1992). [Niu88a] H. Niu, V. P. Degtyareva, V. N. Platonov, A. M. Prokhorov, and M. Ya. Schelev, Proc. SPIE 1032, 79-85 (1988). [Niu88b] H. Niu, H. Zhang, Q. L. Yang, Y. P. Liu, Y. C. Wang, Y. A. Reng, and J. L. Zhou, Proc. SPIE 1032, 472-479 (1988). [Niu81] H. Niu and W. Sibbett, Rev. Sci. Instrum. 52(12), 1830-1836 (1981). [Nix95] R.H. Nixon, S. E. Kemeny, C. 0. Staller, and E. R. Fossum, Proc. SPIE 2415, 117-123 (1995). [Not56] W. B. Nottingham in Encyclopedia Of Physics: Electron-Emission Gas Discharges I, Vol. 21 , S. Fliigge (ed.), Springer-Verlag: Berlin, pp. 1-175, 1956. References 386 [Nov79] V. P. Novikov, J. Mot. Struct. 55, 215-221 (1979). [Oat85] C. W. Oatley, J. Microsc. 139(2), 153-166 (1985). [Ogu77] I. Ya. Ogurtsov, L.A. Kazantseva, and A. A. lschenko, J. Mot. Struct. 41, 243-251 (1977). [Ost85] D. E. Osten, Proc. SPIE 570, 89-94 (1985). [PaD83] D. W. Paul, J. D. Ewbank, 0. J. Benston, and L. Schafer, Appl. Spec. 37(2), 127-130 (1983). [Par89] D. H. Parker and R. B. Bernstein, Ann. Rev. Phys. Chem. 40, 561-595 (1989). [Pau95] L. Pauling, Linus Pauling In His Own Words: Selected Writings, Speeches, and Interviews, B. Marinacci (ed.), Simon and Schuster: New York, 1995. [Pau35] L. Pauling and L. 0. Brockway, J. Am. Chem. Soc. 57, 2684-2692 (1935). [Pau34] L. Pauling and L. 0. Brockway, J. Chem. Phys. 2, 867-881 (1934). [Paw74] J. Pawley, Scan. Elec. Microsc., 28-34 (1974). [Ped94] S. Pedersen, J. L. Herek, and A.H. Zewail, Science 266, 1359-1364 (1994). [Pei69] E. M. A. Peixoto, Phys. Rev. 177(1), 204-211 (1969). [Pen81] W. H. Pence, S. L. Baughcum, and S. R. Leone, J. Phys. Chem. 85(25), 3844-3851 (1981). [Per91] M. D. Person, P. W. Kash, and L. J. Butler, J. Chem. Phys. 94(4), 2557-2563 (1991). [Pos71] J. Pospisil and V. Bumba, Optik 34(2), 136-152 (1971). [Pre92] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd Ed., Cambridge University Press: Cambridge, 1992. [Pro91] A. M. Prokhorov, M. Ya. Schelev, and S. J. Nebeker, Laser Focus World, December, 125-128 (1991). [PrS95] S. Preuss, A. Demchuk, and M. Stuke, Appl. Phys. A 61, 33-37 (1995). [Pru86] A. P. Prudnikov, Yu. A. Brychkov, and 0 . 1. Marizhov, Integrals and Series, N. M . Queen, trans., Gordon and Breech Science Publishers: New York, 1986. [Pul83] P. Pulay, R. Mawhorter, D. A. Kohl, and M. Fink, J. Chem. Phys. 79(1), 185-191 (1983). [Pun90] A. K. Puntajer and C. Leubner, J. Appl. Phys. 67(3), 1606-1609 (1990). [Pus88] D. Puseljic, B. Baumbaugh, J. Bishop, J. Busenitz, N. Cason, J. Cunningham, R. Gardner, C. Kennedy, E. Manne!, R. J. Mountain, R. Ruchti, W. Shephard, M. Zanabria, A. Baumbaugh, K. Knickerbocker, A. Rogers, B. Kinchen, C. G. A. Hill, IEEE Trans. Nucl. Sci. NS-35(1), 475-476 (1988). [Rak96] F. Raksi, K. R. Wilson, Z. Jiang, A. Ikhlef, C. Y. Cote, and J.-C. Kieffer, J. Chem. Phys. 104(15), 6066-6069 (1996). [Ran80] L. M. Rangarajan and G. K. Bhide, Vacuum 30(11,12), 515-522 (1980). Portions of this article were plagiarized from [SpW64]. [ReC67] C. Reinsch, Numer. Mathe. 10, 177-183 (1967). [Rei91] S. E. Reichenbach, S. K. Park, and R. Narayanswamy, Opt. Eng. 30(2), 170-177 (1991). [ReL85] L. Reimer, Scanning Electron Microscopy, Springer-Verlag: Berlin, 1985. [Ren45] H. C. Rentschler and D. E. Henry, Trans. Electrochem. Soc. 87, 289-298 (1945). [Rid78] G. H. N. Riddle, J. Vac. Sci. Tech. 15(3), 857-860 (1978). References 387 [Rif93] D. M. Riffe, X. Y. Wang, M. C. Downer, D. L. Fisher, T. Tajima, J. L. Erskine, and R. M. More, J. Opt. Soc. Am. B 10(8), 1424-1435 (1993). [Riv69] J. C. Riviere, Sol. Sta. Surf. Sci. 1, 179-289 (1969). [RoA92] A. W. Ross, M. Fink, and R. Hilderbrandt in International Tables For Crystallography, Vol. C, A. J. C. Wilson (ed.), Kluwer Academic Publishers: Dordrecht, pp. 245-338, 1992. [RoA88] A. W. Ross and M. Fink, Phys. Rev. A 38(12), 6055-6058 (1988). [RoB87] B. W. Rossiter and J. F. Hamilton, Physical Methods of Chemistry, 2nd Ed., Vol. IIIA, John Wiley and Sons: New York, 1987. [Roe92] B. P. Roe, Probability and Statistics in Experimental Physics, Springer-Verlag: New York, 1992. [RoL94] L. Rosenberg, Phys. Rev. A 49(2), 1122-1130 (1994). [RoM88] M. J. Rosker, M . Dantus, and A. H. Zewail, J. Chem. Phys. 89(10), 6113-6127 (1988). [Roo84] A. P. Rood and J. Milledge, J. Chem. Soc. Faraday Trans. 2 80, 1145-1153 (1984). [RoP92] P. W . Roehrenbeck, Laser Focus World, November, 169-171 (1992). [Ros48] A. Rose, J. Opt. Soc. Am. 38(2), 196-208 (1948). [Ros46] A. Rose, J. Soc. Motion Picture Engineers 47(4), 273-294 (1946). [RoT89] T. S. Rose, M. J. Rosker, and A.H. Zewail, J. Chem. Phys. 91(12), 7415-7436 (1989). [RoW65] W. van Roosbroeck, Phys. Rev. 139(5A), Al 702-Al 716 (1965). [Ruc86] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, J. Busenitz, N. Cason, J. Cunningham, R. Gardner, S. Grenquist, V. Kenney, E. Manne!, R. Mountain, W. Shephard, A. Baumbaugh, K. Knickerbocker, C. Wegner, R. Yarema, A. Rogers, B. Kinchen, J. Ellis, R. Mead, and D. Swanson, IEEE Trans. Nucl. Sci. NS-33(1), 151-154 (1986). [Ruc85] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, N. Cason, J. Cunningham, R. Erichsen, S. Grenquist, V. Kenney, E. Manne!, R. Mountain, W. Shephard, P. Wilkins, A. Baumbaugh, K. Knickerbocker, A. Kreymer, J. Simanton, C. Wegner, R. Yarema, A. Rogers, R. Mead, and D. Swanson, IEEE Trans. Nucl. Sci. NS-32(1), 590-594 (1985). [Ruc84] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, N. Cason, R. Erichsen, V. Kenney, A. Kreymer, R. Mountain, W. Shephard, and A. Rogers, IEEE Trans. Nucl. Sci. NS-31(1), 69-73 (1984). [Ruc83] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, N. Cason, L. Dauwe, R. Erichsen, V. Kenney, A. Kreymer, W. Shephard, D. Potter, and A. Rogers, IEEE Trans. Nucl. Sci. NS-30(1), 40-43 (1983). [Rui92] W. J. de Ruijter and J. K. Weiss, Rev. Sci. Instrum. 63(10), 4314-4321 (1992). [Sai88] N. A. Sainov, Sov. Tech. Phys. Lett. 14(9), 731-732 (1988). [Sal80] K. L. Sala, G. A. Kenney-Wallace, and G. E. Hall, IEEE J. Quant. Elec. QE-16(9), 990-996 (1980). [Sas92] Y . Sasaki, H. Takeuchi, S. Konaka, and M. Kimura, Int. J. Quant. Chem. 43, 701-712 (1992). [Sav85] E. D. Savoye, Proc. SPIE 570, 95-97 (1985). [ScE83] E. Schmied!, P. Wissmann, and E. Wittmann, Surf. Sci. 135, 341-352 (1983). [ScF95] Schott Fiber Optics Inc., Fused Fiber Optic Tapers, (1995). References 388 [ScG80] G. Schmitt and F. J. Comes, J. Photochem. 14, 107-123 (1980). [ScH73] H. Schwarz, Phys. Lett. 43A(5), 457-458 (1973). [ScH65] H. Schwarz, H. A. Tourtellotte, and W.W. Gaertner, Phys. Lett. 19(3), 202-203 (1965). [Sch76] L. Schafer, Appl. Spec. 30(2), 123-149 (1976). [Sch71] L. Schafer, A. C. Yates, and R. A. Bonham, J. Chem. Phys. 55(6), 3055-3056 (1971). [Sch68] L. Schafer, J. Am. Chem. Soc. 90(15), 3919-3925 (1968). [ScJ94] J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73(16), 2180-2183 (1994). [ScL54] L. G. Schulz, J. Opt. Soc. Am. 44(5), 357-362 (1954). [ScM71] M. Ya. Schelev, M. C. Richardson, and A. J. Alcock, Appl. Phys. Lett. 18(8), 354-357 (1971). [Sco88] G. Scoles (ed.), Atomic and Molecular Beam Methods, Oxford University Press: New York, 1988. [ScR96] R. W. Schoenlein, W. P. Leemans, A.H. Chin, P. Volfbeyn, T. E. Glover, P. Balling, M. Zolotorev, K.-J. Kim, S. Chattopadhyay, and C. V. Shank, Science 274, 236-238 (1996). [ScV52] V. Schomaker and R. Glauber, Nature 170, 2~_0-291 (1952). [ScW23] W. Schottky, Z. Physik 14, 63-106 (1923). [Sei73] H. M . Seip in Chapter One of [Sim73]. [Sei67] H. M. Seip in Selected Topics in Structure Chemistry, P. Andersen, 0. Bastiansen, and S. Furberg (eds.), Universitetsforlaget: Oslo, pp. 25-68, 1967. [Sel78] H. L. Sellers, L. Schafer, and R. A. Bonham, J. Mal. Struct. 49, 125-130 (1978). [Sha59] M. H. Shamos, Great Experiments in Physics, Henry-Holt and Co.: New York, 1959. [ShE80] E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22(4), 1612-1628 (1980). [She93] M. H. Sher, U. Mohideen, H. W. K. Tom, 0. R. Wood, G. D. Aumiller, R.R. Freeman, and T. J. Mcllrath, Opt. Lett. 18(8), 646-648 (1993). [Shi72] S. Shibata, Bull. Chem. Soc. Japan 45(6), 1631-1634 (1972). [Shi71] S. Shibata and L. S. Bartell, J. Mal. Struct. 9, 1-9 (1971). [Shi64] S. Shibata, L. S. Bartell, and R. M. Gavin, J. Chem. Phys. 41(3), 717-722 (1964). [Sho38] W. Shockley and J. R. Pierce, Proc. Inst. Radio Eng. 26, 321-332 (1938). [ShP46] P. Shaffer, V. Schomaker, and L. Pauling, J. Chem. Phys. 14(11), 659-664 (1946). [Sib82] W. Sibbett, H. Niu, and M. R. Baggs, Rev. Sci. Instrum. 53(6), 758-761 (1982). [Sim73] G. A. Sim and L. E. Sutton (eds.), Molecular Structure by Diffraction Methods, Vol. 1, The Chemical Society: London, 1973. [SIT95] Scientific Imaging Technologies, Inc., S!Te 512><512 Scientific-Grade CCD, (1995). [SIT94] Scientific Imaging Technologies, Inc., An Introduction to Scientific Imaging Charge-Coupled Devices, (1994). [Sit87a] G. 0. Sitz, A. C. Kummel, and R. N. Zare, J. Chem. Phys. 87(5), 3247-3249 (1987). [Sit87b] G. 0. Sitz, A. C. Kummel, and R. N. Zare, J. Vac. Sci. Tech. A 5(4), 513-517 (1987). References 389 [SmD73] D. W. Smith and L. Andrews, J. Chem. Phys. 58(12), 5222-5229 (1973). [Smi94] V. Smith, 1994. Personal communication from M. Fink. [Som68] A.H. Sommer, Photoemissive Materials, J. Wiley and Sons: New York, 1968. [Spe88] J.C. H. Spence and J.M. Zuo, Rev. Sci. Instrum. 59(9), 2102-2105 (1988). [Spi81] V. P. Spiridonov, A. A. Ischenko, and L. S. Ivashkevich, J. Mol. Struct. 72, 153-164 (1981). [Spi79] V. P. Spiridonov, A. Ya. Prikhod'ko, and B. S. Butayev, Chem. Phys. Lett. 65(3), 605-609 (1979). [SpW64] W. E. Spicer and C. N. Berglund, Rev. Sci. Instrum. 35(12), 1665-1667 (1964). [Sri91] T. Srinivasan-Rao, J. Fischer, and T. Tsang, J. Appl. Phys. 69(5), 3291-3296 (1991). [StE54] E. J. Sternglass, Phys. Rev. 95(2), 345-358 (1954). [Ste89] D. G. Stearns and J. D. Wiedwald, Rev. Sci. Instrum. 60(6), 1095-1103 (1989). [SuJ90] J. J. Su, T. Katsouleas, J.M. Dawson, and R. Fedele, Phys. Rev. A 41(6), 3321-3331 (1990). [Suy88] M. Suyama and K. Kinoshita, Proc. SPIE 1032, 448-452 (1988). [Swo83] E.W. Swokowski, Calculus with Analytic Geometry, Prindle, Wever, and Schmidt: Boston, 1983. [Tag84] M. Taguchi and T. Iijima, Japan. J. Appl. Phys. 23(11), 1509-1517 (1984). [Tak86] M. Takeuchi, M. Nagashima, K. Tanaka, S. Konaka, and M. Kimura, Int. J. Quant. Chem. 30, 821-830 ( 1986). [Tan71] K. Tanaka and F. Sasaki, Int. J. Quant. Chem. 5, 157-175 (1971). [Tav67] C. Tavard, D. Nicolas, and M. Rouault, J. Chim. Phys. 64, 540-554 (1967). [Tav66] C. Tavard, Cahiers. Phys. 20, 397- (1966). [Tav65a] C. Tavard, M. Rouault, and M. Roux, J. Chim. Phys. 62, 1410-1417 (1965). [Tav65b] C. Tavard and M. Roux, C.R. Acad. Sci. Paris. 260, 4933- (1965). [Tek92] Tektronix, Inc., The Imaging CCD Array: Introduction and Operating Information, (1992). [Tek9la] Tektronix, Inc., Thinned, Back Illuminated CCDs for Short Wavelength Applications, (1991). [Tek91b] Tektronix, Inc., Quantum Efficiency Measurements on Charge Coupled Devices (CCDs), (1991). [Tek9lc] Tektronix, Inc., MPP Operation of CCDs, (1991). [Tex94] Texas Instruments, Inc., Area Array Image Sensor Products Data Book, ( 1994). [Tha75] A. Thanailakis, J. Phys. C 8, 655-668 (1975). [ThH96] H. Thomassen and K. Hedberg, 1996. Personal communication. [ThH92] H. Thomassen, S. Samdal, and K. Hedberg, J. Am. Chem. Soc. 114(8), 2810-2815 (1992). [ThJ95] J. R. Thompson, P. M. Weber, and P. J. Estrup, Proc. SPIE 2521, 113-122 (1995). [Tho28a] G. P. Thomson, Proc. Royal Soc. A 117, 600-609 (1928). [Tho28b] G. P. Thomson, Proc. Royal Soc. A 119, 651-663 (1928). [Tho27] G. P. Thomson and A. Reid, Nature 119, 890 (1927). References 390 [ThS90] S. W. Thomas, R. L. Griffith, and A. T. Teruya, Proc. SPIE 1358, 578-588 (1990). [Tom95a] I. V. Tomov, P. Chen, and P. M. Rentzepis, J. Appl. Cryst. 28, 358-362 (1995). [Tom95b] I. V. Tomov, P. Chen, and P. M. Rentzepis, Proc. SPIE 2521, 13-22 (1995). [Ton93] A. Tonomura, Electron Holography, Springer-Verlag: Berlin, 1993. [Tot91] C. Toth, Gy. Farkas, and K. L. Vodopyanov, Appl. Phys. B 53, 221-225 (1991). [Toy64] M. Toyama, T. Oka, and Y. Morino, J. Molec. Spec. 13, 193-213 (1964). [Tre88] J. Tremmel and I. Hargittai in Chapter Six of [Har88a]. [TrF33] F. Trendelenburg, Naturwis. 21, 173-177 (1933). [Tsa93] T. Tsang, Appl. Phys. Lett. 63(7), 871-873 (1993). [Tsa92] T. Tsang, T. Srinivasan-Rao, and J. Fischer, Nucl. Instrum. Meth. A318, 270-274 (1992). [Tsa91] T. Tsang, T. Srinivasan-Rao, and J. Fischer, Phys. Rev. B 43(11), 8870-8878 (1991). [Typ78] V. Typke, M. Dakkouri, and H. Oberhammer, J. Mol. Struct. 44, 85-96 (1978). [Uga94] E. Ugaz, Phys. Rev. A 50(1), 34-38 (1994). [Vac62] Vachaspati, Phys. Rev. 128(2), 664-666 (196?) and erratum in Phys. Rev. 130(6), 2598 (1963). [VaJ86] J. A. Valdmanis and R. L. Fork, IEEE J. Quant. Elec. QE-22(1), 112-118 (1986). [Val66] R. C. Valentine, Adv. Opt. Electr. Microsc. 1, 180-203 (1966). [Val64] R. C. Valentine and N. G. Wrigley, Nature 203, 713-715 (1964). [Var95] S. D. Vartak and N. M. Lawandy, Opt. Comm. 120, 184-188 (1995). [Vie47] H. Viervoll, Acta Chem. Scand. 1, 120-132 (1947). [Vod89] K. L. Vodopyanov, L.A. Kulevskii, Cs. Toth, Gy. Farkas, and Z. Gy. Horvath, Appl. Phys. B 48, 485-488 (1989). [Vol96] M. Volkmer, Ch. Meier, J. Lieschke, A. Mihill, M. Fink, and N. Bowering, Phys. Rev. A 53(3), 1457-1468 (1996). [Vol92] M. Volkmer, Ch. Meier, A. Mihill, M. Fink, and N. Bowering, Phys. Rev. Lett. 68(15), 22892292 (1992). [War93] W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581-1589 (1993). [Wea81] J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Physics Data 18, Mathematik GmbH: Karlsruhe, 1981. [Web95] P. M. Weber, S. D. Carpenter, and T. Lucza, Proc. SPIE 2521, 23-30 (1995). [Whe59] P. J. Wheatley, The Determination of Molecular Structure, Oxford University Press: London, 1959. [WiA91] A. Williams, DOS 5: A Developer's Guide, M&T Books: Redwood City, 1991. [Wie31] R. Wier!, Ann. d. Phys. 8(5), 521-564 (1931). [WiG95] G. M. Williams, A. L. Reinheimer, V. W. Aebi, and K. A. Costello, Proc. SPIE 2415, 211235 (1995). [Wij80] R. W. Wijnaendts van Resandt, J. Phys. E 13, 1162-1164 (1980). References 391 [Wil97] J.C. Williamson, J. Cao, H. Ihee, H. Frey, and A.H. Zewail, Nature 386, 159-162 (1997). [Wil94] J.C. Williamson and A.H. Zewail, J. Phys. Chem. 98(11), 2766-2781 (1994). [Wil93] J.C. Williamson and A.H. Zewail, Chem. Phys. Lett. 209(1,2), 10-16 (1993). [Wil92] J.C. Williamson, M. Dantus, S. B. Kim, and A.H. Zewail, Chem. Phys. Lett. 196(6), 529534 (1992). [Wil91] J.C. Williamson and A.H. Zewail, Proc. Natl. Acad. Sci. USA 88, 5021-5025 (1991). [WiO88] S. 0. Williams and D. G. Imre, J. Phys. Chem. 92(23), 6648-6654 (1988). [WiS84] S. Williamson, G. Mourou, and J.C. M. Li, Phys. Rev. Lett. 52(26), 2364-2367 (1984). [WiS82] S. Williamson, G. Mourou, and S. Letzring, Proc. SPIE 348, 313-317 (1982). [WiS--] S. Williamson, G. Mourou, P. Bado, C. G. Dupuy, and K. R. Wilson (unpublished). [WiT68] T. J. Williamson and R. W. Albrecht, Nucl. Sci. Eng. 33, 141-143 (1968). [Wiz79] J. L. Wiza, Nucl. Instrum. Meth. 162, 587-601 (1979). [Won73] T. C. Wong and L. S. Bartell, J. Chem. Phys. 58(12), 5654-5660 (1973). [Wor73] J. Wormald, Diffraction Methods, Clarendon Press: Oxford, 1973. [WuT62] T.-Y. Wu, and T. Ohmura, Quantum Theory of Scattering, Prentice-Hall, Inc.: Englewood, 1962. [Yam85] T. Yamazaki, T. Noguchi, S. Sugiyama, T. Mikado, M. Chiwaki, and T. Tomimasu, IEEE Trans. Nucl. Sci. NS-32(5), 3406-3408 (1985). [Yan94] Q. L. Yang, H.J. Zhao, Z. X. Song, M. Z. Pan, B. P. Guo, and H. Niu, Proc. SPIE 2513, 112118 (1994). [Yat72] A. C. Yates and A. Tenney, Phys. Rev. A 5(6), 2474-2481 (1972). [Yat69] A. C. Yates and R. A. Bonham, J. Chem. Phys. 50(3), 1056-1058 (1969). [Yat68] A. C. Yates and T. G. Strand, Phys. Rev. 170(1), 184-189 (1968). [Yen80] R. Yen, J. Liu, and N. Bloembergen, Opt. Comm. 35(2), 277-288 (1980). [Yen79] R. Yen, P. Liu, M. Dagenais, and N. Bloembergen, Opt. Comm. 31(3), 334-339 (1979). [Zav95] A. Zavriyev, I. Fischer, D. M. Villeneuve, and A. Stolow, Chem. Phys. Lett. 234(4,5,6), 281288 (1995). [Zew96] A.H. Zewail, J. Phys. Chem. 100(31), 12701-12724 (1996). [Zew94] A.H. Zewail, Femtochemistry: Ultrafast Dynamics of the Chemical Bond, World Scientific: Singapore, 1994. [Zew91] A.H. Zewail, Faraday Disc. Chem. Soc. 91(), 207-237 (1991). [ZhA96] A. A. Zholents and M. S. Zolotorev, Phys. Rev. Lett. 76(6), 912-915 (1996). [Zha88a] J. Zhang and D. G. Imre, J. Chem. Phys. 89(1), 309-313 (1988). [Zha88b] J. Zhang, E. J. Heller, D. Huber, D. G. Imre, and D. Tannor, J. Chem. Phys. 89(6), 36023611 (1988). [Zho97] D. Zhong, S. Ahmad, and A. H. Zewail, J. Am. Chem. Soc. 119(25), 5978-5979 (1997). ,• Ultrafast Gas-Phase Electron Diffraction Volume Two Thesis By J. Charles Williamson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasade1:1,a, California 1998 (Submitted August 21, 1997) Ultrafast Gas-Phase Electron Diffraction ii Ultrafast Gas-Phase Electron Diffraction iii Table of Contents Volume One ACKNOWLEDGMENTS ..................................................................................................................... iv ABSTRACT .......................................................................................................................................... vii TABLE OF CONTENTS ........................................................................................................................ x LIST OF ABBREVIATIONS .............................................................................................................. xvi FUNDAMENTAL CONSTANTS ................................ :: ..................................................................... xvii LIST OF SYMBOLS ......................................................................................................................... xviii CHAPTER ONE: TIME-RESOLVED DIFFRACTION STUDIES ..................................................... I 1.1 FEMTOSECOND TRANSITION-STA TE SPECTROSCOPY ....................................... .. ........ ..... .... ... ..... .... .. 1 1.2 EXTRACTING R(t) FROM FTS TRANSIENTS ..... ............. .... ... ... ..... ....... .... ..... . .... .. .. ........... .. .... ........ . . 6 1.3 STRUCTURE DETERMINATION WITH DIFFRACTION TECHNIQUES ............ ........................... ..... ........ 16 1.4 PICOSECOND X-RA y DIFFRACTION ....... ........ ... ............................. ······ .......................................... 24 1.5 PICOSECOND ELECTRON DIFFRACTION: SURFACES AND FILMS .... ........ ..... ...................................... 27 1.6 TIME-RESOLVED GAS-PHASE ELECTRON DIFFRACTION ...... ... ..... ... .............. ...... .... .... ....... .... ........ . 31 1.7 ULTRAFAST GAS-PHASE ELECTRON DIFFRACTION ... ... ........ .. .......... .... ......... ... .......................... ... . 38 CHAPTER TWO: GAS-PHASE ELECTRON DIFFRACTION THEORY ..................................... 43 2.1 DIFFRACTION FROM ISOTROPIC SAMPLES ..................... .. ..................... ..... ................................. . ... 44 2.2 DEFINITIONS OF INTERNUCLEAR SEPARATION ..... ........ ...... ..... ...... ........... . ..... .. ...... ............. .. ......... 74 2.3 DIFFRACTION FROM SPECIALLY-PREPARED GAS SAMPLES .. ............................................... ...... .. .... 79 2.4 ROTATIONALLY COHERENT SAMPLES ........................ .. ................ ... .... ..... ........ .......................... . .. 85 2.5 VIBRATIONALLY COHERENT SAMPLES ....... ... ................... .. .... ........................................... .... ... ... 120 CHAPTER THREE: LASERS, VACUUMS, AND THE COMPUTER .......................................... 134 3 .1 THE FEMTOSECOND LASER SYSTEM ................................................................ ............... .............. 135 3.2 THE GAS-PHASE ELECTRON DIFFRACTION VACUUM SYSTEM .................................... ... ... ... ... . ..... 143 3.3 THE SAMPLE INLET SYSTEM ............. .. ....... .. ............ .. ............................. ........................... .. ....... 158 3 .4 THE METAL-Ev APO RATION VACUUM CHAMBER ........ ............... ....... .. ........ .. ............... ............. . .. 163 Ultrafast Gas-Phase Electron Diffraction iv 3.5 THECOMPUTERSYSTEM ............................................................................................................ 165 CHAPTER FOUR: ULTRAFAST ELECTRON PULSE GENERATION ...................................... 168 4.1 METHODS OF GENERATING FREE ELECTRONS FROM METALS ...................................................... 169 4.2 THEPHOTOCATHODE ............. ....... ............................................................................................. 180 4.3 THE UGED ELECTRON GUN················ ····················· ··············· ······· ·· ··· ··················· ··· ················ 192 4.4 MEASUREMENT OF THE ELECTRON PULSE WIDTH ............ ..... .... ........................ ... ....................... 217 CHAPTER FIVE: REAL-TIME, SINGLE ELECTRON DETECTION ACROSS TWO DIMENSIONS ........................................................................................... 228 5 .1 Ev ALUATION OF ELECTRON FLux ................................................................... ........................... 228 5.2 REAL-TIME ELECTRONIC METHODS OF GED DETECTION ..... ..................... ............................ ...... 237 5.3 CHARACTERIZING Two-DIMENSIONAL IMAGING SYSTEMS ........ ......................... ... ...................... 241 5 .4 ELECTRON IMAGING COMPONENTS ........................................................................ .................... 256 5.5 DESIGN EXAMPLES AND DETECTIVE QUANTUM EFFICIENCY ................. ... ....................... ..... ... ..... 277 CHAPTER SIX: THE UGED IMAGING SYSTEM.:·...................................................................... 288 6.1 THE FUSED FIBER OPTIC COMPONENTS ....................... .... ...... .............. .......................... ............. 291 6.2 ASSEMBLYOFTHESCINTILLATOR-BASEDIMAGINGSYSTEM .. ... ................................................ .. 292 6 .3 THE ALUMINUM BEAM STOP ... ... ..................... ........ . ··························· ....... .. ............. ········ ·· ....... 300 6.4 THE P20 PHOSPHOR SCINTILLA TOR ............. .. .... ............ ........ .. .. ... .......... .... ................................ 303 6.5 THE PROXIMITY-FOCUSED IMAGE INTENSIFIER ............................................. ... ........ ................... 305 6.6 THE CHARGE-COUPLED DEVICE ........................ .. ....................... ............................................... . 313 6.7 THE SPECTRASOURCE CAMERA HEAD············· ·· ·· ······ ···· ····· ···· ··· ······· ······ ·········· ····· ···· ················· 328 6.8 THERMOELECTRIC COOLING SYSTEMS .............. .. .. .... ....................... ... ......... ....................... ..... .. . 355 6.9 CHARACTERIZATION OF THE DETECTORS ........... .................................... ................................. .... 361 REFERENCES ................................................................................................................................... 371 Volume Two TABLE OF CONTENTS ....................................................................................................................... iii LIST OF ABBREVIATIONS ................................................................................................................ ix FUNDAMENTAL CONSTANTS ........................................................................................................... x LIST OF SYMBOLS ............................................................................................................................. xi Ultrafast Gas-Phase Electron Diffraction V CHAPTER SEVEN: METHODS OF DIFFRACTION DATA ANALYSIS .................................... 392 7 .1 EXTRACTION OF RAW INTENSITY CURVE: RADAR2 ................................................................... 393 7.1.1 Finding the Diffraction Pattern Center 7.1.2 Limits of the Active Area 7.1.3 Background Offset Correction 7.1.4 Gain and Flat-Field Image Corrections 7.1.5 Data Point Filtering 7 .2 BACKGROUND CORRECTION TECHNIQUES ................................. .. ........................................... ..... 405 7.2.1 Standard GED Methods 7.2.2 The UGED Approach to Background Correction: PROC5 7.3 DETERMINATION OF THE CAMERA CONSTANT ................................................ .............. .... ..... ...... 414 7.3.1 Diffraction From Thin Metal Films 7.3.2 Preparation of the Aluminum Film 7.3.3 Camera Constant Measurement CHAPTER EIGHT: GROUND-STATE ELECTRON DIFFRACTION DATA ............................. 421 8.1 THEEXPERIMENTALMETHOD ..................................... .. ....................... ...................................... 422 8.1 .1 Preparing the UGED Instrument 8.1.2 Recording the Diffraction Data 8.1.3 Shutting Down the UGED Instrument 8. 1.4 Analyzing the Diffraction Data 8.2 CARBON TETRACHLORIDE ............................................................................................ ............. 427 8.3 TRIFLUOROMETHYL IODIDE ................. ........ ............................................................................ .. 430 8.4 SULFUR lIEXAFLUORIDE ................................ ... ....... ....................................... .... ... ...... .. ......... .... 433 8.5 DIIODOMETHANE ............ .......... ..... .... ... ...... ..................................... ... .... ................................. .. 436 8.6 DIIODOTETRAFLUOROETHANE ..... ..... ................................................. .. ................................ .. ..... 439 8 .7 PHOTODISSOCIATION OF TRIFLUOROMETHYL IODIDE ............................................ .... ... ... .. .. ......... 441 8.8 POSSIBLE SOURCES OF ERROR ................................................................... ................ ..... .... ........ 443 8.8.1 Finite Beam Dimensions 8.8.2 Multiple Scattering 8.8.3 Chemical Binding Effects CHAPTER NINE: TOTAL EXPERIMENTAL TEMPORAL RESOLUTION AND ESTABLISHMENT OF TIME ZERO ...................................................... 448 9.1 VELOCITY MISMATCH ............ ...... ...................... ... .............................................. ...................... 450 9. 1. 1 Theoretical Analysis of Velocity Mismatch 9.1.2 Impact of Velocity Mismatch on the UGED Experiment 9.2 PURE ELECTRON-PHOTON INTERACTIONS .. ..... ............... ... .......................................................... 461 9.2.1 Thomson Scattering 9.2.2 Second Harmonic Generation 9.2.3 Ponderomotive Scattering 9.2.4 Kapitza-Dirac Scattering 9 .3 ELECTRON-PHOTON INTERACTIONS VIA INTERMEDIARIES ..... .................. ..... ... ............... .. ........... 472 9.3.1 Photoconductive Switches 9.3.2 Photoionization-Induced Lensing Ultrafast Gas-Phase Electron Diffraction vi CHAPTER TEN: ULTRAFAST GAS-PHASE ELECTRON DIFFRACTION ............................... 486 10.1 SELECTION OF THE PROTOTYPE MOLECULE: CH2l2 ................................................................... 487 10.2 EXPERIMENTAL SETUP AND METHOD ........ .. ... ............... .. .. .. .......... .. .................................. ... .... 490 10.3 DATA ANALYSIS ANDTHEFIRSTUGED TRANSIENTS .. .................. ... ..... ... ....... .. ...... ...... ... ......... 494 10.3.1 CH2I2 Photodissociation: Trial #1 10.3.2 CH2I2 Photodissociation: Trial #2 CHAPTER ELEVEN: CONCLUSIONS AND FUTURE DIRECTIONS ........................................ 512 11.1 SUMMARY OF RESULTS ................... ........ .. ............... .. .............. ............ ... ........... ........ ...... ........ 512 11.2 THE THIRD-GENERATION UGED INSTRUMENT ......................................................................... 514 11.2.1 The Laser System 11.2.2 The Sample Inlet System 11.2.3 The Electron Gun 11.2.4 The Streaking Experiment 11.2.5 The Imaging System 11.2.6 Establishing Time Zero 11.2. 7 Data Analysis Techniques APPENDIX A: DERIVATION OF ELECTRON WAVELENGTH ................................................ 527 A.1 INTRODUCTION .. .... ..... ........ ... ........ .............. ..... ..... ..... .... ...... .. ......... .. ...... .. ....... ................. ...... . 527 A.2 NONRELATIVISTIC ELECTRON WAVELENGTH .................................................. ........................... 528 A.3 RELATIVISTIC ELECTRON VELOCITY .................. .. ....................... .... ........ ... .. ...... .......... ..... .. ....... 528 A.4 RELATIVISTIC ELECTRON WAVELENGTH ..... ........ .... .. ..... ..... .... ................................................... 529 APPENDIX B: DERIVATION OF ROTATIONAL COHERENCE DIFFRACTION INTEGRALS .............................................................................................. 531 B .1 INTRODUCTION AND PRELIMINARY MATHEMATICS ................................................................ .... 531 B.1.1 Series Expansions B.1.2 The Double Factorial Notation B.1.3 The Gamma Function B.1.4 Bessel Functions Of Integer Order B.1.5 Bessel Functions Of Fractional Order B.2 1 211: s:11: exp(ia cos lfl + ib sin lf/ )dlfl ................................................................................. 534 B .3 2~ s:11: COS2 lf/ exp(ia cos lf/ + ib sin lf/ )dlfl ................................................................... 536 B.4 ½ (sinny+i Jn (bsin.O)exp(iacosO)dQ .... ...... .................... ........... .......... ................ . 539 s: APPENDIX C: INTERPOLATING THE SCATTERING FACTORS ............................................ 543 C.1 INTERPOLATION ALONG ENERGY ...................................................................... .......... .......... .. .. 544 C .2 INTERPOLATION ALONG MOMENTUM TRANSFER ....... ...... .............. .......... .......... ... ....... ........ .. ..... 545 Ultrafast Gas-Phase Electron Diffraction vii APPENDIX D: SOFTWARE DEVELOPED FOR ULTRAFAST GAS-PHASE ELECTRON DIFFRACTION ......................................................................................... 547 D.1 INTRODUCTION ......................................................................................................................... 547 D.1.1 The Programming Environment D.1.2 General Characteristics of the Software D.2 READING AND WRITING CCD IMAGES ...................................................................................... 418 D.1.1 The SpectraSource CCD Image File Structure D.1.2 Accessing Extended Memory D.3 RADAR2 ................................................................................................................................. 421 D.3.1 RADAR2 Option One: Load CCD Image D.3.2 RADAR2 Option Two: Calculate Radial Intensity D.3.3 RADAR2 Option Three: Automatic Radial Intensity Processor D.3.4 RADAR2 Option Four: Automatic Beam Center Search D.3.5 RADAR2 Option Five: Create Bitmap From Image D.3.6 RADAR2 Option Six: Calculate Regional Mean And RMS Values D.3.7 RADAR2 Option Seven: Automatic Mean And RMS Values D.4 PROC5 .................................................................................................................................... 446 D.4.1 PROC5 Background Correction Technique D.4.2 PROC5 Input Data Files D.4.3 "?" -Activate Help Screen D.4.4 "C" - Change Calculation Parameters (Molecular Scattering Screen) D.4.5 "C" - Change Calculation Parameters (Radial Distribution Screen) D.4.6 ''N" - Select New Raw Data Set D.4. 7 ''M" - Select New Molecule D.4.8 "S" - Seal Experimental Data Relative To Theory D.4.9 "A" -Append Theoretical Data Over Experimental D.4.10 "R" - Select Range For Sine Transform D.4.1 I "T" - Transform Molecular Scattering Curve D.4.12 "B" - Get Best Fit To Mixture Composition D.4.13 "L" - Get Best Fit To Camera Length D.4.14 "D" -Do MS Calculation On All Molecules D. 4. I 5 "F" - Save Data To File D.4. I 6 "p" - Change Path D.4.17 "/" -Switch Between MS And RD Screens D.4. I 8 "H" - Restrict Horizantal Viewing Range D.4.19 "V" -Restrict Vertical Viewing Range D.4.20 "E" - Enlarge To Full Screen D.4.21 "Q" - Quit D.5 ADDER ................................................................................................................................... 488 D.5.1 ADDER Option One: Sum Or Average CCD Images D.5.2 ADDER Option Two: Sum Or Average With Batch File D.5.3 ADDER Option Three: Divide One CCD Image By Another D.5.4 ADDER Option Four: Correct CCD Images With Background Curve D.6 PROFILE ................................................................................................................................ 503 D.6.1 PROFILE Option One: Load CCD Image D.6.2 PROFILE Option Two: Create X And Y Profiles D.6.3 PROFILE Option Three: Simple Batch File Processor D.6.4 PROFILE Option Four: Aligned Batch File Processor D.7 S1REAK ............... .......................... ... ............................... .......................................... ............ 518 D. 7. I STREAK Option One: Load A CCD Image Ultrafast Gas-Phase Electron Diffraction viii D.7.2 STREAK Option Two: Analyze Single CCD Image D. 7.3 STREAK Option Three: Batch File Processor D .8 PROC4 ..................................................... .. .. ....... .. ................. .. ...... ........... ..................... ....... .. 529 D .9 R-K .. ........... ........... ........................... ....... ... .............................................. .............................. 532 D.9.1 R-K Option One: Calculate Vibrational Trajectories D.9.2 R-K Option Two: Convolve Electron Pulse Time D.9.3 R-K Option Three: Load Old Trajectories D.9.4 R-K Option Four: Change Path D.9.5 R-K Option Five: Test Initial Conditions D.9.6 R-K Option Six: Check The Total Count D.10 PROC3 .............................. ..................... .................. .... ..................... .............. ... .. ................. 544 D.10.1 PROC3 Option One: Change Path D.10.2 PROC3 Option Two: Select Input Position Array D.10.3 PROC3 Option Three: Molecular Scattering Filename D.10.4 PROC3 Option Four: Radial Distribution Filename D.10.5 PROC3 Option Five: Damping Constant D.10.6 PROC3 Option Six: Calculate Scattering D.10.7 PROC3 Option Seven: Calculate Scattering For Specific Times D.10.8 PROC3 Option Eight: Calculate 2-D Scattering (IODINE) D.10.9 PROC3 Option Nine: Calculate 2-D Scattering (CF3I) D.10.10 PROC3 Option Ten: Calculate 2-D Scattering (CH2I2) D.10.11 PROC3 Option Eleven: Calculate 2-D Transform (IODINE) D.10.12 PROC3 Option Twelve: Calculate 2-D Transform (CF3I) D.11 CONV ........................... ..... ........... .... ...... .... .......... .......................... ............... ......... ........... ... 554 D.11.1 CONV Option One: Change Path D.11.2 CONV Option Two: Select Binary File D.11.3 CONV Option Three: ASCII Filename D.11.4 CONV Option Four: Convert Floating Point Data D.11.5 CONV Option Five: Convert Unsigned Integer Data D.12 CIRC ... ...... ..... ............... ............................................ ............................................ .. ........... .. . 556 D.12.1 CIRC Option One: Conduct A Translation Stage Scan D.12.2 CIRC Option Two: Conduct A Monochromator Scan D.12.3 C/RC Option Three: Conduct A Time Scan D.12.4 C/RC Option Four: View Scanned Data D.12.5 C/RC Option Five: Control The Translation Stage D.12. 6 CIRC Option Six: Control The Monochromator D.13 AUTOHOME AND AUTOSCAN .. ........................ ................... ... .... ....................... ................. 569 APPENDIX E: EXCEL MACROS FOR AUTOMATING UGED EXPERIMENTS ...................... 571 E.1 INTRODUCTION ............. ......................... ............ .... ......... .............. ........ .. ...................... .. .. ........ 571 E.2 MACRO FOR EXAMINATION OF CCD IMAGES ...... .................... ......... .. .................... .................... 572 E.3 MACRO FOR THE UGED EXPERIMENT ... .. ............... .......... ....... ............. .... .. ... ....... .. .............. ..... 574 E.4 MACRO FOR DETERMINATION OF TIME ZERO ........... .............. ............... ............ .. .... ... .. ........... ... 577 APPENDIX F: CLOCKING TRANSIENT CHEMICAL CHANGES BY ULTRAFAST ELECTRON DIFFRACTION ................................................................... 581 REFERENCES ................................................................................................................................... 585 Ultrafast Gas-Phase Electron Diffraction List of Abbreviations A➔D ADU APS ASE ATI CCD CCE CDS CTE CFF CPM csv DQE DSCS BBS BHP EMF e-p EPH FTS FWHM GED 1AM ID LEED LIP MAV MOSFET MS MTF Nd:YAG Nd:YLF OAR OD ODE OM PC PCS PDA PBS analog to digital A➔D conversion unit active pixel sensor amplified spontaneous emission above-threshold ionization charge-coupled device charge-collection efficiency correlated double sampling charge-transfer efficiency Conflat flange colliding-pulse, mode-locked, ring dye laser comma-separated variables detective quantum efficiency differential scattering cross section electron-bombarded semiconductor cascade process electron hole pairs electromagnetic fields encoder pulses extraction pinhole femtosecond transition-state spectroscopy full-width at half-maximum gas-phase electron diffraction independent atom model inner diameter low-energy electron diffraction laser-induced fluorescence mean amplitude of vibration metal-oxide-semiconductor field-effect transistor molecular scattering modulation transfer function neodymium yttrium aluminum garnet laser neodymium yttrium lithium fluoride laser open area ratio outer diameter ordinary differential equation order of magnitude photocathode photoconductive switch pulsed dye amplifier potential energy surface ix Ultrafast Gas-Phase Electron Diffraction PGF PHD PIL pix pixel PLE PLU PPE PPU PSF RAM RD RHEED RMS SITe SNR sr SSD TEC TI TOF UGED YAG ZEKE X probability generating function pulse-height distribution photoionization-induced lensing see "pixel" picture element; the smallest unit of resolution of a CCD parallel / excited parallel / unexcited perpendicular / excited perpendicular/ unexcited point spread function random access memory radial distribution reflection high-energy electron diffraction root mean square Scientific Imaging Technologies, Inc. (CCD manufacturer) signal-to-noise ratio steradian (unit solid angle) sum of the square of the differences thermoelectric cooler Texas Instruments (CCD manufacturer) time of flight ultrafast gas-phase electron diffraction yttrium aluminum garnet zero electron kinetic energy Fundamental Constants Bohr radius speed of light charge of electron permittivity of vacuum Planck's constant Boltzmann constant mass of electron electron mass energy mass of neutron Avogadro's number ao C e co h k me 2 m eC mn NA gas constant R classical electron radius Thomson cross section re <JT 5.29177 X 10-ll m 299792458 mis 1.602189 X 10· 19 C 8.854188 X 10"12 F/m 6.626176 X 10·34 Js 1.38066 X 10·23 J /K 9.109534 X 10·31 kg 511.003 keV 1.674929 X 10·27 kg 6.022045 X 1023 #/mol 0.08206 f atm/mol K 8.3145 J /mol K 2.817938 X 10· 15 m 6.652448 X 10-29 m2 List Of Symbols xi List of Symbols ae ~ r r( ) y ~E ~Tl ~v ~cr ~t ~tt.e ~tg ~te ~tL ~tTor ~tvM o o( ) Og or E co angle; rotational angle of ru about the excitation axis during integration of Fij( ) vibrational-rotational interaction constant velocity ratio volume Euler's gamma function constant; relativistic constant; Keldysh parameter FWHM of initial electron energy distribution difference in elastic scattering phase factors frequency bandwidth scattering cross section difference time delay between pump and probe laser pulses temporal broadening due to initial electron energy distribution temporal broadening due to pumpprobe geometry temporal pulse width (FWHM) of the electron beam temporal pulse width (FWHM) of the laser total temporal resolution of UGED experiment temporal broadening due to velocity mismatch phase shift; mean number of secondary electrons Dirac delta function transverse displacement shrinkage of internuclear separation centrifugal distortion energy; radiant efficiency; KapitzaDirac theory constant permittivity of vacuum 0 e 0s 1( 'A fl.e /1.n Apr fl.pu µ V p p() pt O' O'eb O'e/ 't Fermi energy quantum efficiency; probability phase of electron elastic scattering factor for element a Euler angle angle; scattering angle Bragg scattering angle internuclear separation asymmetry constant wavelength electron de Broglie wavelength neutron de Broglie wavelength probe laser wavelength pump laser wavelength reduced mass frequency density; potential density function density distribution mass-thickness parameter standard deviation; scattering cross section standard deviation of single electron pulse-height distribution; elastic scattering cross section standard deviation of electron beam pulse width elastic electron scattering cross section second harmonic generation cross section inelastic electron scattering cross section molecular electron scattering cross section time; kinetic time constant; Kapitza-Dirac theory constant; photoelectric absorption cross section List Of Symbols temporal resolution combining electron pulse width and velocity mismatch ionization potential rotational angle of detection (relative to x-axis); metallic work function azimuthal Euler angle X wave function; azimuthal angle of 'I' internuclear separation (relative to x-axis) incident wave function \j/1 scattered wave function 'l's Q solid angle; altitude angle of internuclear separation (relative to z-axis) angle between internuclear separation ru and excitation axis spatial or vibrational frequency fundamental vibrational frequency constant; rotational constant; area; Richardson constant constant; anharmonicity constant; a atomic element; acceleration; pixel dimension Bohr radius ao rotational constant B BoJ/) row-dependent background offset function of CCD image change of background offset from BRng top to bottom of CCD image; also range of pulse-height distribution background offset value at top of Braff CCDimage constant; atomic element b constant; rotational constant; flow C conductance CJ() x-y array of CCD pixel count values after A~D conversion pixel count value offset Cloff CP() average profile of CCD pixel array speed of light C rate of background noise accrual D D() radial distribution function xii dissociation energy diameter; distance differential solid angle energy; electric field one-half potential energy change of bringing atoms to molecular positions E,,_ energy of wavelength 'A, photon binding energy Eb correlation energy Ecorr total energy Eror charge of electron e e() edge spread function internuclear force constant; Fano F factor generic function; Fowler function F() Fu() spatial orientational average of scattering function for internuclear separation ru x-ray scattering function Fx() focal point distance; fraction f generic function; modified radial f() distribution function electron elastic scattering factor for element a !fa( )I amplitude of electron elastic scattering factor for element a probability generating function; G() Green's function gain g generic function; normalization g() function; spin-flip scattering amplitude scaling factor between experimental and theoretical sM(s) curves user-defined rescaling factor for CCD pixel intensities relative gain variation between top and bottom of CCD image relative CCD gain as a function of row number Planck's constant h point spread function h() current; intensity I intensity distribution I() xiii List Of Symbols moment of inertia about axis a atomic scattering intensity IA() background scattering intensity IB() IE() experimental scattering intensity IM() molecular scattering intensity IT() theoretical scattering intensity integer index; i rotational quantum number; J current Bessel function of integer order integer index Bessel function of fractional order transverse displacement of thermally-averaged internuclear separation; time-bandwidth product kinetic energy KE scattered electron beam wave k vector integer index; Boltzmann constant; k optical extinction coefficient; wave constant incident electron beam wave vector ko magnitude of incident electron ko beam wave vector damping constant used during the generation of a radial distribution curve voltage sweep rate ks length; camera length L LAe camera constant integer index; mean amplitude of l vibration; length line spread function mean amplitude of vibration of lowest vibrational state mean amplitude of vibration of harmonic oscillator mean amplitude of vibration between atoms i and j effective mean amplitude of vibration M() modified molecular scattering function; modulation transfer function MW molecular weight Ia m m H Nr n n() p P() Pn() p Q q R R R() r ro integer index integer index mass of electron mass of neutron relativistic mass number number of CCD images number of different internuclear separations in a molecule number of regions selected from a CCDimage number of trajectories integer index; refractive index population distribution number of internuclear separations with atoms a and b pressure; probability; point of detection probability distribution Legendre polynomial momentum; probability flow throughput momentum transfer magnitude; Kapitza-Dirac theory constant detection vector reflectance; distance to point of detection; gas constant set of molecular coordinates; radial probability function radius; repetition rate distance determined from groundstate rotational constants distance between average nuclear positions at thermal equilibrium structure defined with r8 bond distances and ra. bond angles internuclear separation determined with electron diffraction equilibrium internuclear separation; classical electron radius thermal average of internuclear separation vector from atom i to atomj distance between atoms i and j List Of Symbols s S() s s Smin Smax T T() t to U() Uo u u() V V() V distance determined from spectra with Kraitchman's method distance between average nuclear position at vibrational level v distance between two CCD pixels distance between average nuclear positions at T = 0 K. pumping speed or flow rate; signal molecular sample spatial distribution function electron inelastic scattering factor for element a momentum transfer vector momentum transfer magnitude lowest s position containing valid experimental scattering data largest s position of scattering data used during radial distribution transformation period; temperature molecular trajectory array (internuclear coordinate versus time) molecular trajectory array convoluted with electron pulse width time; thickness zero of time modified potential function ponderomotive potential variable axis modified radial probability function voltage; volume potential energy function velocity; vibrational quantum number electron velocity relativistic velocity xiv streak velocity well depth WB() Windows bitmap x-y array of pixel count values w weighting constant; width width of electron beam Web pre-alignment window width in Wp PROFILE software CCD pixel width Wpix X coherence length X variable axis x-axis position on CCD of unscatXeb tered electron beam x-coordinate from lower-right corXt ner selected region on CCD x-axis range of selected region on Xr CCD x-coordinate from upper-left corXu ner of selected region on CCD Xffie anharmonicity constant Y() angular probability function yij Dunham coefficient variable axis y y-axis position on CCD of unscatYeb tered electron beam y-coordinate from lower-right corYt ner of selected region on CCD y-axis range of selected region on Yr CCD y-coordinate from upper-left corYu ner of selected region on CCD z atomic number variable axis z position of ith zero in modified Z; molecular scattering curve Vs w 392 Chapter Seven Methods of Diffraction Data Analysis With the installation of the 2D single-electron detection system described in Chapter Six, construction of the second-generation UGED instrument was complete. The instrument had continuous and pulsed nozzle systems for introducing sample molecules into the scattering chamber; differential pumping to protect fragile components from the same sample molecules; a calibrated source of collimated, ultrafast electron pulses; and a dual imaging system suitable for both electron diffraction and high-spatial-resolution studies of the electron beam. This chapter discusses the last element needed to obtain structural parameters of gas-phase molecules: a method of analyzing the diffraction images downloaded from the charge-coupled device and stored on the computer hard drive. The software required to complete these tasks was part of a package of in-house, custom programs written expressly for the UGED laboratory (D.1). Chapter Seven: Methods of Diffraction Data Analysis 393 Data analysis was broken down into ·two major steps. First, a one-dimensional data file of raw scattering intensity had to be extracted from the dozens of twodimensional CCD images taken during a single experiment (7.1). Second, the raw scattering intensity had to be corrected for the background intensity in order to generate the modified molecular scattering function sME(s) and the radial distribution function/Cr) (7.2). These functions could then be compared with theoretical curves. In addition, the UGED instrument's camera constant L'A. had to be measured in order to calibrate the conversion from CCD pixel distance to the momentum transfer variables. This was done by recording diffraction patterns from a 460-A aluminum film (7.3). Ground-state structural data of several molecules studied with the UGED apparatus are reported in the next chapter. 7.1 Extraction of Raw Intensity Curve: RADAR2 Each raw image in a set of diffraction data was subject to a number of tests and measurements. First, the images underwent a cursory visual examination in order to identify blatant problems such as electron gun arcing, sudden shifts in the electron beam position, or CCD readout failures. This review could occur as the data was taken or after the fact, using SpectraSource's HPC-1 program and the EXAMINE.XLM macro (E.2). Images were then analyzed with RADAR2 to determine the count value of the background offset (necessary for gain and uniformity corrections) and the position of the unscattered electron beam. With this information, RADAR2 could operate on the CCD images as a virtual microdensitometer, computing the average image intensity as a Chapter Seven: Methods of Diffraction Data Analysis 394 function of pixel distance from the center of the pattern. The program evaluated each image over several passes, comparing the intensity of a particular pixel to the mean value of all pixels at that distance from the pattern's center. In this way, abnormally high or low values, caused by blooming or certain forms of spontaneous emission from the image intensifier, could be filtered out. Finally, RADAR2 combined the results from all images in a weighted average and created a single, one-dimensional data file: the experimental scattering intensity curve /£(pix). Explicit details on the use of RADAR2 are provided in D.3. With a few additional lines of code, RADAR2 could be modified to calculate /£(pix) from specific angular regions of the images. This would be necessary for rotational coherence studies, where the diffraction patterns lose their circular symmetry (2.4). 7.1.1 Finding the Diffraction Pattern Center In standard gas-phase electron diffraction instruments, the central region of the image is blocked by a Faraday cup to monitor the current of the primary electron beam and prevent overexposure of the detector. The center of the diffraction pattern is found after the experiment is complete, usually by spinning the photographic plate in the microdensitometer and gently adjusting the plate's position [Ben84], [MoR80]. The center was much easier to find in the UGED instrument because the unscattered electron beam was not completely blocked, and its position could be measured exactly from the image. Ideally the aluminum beam stop on the large fiber optic taper transmitted only a fraction of a percent of the scintillation from the unscattered electron beam, but if the coating were not thick enough, then the central pixels would bloom. This obscured the electron beam's position. Under such circumstances a short, unsaturated exposure of the Chapter Seven: Methods of Diffraction Data Analysis 395 beam stop pixels was recorded every five or ten diffraction images in order to monitor the electron beam position as a function of time. An example of this type of image is shown in Figure 7-1. RADAR2 determined the beam's horizontal position in these images by calculating the average horizontal profile over the beam stop region. A three-point boxcar smooth was applied to the profile, and the program noted the maximum intensity. RADAR2 then found the pixel Figure 7-1: Sample electron beam image recorded on the SITe CCD during a diffraction e~periment. The dark ring is the boundary of the beam stop; intensity outside of this region is due to scattered electrons. A horizontal intensity profile across the center of the image is plotted along the bottom . The image was used to identify the center of the diffraction pattern. Exposure time: 1 s. Image dimensions: 60x60 pix2. positions (interpolated to a tenth of a pixel) on either side of the peak corresponding to half the maximum intensity, and the profile center was identified as the half-way point between these two positions. The same procedure was used to find the vertical position. This method did require a value for the background offset correction of each image. Over the course of an experiment, the electron beam position usually varied by no more than a pixel. The distance from the center position to a particular pixel was rounded to the nearest whole pixel. Since the electron beam FWHM was four to five pixels, there was no need to calculate the fraction of overlap a particular pixel had with different integer distances and then split the pixel's intensity accordingly. Chapter Seven: Methods of Diffraction Data Analysis 396 Figure 7-2: Sample raw diffraction image of CF3I recorded on the SITe CCD. Exposure time: 90 s. An intensity profile across the center of the pattern is shown at the bottom. The thin dark circles are the inner and outer limits of the active area specified for RADAR2. Just to the right of the cross hairs is a large, spontaneous emission event approximately 160 pixels from the center of the diffraction pattern (see text). Background offset values were measured in the upper left and lower right corners of the CCD image. 7.1.2 Limits of the Active Area In order to decide whether a particular pixel should be included in the calculation of / E(pix), RADAR2 needed to know the limits of the CCD images' active area. The inner Chapter Seven: Methods of Diffraction Data Analysis 397 edge of the active area ended at the electron beam stop; the outer edge was determined by the dimensions of the CCD, the small fiber optic taper, and their overlap. The overlap was different every time the detector system was reassembled, and could change slightly as components settled into position. These limits were identified by two rings, not necessarily concentric, whose centers and radii were found iteratively using a feature in RADAR2 (D.3.2.1). The program created a faux-CCD image of these rings which was visually compared with an actual image using subtraction features in HPC-1 (Figure 7-2). Typically the inner limit had a 12-pixel radius and the outer limit had a 245-pixel radius. The final coordinates and dimensions were entered into RADAR2 and used during the microdensitometry calculations. 7.1.3 Background Offset Correction Processing a CCD image for gain or uniformity variations required a correction for the "constant" background offset. Despite careful tuning of the camera head electronics, zero electron-hole pairs registered as a finite number of ADUs at output, with values on the order of 3,000 ADU. This value increased with exposure time due to dark current, and also varied across the image, slowly increasing from the top to the bottom, due to the accumulation of dark current during readout. The background offset for diffraction images was calculated with RADAR2 by averaging the intensity of several hundred pixels in the inactive regions at the top and bottom of each image (see Figure 7-2). The offset fluctuated with time for unknown reasons, but Figure 7-3 shows that the difference between top and bottom values (due to dark current) remained constant. Plotting a graph such as Figure 7-3 for each set of Chapter Seven: Methods of Diffraction Data Analysis 398 3250 3240 ::::, C <( 3230 3220 3210 3200 1: Upper Background Offset t 0 Difference Curve I 20 40 Image 60 80 Figure 7-3: Background offset values of SITe CCD diffraction images at the top and bottom of the image. Exposure time: 75 s. The difference curve was due to the continued accumulation of dark current during readout, and remained constant despite the offset fluctuations. Spikes in the difference curve (images 6 and 9) were due to random events occurring within the offset sampling regions. The 88 exposures were recorded over an eleven hour time span (three other sets of 88 exposures were taken during this time too). diffraction data was important to make sure that random events did not occur within the sampling regions and artificially increase the offset values. 7.1.4 Gain and Flat-Field Image Corrections A major advantage that direct electron bombardment had over the secondgeneration imaging system was uniformity. The gain of the new irnager varied across the active area due to variations in the P20 phosphor, the transmission of the fused fiber optics, the "chickenwire" pattern inherent to fiber optics, and errant bubbles trapped within the optical coupling compound, particularly at the interface between the large taper and the image intensifier. Two-dimensional gain variations can be corrected by Chapter Seven: Methods of Diffraction Data Analysis 399 Figure 7-4: Sample image before and after flat-field gain correction. The images were recorded before the scintillator was installed. A photocopied picture of Dr. Zewail was placed against the fiber optic window and back-illuminated with very dim light. Flatfield correction removed the electron beam stop from Dr. Zewail's nose and the coupling compound air bubbles from his tie. proccessing each image using the following equation [Dab91], [Kuj92], [Rui92]: CI Raw ( X, Y) - CI Off ( X, Y) CIFF(x,y) - CI 0ff (x,y) (7.1) where Cioff is the background offset and ChF is the intensity of a flat field image. A flat field image is the response of the detector system to illumination with a uniform intensity. Figure 7-4 shows the results of flat field correction on a light image recorded in the UGED detector before the phosphor scintillator was installed. Gain variations due to the electron beam stop in the center of Dr. Zewail's nose and coupling-compound bubbles in his necktie were eliminated after correction with Eq. 7.1. Unfortunately a flat field image for UGED was not created. A highly uniform light source was constructed with rectangular LEDs and a pair of flashed-opal diffusers, but the Chapter Seven: Methods of Diffraction Data Analysis 400 resulting flat field images were useless for electron diffraction because the response of the aluminum overcoat and scintillator to photons is fundamentally different than their response to electrons. Instead, a two-dimensional, uniform electron source was required to create the flat field image. Possibly this could be done by defocusing the electron beam and rapidly rastering it across the scintillator, averaging over many images. The deflection electrodes would not have to be located at the nozzle position because the interaction of the incident electrons with the aluminum overcoat and the P20 phosphor has only a slight dependence on the incidence angle for small 8. At the instrument's maximum scattering angle of 12°, the travel distance through the aluminum overcoat increases by only 2%. Data presented by Reimer showed that increasing the thickness of a 3,000-A aluminum film by 2% (pt= 81 µg/cm 2) causes less than an 0.1 % change in the kinetic energy of a 20 ke V electron, which is insignificant [ReL85]. Since the penetration depth of the electrons into the P20 phosphor is only a few microns, scintillation from the phosphor should also exhibit no dependence at small angles. RADAR2 was written to include the flat field correction, once such an image is obtained. The program also automatically corrects for a linear, 30% gain decrease that occurs from the top to the bottom of CCD images. The source of this inhomogeneity was not found but must occur either within the SITe CCD or the camera head. The fit between experimental and theoretical diffraction data improved by correcting the experimental scattering intensity according to (see Figure 8-12): (7.2) Chapter Seven: Methods of Diffraction Data Analysis 401 where r is the pixel distance from the center of the pattern. This first-order approximation to a flat field image was made by measuring the electron beam intensity at several points along a radius of the detector. 7.1.5 Data Point Filtering Once RADAR2 was provided with the center of the diffraction pattern, the limits of the active area, the background offset, the uniform gain correction, and also the pixel coordinates of any particular regions which should be ignored, the program was ready to perform the microdensitometry calculation. A data storage array containing pixel intensity as a function of distance from the center was cleared to zeros. RADAR2 scanned through the diffraction image, pixel by pixel, and added the corrected intensity of each valid pixel into the array bin corresponding to the pixel's distance from the center (to the nearest whole pixel). Finally, after all pixels were evaluated, the program normalized the array relative to sampling area by dividing by the number of valid pixels which contributed to each bin. The data array then contained !\pix) and could be written to the hard drive. Unfortunately, this method proved inadequate because of irregularities in the CCD images. Some pixels in the active area became saturated due to blooming, and others had abnormally high count values due to events such as spontaneous emission from the image intensifier (most likely ion emission). A single experiment involved hundreds of diffraction images, and it was impractical to manually identify and block out all anomalous regions in each image, but the impact of these regions could not be ignored. As an illustration, Figure 7-5 presents the pulse-height distribution of all pixels contributing to r = 160 pix in the diffraction image shown in Figure 7-2. Two pixels have count values far removed 402 Chapter Seven: Methods of Diffraction Data Analysis 120 100 "' 80 Cl) Mean: Std. Dev.: (.) C Cl) :r... :r... ::::, Without "Bad" Pixels 217 187 210 85 60 - (.) (.) 0 With "Bad" Pixels ~~ ~ 40 - =l:t:: "Bad" Pixels ~ / 20 0 0 1000 2000 3000 4000 5000 Signal (ADU) Figure 7-5: Offset-corrected pulse-height distribution of the diffraction image in Figure 72 at a radius of 160 pixels from the center. Tw0 pixels have unusually high count values due to random noise, and they significantly distort the mean and standard deviation of the PHD. The vertical bars show that the majority of the PHD lies within four standard deviations (85 ADU) of the mean. from the background-corrected main distribution, one at 1,810 ADU and one at 5,150 ADU. These two pixels alone raise the average intensity at r = 160 pix by 5 ADU, which is of the same magnitude as the molecular scattering intensity at that position. The sM(s) from this diffraction image is plotted in Figure 7-6, and the influence of the two "bad" pixels caused the spike at s = 8.24 A- 1. Removing those pixels from the RADAR2 calculation eliminated the spike. A filtering procedure was added to RADAR2 to automatically ignore pixels with unusually low or high count values. RADAR2 scanned each image at least three times: once to calculate the mean count value as a function of r, once to calculate the standard deviation about the mean at each r, and once to compare the values of individual pixels with the mean value. Those pixels with count values too far from the mean were declared "bad" and removed from consideration; RADAR2 repeated the process until a self- Chapter Seven: Methods of Diffraction Data Analysis - - Raw Data 0 1 2 3 - Filtered Data 403 - Theory I 7 8 9 10 Figure 7-6: Modified molecular scattering curves for the single diffraction image of CF3 I shown in Figure 7-2. The two "bad" pixels in the PHO at r= 160 pixels (Figure 7-5) cause a spike in the sM(s) curve. Once the raw data is filtered, the experimental curve is closer to the theoretical curve. consistent pixel set was obtained. Two types of limits were established to weed out the "bad" pixels. Often the central columns of the diffraction image were dominated by blooming, caused by saturation of the beam stop pixels by the unscattered electron beam signal. Bloomed pixels all had high count values, higher than the diffraction signal even at small s, so an upper cutoff of valid pixel intensities (35,000 ADU) was set to remove bloomed pixels. To remove "bad" pixels such as those shown in Figure 7-5, the count value of valid pixels had to be within n standard deviations of the mean value at that radius. A lower limit was set for the standard deviation so that valid pixels would not be thrown out in high s regions of the diffraction pattern, where the number of scattered electrons might be small compared to the number of pixels. The lower limit corresponded to the average signal per Chapter Seven: Methods of Diffraction Data Analysis pixel caused by one electron. The 6.9 Smax distribution pulse-height C 0 ; showed ~ 5.4 one electron registered as 1,600 ADU spread cu 5.9 -~ _________________ _SfT1<P< _=_ 1_0_~-~ :E a: 4.9 __________________ over ~4 pixels when the image Most diffraction images were recorded with the dial position at 8, a factor of ten lower in gain (Figure 6-10), and the lower limit s_ max _=_a__ A· 1_ 4.4 - t - - - + - - - t - - - - + - - - + - - 1 - - - - 1 - - ~ 3 intensifer gain was at maximum (dial position at 10). = 12 A1 6.4 measurement discussed in 6.9.3 that 404 4 5 6 7 8 9 10 # of Standard Deviations Retained Figure 7-7: Change in the RMS deviation between experiment and theory of a complete CF3 1 diffraction data set as a function of the number of standard deviations retained by RADAR2 during the filtering process. Calculations were done for three different ranges of s. The horizontal dashed line shows the RMS values with no filtering. on the standard deviation in RADAR2 was set at 40 ADU. The limit would have to be adjusted if a different image intensifier gain setting were used, or if flat field corrections were initiated. In order to select a proper value for the number of standard deviations n, sM\s) curves were generated for a complete set of diffraction data as a function of n. The RMS difference between theoretical and experimental sM(s) curves were calculated using different values of Smax, and the results are presented in Figure 7-7. The optimum value of n was found to be 4, representing a balance between noise due to anomalous pixel intensities (n too big) and noise due to the removal of valid pixel intensities (n too small). The thick vertical bars in Figure 7-5 show how far four standard deviations extend from the mean in a typical pulse-height distribution. Chapter Seven: Methods of Diffraction Data Analysis 405 In practice, each diffraction image went through five or six passes of the filtering process because removal of one "bad" pixel could cause a large drop in the accepted standard deviation. Pixels which would have been acceptable in the first pass, like the one with 720 ADU in Figure 7-5, would be removed in subsequent passes. All gas-phase diffraction data recorded with the second-generation UGED instrument (and presented in this thesis) were extracted from the raw CCD images with the filtering microdensitometer option of RADAR2. In addition to the /E(pix) data file, RADAR2 also created a diagnostic data file which reported the electron beam position and background offsets used for each image, followed by the number of filtering passes, the number of "bad" pixels, and the cumulative, background-corrected scattered intensity of each image in ADU. 7.2 Background Correction Techniques: The second phase of UGED data analysis was to obtain molecular structure parameters from the newly generated /E(pix) data file. The total experimental scattering intensity is commonly described as a sum of three components: (7.3) where /M(s) is the molecular scattering intensity (Eq. 2.69), /A(s) is the atomic scattering intensity, including inelasitic terms (Eq. 2.43), and lver(s) represents contributions from the detector and experimental artifacts. Since /M(s) is the only term containing structural information, IA(s) and lver(s) are sometimes lumped together as a single, generic background term, ls(s): Chapter Seven: Methods of Diffraction Data Analysis 406 (7.4) With an ideal experimental apparatus, lver(s) would be the same for every molecular system studied. IA(s) varies with each type of molecule, however, so the background function must be determined for every system when steady-state structures are examined with conventional GED methods. Most analytic treatments make the reasonable assumption that ls(s) is a smooth function compared to IM(s), and all higher frequency oscillations in the scattering intensity are due solely to molecular interference terms. A brief review of different approaches diffractionists have used to remove J8 (s) from Eq. 7.4 is presented in 7.2.1. With UGED experiments, however, h(s) should not change as a function of time because all atoms remain within the interaction region, regardless of the photochemistry. Therefore, 18 (s) could in principle be eliminated from time-resolved data by taking the difference between scattering intensity curves from different data points (time steps); the analysis procedure would be greatly simplified (10.3). Of course, the UGED technique had to be tested first by recording diffraction data of ground-state molecules, where difference curves could not be generated, so the program PROC5 was written to remove 18 (s) from UGED data. Obtaining highly-refined structural parameters was not the goal of PROC5, unlike other software used by conventional diffractionists, so the mechanics of background correction in PROC5 were also different. PROC5 is discussed further in 7.2.2. 7.2.1 Standard GED Methods The sophistication of GED data background removal procedures has increased Chapter Seven: Methods of Diffraction Data Analysis steadily with improvements in computational power. 407 In the early years of molecular structure investigation, diffractionists relied on the visual method of interpretation [Pau34]. The positions of interference maxima and minima were determined directly from the photographic plates using the human eye's logarithmic intensity response, and these positions were compared with theoretical modified scattering curves. The background curve was just part of the experimentalist's subconscious manipulations, and never explicitly drawn. Shaffer et al. developed a complementary approach which was perhaps the frrst analysis method to exploit computers [ShP46]. The authors drew a modified molecular scattering curve based on the plate images, this time estimating an experimental background curve in the process. The sM\s) was entered into the computer (with punched cards!), and the computer calculated the radial distribution curve from which the internuclear separations could be immediately identified. Later versions used microdensitometer traces of the raw data and actually refined the background iteratively such that the radial distribution curve had a flat baseline and was always positive [KaJ50]. Problem regions in the background estimate could be identified by a frequency analysis of residual oscillations in the f(r). As computational power and speed increased, diffractionists sought to completely remove the "human factor" from data analysis such that every research group would concur on the structure identified by a particular set of data. Several automated background refinement procedures were tested [Shi64]. For example, Bartell and coworkers conducted a least squares fit on the total experimental scattering intensity l(s) by minimizing the function [Bar65a]: Chapter Seven: Methods of Diffraction Data Analysis I, wj(IT(s) - IE(s))2 408 (7.5) j where wi were weighting factors over different regions of the pattern, /T(s) was given by: (7.6) and the parameterized background curve was: (7.7) n MT(s) was the theoretical modified molecular scattering function (Eq. 2.80) according to the "American school" (Eq. 2.88), and R was a fitting variable called the index of resolution. In an ideal fit, R approached unity. The order of the polynomial in the background curve was limited to prevent the introduction of spurious oscillations. A similar approach was also used by the "Norwegian school" (Eq. 2.87) [AnB69]. Other variants on background-correction techniques included refinement of the radial distribution curve [Bon59], least squares fitting of the background curve (rather than /T(s)) [Shi72], and optimization of the smoothness of the background curve [Shi71]. More recently, various fitting mechanisms have replaced the single background function (like Eq. 7.7) with a series of splines, third- or fifth-order polynomials applied piecewise across the scattering intensity curve [ReC67], [Mij75], [Nov79], [Spi79]. The splines have been optimized for smoothness and continuity of the first and second differentials at the joints. All of these refinement procedures also include a feedback loop of structure optimization as well. The number of structural parameters NFic is equal to two (r, l) or three (r, l, K) times the result of the summation: Chapter Seven: Methods of Diffraction Data Analysis 409 (7.8) where N is the number of atoms in the molecule. Clearly NFir becomes large very quickly as the number of atoms increases. NFir is often reduced in advance by assuming a particular symmetry for the molecule, fixing certain internuclear distances or mean amplitudes of vibrations, or even neglecting weak contributors such as H •••H atom pairs. Spectroscopic data is sometimes incorporated as well [Kuc88]. 7.2.2 The UGED Approach to Background Correction: PROCS The motivation behind the analysis of cqpventional gas-phase electron diffraction data experiments has been to obtain high structural resolution(< 0.01 A) of the sample molecules. Ultrafast GED had a markedly different perspective, however, because the goal was to determine the function R(t) with moderate structural resolution (< 0.1 A) on the time scale of fundamental chemical dynamics (< 10 ps). This difference in perspective was reflected in the way the UGED data was treated upon collection: the analysis program PROC5 was written with the intent of correcting l(s) for Is(s), but not of making a finetuned refinement of structural parameters. After all, with a temporal resolution of a few picoseconds or greater, UGED experiments would follow ultrafast kinetic processes between parents and products, and not observe coherent vibrational intermediates. The atomic positions of the reactants and products would be more or less static, except for thermal averaging. Since structural parameters for these species were usually available from conventional GED, spectroscopy, or calculations, PROC5 could start from the assumption that the structures were known, but the background curve and composition Chapter Seven: Methods of Diffraction Data Analysis 410 were not. • The program PROC5 (D.4) completed a number of different tasks: (1) it calculated the experimental background curve h(s) based on a theoretical model for the molecular structures, (2) it converted the scattering data from detector coordinates (pixels) to units of momentum transfer (A- 1), (3) it generated experimental and theoretical sM(s) curves, and (4) it calculated the radial distribution functions. Simple least squares fitting routines were included for optimizing the fit of a mixture of two or more components and for finding the camera length. PROC5 also had special scattering intensity normalization options, not found in conventional GED software but necessary for the analysis of UGED transients (10.3). The UGED background correction method was based on the oscillatory nature of the molecular interference functions. IM(s) cycles back and forth about the zero line, crossing several times within the UGED range of 15 A- 1. At each of these crossings or zero points, Eq. 7.4 shows that the raw experimental scattering intensity must be equal to J8 (s). The theoretical zero points can be identified with an adequate model of the molecular structure, and a smooth curve can be fit through l(s) at those zero points. This fitted curve is the experimental background curve. The questions remaining during the design of PROC5 was what functions and constraints to use while fitting the zero points, and how to prepare the data (should • As the temporal resolution of UGED improves, vibrational coherence studies will become possible and the analysis methods would have to change, becoming more like conventional GED, so that unknown transient structures could be determined. Chapter Seven: Methods of Diffraction Data Analysis Fitting Method Spline Function D'Antonio exp(a 1 + a 2 Sa 3 ) # Other OverZeros Constraints lap? 411 First Segment Last Segment 3 None y - - Option 1 Cubic 2 Slope, Curvature at z1 N f"(z1) = 0, Closeness - Option 2 Cubic 3 Closeness y - - Option 3 Cubic 4 None y - - - - Option 4 Quadratic 2 Closeness y Option 5 Cubic 3 Smoothness y - - Option 6 Cubic 2 Slope at z1, z2 N Slope at z2, Smoothness Slope at z1, Smoothness Option 7 Cubic 2 Slope at z1 , Smoothness N - Fit Line Option 8 Quartic 2 Slope at z1, z2, Smoothness .. N Fit Cubic, Slope at z2, Smoothness Fit Cubic, Slope at z1, Smoothness Option 9 Cubic 2 Slope at z1, z2 N Fit Quadratic, Fit Quadratic, Slope at z2 Slope at z1 Table 7-1: Summary of the experimental background fitting methods tested in the PROCS software. "Overlap?" indicates that overlapping spline curves were linearly mixed. The first and last segment often required additional or alternative fitting constraints. Zi refers to the ilh zero spanned by the spline. were tested (Table 7-1). Each spline segment was fit across two or more zero points with additional constraints added as necessary. These constraints included matching slopes at the joints, smoothing the segment, or optimizing the closeness of the segment to the experimental data [Hay70]. The data was always fit as a function of pixel position; conversion to regular units of s took place after background correction. Early versions of PROC5 relied solely on a method suggested by D' Antonio et al., where three-zero-point segments were fit to an exponential function exp(a 1 + a 2 sa 3) [DAn71]. Overlapping segments were then linearly mixed to give a composite background curve, which guaranteed that the slopes all matched at the joints. This approach worked fairly well on the UGED data as long as the experimental intensity at Chapter Seven: Methods of Diffraction Data Analysis 412 each zero point was always lower than at the previous zero point. The exponential cannot fit a local minimum or maximum, so the raw data could never be prepared with s/lfa IIJb I, which makes the data go to zero at smalls. The remaining fitting methods all used polynomial spline segments. Option 1 fit a cubic across two zero points. At the first zero point, the first and second differentials of the cubic had to match those of the spline from the previous segment. In the very first segment, the two extra constraints were a zero second differential at the first zero point and optimization of closeness to the raw experimental data. Option 2 fit a cubic across three zero points and optimized for closeness to the raw experimental data. Overlapping segments were linearly mixed. Option 3 fit a cubic across four zero points, and overlapping segments were linearly mixed. Option 4 fit a quadratic across the end zero points of a three-point segment and optimized for closeness. Overlapping segments were linearly mixed. This method did not guarantee that the background curve would actually pass through the zero points. Option 5 fit a cubic across three zero points and optimized for smoothness of the segment. Overlapping segments were linearly mixed. Option 6 fit a cubic across two zero points and matched the slopes at each zero point to the slope between the two surrounding zero points. The first and last segments needed an additional constraint and were optimized for smoothness. Option 7 fit a cubic across two zero points, optimized for smoothness, and fit the slope at the first zero point to the slope of the preceding segment. The last segment needed an additional constraint and was assumed to be a line for 1/lfa llf I or s/lfa llf I b b Chapter Seven: Methods of Diffraction Data Analysis 413 preparation, and assumed to have a final slope of zero when fitting IE(s). Option 8 fit a quartic across two zero points, matching slopes as in Option 6 and also optimizing for smoothness. The first and last segments were fit as cubics, matching the slope at the innermost zero point and then optimizing for smoothness. Finally, Option 9 fit a cubic across two zero points as with Option 6, except the first and last segments were fit as quadratics. Option 2 was a disaster because the closeness constraint followed the raw data too closely, and the resulting background curve contained many wiggles. The background curve from Option 4 was not guaranteed to pass through the zero points, and the spline order of Option 8 was found to be too high, resulting in a sequence of nearly linear segments. Options 5 and 7 exhibited much stronger deviations from the ideal than other methods and were also removed from consideration. To evaluate the remaining methods (D' Antonio and Options 3, 6, and 9) and the choice of data preparation, a theoretical molecular scattering curve for CF3I was superimposed on top of an actual experimental background curve generated with Option 3. This faux l(s) curve was fit using each method under two types of preparation, and the resulting background curves were compared by taking the difference relative to a reference method (in this case, the results from the D' Antonio method with no data preparation). The difference was taken because the original background was generated by PROC5, and was not necessarily the best. The best fitting method would be the one which exhibited the least deviation of all others; this was found to be Option 9 under s/lfa llfb I data preparation. Option 9 also provided some of the best fits in the first and last segments; other approaches tended towards extremes, particularly at larges. Chapter Seven: Methods of Diffraction Data Analysis 414 All diffraction data presented in this thesis were fit using Option 9 and s/lfa IIJb I data preparation. Other, better methods should be sought in the future. One glaring difficulty in relying on the zero points to fit the background curve (with no explicit dependence on all the raw data) was that the shape of the curve could suddenly jump when fitting for composition. As composition changed, a pair of zeros might disappear as a maximum or minimum in the sM(s) curve dipped below or above the baseline. This did not affect the time-resolved data presented in Chapter Ten. 7.3 Determination of the Camera Constant In order for PROC5 to make the conversion from CCD pixels to momentum transfers, the program needed values for the camera length Land the de Broglie electron wavelength "-e• At small scattering angles, the product of these two variables is sufficient to make the conversion because: (7.9) where Wpix is the effective CCD pixel width at the scintillator (76.8 µm), r is in pixels, and LAe is known as the camera constant. With L ~ 100 mm, the maximum UGED scattering angle was ~ 12 °, and the approximation in Eq. 7. 9 gave a 1.5 % error in s. This error seemed too big to ignore, so Land Ae were determined individually. The camera length was measured as 100.1 ± 0.5 mm using a ruler, but the 0.5% uncertainty was an order of magnitude larger than in standard GED values for L [Tre88]. The electron accelerating voltage was measured with a multimeter to be 18.1 ± 0.2 keV (4.3.1), corresponding to a Chapter Seven: Methods of Diffraction Data Analysis relativistic de Broglie wavelength of 0.0904 ± 0.0005 A (Eq. A.12). 415 Again, the uncertainty was larger than for traditional GED experiments, and an alternative camera constant calibration method was sought. GED laboratories calibrate their instruments with diffraction studies of highly symmetric gas molecules such as CO2, CCLi, SF6 , or benzene, or with thin, polycrystalline films [Ewb84], [Tag84], [Tre88]. Calibration with gas-phase diffraction was prone to too many errors in the UGED instrument because of the short range of s (~ 15 A- 1), nonuniform gain, and the difficulties associated with background correction. Instead, confirmatory measurements of L and "Ae were made by diffracting electrons from a thin, amorphous aluminum film, as described in the next three sections. Unfortunately, the uncertainty in the values of L and "Ae did not improve. 7.3.1 Diffraction From Thin Metal Films The diffraction image from a polycrystalline or amorphous film is a series of sharp, concentric rings, called a Debye-Scherrer pattern (1.3). The ring pattern occurs because the crystal planes within the film are randomly oriented with respect to the electron beam. The radius of a particular ring at the detector (in mm) is given by [AnK71], [Hir77]: (7.10) where d is the interplanar spacing. For a face-centered cubic crystal structure, values of d are given by: (7.11) 416 Chapter Seven: Methods of Diffraction Data Analysis where a is the lattice constant of the material and h, k, and l are integers known as the Miller indices. Aluminum, silver, and gold all have FCC structures, and their lattice constants are 4.049, 4.086, and 4.078 A, respectively [AnK71]. Table 7-2 summarizes the values of d for the first sixteen aluminum Debye-Scherrer nngs, their relative intensities, and the ring radii, using 18 ke V electrons and a camera length of 100.6 mm as an example. The error in r caused by the approximation in Eq. 7.10 is 0.5% by the ninth ring. hk/, 111 200 220 311 222 400 331 420 422 511 333 440 531 600 442 620 ,<a) r<b) (A) loix) (pix) 2.338 50.8 50.8 2.025 1.432 1.221 1.169 1.012 0.929 0.905 58.6 82.9 97.2 101 .6 117.3 127.8 131.1 0.826 0.779 0.779 0.716 143.6 152.3 152.3 165.8 0.684 0.675 0.675 0.640 173.4 175.9 175.9 185.4 58.7 83.0 97.4 101.8 117.6 128.2 131.6 144.3 153.1 153.1 166.8 174.6 177.1 177.1 186.8 d 0 Table 7-2: Miller indices, interplanar spacings, and radii of Debye-Scherrer rings for aluminum (a = 4.049 A) [AnK71]. L = 100.6 mm; Ae = 0.09062 A; 1 pixel = 0.0768 mm. (a) r = L'Ae/d. (b) r corrected for a planar detector (Eq. 7.10). 7.3.2 Preparation of the Aluminum Film The thin, polycrystalline aluminum target was fabricated in the UGED laboratory. The quality of the diffraction pattern depends on the film thickness; diffraction is weak if the film is too thin, but thicker films decrease the electron kinetic energy, broaden the output energy PHD, and thereby decrease resolution of the ring pattern. Aluminum films with mass-thickness parameters on the order of 10 to 20 µg/cm 2 ( 400 to 700 A) perturb the energy distribution of 20 ke V electrons only slightly [ReL85], but still have a substantial number of atomic layers. Thicknesses of 220, 470, and 1200 A were tested in the UGED instrument. Chapter Seven: Methods of Diffraction Data Analysis 417 Aluminum films were prepared in the following manner. Rock salt crystals were cleaved with a razor blade to give mirror-like surfaces with areas of ~20 mm2 . The crystals were glued face-up to a metal plate, mounted upside-down in the metal evaporation chamber (3.4), and coated with aluminum (Aldrich; 99.999%). The aluminum films were removed from the salt crystals by slowly lowering the crystals into water at an angle, allowing the salt to dissolve and the aluminum to float on the surface. Fine nickel mesh (70 lpi; Interconics) was superglued over the ~3-mm openings of metal washers, and the aluminum films were picked up with the mesh-covered washers to make the diffraction target. Several targets were prepared simultaneously because the films sometimes fractured as the water dried. Good targets were mounted on the nozzle tip in the scattering chamber, and the attachment method displaced the targets an extra 0.5 mm from the detector, giving a value of 100.6 ± 0.5 mm for L. The best diffraction patterns were obtained with the 470-A film. 7.3.3 Camera Constant Measurement The plan for measuring L and Ae was to record aluminum diffraction patterns at several camera distances. Since the change in camera length could be adjusted with 5micron precision using the Thermionics high-precision positioning stage, the uncertainty in M was negligible compared with the uncertainty in L, and L could be calculated from: (7.12) where ~r is the change in a Debye-Scherrer ring's radius as the camera length shifts from L to L+M. After determining L, Ae could be found by using an alternate form of Eq. 7.10: Chapter Seven: Methods of Diffraction Data Analysis 418 (7.13) where the term in brackets has only a small dependence on Ae and is essentially constant across the expected uncertainty range of AeDiffraction patterns were recorded for three distances: L, L+0.2500", L+0.5000". camera and Forty images were taken at each camera distance, 60 s per exposure, with standard image intensifier settings (gain dial 0 100 window). The raw scattering 200 300 r (pix) at 8 V; 6.4-µs delay; 210-µs Figure 7-8: Raw scattering intensity profile l(pix) from a 470-A aluminum film. Total exposure time: 40 min. intensity curves were extracted as described in 7.1 using the filtering option of RADAR2, and !\pix) at Lis shown in Figure 7-8. The background intensity was removed by fitting !\pix) to a biexponential function at selected points, and the corrected curves multiplied by r2 are plotted in Figure 7-9. Table 7-3 summarizes the radii of five prominent rings for each set of diffraction patterns. Determining L with this data according to Eq. 7 .12 was hkl 111 220 311 331/420 600/442 L L+0.25" L+0.50" 49.8 81.4 95.3 126.4 172.3 53.0 86.7 101.4 135.1 184.0 56.2 91.7 107.3 143.0 194.5 Table 7-3: Ring radius in pixels for 470-A polycrystalline aluminum diffraction pattern. 111, 220, and 311 rings have an uncertainty of ±0.5 pix; other rings are ±1 pix. Chapter Seven: Methods of Diffraction Data Analysis 419 111 600 L + 0.2500" L 0 50 100 150 200 250 300 r (pix) Figure 7-9: Background-corrected intensity profiles for 470-A aluminum foil diffraction data recorded at three camera lengths L, L+0.2500", and L+0.5000". Most of the Debye-Scherrer rings listed in Table 7-2 are evident. The rings move out to higher pixel positions as the camera length increases. Total exposure time for each data set: 40 min. unsatisfactory because the uncertainty was on the order of 3 mm or more, depending on the number of rings included in the calculation. Furthermore, L was dependent on which pairs of ring distances were used; the three values found using Eq. 7.12 were 95, 99, and 103 mm. A greater range of motion for L or better spatial resolution would be necessary to refine these results. In the mean time, the camera length of 100.1 ± 0.5 mm found with a ruler seemed to be the best measurement for L. Using the ruler value, then, the electron wavelength was calculated with Eq. 7 .13 for the five prominent rings in each set of diffraction data. The average electron kinetic energy derived from these wavelengths was 18.8 ± 0.3 keV, different from the direct voltage measurement, but with a similar uncertainty. Since KE= 18.8 keV was the result of a diffraction experiment, this value was used to analyze the GED patterns. Although measuring the values of L and Ae with greater precision and accuracy is an important Chapter Seven: Methods of Diffraction Data Analysis 420 future goal for the UGED laboratory, the high uncertainties do not have much influence on the results reported in this thesis. Excellent agreement between experimental and theoretical modified molecular scattering curves was still obtained (Chapter Eight). 421 Chapter Eight Ground-State Electron Diffraction Data Ground-state diffraction patterns were recorded with picosecond electron pulses to test both the second-generation instrument's capabilities and the data analysis techniques. The laboratory procedure used during these benchmark experiments is outlined in 8.1. Four molecules were studied (repeatedly) - CC4, CF3I, SF6 , and CH2Ii - and the modified molecular scattering curves and radial distribution functions obtained for each of these systems are presented in 8.2 through 8.5. In addition, the results from two experiments conducted in the first-generation apparatus are also included: ground-state diffraction data of C2F4Ji (8.6) and a nanosecond time scale photodissociation study of CF3I (8.7). These results were originally published in [Wil92] and [Dan94]. This chapter concludes with a brief analysis of some discrepancies between experimental and theoretical sM(s) curves. Chapter Eight: Ground-State Electron Diffraction Data 422 8.1 The Experimental Method The basic protocol for obtaining scattering data could be broken into four phases: (1) preparation of the instrument, (2) recording two-dimensional electron diffraction images, (3) shutting down the instrument, and (4) analyzing the images to obtain sM(s) andf(r). The details of each of these phases are described below. 8.1.1 Preparing the UGED Instrument Several components required a half-hour or more of warm up time and were turned on early in the day, such as the CPM/PDA laser system, and the image intensifier and electron gun power supplies. The liquid-nitrogen reservoir for the trap inside the scattering chamber was charged, and the molecular beam system heaters were started if the sample required heating. Generally, the camera head power supply and SITe CCD thermoelectric cooler ran continuously, so the SITe CCD should already have been stabilized at a temperature of -40 °C. The electron gun was slowly brought up to 18 kV. Once the laser was running well, the first order of business was to maximize the electron beam intensity by tweaking the input mirror which directed the 310-nm laser onto the photocathode. The electron beam intensity was monitored by switching the camera head to the TI CCD. Since the heat sink for the TI CCD thermoelectric cooler was thermally coupled through the scintillator gate cover to the scattering chamber wall, the cooler was not left on continuously, like the SITe CCD's cooler. However, equilibration to -20 °C took only a few minutes. SpectraSource's HPC-1 program was run in SubFrame Focus Mode, which continuously downloads images from the CCD without saving them to disk. In this way, feedback about the electron beam intensity as a function of the Chapter Eight: Ground-State Electron Diffraction Data 423 input mirror tilt position was immediately available, and the intensity could be tweaked in real time. If the intensity became too high (corresponding to electron pulses longer than ~ 10 ps), then NG filters were installed in the 620-nm portion of the electron-generation laser path. After optimizing the electron beam intensity, the horizontal and vertical deflection plate voltages were adjusted to bring the electron beam onto the center of the beam stop. This required shutting down the TI CCD cooler, opening the scintillator gate cover, switching the camera head over to the SITe CCD, and activating the image intensifier. Since this was the first use of the image intensifier for the day, it was also a good time to confirm that the II's gate window was 210-µs wide and began 6.4 µs after the end of the Nd:YAG laser lamp synchronization pulse. The gain-adjustment voltage on the intensifier was usually set to 8 V (Figure 6-10). With the electron path now fixed, the molecular beam had to be moved into position. The y-axis setting for the high-precision positioning stage was not changed from experiment to experiment in order to keep the camera length L constant, but the x- and zaxis settings were adjusted each time based on how the nozzle tip clipped the electron beam. First, the detector system was switched back to the TI CCD. Second, the nozzle tip was lowered and centered side-to-side in the electron beam path to determine the xaxis setting. Third, the nozzle was moved up until clipping was barely evident, and then the nozzle was raised an additional 100 µm or so. The electron beam had a FWHM We of ~300 µmat the nozzle tip. The molecular beam width was estimated to be 380 µmusing: (8.1) Chapter Eight: Ground-State Electron Diffraction Data 424 where z is the distance from the nozzle tip (approximately wef2), l.53z is the FWHM of a thin-walled effusive point source (see Eq. 9.12), and WN is the width of the nozzle orifice. The final preparatory task was to start the flow through the molecular beam. To be safe, the Tl CCD was allowed to warm up and the electron gun chamber butterfly valve was closed. The inlet-system input valve was adjusted until the scattering chamber ionization gauge reported a pressure on the order of 2x 104 torr; the actual value used was sample-dependent since the ion gauge response varies with chemical [Moo89]. Once the pressure stabilized, the butterfly valve was reopened and the detection system was switched to the SITe CCD. 8.1.2 Recording the Diffraction Data A starting value for the exposure time was 60 s, but this value was adjusted up or down based on the scattered electron intensity in a test diffraction image. The central part of the diffraction pattern should not saturate and exceed the dynamic range of the CCD. At the same time, though, the ratio between the exposure and CCD image readout times ( ~ 10 s) should be maximized, so the sample flow was often attenuated if the scattering intensity was too strong, rather than shortening the exposure time. The image intensifier gain could be lowered instead, but strong scattering possibly indicated that the molecular beam density was too high, causing greater than 10 to 20% scattering and increasing the probability of intermolecular multiple scattering. The percent scattering was easily checked by comparing the unscattered electron beam intensity with and without the molecular beam flow. Once the exposure conditions were selected, five to ten diffraction images were Chapter Eight: Ground-State Electron Diffraction Data 425 recorded one after another using an EXCEL macro similar to (but simpler than) UGED_EXP.XLM (E.3). There was no need to move the Aerotech translation stage since the pump laser was not used. Images were given a quick, visual check as they appeared on the computer screen to confirm that the experimental conditions remained constant and that no problems occurred, such as electron gun arcing, loss of molecular beam flow, or a sudden shift in the electron beam position. Each set of diffraction images included a short, 1-s exposure of the beam stop region for later identification of the unscattered electron beam position. This entire process was repeated for as long as desired, shortened only if the sample was used up or some other major system failure happened. The LN2 reservoir had to be refilled every few hours. 8.1.3 Shutting Down the UGED Instrument After data collection was complete, the first priority was to secure the vacuum chambers: the molecular beam flow was stopped, the butterfly valve was closed to isolate the electron gun chamber, and the scintillator gate cover was locked into place. The electron gun was turned off and the image intensifier was deactivated. Once the scattering chamber pressure returned to standard operating conditions of 10-6 torr, the gate valve was closed and the liquid-nitrogen trap was allowed to warm up, causing a sudden boil-off of sample. The oil in the scattering chamber roughing pump had to be changed regularly, as often as every experiment when high-melting point samples containing iodine were studied. 8.1.4 Analyzing the Diffraction Data With the UGED instrument quiescent, the next highest priority task was to back Chapter Eight: Ground-State Electron Diffraction Data 426 up the diffraction images on Zip disks and the magnetic tape archive. The experimental raw scattering intensity curve I\s) was then extracted from the images using RADAR2 as described in 7.1, and sM(s) and f(r) curves were generated with PROC5 (7.2). Unless otherwise specified, L = 100.1 mm, Ae =0.0886 A (18.8 keV), We= 3 to 5 pixels, and kd = 0.01 A2 for these calculations. The experimental background curve was also saved to disk, and a two-dimensional sM(pix) image was created with it using the original data and the program ADDER (D.5). In addition to this image's aesthetic appeal, the 2-D sM(pix) curve was an important diagnostic tool for identifying inferior regions in the diffraction patterns, problems that might not be seen in the raw images alone. Depending on the quality of the 2-D image, l(s) might be recalculated by ignoring certain regions in the active area. The average number of scattered electrons per pulse during the experiment could be estimated by summing the cumulative scattered intensities recorded for each image in the diagnostic data file created by RADAR2 (7.1.5). The sum was then divided by the total exposure time, the laser repetition rate (30 Hz), and the average number of ADU per incident electron (160 at an 8-V image intensifier gain setting). Spontaneous emission from the image intensifier made a negligible contribution to the sum, and the calculation did not account for non-uniform gain across the detector. If the percent scattering was measured, then the average total number of electrons per pulse was known, and the electron pulse duration could be read from Figures 4-23 or 4-24. Chapter Eight: Ground-State Electron Diffraction Data 8.2 Carbon Tetrachloride A round glass bulb half-filled with carbon tetrachloride (Fisher; 99.9% purity; 427 0 0 Atom Pair # ra (A) l (A) C-Cl Cl···Cl 4 6 1.765 2.886 0.0505 0.0696 Table 8-1: Structural parameters for carbon tetrachloride [Mor60a]. mp: -23 °C; bp: 76.5 °C) was attached to the sample inlet system and subjected to several freeze-thaw evacuation cycles to remove dissolved gases. The room temperature vapor pressure after evacuation was high enough that no heating was necessary. The scattering chamber ionization gauge read 2.4xl0-4 torr during the diffraction experiment. 60-s images were recorded for a total exposure time of 80 min. The sM(s) andf(r) curves derived from this data are shown in Figure 8-1, and the 2-D sM(pix) curve is shown in Figure 8-2. Structural parameters for CC4 are summarized in Table 8-1 and were obtained from Morino et al. [Mor60a]. The experimental and theoretical sM(s) intensities were leveled using the Norwegian format (Eq. 2.87) with a, b = Cl, and scaled together at the top of the third peak (-4.8 A- 1). The f(r) was calculated from experimental data over a range of 1.28 A- 1 to 13.24 A- 1 (as always, the theoretical curve was appended up to Sm;n). A total of 41-million electrons were detected with an average of 280 electrons per shot. The percent scattering was not measured. Two main defects were observed in the two-dimensional sM(pix) curve. Firstly, the diminished intensity to the left of the beam stop was a scattering shadow caused by the nozzle tip. (The camera head flips the CCD image along a diagonal from the upper left to the lower right.) Since the shadow presumably affected atomic and molecular scattering equally, these regions were usually left in RADAR2's calculation. Secondly, residual blooming effects from the central region of the image were seen in later pixels in those Chapter Eight: Ground-State Electron Diffraction Data 428 -Cl) :Cl)E Difference Curve 2 0 4 10 14 Cl···Cl • Theory - 12 Experiment C-Cl 1 2 Internuclear Separation (A) 3 4 Figure 8-1: Experimental and theoretical diffraction data for carbon tetrachloride. (Top) Modified molecular scattering curves and their difference (experiment minus theory). (Bottom) Radial distribution functions. Chapter Eight: Ground-State Electron Diffraction Data Figure 8-2: Two-dimensional sM(pix) image of carbon tetrachloride. 429 Chapter Eight: Ground-State Electron Diffraction Data 430 columns, and became more pronounced towards the bottom of the image as the scattering intensity decreased. These regions were blocked out during recalculation of I\s). 8.3 Trifluoromethyl Iodide A gas canister of compressed trifluoromethyl iodide (Aldrich; 99% purity; bp: -22.5 °C) was attached to the sample inlet system using a regulator. The scattering chamber ionization gauge read 3.0xl0-4 torr during the diffraction experiment. 50-s images were recorded for a total exposure time of 83 min. The sM(s) andf(r) curves derived from this data are shown in Figure 8-3, and the 2-D sM(pix) curve is shown in Figure 8-4. Structural parameters for CF3I are summarized in Table 8-2 and were obtained from two sources [AnA72], [Typ78]; the values reported by Andreassen and Bauer gave a superior fit. The leveling atoms for calculating sM(s) were a = F, b = I, and the experimental Atom Pair # C-F C-I F···F F···l [AnA72] [Typ78] 0 0 (A) l (A) fa (A) l (A) 3 1 3 1.341 2.098 (2.167) 0.0583 0.0789 0.0678 1.331 2.141 2.154 0.0510 0.0465 0.0547 3 (2.874) 0.0821 2.892 0.0812 fa Table 8-2: Structural parameters for trifluoromethyl iodide. Bracketed values were calculated assuming °-3v symmetry. and theoretical intensities were scaled together at the bottom of the fourth peak (-8.1 A- 1). The experimental range of s 1 used for the f(r) calculation was from 1.40 A- 1 to 12.64 A- • A total of 74-million electrons were detected with an average of 516 electrons per shot. The percent scattering was not measured. Chapter Eight: Ground-State Electron Diffraction Data 431 -U) :U)E Difference Curve 0 4 2 6 s (A-1) 8 F···F '" Theory Experiment 10 12 14 p ... J C-1 C-F --.... i... 1 2 Internuclear Separation (A) 3 4 Figure 8-3: Experimental and theoretical diffraction data for trifluoromethyl iodide. (Top) Modified molecular scattering curves and their difference (experiment minus theory). (Bottom) Radial distribution functions. Chapter Eight: Ground-State Electron Diffraction Data Figure 8-4: Two-dimensional sM(pix) image of trifluoromethyl iodide. 432 Chapter Eight: Ground-State Electron Diffraction Data 433 8.4 Sulfur Hexafluoride A gas canister of compressed sulfur hexafluoride (Matheson; 99.8% purity) was attached to the sample inlet system using a regulator. The scattering chamber ionization gauge read l .5x 10-4 torr during the diffraction experiment. 60-s images were recorded for a total exposure time of 80 min. The sM(s) andf(r) curves derived from this data are shown in Figure 8-5 . The 2-D sM(pix) curve shown in Figure 8-6 is from a different set of SF6 data after 67 min of exposure. Structural parameters for SF6 are summarized in Table 8-3 and were obtained from Bartell and Doun [Bar78]. The leveling atoms for calculating sM(s) were a= F, b = S, and the experimental and theoretical intensities were scaled together 0 I at the top of the fourth peak (-9 .1 A ) . The Atom Pair # ra (A) l (A) experimental range of s used for the f(r) S-F F···F (cis) F· •·F (trans) 6 12 1.560 (2.206) 0.044 0.061 3 (3.121) 0.056 o 1 calculation was from 1.76 A- 1 to 13.52 A- • A total of 47-million electrons were detected with an average of 327 electrons per shot, and almost 20% of all electrons were scattered. Table 8-3: Structural parameters for sulfur hexafluoride [Bar78]. Bracketed values were calculated for an octahedral symmetry. Chapter Eight: Ground-State Electron Diffraction Data 434 -Cl) ~ Cl) Difference Curve 2 0 4 S-F , ·Theory - 6 Experiment s (A-1) 8 10 12 14 F···F (cis) p ... p (trans) 0 1 2 Internuclear Separation (A) 4 Figure 8-5: Experimental and theoretical diffraction data for sulfur hexafluoride. (Top) Modified molecular scattering curves and their difference (experiment minus theory) . (Bottom) Radial distribution functions. Chapter Eight: Ground-State Electron Diffraction Data Figure 8-6: Two-dimensional sM(pix) image of sulfur hexafluoride. 435 Chapter Eight: Ground-State Electron Diffraction Data 436 8.5 Diiodomethane A round glass bulb half-filled with diiodomethane (Aldrich; 99% purity; mp: 6 °C; bp: 182 °C) was attached to the sample inlet system and subjected to several freeze-thaw evacuation cycles to remove dissolved gases. Heating was necessary to generate sufficient vapor pressure; the bulb was heated to 108 °C, the external tubing of the inlet system was heated to 150 °C, and the temperature of the nozzle tip was 166 °C (439 K) . The scattering chamber ionization gauge read l.7x10-4 torr during the diffraction experiment. 50-s images were recorded for a total exposure time of 213 min. The sM(s) and f(r) curves derived from this data are shown in Figure 8-7, and the 2-D sM(pix) curve is shown in Figure 8-8. Structural parameters for CH2l2 at 360 K are summarized in Table 8-4 and were obtained from Thomassen and Hedberg [ThH96]. The leveling atoms for calculating sM(s) were a, b = I, and the experimental and theoretical intensities were 0 scaled together at the top of the third peak (~3.8 A- 1). The experimental range of s used for the j(r) calculation was from 1.12 A- to 1 12.40 A- . 1 A total of 191-million electrons were detected with an average of 499 electrons per shot. The percent scattering was not measured. 0 Atom Pair # ra (A) l (A) C-H H .. ,H 2 2 1 1.046 2.119 1.700 0.078 0.045 0.130 H···I 4 2.628 0.126 1···1 1 3.579 0.094 C-1 Table 8-4: Structural parameters for diiodomethane at 360 K [ThH96]. Chapter Eight: Ground-State Electron Diffraction Data 437 Difference Curve 2 0 - 4 6 s (A-1) 8 10 12 14 I·· ·I Theory Experiment C-I -.-... '- 0 1 2 3 Internuclear Separation (A) 4 5 Figure 8-7: Experimental and theoretical diffraction data for diiodomethane. (Top) Modified molecular scattering curves and their difference (experiment minus theory). (Bottom) Radial distribution functions. Chapter Eight: Ground-State Electron Diffraction Data Figure 8-8: Two-dimensional sM(pix) image of diiodomethane. 438 Chapter Eight: Ground-State Electron Diffraction Data 439 8.6 Diiodotetrafluoroethane A round glass bulb half-filled with diiodotetrafluoroethane (PCR Inc.; 97% purity; liquid at room temperature; bp: 112 °C) was attached to the sample inlet system and subjected to several freeze-thaw evacuation cycles to remove dissolved gases. Heating was necessary to generate sufficient vapor pressure; the bulb was heated to 40 °C, and the temperature of the nozzle tip was 75 °C (348 K). The scattering chamber ionization gauge was ~2x 10-4 torr during the diffraction experiment. This molecule was studied in the first-generation UGED apparatus (17 keV; L = .. 46.0 mm; We = 30 pixels) and analyzed with less sophisticated versions of RADAR2 and PROC5. 50- to 60-s images were recorded for a total exposure time of 55 min, and the sM(s) andf(r) curves derived from this data are shown in Figure 8-10. The leveling atoms for calculating sM(s) were a, b = I, and the experimental and theoretical intensities were scaled together at the top of the second peak (~2.7 k 1). The experimental range of s used for the f(r) calculation was from 2.22 k 1 to 45 (1) '§ 35 ~ ~ ~ 0 25 10.00 k 1. Structural parameters for C2F4Ji 250 at various temperatures were reported by Thomassen et al. [ThH92]. The analysis was complicated by the presence of both anti and gauche isomers, and the 300 350 400 450 500 Temperature (K) Figure 8-9: Mole fraction of gauche isomer as a function of temperature in anti I gauche mixture of diiodotetrafluoroethane. Data points were taken from [ThH92] and fit to a parabola. Chapter Eight: Ground-State Electron Diffraction Data 440 i I I ; I ......... -~ Cl) _ ! 1 :E ' Cl) Difference Curve 0 2 4 6 s (A-1) 8 10 F···l - Theory Experiment C-I --.... C-F I .. I··· I (anti) 2 4 3 Internuclear Separation (A) 5 6 Experimental and theoretical diffraction data for diiodotetrafluoroethane recorded with the first-generation UGED apparatus. (Top) Modified molecular scattering curves and their difference (experiment minus theory). (Bottom) Radial distribution functions. Only some of the internuclear separations are identified; the anti isomer has 11 and the gauche isomer has 13 different internuclear separations [ThH92]. Figure 8-1 O: Chapter Eight: Ground-State Electron Diffraction Data composition was dependent on temperature as shown in Figure 8-9. 441 The UGED diffraction data fit best to a 72% anti I 28% gauche (±5%) mixture, and the expected composition was 78/22. 8. 7 Photodissociation of Trifluoromethyl Iodide In order to demonstrate that ultrafast gas-phase electron diffraction was sufficiently sensitive for monitoring chemical changes, a simple photodissociation experiment was carried out in the first-generation apparatus (17 keV; L = 46.0 mm; We = 30 pixels). Trifluoromethyl iodide loses its iodine atom through one of two possible channels when illuminated in the ultraviolet [Per91], [FeP91], [Hwa92], [FeP92]: hv (8.2) hv (8.3) The absorption cross section of CF31 reaches a maximum value of 7xl0- 19 cm2 at 270 nm, but is only 3x 10-20 cm2 at the more convenient CPM wavelength of 310 nm [Dvo89], [FeP92]. The cross section at 310 nm was estimated to be too low given the available laser energy, so the molecular beam sample was instead excited with quadrupled output from the Nd:YAG laser (266 nm; 1 mJ; 7 ns). The pump laser preceded the electron pulse by 14 ns. With only 10 min of exposure time, a clear difference was observed between the diffraction patterns with and without the pump laser, and the radial distribution curves are compared in Figure 8-11. The leveling atoms for calculating sM(s) were a= F, b = I, and the experimental range of s used for the f(r) calculation was from - 1.5 A- 1 to -8.0 A- 1. Chapter Eight: Ground-State Electron Diffraction Data F-··1 C-1 Experiment '- Theory ·No Laser -Laser C-F .-... 1···1 442 F···I C-1 C-F 1···1 I\\ ff I\ \ ~ :( / \ I I I I I I I I 2 4 3 Internuclear Separation (A) l I I I ii I I I I I I I I 2 3 4 Figure 8-11: Experimental and theoretical radial distribution functions for the photodissociation of trifluoromethyl iodide into CF3 and an iodine atom. Dissociation is marked by a decrease in the C-1, F·••I, and 1···1 peak amplitudes. The C-F peak amplitude also appears to drop, but this is due to a shift in the baseline. The theoretical curve of the laser-pumped sample was calculated for a 74/26 mixture of parent and product. Loss of an iodine atom eliminates interference terms from C-1, F···I, and 1···1 internuclear separations, and the amplitudes of those peaks inf(r) decrease. The amplitude of the C-F peak should remain constant, but Figure 8-11 shows a drop in both the experimental and theoretical curves. This drop is artificial and caused by the choice of a = F, b = I for the leveling atoms, which are good for CF3I but not for CF3 radical; as a result, the f(r) baseline curve for the laser-pumped system, where CF3 is present, is not flat. The modified molecular scattering curve fit best to a composition containing 26±5% CF3 (structure parameters from [HiE83], [Moc86]), although the total relative scattering intensities could not be evaluated as they are in 10.3. The percent composition may have been artificially high due to an oversight in the fitting process. Chapter Eight: Ground-State Electron Diffraction Data 443 Raw -- Correcte fl) ~ fl) Raw -<l Corrected • 0 •••••••• 2 4 6 8 10 Figure 8-12: Differences between experimental and theoretical sM(s) curves before and after the one-dimensional gain correction (Eq . 7.2) . 8.8 Possible Sources of Error As shown in the previous sections, the fit between the experimental and theoretical sM(s) curves was very good, but not perfect; the !isM(s) difference curves were comparable to results from other low electron flux GED studies [Ewb93], [Ewb92], [Isc94c]. However, by taking diffraction patterns of each molecule on several occasions and comparing trends in the !isM(s) curves of different molecules, it became apparent that some type of systematic error was present. First of all, the !isM(s) curves for a particular molecule were similar from experiment to experiment. Secondly, for most molecules the oscillation amplitudes could not be matched across the entire range of s because early oscillations tended to have larger amplitudes than later oscillations (relative to theory). The experimental sM(s) curves were scaled to the theoretical curves using maxima or minima near the center of the range of available s to reduce these amplitude differences. Chapter Eight: Ground-State Electron Diffraction Data 444 As Figure 8-12 shows, the problem was worse before the one-dimensional gain correction was incorporated into the data analysis procedure (Eq. 7.2), particularly at lows. Sources of systematic and random error in gas-phase electron diffraction have been reviewed by several authors [Kuc72a], [Sim73], but not all are relevant here since determining internuclear separations to within 0.001 A was not the goal of UGED. A few potential problems are considered in this section, but the most likely candidate for the discrepancies between theory and experiment was still the two-dimensional non-uniform gain across the imaging system. 8.7.1 Finite Beam Dimensions The spatial resolution of diffraction patterns recorded in the UGED instrument is limited by the electron beam width according to the modulation transfer function shown in Figure 6-55. As was seen in the first-generation instrument, this type of damping changes the relative contribution each internuclear separation makes to the total interference pattern; the mean amplitudes of vibration are broadened to some extent, but most likely the determination of r would not suffer. Regardless, the electron beam dimensions have been accounted for when calculating the theoretical sM(s) curve with PROC5, and no effects should be seen in the difference curve. The molecular beam is not a point scattering source, and several authors have considered the effect this has on diffraction patterns [Kar50], [Mor65], [Bon74], [Tag84]. (The values for the UGED camera length and molecular beam width are common to many diffraction instruments.) In all analyses, the beam width broadened the mean amplitudes of vibration by at most a few percent, and the internuclear distances were unaffected. The Chapter Eight: Ground-State Electron Diffraction Data 445 effects of the molecular beam dimensions on structural parameters therefore can be ignored in UGED. 8.7.2 Multiple Scattering Intramolecular multiple scattering was described in 2.1.8 and should make only small contributions to the sM(s) curve for 18 keV electrons. Intennolecular multiple scattering occurs when the number density of the molecular beam sample is high, and an incident electron is diffracted by more than one molecule while passing through the interaction region. The single-scattering probability is given by: P = PNA (8.4) (jTotL-- RT where P and T are the pressure and temperature in the interaction region, NA is Avogadro's number, Lis the distance the electron travels through the interaction region, and CTTor is the total scattering cross section of one molecule. The probability of a doublescattering event is p212, and the fraction of double-scattering events in the total scattered intensity is p/2. For the SF6 experiment described in 8.4, 10% of the diffracted electrons were doubly scattered. Karle and Karle estimated the effects of double scattering on GED for a high value of p, 25% [Kar50]. The primary observation was that the background scattering intensity shifted away from the central region and out towards larger s, but the shift was smooth and introduced no artificial oscillations. In the molecular scattering equation, an additional damping term appeared that was dependent on r. The authors predicted that this damping o I term would alter the sM(s) curve by 2% at s = 4 A, and less at larger s. Perhaps intramolecular multiple scattering is the source of some error in the UGED data, but it is Chapter Eight: Ground-State Electron Diffraction Data o [Nag82] - - - - -Fit to [Nag82] 10 446 - - - - - - [Nag82] After PROC5 --UGED Data 5 _o Cl) t) <1 -5 ,,--.o--_____ ./ -10 ···o,__ _1::/ / p b _______o····· •15 -h-TTTTrrr1-rrr,rr-rrrr-+rrrrr1""TTT+-r--rrrrrTTT"l-rrr""TTTT""T""T"1h-,-,-,..,,...,...,....,-l~~rrrl~~-.-,-I 0 1 2 3 5 6 7 8 Figure 8-13: Experimental ~cr(s) curves for carbon tetrachloride. Polynomial curves were fitted through the small angle scattering data recorded by Nagashima et al. [Nag82]. After treating this data with PROC5, very little of the chemical binding effects remained. unlikely the main problem since p was less than 25%. One method of testing would be to record diffraction patterns of the same molecule for two different sample pressures and compare the difference curves. 8. 7 .3 Chemical Binding Effects Since the GED theory is based on the Independent Atom Model, the influence of chemical bonds is not included in the theoretical sM(s) curve (2.1.8). These effects are strongest at small scattering angles and could be a source of error in the UGED diffraction data, although chemical bonds reduce the scattering intensity and probably would not cause the amplitude increase that was observed in the UGED difference curves at smalls. To test the significance of chemical bonding, L1cr(s) curves (Eq. 2.92) were calculated for both UGED carbon tetrachloride diffraction data and the 50 ke V smallangle scattering data recorded by Nagashima et al. [Nag82] . Since differences in atomic Chapter Eight: Ground-State Electron Diffraction Data 447 scattering intensities are eliminated by the background correction methods in PROC5, only molecular scattering intensities were used in ~cr(s). Nagashima et al.'s data was first added on to a theoretical (1AM) total scattering curve for CCLi, and this data was analyzed with PROC5 to generate sM(s), and then ~cr(s). Figure 8-13 shows that the PROC5 fitting procedure eliminated most of the chemical bonding effects once the theoretical (1AM) and experimental ([Nag82] + 1AM) sM(s) curves were scaled together at ~4.8 A- 1. Similar results were seen for SF6 using theoretical small-angle scattering data from Pulay and co-workers [Pul83], and so most likely chemical binding effects are not major contributors to the UGED difference curves. 448 Chapter Nine Total Experimental Temporal Resolution and Establishment of Time Zero The ground-state diffraction data presented in Chapter Eight demonstrated that structural information about gas-phase molecules could be obtained with picosecond electron pulses, despite an extremely low beam current of ~50 fA. The earlier nanosecond pump-probe dissociation study of CF3I had shown that the structural resolution obtained with the first-generation UGED detection and data analysis techniques was sufficient to observe laser-induced chemical changes; presumably the same would be true of the second-generation system. In order to complete the initial goal set in Chapter One of following chemical changes with GED on the ultrafast time scale, two timing issues had to be addressed. First of all, the incident electron velocity was only one-fourth the speed of light. As a result, the arrival times of electrons and photons across the interaction region could not be perfectly matched, for any intersection angle, and the temporal resolution Chapter Nine: Total Experimental Temporal Resolution and Time Zero 449 suffered. Even if the electron and laser pulses were delta functions in time, the total experimental temporal resolution would be limited by l!:.tvM, the broadening due to velocity mismatch. A theoretical model of velocity mismatch, applicable to any two-particle, pump-probe geometry, is presented in 9.1. Based on the laser, electron, and molecular beam dimensions at the interaction region of the UGED apparatus, l!:.tvM was calculated to be 3.4 ps. The second issue was one of synchronization: how to determine when the electron and laser pulses overlapped temporally within the interaction region. The ultrafast resolution of the UGED experiments would be of little significance unless time zero (t0 ) could also be established to within a few picoseconds, preferably using any convenient pump laser wavelength. One approach would be to rely on a direct interaction between the incident electrons and the pump laser photons. Such a method would provide a true cross-correlation measurement of the UGED experiment; the width of the response curve would correspond to the total experimental temporal resolution, l!:.tror, incorporating velocity mismatch and any additional space-charge broadening the electron pulses experienced while traveling from the streak plates to the nozzle tip. Four types of electron-photon interactions are described in 9.2, and estimates of signal intensities indicate that at least one of these interactions may be detectable given the existing electron and photon fluxes. 9.3 discusses alternative approaches to finding t 0 , where the electrons and photons interact through an intermediary. In particular, photoionization-induced lensing (PIL) of the electron beam has allowed time zero to be determined with ps resolution under experimental conditions nearly identical to UGED. Preliminary evidence indicates that the resolution of to could be improved to just 1 or 2 ps using PIL. Chapter Nine: Total Experimental Temporal Resolution and Time Zero 450 9. 1 Velocity Mismatch* Sample molecules within the interaction region of a pump-probe experiment will experience a distribution of time delays between the pump and probe pulses, a distribution (with FWHM D..tvM) which is dependent on the velocity vectors of the two beams. Velocity mismatch broadening is significant on the ultrafast time scale because the physical dimensions of the sample are comparable to picosecond light-distances (1 ps = 300 µm). If the magnitudes of the pump and probe velocity vectors are the same (e.g., two laser pulses traveling through a gas), then D..tvM is zero when the beams copropagate. This is the standard experimental arrangement in Femtosecond Transition-State Spectroscopy. For all other intersection angles 0, the time delay due to velocity mismatch varies linearly across space (see Eq. 9.4 in 9.1.1 below), and some authors have exploited this dependence to record complete ultrafast transients with single-shot pump-probe experiments [Dha94 ], [Fou95]. When the pump and probe beams have different velocities, however, M vM can never be reduced to zero. In principle, the total experimental temporal resolution might be limited by D..tvM, and not the duration of the pump or probe pulses. As an extreme example, velocity mismatch prevents the time-resolution of thermal neutron diffraction experiments from improving beyond nanoseconds, even if an ultrafast neutron source becomes available (1.3). 18-keV electrons are orders of magnitude faster than thermal neutrons, however, with velocities of 0.259c according to the relativistic equation (A.3): • A version of this section was first published in [Wil93] . Symbols for some parameters, such as the velocity ratio ~, have been changed to coincide with the designation in other references. Chapter Nine: Total Experimental Temporal Resolution and Time Zero = C 1 - (1 + KE2 J-2 451 (9.1) me c The question then remains as to how large /).fvM will be for UGED. This section provides an estimate for the magnitude of velocity mismatch using a geometrical model of a generic pump-probe experiment. The purpose of the model is to generate an analytical form of /).tvM which is written as a function of experimental parameters. A numerical estimate for /).tvM under typical UGED conditions is calculated from these results. 9.1.1 Theoretical Analysis of Velocity Mismatch A generic crossed-beam experiment consists of two pulses, CD and 0, which overlap at the center of a molecular beam (Figure 9-1). The direction of the molecular beam is orthogonal to the plane formed by CD and 0, and the intersection angle between CD and 0 is e. The nature of these two pulses (e.g., photons or electrons) is not important to the model, except that the molecular beam particles are assumed to be stationary during their interaction with the pump and probe pulses, and that the molecular beam does not significantly attenuate either CD or 0. To simplify the problem, CD and (2) are initially defined to be delta functions in time with transverse spatial distributions given by p1(x) and p2 (u). The actual temporal distributions of the pulses will be accounted for later. Time zero for CD is defined to be the x-axis, and time zero for 0 is defined to be the u-axis. A molecule at the center of the molecular beam, where CD and 0 intersect, will see no delay between the arrival of pulse CD and the arrival of pulse 0 . A molecule at point P, however, observes a time delay between CD and (2) as defined by: Chapter Nine: Total Experimental Temporal Resolution and Time Zero 452 P1 (x) X Figure 9-1: Geometry of a crossed-beam experiment. The trajectories of pulses CD and a> intersect at angle 0 within the center of a molecular beam. The molecular beam flow is normal to the page, and a cross section of the beam is represented by the shaded coincident circles. If time zero is defined at the origin, then a molecule at point P observes a time delay M between CD and a> of d,!Vi - ch.lv2. (9 .2) In this equation, d 1 and d2 are the distances from P to the x- and u-axes, respectively, and v1 and v2 are the pulse velocities. Note that !it is not a delay time chosen by the experimentalist (e.g., a scan delay); l::,,.t is actually an experimental artifact, dependent on the velocity mismatch and the intersection angle 0, which occurs even when the experimental delay line is set at time zero. As shown in Figure 9-1, d 1 is they-coordinate of P. Using trigonometry, it can be Chapter Nine: Total Experimental Temporal Resolution and Time Zero 453 determined that d2 is related to x, y, and e by: d2 = ycos0 - xsin0 (9.3) The time delay observed by a molecule at P thus takes the form: L\t(P) = x sin 0 + y(/3 - cos 0) (9.4) where Bis the velocity ratio of the pulses: (9.5) The goal of this analysis is to find an analytical function, l(L\t), which represents the distribution of time delays (between CD and 0) from the molecular beam's frame of reference. Since CD and 0 are delta functions in time, the width of this distribution is the temporal broadening due solely to velocity mismatch. Eq. 9.4 may be rearranged to show that there is a linear relationship between x and y for a specific L\t: y v 2 L\t - x sin 0 /3 - cos0 (9.6) All molecules along this line in the x-y plane see the same time delay between CD and 0 . For example, if the velocities are identical CB= 1) and pulse CD is perpendicular to pulse 0 (0 = n/2), then all molecules along the line x + y = 0 see no time delay between the pulses. Molecules along x + y = a, however, see a time delay of a/v2 . Specific delay times L\t occur as parallel lines across the x-y plane, and integration along the line defined by Eq. 9.6 gives the total molecular population observing an arbitrary L\t for a fixed angle 0. The distribution of time delays is therefore defined by a line integral, which takes the general form: Chapter Nine: Total Experimental Temporal Resolution and Time Zero 454 (:J (9.7) I(llt) = If(x, y)✓I + dx Not all regions of space contribute equally to /(~t) because the molecular beam density varies across the x-y plane, and because CD and C2> have spatial intensity distributions along x and u. The function f(x, y) is a weighting factor which takes these distributions into account: (9 .8) Pulses CD and C2> are assumed to have gaussian spatial distributions with FWHM given by p,(x) = exp(-4ln2 :; J (9.9) p,(u) = exp(-4ln2 :; J (9.10) To obtain an analytical solution for /(M), the planar cross section of the molecular beam is also assumed to be gaussian (FWHM = WM): 2 PM(x, y) = + y2J exp( -4ln2 x w~ (9 .11) The gaussian distribution is not too different from the horizontal spatial distribution derived for a thin-walled effusive orifice [Sco88]. oc cos¢ 4m-2 = z (9.12) where z is the vertical distance from the orifice. For simplicity, p 1, p2 , and PM have not been normalized. Note that if this model Chapter Nine: Total Experimental Temporal Resolution and Time Zero 455 were applied to liquid or solid samples, PM would be a constant within the limits defined by the cell or crystal dimensions, and zero everywhere else. Since x and y have a linear relationship, the radical in Eq. 9.7 is a constant and can be removed from the integral: (9.13) As shown in Figure 9-1, the u-axis is related to the x- and y-axes by a rotation: U = • y sin 0 + X COS 0 (9.14) With this relation, integration of Eq. 9.13 yields the following gaussian function: 2 n(/3 - 2/3cos0 + 1) V22 ( 2 2 WM Sl·n where: (( ) - - - - - - - e x p - 4ln2 a1'1t 2 a2 ln2 I(L1t) = ) J 0 + w,2 + W22 + -w,2w22 -2- ' ~ (9.15) (9.16) WM The FWHM of Eq. 9.15 is given by: (9.18) Eq. 9.18 represents the temporal broadening due to velocity mismatch. This function must be analyzed to determine how experimental parameters (P, 0, w1, w2, WM,) affect the temporal broadening. The influence of the intersection angle is evaluated by taking the first derivative of Eq. 9.18 with respect to 0. Three pairs of local extrema are found: sin0 0 (9.19) Chapter Nine: Total Experimental Temporal Resolution and Time Zero and: cos0 = /3( w; :~wt) cos0 = w22 + w2M f3w~ 456 (9.20) (9.21) Eq. 9.19 shows that there are local extrema at 0 = 0 and 0 = rt. Two solutions arise from Eq. 9.20 when the following condition is met: (9.22) and the solutions to Eq. 9.21 have a similar condition: (9.23) These two conditions are simultaneously satisfied when p = 1 and the pulse widths are zero, but no additional extrema result. There is a possibility of two additional extrema when p t= 1. For the remainder of this analysis, it will be assumed that pulse @ is faster than pulse CD (P > 1). With this assumption, the solutions to Eq. 9.20 never exist, and the two solutions to Eq. 9.21 exist only if the condition in Eq. 9.23 is satisfied. A second-derivative analysis of the FWHM reveals whether the four possible extrema are local minima or maxima. The counterpropagating arrangement, 0 = rt, is a local maximum and represents the geometry which gives the greatest temporal broadening. At this angle, the FWHM is: (9.24) A local minimum occurs at 0 = 0 when there are no solutions to Eq. 9.21; a local maximum occurs when there are. /::,,,,tvM at 0 =0 is always smaller than MvM at 0 =rt: Chapter Nine: Total Experimental Temporal Resolution and Time Zero 457 (9.25) As expected, if pulses CD and@ have identical velocities(~= 1), and are copropagating (0 = 0), then there is no velocity mismatch and no temporal broadening. When the solutions in Eq. 9.21 do exist they are local minima, and therefore of potential importance to the design of the pump-probe experiment. If the spatial width of pulse (2), the •faster pulse, is less than the width of the molecular beam multiplied by ~ , then the smallest amount of temporal broadening occurs at an angle 0min defined by Eq. 9.21. The broadening at 0min is: 2 Wz 2 (9.26) + WM Eq. 9 .26 is independent of w 1, the width of the slower beam. Up to this point the analysis has assumed that CD and (2) are delta functions in time, but including their temporal profiles is straightforward with a double convolution of the gaussian /(M) from Eq. 9.15. If the temporal profiles of CD and @ are assumed to be gaussian with FWHM of M 1 and /1t2 , then the total experimental temporal resolution is: (9.27) Since ~t 1 and ~t2 are constants, ~tror will have the same extrema as found when using delta functions for the temporal profiles of CD and @. The interaction between CD, (2), and the molecular beam takes place in three dimensions, but this model has considered only the plane which bisects CD and @. To carry the analysis one step further, /(M) would be integrated along the molecular beam Chapter Nine: Total Experimental Temporal Resolution and Time Zero 458 axis, z, with the understanding that p 1, p2 , and PM are all functions of z. Most likely, the time resolution will not increase significantly as a result of this calculation. Perfectly skimmed molecular beams will maintain a constant width along z, and therefore velocity mismatch broadening would be unaffected. For an expanding nozzle source, the width of the molecular beam will be narrower above z = 0 and broader below z = 0. Increases in temporal broadening due to the larger molecular beam width below z = 0 may not be severe, however, because the number density will be less in the regions of large WM and greater in regions of small WM . It is therefore reasonable to assume that the two- dimensional result is a good representation of the actual three-dimensional system. 9.1.2 Impact of Velocity Mismatch on the UGED Experiment The magnitude of velocity mismatch broadening in UGED experiments can be estimated with Eq. 9.18. In a typical experiment, the excitation laser pulse is focused to w2 = 350 µm, the 18-keV electron pulse (P = 3.866) is focused to w1 = 300 µm, and the molecular beam has a width of WM = 380 µm. With these values, temporal broadening is minimized at 0min = 61.4° (Eq. 9.21) where 13.tvM at 0min is 3.1 ps (Eq. 9.26). For the UGED apparatus described in this thesis, 0 = 90° and 13.tvM is 3.4 ps. Convolution of a 300 fs pump pulse and a 10 ps electron pulse with the broadening due to velocity mismatch raises the total experimental temporal resolution to 11 ps. If the data were recorded with 1 ps electron pulses, the resolution would only decrease to 3.6 ps because of velocity mismatch limits. Velocity mismatch can be reduced by modifying the experimental parameters p, 0, w w2 , and , 1 WM. Figure 9-2 demonstrates that M v M is insensitive to w the spatial width of , 1 Chapter Nine: Total Experimental Temporal Resolution and Time Zero the slower pulse. The position 459 7 6 and magnitude of all extrema are _5 unaffected, and the overall curve undergoes little change. This is (/) S4 - ~ 3 <] good news for UGED - the 2 1 0 electron beam width (w 1) can be 0 dimensions beam without compromising the 60 90 120 150 180 Intersection Angle (Degrees) freely optimized to the laser and molecular 30 Figure 9-2: Effect of the transverse width w1 of the slower beam (Q)) on velocity mismatch broadening as a function of intersection angle. There is only minimal dependence on w1. Curves are calculated for~ = 3.866 (18 keV electrons); w2 = 350 µm; WM= 380 µm . temporal resolution. /:J.tvM is very sensitive, however, to changes in the focal width of the pump pulse, w2 (Figure 9-3), and the width of the molecular beam, WM (Figure 9-4). 7 6 For large w2 , the minimum of Eq. _5 (/) 9.21 disappears and the optimum angle of intersection is 0. As w2 decreases, the minimum moves S4 - ~ 3 <] 2 W2 1 = 150 µm 0 towards cos0 = 1/~ and the temporal resolution improves. Similarly, the temporal resolution improves for small WM where the optimum angle is 0. For large WM, 0 30 60 90 120 150 180 Intersection Angle (Degrees) Figure 9-3: Effect of the transverse width w2 of the faster beam (0) on velocity mismatch broadening as a function of intersection angle. Decreasing w2 reduces MvM and moves 0m;n away from 0 and out towards an upper limit of arccos(1/~)- Curves are calculated for ~ = 3.866 (18 keV electrons); w1 = 300 µm; WM= 380 µm. Chapter Nine: Total Experimental Temporal Resolution and Time Zero the minimum in Eq. 9 .21 460 10 9 reappears. These factors must be 8 taken into account when altering the interaction region of the 7 u,6 C. -s UGED experiment. Small w2 and ~ <:] WM are obviously desirable. 4 0min .• •• ... ... ···wM = 380 µm . ..-- 3 2 Practically, it may be difficult to 1 copropagate the laser and electron 0 beams, as might be required if the solutions to Eq. 9.21 do not exist and 0 = 0. However, Figure 9-4 shows that MvM does not change WM= 150 µm 0 30 60 90 120 150 180 Intersection Angle (Degrees) Figure 9-4: Effect of the transverse molecular beam width WM on velocity mismatch broadening as a function of the intersection angle between CD and @. Decreasing WM reduces MvM and moves 8m;n in towards 0 as shown. Curves are calculated for p = 3.866 (18 keV electrons); w1 = 300 µm; w2 = 350 µm. much as a function of 0 when WM is small. There is an additional degree of freedom in UGED which may be exploited to decrease velocity mismatch. The ratio of beam velocities, p, is reduced when the kinetic energy of the electrons increases, as follows from Eqs. 9.1 and 9.5. The velocity ratio becomes 3 with 31 keV electrons and 2 with 79 ke V electrons. Using the parameters for recent experiments, the velocity mismatch broadening of a 79 ke V experiment would improve from 3 .4 ps to 1. 9 ps. Chapter Nine: Total Experimental Temporal Resolution and Time Zero 461 9.2 Pure Electron-Photon Interactions A cross-correlation measurement of electron and laser pulses depends on the detection of energy or momentum transfer following collisions between the electrons and photons. The likelihood of a collision between a photon and a free electron scales according to the Thomson scattering cross section crr: Sn r 2 3 e = 6.65 x 10-29 m2 = 0.665 barns (9.28) where re is the classical electron radius: e 2 2.82 X 10- 15 mt (9.29) Clearly electron-photon collisions are rare; O"r is orders of magnitude smaller than the cross sections for electron-atom scattering or molecular absorption of a photon. Still, if the particle fluxes are high enough, a number of interesting interactions can take place between photons and free electrons [BrS64], [Kib66b], [Fed91], [Fed97]. Incident photons can be emitted from the interaction region changed in wavelength and direction; incident electrons can be scattered from the interaction region, either elastically or inelastically. The next few sections evaluate several electron-photon interactions (Thomson scattering, second harmonic generation, ponderomotive scattering, and Kapitza-Dirac scattering) in terms of electron beam and laser intensities currently available in the UGED laboratory. Of these four processes, Kapitza-Dirac scattering is predicted to t The classical electron radius corresponds to a sphere of uniform charge density, with total charge e, where the sphere's potential energy is equal to the electron self-energy. Depending on the units, the 41tf{) term is sometimes dropped and substitutions of r, = e2!m,c2 are made in equations. Chapter Nine: Total Experimental Temporal Resolution and Time Zero 462 give the most readily detectable signal: deflection of the incident electron beam by one or more pixels on the direct bombardment CCD. 9.2.1 Thomson Scattering ty Thomson scattering is a classical electron-photon e· collision involving the transfer of energy and momentum. (Compton scattering is the same process except the ~ / ~' _ _ _ ___:, •-+--- X 2 photon energy is on the order of mec [MoC95] .) Figure 9-5 shows a schematic for Thomson scattering in a plane. e An incident photon of energy £ 1 collides with an electron at an intersection angle 0 1. Because of energy and momentum conservation, the scattered photon emitted at an angle 02 has a new energy £ 2 equal to [Aru63], Figure 9-5: Geometry for inplane Thomson scattering. An electron collides with a photon of energy IN, at angle 0,. The photon scatters at angle 02 with energy IN2. [Yam85], [ChJ94]: (9.30) where E 101 is the sum of the electron's mass and kinetic energies and ~ is the ratio of the relativistic electron velocity to the speed of light, Vele (as in Eq. 9.5). The differential scattering cross section (DSCS) for Thomson scattering is [Kle29], [Yam85], [ChJ94]: where: dar dQ = x, = 3a r E2 1 1 1 1 ]2 ( 2 ] 2{( ( - ; - X1 mec ~ + X2 - ~ + X2 - 2 y ~ 1 (1 - /3cos0 1 ) mec J 41(x + ~x J} 1 - 2 (9.31) X2 (9.32) Chapter Nine: Total Experimental Temporal Resolution and Time Zero 463 (9.33) and: r = 1/ ✓1 - /3 2 (9.34) When E1 is a few eV (UVNIS) and the electron kinetic energy is on the order of Me V or greater, scattered photons are fairly well-collimated about 02 = 0, with a maximum DSCS of 10-26 or greater. The scattered photons have ke V energies, corresponding to the x-ray region of the spectrum. Colliding femtosecond laser pulses with high-energy electron beams has proven to be a successful method for generating ultrafast x-ray pulses [Kim94], [ScR96] (1.4) . If the electron kinetic energy is keV, however, Eqs. 9.30 and 9.31 predict that the scattered photons will be emitted with comparable probabilities in all directions, and the energy transfer will be on the electron-volt scale. This was observed as early as 1963, when Fiocco and Thompson crossed the paths of 2-kV electrons with a ruby laser and detected scattered photons shifted by 26 nm from the fundamental wavelength (693 nm) [Fio63]. Detection of Thomson scattering under UGED conditions therefore requires only UVNIS optical components. Figure 9-6 plots emitted wavelength and the DSCS as a function of the angle 02 for 18-keV electrons colliding with 620-nm photons at 0 1 = 90°. The maximum wavelength shift is ±160 nm. The total scattering cross section for photons collected from a 30° half-angle about the maximum in the DSCS curve is on the order of 0.1 barns. Under typical UGED conditions for 620-nm laser pulses (2 mJ, 300 fs, 30 Hz) with the beam waist matched to an electron beam diameter of 300 µm, one Thomson-scattered photon can be expected within the collection angle every 200 laser shots. This assumes Chapter Nine: Total Experimental Temporal Resolution and Time Zero 0.11 . 0.1 -"' 0.08 C 0.07 800 • • • • • ·Wavelength •, ' ... 0.09 -..."' - --DSCS 700 - E -C .c cu .c 0.06 - 600 c, Cl 0.05 "C I- t) "C 464 0.04 .. 0.03 .' ' , C Cl) ... ,. "ii> 500 > cu 3:: 0.02 0.01 -+--.--+---+--+---.----+-~---+--~>------,..__.__ 180 150 120 90 60 30 0 -30 _,____,__ _,__ _,______-----U.. 400 -60 -90 -120 -150 -180 Emission Angle 02 (Degrees) Figure 9-6: Emission wavelengths and the corresponding differential scattering cross section (DSCS) for planar Thomson scattering as a function of emission angle 02. The electron kinetic energy is 18 keV, hv1 = 2.0 eV (620 nm), and the two beams intersect at goo. that the electron pulse is 4-ps long (a spatial length of 300 µm) and contains ~5,000 electrons (according to streaking experiments - 4.4). Realistically, the quantum efficiency of detection would be 0.1 at best, so a scattered photon would be detected only once a minute. Still, if the laser repetition rate were increased or the electron beam diameter were reduced, detection of Thomson scattering might be a reasonable method of finding to in the future, but not under current conditions. For 310-nm laser pulses (300 µJ), the calculated yield of Thomson-scattered photons is an order of magnitude less because the of the drop in laser intensity; cr at 310 nm is still ~0.1 barn over the collection solid angle. Effects of Thomson scattering on the electron beam should also be considered. There is no energy analyzer in the UGED detection system so changes in the electron KE (at most 0.7 eV) cannot be detected, but the direct bombardment CCD located 50 mm Chapter Nine: Total Experimental Temporal Resolution and Time Zero 465 from the nozzle tip has very high spatial resolution (13.75 µm along one axis; 16.00 µm along the other) with which changes in momentum might be observed. A backscattered 620-nm photon imparts 4 eV/c of momentum to an incident electron, giving the electron a transverse velocity of 2.3 km/s. During the 0.64 ns of flight time from the nozzle tip to the CCD, the electron will be displaced 1.5 µm from the beam center. Unfortunately, this displacement is too small to be resolved. 9.2.2 Second Harmonic Generation The electron beam can serve as a medium for frequency-doubling photons. Under a classical interpretation, electrons can oscillate at twice the frequency of the incident radiation and then emit the second harmonic upon relaxation. For stationary electrons, the DSCS of this process is given by [Vac62], [Eng83], [Uga94]: (9.35) where 0 is the angle between the trajectories of the incident and emitted photons, and a is the angle between the electric field vector of the incident photon and the trajectory of the emitted photon. The total scattering cross section is [Vac62]: 2.1 r /},} e 3 (J' T (9.36) lrmec Other theories have been developed which incorporate non-zero electron kinetic energies or are based on semiclassical or quantum electrodynamical interpretations, but these refinements shift the angular distribution by at most 20%, and the value of <JH is not altered significantly [Jaf75], [Ehl87], [Pun90]. Englert and Rinehart have reported experimental observations of frequency- Chapter Nine: Total Experimental Temporal Resolution and Time Zero 466 doubling during electron-photon collisions [Eng83]. A 1060-nm ps laser, focused to give intensities of l.7xl0 14 W/cm2 at the beam waist, collided head-on with a 1.6-keV electron beam. The number density of the electron beam was very high, 10 10 e"/cm3 , as compared to typical UGED electron number densities of 108 e·/cm3. Doppler-shifted photoernission was collected from 2% of the total solid angle at 90° to the collision axis, filtered with an interference filter, and detected on a photomultiplier tube. The authors observed a second-harmonic photon approximately once every 32 laser shots. Under UGED conditions, cross-correlation measurements by detection of the second harmonic are simply not feasible. With the 620-nm laser (2 rnJ, 300 fs) focused to a beam waist of 50 µm, the total second-harmonic scattering cross section over all angles is calculated to be 7x10·5 barns (Eq. 9.36), and a second-harmonic photon can be expected only once every 300,000 shots. For 310-nm laser pulses (300 µJ), crH is only 3x10·6 barns and there is the additional experimental challenge of collecting and detecting 155-nm photons. 9.2.3 Ponderomotive Scattering Free electrons will scatter from electromagnetic field gradients of intense light beams as if there were a potential energy V0 equal to [Buc87], [Buc88] : = rJ},} V 0 (9.37) 2nc V 0 is known as the ponderomotive potential. An alternative description is that the light beam is a refractive medium for the electron, with index of refraction [Kib66a], [Kib66b]: (9.38) Chapter Nine: Total Experimental Temporal Resolution and Time Zero 467 Under either interpretation, a free electron will be unable to pass through the light beam if the electron's kinetic energy is less than U0 . Ponderomotive effects are noticeable in experiments such as time-resolved zero kinetic energy photoelectron spectroscopy (ZEKE), where the intensities of the fs lasers perturb atomic and molecular energy levels, and limit energy resolution and state selectivity [Zav95]. Hora et al. have suggested characterizing ultrafast lasers by the ponderomotive effects on an electron beam [Hor96]. Experimental studies of the ponderomotive potential have used free electrons with a few eV of kinetic energy, created by above-threshold ionization (ATI) within a highintensity laser beam [Fre86], [Buc87], [MoC95]. If the light beam is continuous on the time scale of the interaction, the ponderomotive potential is conservative to first order and the ATI photoelectrons are scattered elastically. Freeman and co-workers found that the angular distribution of xenon ATI photoelectrons broadened with increasing laser intensity [Fre86]. The distribution was oriented along the laser polarization vector when U0 was less than the electron KE, but became more and more isotropic as U0 exceeded KE. The kinetic energy distribution of the electrons remained constant. If the light beam intensity varies in time, however, then kinetic energy can be transferred to and from free electrons through ponderomotive effects. To demonstrate this, Bucksbaum and co-workers used two parallel, non-coincident lasers whose focal points were transversely separated by 180 µm [Buc87]. Xenon ATI photoelectrons were created within the focal point of the first laser (532 nm, 100 ps, 6xl0 13 2 W/cm , linearly polarized) and the angular distribution of the electron trajectories was peaked in the direction of the second laser's focal point (U0 for the first laser was -1.6 eV). A time-offlight energy analyzer was located 40 cm downstream, and the authors studied the Chapter Nine: Total Experimental Temporal Resolution and Time Zero 468 photoelectron kinetic energies as a function of the time delay between the two laser pulses. Since U0 for the second laser (1064 nm, 140 ps, l.3xl0 14 W/cm2 , circularly polarized) was 8 eV (Eq. 9.37 predicts 13.4 eV), the photoelectrons were reflected from the temporal center of the second pulse and no signal was detected. When the photoelectrons arrived at the leading or trailing edges of the second laser pulse, however, they were accelerated by the time-dependent ponderomotive potential. Electron kinetic energies changed up to 0.2 eV, increasing on the leading edge of the second pulse and decreasing on the trailing edge. At high light intensities, nonlinear ponderomotive scattering effects are predicted [HaF95]. Moore et al. observed that ATI photoelectrons were ejected with ke V of kinetic energy from the focal point of an extremely intense laser (1053 nm, 1 ps, 10 18 W/cm2 , U0 = 100 keV) [MoC95] . They described their results as a transition from Thomson scattering to multi-photon Compton scattering, where the energy 2 transfer approaches mec . In the UGED laboratory, the ponderomotive potential approaches 12 eV at 620 nm and 0.5 eV at 310 nm, assuming a 50-µm focal width, but a general treatment of ponderomotive scattering when the incident electron KE is much greater than U0 has been addressed only indirectly [Hor96]. As explained in 9.2.1, the direct bombardment detection system is sensitive to changes in momentum, and shifts of one pixel (13.75 µm) are resolvable. A one-pixel shift of an electron's trajectory corresponds to a transverse momentum change of 36 eV/c. The momentum transfer of ATI photoelectrons in Freeman et al.'s experiment was as much as 1,500 eV/c in a ponderomotive potential of 6 eV [Fre86]. Since the length of time the ATI photoelectrons remained in the laser beam is comparable to the transit time of an 18-keV electron across a 50-µm beam waist, Chapter Nine: Total Experimental Temporal Resolution and Time Zero 469 ponderomotive effects would be observable with the UGED detector if the degree of momentum transfer were not strongly dependent on the initial electron kinetic energy. This experiment would be simple to test. 9.2.4 Kapitza-Dirac Scattering In 1933, Kapitza and Dirac predicted that electrons could be scattered from a standing light wave as shown in Figure 9-7, where the scattering angle 0s satisfies the Bragg condition [Kap33], [Gus71], [Fed81]: (9.39) The mechanism has been described as stimulated Thomson scattering. Following the diagram in Figure 9-7, the incident electron first absorbs a photon traveling away from the Laser mirror, and then the presence of the laser stimulates emission in the opposite direction; the total amount of momentum transferred to the electron is 2hvlc. At low laser intensities, the probability for Kapitza-Dirac scattering is Figure 9-7: Kapitza-Dirac scattering geometry. An electron entering the laser beam at Bragg angle 88 is reflected by the standing light wave. The process also works with atoms [MaP87]. equal to: u2 __ o_t li 2 t::..v (9.40) where tis the transit time of the electron through the laser and t::..v is the laser's frequency bandwidth. Attempts at observing Kapitza-Dirac scattering were made as early as 1965, Chapter Nine: Total Experimental Temporal Resolution and Time Zero 470 when keV electron beams were directed through laser cavities [Bar65b], [ScH65], but the results from these and similar experiments were vigorously debated by the various participants [Bar68], [ScH73], in part because PKv was low [ChY79] . Subsequent improvements in pulsed laser technology yielded laser intensities at which the classical model of Kapitza-Dirac scattering failed because PKD would be greater than one according to Eq. 9.40. Fedorov characterized the transition to the high-intensity regime with two unitless variables q and 't [Fed67]: q (9.41) (9.42) q is proportional to the number of photons in a cylinder of length 2re and radius A, and 't is proportional to the interaction time. If q << l, then Kapitza-Dirac scattering would occur only when the product q't is much greater than one. If q >> l, however, Fedorov predicted that maxima in the diffraction pattern would be washed out, and that the incident electron beam would spread out like a fan due to higher-order scattering. Gush and Gush calculated that the probability of second-order scattering would become significant for intensities on the order of 108 W/cm2 [Gus71] . Coutsias and Mciver have defined the onset for high-intensity Kapitza-Dirac scattering by the product q£, where [Cou85]: t: = ~2 2me c (9.43) When q£ "'" l, then approximately one photon is in the vicinity of an electron at all times and stimulated emission is highly likely to occur. Other theoretical treatments have been developed [GuD92], [RoL94], [GuD96], but formulas for higher-order Kapitza-Dirac Chapter Nine: Total Experimental Temporal Resolution and Time Zero scattering probabilities or cross sections that are as simple as Eq. 9.40 are unavailable. Bucksbaum and co-workers provided the first experimental evidence of high-order Kapitza-Dirac scattering of electrons •[Buc88]. Photoelectrons were generated with a few eV of kinetic energy by ATI of xenon gas with a 1064-nm laser (100 ps, 8x10 13 W/cm2). The angular photoelectrons distribution separated into of two distinct, broad peaks (in Fedorov's [Buc88] (nm) E,. (eV) r (µm) ~tL (ps) ~v (Hz) 'A, 1064 1.17 7.5 100 I (W/cm ) t (ps) (rad) ea (J) Uo (eV) PKo [Fed67] q UGED Laboratory 620 2.0 25 1 9 2 471 310 4.0 25 1 11 4.4x 10 12 7.7x10 0.6 5 2.9x10' 4.4x10 13 8.0x 10 4(a) 4.4x 10 13 5.1x10 0.6 3.7x 10-4 (a) 1.5x10' 18 1.4x 108.5 11 1.5x10 2.9x101.8 7 1.0x 10 6 11 1.1x10' 0.069 4 1.5x10 20 6.4x 10 4 5.1 x 10 11 3.3x10 4.6x10 1640 5 4390 63 7.5x10 8 2.8x10 £ 1.1 x10·5 2.ox10·5 q£ 7.0 0.9 3.9x100.02 't qt 5 19 5 [Cou85] 6 Table 9-1: Comparison of Kapitza-Dirac variables for standard conditions in the UGED laboratory versus conditions in the experiment of Bucksbaum et al. (a) Values calculated for photoelectrons with 10 eV of kinetic energy. terms, fan-like) when the electrons were created from two counterpropagating laser pulses which intersected to form a standing optical wave. The position of the peaks on their detector corresponded to a total momentum transfer of 1 keV/c or more - 500th-order scattering! To detect Kapitza-Dirac scattering on the UGED direct bombardment CCD, an electron's trajectory must shift by at least one pixel, about 0.28 mrad, or a change in the transverse momentum of 36 eV/c. Table 9-1 compares laser parameters of the UGED laboratory with the experimental conditions of Bucksbaum et al. In order to create a standing wave with a length matched to the electron beam waist, two transform-limited, 1ps laser pulses are required (rather than one 300-fs pulse used in previous estimates). The Chapter Nine: Total Experimental Temporal Resolution and Time Zero 472 temporal delay between the pulses should be 2d/c, where d is the distance from the electron beam center to the mirror (Figure 9-7). As shown in the table, multiple-order effects are expected because PKD >> 1, q >> 1, and qE z 1, at least at 620 nm. Based on the results of Bucksbaum et al., it is reasonable to expect that Kapitza-Dirac scattering of at least 20th-order (40 eV/c) would occur under UGED conditions. 9.3 Electron-Photon Interactions Via Intermediaries The Thomson scattering cross section <JT may be small, but the cross section for pure photon-photon scattering is virtually nonexistent in the visible region of the spectrum; at 620 nm, cr = 5x10·40 barns according to [BeW88]: 6 a = 1.3 x ( £\ J x 10- 31 mec cm 2 (9.44) The standard approach for finding time zero m Femtosecond Transition-State Spectroscopy is to use the interaction between the pump and probe laser pulses and an intermediate (e.g., molecules). Transients are recorded from a chemical species which exhibits an immediate, fs response to the pump and probe laser pulses, and t 0 is determined from the initial rise. In theory, t 0 for UGED experiments could be measured from diffraction data in a similar way, but this method is not practical. A cursory FTS transient can be recorded within minutes; in contrast, each UGED data point along the temporal axis requires several hours of laboratory work, and several more of analysis. Hunting for to by following changes in the diffraction data would be tedious, and also unreliable because the time zero position can shift day to day due to minor adjustments of the laser Chapter Nine: Total Experimental Temporal Resolution and Time Zero 473 paths. Ultrafast x-ray experiments have the same difficulty because low particle flux and long integration times inhibit determining time zero from the structural transients themselves. The intermediate used in this field has been a streak camera with a dual photocathode, sensitive to both x-rays and UVNIS photons [Tom95a], [Rak96]. Time zero can be identified to within 10 ps or better by adjusting the delay between the two pulses until their streak profiles overlap. FfS and ultrafast x-ray experimentalists determine time zero from the response of the intermediate (molecules; streak camera) to the combined effects of the pump and probe pulses. A different strategy can be employed for ultrafast electron experiments: a laser pulse excites the intermediate, and the intermediate then perturbs the electron beam trajectory. This is akin to some of the detection schemes for pure electron-photon interactions. Photoconductive switching is one method of deflecting the electron beam with an intermediate (9.3.1), but the interaction geometry is not identical to a pump-probe diffraction experiment and the temporal resolution is limited. Instead the Zewail group's UGED laboratory has used photoionization-induced lensing to establish time zero to within a few ps. With PIL, the intermediate is not a voltage pulse, but a collection of ionized molecules - the same molecules which are to be studied by diffraction. Experimental characteristics and the temporal response of PIL are described in 9.3.2. 9.3.1 Photoconductive Switches To determine time zero for their ps laser-melting studies of thin aluminum films, Williamson and co-workers installed a pair of deflection plates in their electron diffraction apparatus at the position of the Al film [WiS82], [WiS84]. Both deflection plates were Chapter Nine: Total Experimental Temporal Resolution and Time Zero 474 grounded initially, but the upper plate was connected to a voltage source through a thin GaAs photoconductive switch. The temporal response of the PCS was comparable to the duration of the electron pulses (20 ps). The PCS was triggered by the ultrafast heating laser, and time zero was identified to within 5 to 10 ps based on the deflection of the electron beam profile on the detector. The primary drawback of using a photoconductive switch intermediate is that the to obtained from the measurement tells when the electron pulse and the voltage gradient coincide, and not when the electron pulse and laser pulse overlap. Because of basic geometrical differences and limitations in the temporal response, it is unlikely that the true time zero could be established with uncertainties of less than 5 ps using photoconductive switching. 9.3.2 Photoionization-Induced Lensing Electron beams in high-energy particle accelerators can be focused by plasmas created with an electrical discharge or photoionization [SuJ90], [ChP87]. As the relativistic electron pulse enters the plasma, free plasma electrons are pushed out of the way by the front of the pulse, leaving only positive ions. The ions counteract azimuthal space-charge broadening within the electron pulse, but not the magnetic self-lensing effect, and the net result is that the electron pulse becomes focused [Nak91], [Kat92]. A slightly different process occurs within the interaction region of the UGED experiment since magnetic self-focusing is not very large for keV electrons. The photoionization plasma is located only at the intersection of the excitation laser and the molecular beam, and does not completely surround the electron beam. Nascent photoelectrons receive the excess kinetic energy of the ionization process and leave the interaction region on the ps time Chapter Nine: Total Experimental Temporal Resolution and Time Zero 475 scale. The leftover horizontal column of Excess Energy (eV) Velocity (µm/ps) Escape Time (ps) positive charge, the ions, then acts as a 1.0 2.5 4.0 0.59 0.94 1.19 85 53 42 coulombic cylindrical lens for the incident ultrafast electron pulse (Figure 9-8), and changes in the beam shape are detected on Table 9-2: Plasma electron velocities as a function of excess energy. Escape times are calculated for leaving the center of a region 100 µm in diameter. the CCD. Assuming that the incident electron pulse is too short in time to "push" the plasma electrons out of the interaction region, the time scale of photoionization-induced lensing (PII..,) can be estimated from the equation for the plasma electrons' initial velocity: V = m, (9.45) Here, n is the number of absorbed photons, E"- is the photon energy, and <Pi is the ionization potential of the molecular sample. Table 9-2 lists plasma electron velocities and escape times under typical UGED conditions. Lensing effects become progressively stronger over a time period of 50 to 100 ps as more and more plasma electrons leave the interaction region and the electrostatic potential increases. After the initial rise, lensing effects should persist for ns because the kinetic energies of the molecular ions are not significantly different from thermal values. 9.3.2.1 Experimental Details The first observation of photoionization-induced lensing in the Zewail laboratory was a fortuitous byproduct of the nanosecond CF3I dissociation experiment (8.7). The diffraction patterns were detected by direct bombardment on a CCD with a spatial Chapter Nine: Total Experimental Temporal Resolution and Time Zero 476 Direct Bombardment CCD a:ffi Il-1,1 Figure 9-8: Sequence of photoionization-induced lensing. (Top Left) Excitation laser is incident on the molecular beam. (Top Right) Excitation laser ionizes molecules within the sample through multiphoton absorption. The nascent electrons exit the interaction region within picoseconds, while the positive ions remain behind. (Bottom) The incident electron beam is deflected by the horizontal column of positive charge, and the altered beam shape is detected on the direct bombardment CCD. resolution of 12 µm, and the unscattered electron beam (a fraction of which penetrated a 2,000-A-thick aluminum beam stop) showed a pronounced horizontal stripe of increased intensity when both the laser and the molecular beam were present (Figure 16 in [Dan94]). The effect was weaker but still evident using femtosecond laser pulses. The degree of lensing depends on many parameters, including the detector position; the electron beam velocity, width, and collimation; the laser beam waist, intensity, and wavelength; the molecular beam density and ionization potential; and the physical overlap of the three beams within the interaction region. Systematic studies of Chapter Nine: Total Experimental Temporal Resolution and Time Zero 477 PIL were carried out in both the first- and second-generation UGED apparatus. By design, the experimental arrangement was identical to that of UGED experiments (Figure 10-2); after establishing time zero with PIL, time-resolved diffraction could be carried out immediately without altering the optical path lengths. The 18-keV electron beam diameter was on the order of 200 to 300 µm at the nozzle tip. The diameter of the 310-nm excitation laser was calibrated as a function of the longitudinal translation position of the 200-mm input lens (see Figure 10-3). A laser beam diameter of 350 µm was used during UGED experiments, but the diameter was reduced to ~ 100 µm for PIL in order to increase the ion density and the strength of the lensing effect. A smaller beam diameter also improved the resolution of time zero measurements because velocity mismatch was less - only 1. 3 ps according to Eq. 9 .18. Translating the input lens position did not alter the optical path length. For all PIL data reported here, the molecular sample was CH2I2 (<I> 1 = 9.46 eV [Lid92]), so the kinetic energy available to the plasma electrons was 2.5 eV for three-photon absorption at 310 nm. Background pressures in the scattering chamber were between 2 and 4xl0-4 torr, the same as during UGED, and the sample pressure at the needle tip was 6 to 12 torr (3.2.2). The pump laser power was ~ 100 µJ. The PIL dynamics of other molecules with ionization potentials spanning a range of 8 to 12 eV were studied in the first-generation apparatus, but attempts at correlating PIL rise times with plasma electron velocities were inconclusive [Dan94]. In the second-generation apparatus, the beam cross section of the electron pulse was detected by direct bombardment on the TI CCD, five cm from the nozzle tip. (The spatial resolution of the phosphor screen detection system was too poor to detect lensing effects.) The TI CCD pixels were rectangular, 13.75 µm by 16.00 µm, and the CCD was Chapter Nine: Total Experimental Temporal Resolution and Time Zero 478 I,., Cl) 0 u, C. 0 NI u, C. 0 'd' u, C. 0 'd' N u, ca .J z + + Figure 9-9: Electron beam surf ace plots during photoionization-induced lensing. The nozzle tip is just above the electron beam at the top of each image and the laser passes through horizontally. (Upper Left) No excitation laser. (Upper Right) -20 ps: The electron beam looks very similar to when no laser is present. (Lower Left) +40 ps: The upper portion starts to distort due to PIL. (Lower Right) +240 ps: PIL has caused the electron beam density to shift towards a horizontal strip above the center of the beam. oriented to provide the greatest spatial resolution along the laboratory's vertical axis, where lensing effects occurred (Figure 9-8) . Horizontal beam profiles were unchanged by PIL. To avoid saturating the CCD, brief exposures (< 1 s) of short electron pulses (~ 1 ps) were recorded. Electron beam cross sections were imaged as a function of the delay time between laser and electron pulses by varying the position of the Aerotech translation stage. Typically ten images were taken per temporal data point: the stage was scanned five times, exposing two electron beam images at each position. The laser was blocked every scan Chapter Nine: Total Experimental Temporal Resolution and Time Zero - No Laser - - Laser 479 - - Difference -20 ps 0 10 20 30 40 50 60 Pixels 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Pixels Pixels Figure 9-10: Change in the electron beam vertical profile with time. The nozzle tip is located on the left side of each profile. Profiles were calculated from the electron beam images shown in Figure 9-9. for the first data point to create a control image of the electron beam. A preliminary scan with large time steps (-20 ps) would be recorded first to narrow down the location of time zero, and a second scan of smaller time steps would be recorded to establish to to within a few ps. Data collection was automated with the EXCEL macro TIMEZERO.XLM (E.4). Figure 9-9 compares electron beam cross sections at different times in the lensing process. The nozzle tip was just above the electron beam in these images, and the laser traveled along the horizontal axis, slightly above the center of the electron beam. At negative times (electron pulse preceded laser pulse), the beam shape was indistinguishable from control exposures in which the excitation laser was blocked. At positive times, however, PIL caused the electron beam density to shift towards the laser position, where the positive charge was located. The integrated signal intensity (the total electron count), however, did not change. The density shift is seen more distinctly in the averaged vertical profiles of the images (Figure 9-10), where the needle tip would be located just to the left of each profile. Chapter Nine: Total Experimental Temporal Resolution and Time Zero 480 4.0 3.0 --e- Gas Present -o-No Gas t.D 0 ,- C 2.0 en en 1.0 o.o Ll~~~~~~~~~~~-;:;2.::=;:::;:::;:Q::i=;:::::;::~:;::;:::;~=!2--. -200 -100 0 100 200 300 Time Delay (ps) Figure 9-11: Typical PIL transient. The arrows correspond to electron beam images and profiles shown in Figure 9-9 and Figure 9-10. No lensing occurs in the absence of the molecular beam. Figure 9-11 shows the photoionization-induced lensing transient obtained from these electron beam images. (The method for quantifying electron beam lensing is discussed in the next section.) The transient exhibits a 100-ps rise consistent with the expected plasma electron velocities and interaction region volume, followed by a plateau of constant lensing which persists for at least 250 ps. No lensing occurred when the molecular beam flow was stopped. The amount of lensing was compared using three different laser beam diameters, 40 µm, 75 µm, and 150 µm. Lensing was similar for the larger beam diameters and significantly less for the 40-µm laser, presumably because the horizontal column of positive charge was narrower and affected a smaller portion of the electron beam. The rise time of the transients was independent of the laser beam diameter. As shown in Figure 9-12, the position of greatest lensing along the vertical profile followed the laser's vertical position relative to the electron beam and nozzle tip. Chapter Nine: Total Experimental Temporal Resolution and Time Zero 481 9.3.2.2 Methods of Data Analysis The effects of PIL are subtle difficult to and - --Laser No Laser - - Difference quantify because the transient signal is a change in a three-dimensional shape, rather than a change in parameter fluorescence a single (such as 0 10 20 30 40 50 60 0 Pixels 10 20 30 40 50 60 Pixels Figure 9-12: Vertical electron beam profiles perturbed by PIL. (Left) Laser passes above the electron beam and only the upper edge is affected. (Right) Laser passes through the center of the electron beam. intensity or number of detected ions). Since lensing effects occur only along the vertical axis, the data could be reduced to two dimensions by calculating the average vertical profile of all electron beam images for a given time delay, like those shown in Figure 9-10. To correct for fluctuations in electron beam intensity, these profiles were normalized to have an ADU area of 100,000 counts. A single, numeric value for the "degree of lensing" was then calculated by summing the square of the differences (SSD) in the average pixel intensities, row by row, between the profile of images at time lit and the profile of electron beam images taken with the excitation laser blocked. An additional complication hindered the analysis. Shot-to-shot jitter in the electron beam position was on the order of one or two pixels, or -20 µm. While such jitter was inconsequential for GED data, the jitter was of the same magnitude as PIL effects on the electron beam and greatly affected calculation of the SSD. Three different Chapter Nine: Total Experimental Temporal Resolution and Time Zero 3.0 (0 - • Average / No Align 2.5 - - o - -Average/ Edge - - -t:r - -Average I Minimum 2.0 --0-Align / Edge -----tr----Align / Minimum 0 482 T"" C 1.5 en en 1.0 0.5 0.0 -200 -100 0 100 200 300 Time Delay (ps) Figure 9-13: Comparison of the same PIL transient analyzed with different techniques. See the text for further details. analysis techniques were considered: 1. Average the images together, determine the vertical profile, and calculate the SSD without any profile alignment. 2. Average the images together, determine the vertical profile, and align with the average background profile before calculating the SSD. 3. Determine individual vertical profiles, align the profiles to each other before determining the average vertical profile, and then align with the average background profile before calculating the SSD. Furthermore, aligning the average profile at a given time step to the average background profile could be done either by minimizing the SSD value or by matching the profiles at an edge. Images were averaged with the program ADDER (D.5), and profiles were calculated, aligned, and converted to SSD values with the program PROFILE (D.6). PROFILE allowed 0.1 pixel precision in profile alignment using a cyclic interpolation scheme. The five possible methods were applied to the same set of lensing data, and the Chapter Nine: Total Experimental Temporal Resolution and Time Zero 483 • • t:,,. • • Vertical Profile (Coarse Scan) --0-Vertical Profile (Fine Scan) • Horizontal Profile (Fine Scan) C (J) (J) -40 -20 0 20 40 Time Delay (ps) 60 80 -30 -15 0 15 30 Time Delay (ps) Figure 9-14: Examples of PIL transients, recorded on different days, which exhibit very fast initial rises. The left-hand figure shows that the horizontal electron beam profile is unaffected by lensing. resulting SSD transients are compared in Figure 9-13. Introducing alignment in at least the final step of calculating the SSD greatly improved the signal-to-noise, and negative time profiles were almost identical to the background profile. There was little difference between SSD curves calculated with either partial or full profile alignment, but minimizing the SSD value in the final step led to more consistent results than aligning by an edge. The analysis methods used in the PIL transients shown throughout this thesis were therefore either full or partial alignment with a minimization of the SSD in the final step. 9.3.2.3 The Fast Rise in the Photoionization-Induced Lensing Transients Even when using smaller time intervals during data collection, the t0 estimated from PIL transients such as those shown in Figure 9-11 and Figure 9-13 had an uncertainty on the order of several picoseconds, comparable to time zero measurements made with photoconductive switches. On more than one occasion, however, transients were recorded which exhibited a very fast lensing rise leading to a "spike" only a few ps Chapter Nine: Total Experimental Temporal Resolution and Time Zero 484 7.0 • -25 µm - - o • - O µm 6.0 ■ 5.0 +25 µm ··0··+75µm .o·. - .o <D - 0 ,- 4.0 C u, 3.0 U) 2.0 1.0 0.0 -20 -10 0 10 20 30 40 Time Delay (ps) Figure 9-15: Changes in the PIL transients with the distance between the upper edge of the laser beam and the nozzle tip. The fast rise only occurs when the laser overlaps with the nozzle. wide (Figure 9-14). The slower rise due to diffusion of the plasma electrons continued beyond the spike, just like in other transients. The presence of the spike allowed a much more precise determination of to, and efforts were made to reproduce it regularly. First of all, the lensing spike was found to be confined to the vertical axis, as shown by the horizontal SSD values in Figure 9-14. Transients generated with p rather than s polarization under otherwise identical conditions were not significantly different. PIL transients were recorded as a function of the distance between nozzle tip and the upper edge of the laser beam, with the electron beam position held constant. As shown in Figure 9-15, the fast rise occurred consistently when the laser beam overlapped with the nozzle tip, although not always with a pronounced "spike." There was no fast rise evident when the gas flow was shut off, but sometimes a slow lensing rise appeared, presumably due to ablation and/or ionization of the nozzle tip. Laser damage on the Chapter Nine: Total Experimental Temporal Resolution and Time Zero 485 nozzle tip occurred regularly under these conditions. Several features of the fast PIL transient remain unexplained. The fast rise appears to be the result of a combined interaction between the excitation laser, the molecular beam, and the stainless steel nozzle tip, but no mechanisms have been proposed. Although the start of the rise can often be identified to within 1 ps, it is unclear whether this point is the location of time zero, or whether cross-correlation effects place t0 somewhere within the spike or rise. Exploration of this phenomenon continues. 486 Chapter Ten Ultrafast Gas-Phase Electron Diffraction The second-generation UGED instrument was ready for a true picosecond study of structural dynamics once time zero had been established to within a few picoseconds using photoionization-induced lensing transients. Careful consideration was given to the selection of the first molecular system, and diiodomethane satisfied all of the criteria admirably (10.1). The experimental methodology described in Chapter Eight required some additional steps: the pump laser had to be incorporated into the setup, and then synchronized with the electron pulses using PIL (10.2). In addition, new approaches to diffraction data analysis had to be developed to compare scattering intensities as a function of time (10.3). Data from two successful time-resolved diffraction studies of CH2Ii are discussed at the conclusion of this chapter. The results showed that the photodissociation of diiodomethane was observed by following structural changes as a function of time with Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 487 a temporal resolution of less than or equal to 1O ps. 10. 1 Selection of the Prototype Molecule: CH2 12 The UGED technique has the potential for general application to a wide range of chemical systems, but in the second-generation apparatus the number of viable samples was limited by the laser wavelength and energy, and the relatively simple molecular beam source. Selection of the prototype system was guided by three criteria: 1. The molecule had to be sufficiently volatile under modest heating (< 200 °C) to provide a few torr of pressure at the molecular beam nozzle orifice. 2. The molecule had to have a high absorption cross section at the fundamental CPM / PDA wavelength of 620 nm, or its second harmonic. 3. The dynamics had to be ultrafast and involve a pronounced structural transformation, such as a dissociation or isomerization. A variety of organic and inorganic molecules were considered (e.g., 12, IBr, CS 2, CF2h, CF3I, C2F4h, Fe(CO) 5 , CF3NO, NOCl), and CH2h emerged as the best candidate. Diiodomethane is a yellowish liquid at room temperature (mp: 6 °C) and has boiling points of 182 °Cat atmospheric pressure and 60 °Cat 10 torr [Lid92]. In order to diffract ~ 10% of the incident electrons, the CH2I2 sample bulb and inlet system required moderate heating (8.5) and the temperature at the nozzle tip in the scattering chamber was 166 °C. The extinction coefficient E at 310 nm is ~850 f, I mol cm [BaL80], [ScG80], [Kof81], [Pen81], [Hun82]. E and the absorption cross section cr are related by: Chapter Ten: Ultrafast Gas-Phase Electron Diffraction (j 1000 ln 10 £ = 3.8236 x 10-21 £ 488 (10.1) NA where cr has units of cm2 . cr310 = 3.25xl0- 18 cm2 for diiodomethane. UGED is not a background-free experiment because the incident electrons scatter indiscriminately from excited and unexcited molecules, so a high absorption cross section was necessary to ensure that a large fraction of the sample molecules were prepared on the upper state. A simple estimate for the amount of energy per laser pulse required to excite "every" molecule within the interaction region is given by: 2 E nwL h v-- 4a (10.2) where WL is the diameter of the pump laser. Using WL = 350 µm, E was estimated to be 190 µJ, towards the upper edge of what the CPM/PDA could produce after doubling 620 nm to 310 nm. The required power density was -2 rnJ/mm2 . The laser was not significantly attenuated by the sample since there were 10 14 photons per pulse and only 10 12 molecules within the interaction region. Even with a pulse energy given by Eq. 10.2, the actual fraction of molecular scattering intensity due to excited molecules was expected to be significantly less than one. The CH2Ii molecules do not rotate on the time scale of the laser pulse, so at most 1/3 of the molecules could be excited by the linearly-polarized pump laser, assuming no saturation. (If the upper state were bound instead of dissociative, the fraction would drop by another factor of two.) In addition, the overlap between pump laser and molecular beam cannot be perfect, and some molecules which never see the laser would be in the path of the incident electrons. Considering these caveats, a more realistic expectation for Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 489 percent completion of photodissociation within the interaction region was only 10 to 20%. The spectroscopy of diiodomethane has been the subject of a moderate amount of study.* The absorption spectrum begins in the near UV and consists of four or five bands, and three electronic transitions are energetically accessible at 310 nm: hv CH 2I + I (21112 ) (10.3) hv CH 2 I + 1* (2Pi 12 ) (10.4) hv (10.5) The creation of iodine molecule (Eq. 10.5) is actually symmetry-forbidden in the UV, so only the first two channels are available. (A recent fs VUV study of CH2l 2 captured the emergence of nascent Ii undergoing coherent vibrational motion [MaU96].) I and i* are formed on the lowest electronic states (both with B 1 symmetry), and the transition moments lies along the 1···1 internuclear separation. At 310 nm, between 20 and 25 % of the reaction proceeds along the i* channel [BaL80], [Kof81], [Hun82] . Experimental evidence [Kaw75] and quantum mechanical modeling [Zha88b] both contend that the dissociation processes are direct and occur within a few hundred fs. The UGED experiment was too slow to resolve a coherent dynamical process such as the steady increase of a C· ••I internuclear separation during dissociation, but CH2Ii was nonetheless ideal for demonstrating that chemical dynamics could be observed with ps resolution. As shown in Figure 10-1, loss of one iodine atom significantly alters the radial distribution function even when the fraction of excited molecules is only 10%. The peaks • See, for example, [KaM75], [Kro76], [BaL80], [ScG80], [Kof81], [Pen81], [Hun82] , [Zha88a] , and [Zha88b] . Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 490 I··· I 0.1 C-I 0.0 -- 0.3 lo,,, ..... I .~'. I ., '.• 0 1 2 3 Internuclear Separation (A) 4 5 Figure 10-1: Theoretical radial distribution curves for mixtures of CH2l 2 and CH2I + I. The fraction of CH2I is indicated for each curve. Smax = 15 A1; a, b = I; kd = 0.01 A2. due to C-1, H•••I, and I••• I internuclear separations all decrease, while the C-H peak remains unaffected. The I••• I internuclear separation offers the strongest signature about compositional change within the system because the CH2I radical has no such atom pair. Spectroscopic studies of CH2I in an argon matrix indicate that the radical is planar [SmD73], [BaL80], but for the calculations presented here the structure was assumed to be unchanged after the iodine atom left. 10.2 Experimental Setup and Methods The optical table was arranged for UGED experiments as shown in Figure 10-2, and also Figure 3-6. Output from the PDA was split into a pump laser arm (95% of the laser intensity) and an electron generation arm (5% ). The electron generation laser passed Chapter Ten: Ultrafast Gas-Phase Electron Diffraction PDA ➔ {\ Output 'J \. Camera Head D Shutter 491 M -0 Aerotech Translation Stage Figure 10-2: Optical table arrangement for UGED experiments. 5% of the PDA output went towards the electron gun to generate the ultrafast electron pulses, and the remaining 95% of the PDA output excited the molecular beam sample. Both arms were frequencydoubled to 310 nm. The pump laser and electron beam intersected with the molecular beam (not shown) in the interaction region. The delay between pump and probe was adjusted with a computer-controlled translation stage. The diffraction patterns were detected on the phosphor screen. BS: beam splitter; M: mirror; OM: dichroic mirror; F: filter; C: white card; SHG: second harmonic generation crystal (KD*P or KDP). through a Michelson interferometer and was focused by a 100-mm lens into an 0.5-mm KD*P doubling crystal. The interferometer was needed only for streaking experiments (4.4.2), so one arm was blocked during UGED. The 310-nm output from the doubling crystal was recollimated with a second lens and any leftover fundamental was blocked with an UG-11 filter. The laser was then directed through a 150-mm lens and vacuum window onto the electron gun photocathode using a mirror in a high-precision mount (Klinger; SL 51, 133-011), and the resulting electron pulse continued through the gun and into the scattering chamber as described in Chapter Four. After traveling along an optical delay line, the pump laser passed unfocused through a 2-cm KDP crystal and compensator (Quanta-Ray; Crystal Module 1) to convert the wavelength to 310 nm. The efficiency was ~ 10%. The fundamental was removed by Chapter Ten: Ultrafast Gas-Phase Electron Diffraction reflecting the output laser off of three dichroic mirrors coated to transmit 620-nrn 492 500 -- 0 400 E 300 light, and the tilt of the second-harmonic ::i. ..J generation crystal in the pump arm was optimized to give the greatest amount of 310-nrn laser power by monitoring the output energy with a Joule meter (Molectron; 14-09). The last dichroic was s: 0 0 200 100 0 0 +..,...,r-r+--~+-,-,-..,..+-~h--,.-...--l--.~1---.---.----.-1 0 2 4 6 8 10 12 14 Stage Position (mm) Figure 10-3: Calibration curve for the pump laser beam waist at the nozzle tip as a function of the longitudinal position of the input lens. installed in a high-precision mirror mount (Klinger; SL 25.4 133-010) which directed the laser through an iris, a 200-mm lens, and into the scattering chamber via a 0.25"-thick window. Both the window and the lens had broadband UV anti-reflection coatings. The lens was mounted on a hand-adjusted translation stage such that the 310-nm laser focal point could be moved back and forth longitudinally under the nozzle tip without changing the optical path length (a calibration curve is shown in Figure 10-3). Generally the focal point was located beyond the nozzle tip. The diameter of the pump laser in the interaction region was about 350 µm. The pump laser exited the scattering chamber through a baffle tube with a Brewster-angle window and Wood's horn (Figure 3-11), and was blocked with a white card which fluoresced to show the 310-nm beam shape. The computer-controlled Aerotech translation stage installed in the pump laser arm varied the arrival time of the pump laser relative to the electron beam at the interaction region under the nozzle tip. The hollow retroreflector mounted on the translation stage was specially-coated to have 99% reflectance in the neighborhood of 620 nm (CVI). Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 493 (Standard comer cubes reflect only ~60% and that power loss would be too big for UGED.) The path of the laser through the delay line was tested carefully to ensure that the position of the pump laser in the interaction region remained fixed for the full length of the translation stage's travel. The methodology outlined in 8.1 to record GED data was modified for ultrafast work because of the addition of the pump laser to the experiment. Once the electron beam was centered on the beam stop and the molecular beam nozzle was aligned relative to the electron beam, the pump laser was aligned relative to the nozzle. To do this, the laser energy was first attenuated with filters, and the nozzle tip was lowered into the laser path. The horizontal position of the laser was adjusted based on the nozzle's shadow, which could be seen in the white card fluorescence at the output. The nozzle was then raised back to its original height and the laser's vertical position was tweaked until the laser just clipped the nozzle tip; the laser was lowered about 50 µm from there. The filters were removed, the molecular beam flow was started, and the arrival times of the pump laser and electron beam at the nozzle tip were synchronized using photoionization-induced lensing (9.3.2.1). The beam waist of the pump laser was reduced to 100 µm for this experiment by translating the input lens. Typically one or two PIL transients were recorded - a coarse scan with 5-ps resolution, followed sometimes by a fine scan with 2-ps resolution - and the data were analyzed immediately in order to establish time zero for the UGED experiment. Usually the molecular beam flow was stopped during the analysis phase. Once the time zero position of the Aerotech translation stage was determined, the programs AUTOHOME and AUTOSCAN (D.13) were recompiled with the desired offset Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 494 position and step size of the UGED transient. The molecular beam was restarted, test diffraction patterns were recorded to set the exposure time, and UGED images were collected using the EXCEL macro UGED_EXP.XLM (E.3). This macro started by sending the delay line first to home and then to the offset position. A short exposure of the beam stop region was recorded to track the electron beam position, and then diffraction images were taken for each data point in the transient, with the Aerotech translation stage automatically moving by the pre-set step size between each exposure. The macro was run repeatedly to take as many diffraction images at each data point as possible. Periodically the power of the pump laser was tested with the Joule meter, the molecular beam flow was monitored with the ionization gauge, and the alignment of the laser and nozzle tip was checked by lowering the nozzle and looking at the white card fluorescence shadow. The constancy of the electron beam position could be confirmed every time the macro ran using the short test exposure. After the experiment was complete, the UGED instrument was shut down as described in 8.1.3. 10.3 Data Analysis and the First UGED Transients The computational methods for generating radial distribution functions of groundstate molecules from the raw UGED scattering intensities is described D.4.1. To briefly summarize, the experimental modified molecular scattering curve is calculated from: (10.6) where / 8 (s) is the background curve estimated by fitting a smooth function to the sM(s) Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 495 zero positions in the theoretical structure, gE is a constant which scales the experimental amplitudes down to the theoretical amplitudes, and the Norwegian school (2.7). s/ifallfbl levels the data according to gE can be estimated by scaling sM\s) to sM\s) at a maximum or minimum, or by matching the amplitudes of a particular internuclear separation in the corresponding radial distribution functions. A different strategy was necessary for evaluating transient structural data. First of all, the various IE(s,ti) had to be normalized with respect to the total number of scattered electrons NE detected at each time step. Usually NE did not vary by more than one percent. Since the percent scattering should be the same for all time steps, the scaling factor gE which normalizes experimental molecular intensities to their theoretical counterparts should also be invariant. gE must be determined at negative time and then applied to all other time steps. To see why this is so, consider the simple example of molecular iodine photodissociation where the only structural evidence for the reaction is a decrease in the molecular scattering amplitude. If gE is overlooked and allowed to vary, then the diffraction data after to will still fit perfectly with the 12 structure (although the noise level in the signal should increase). The structural transient will mistakenly indicate that nothing happened. For the case of CH2Ii photodissociation, the shape of the sM(s) curve does vary with the percent completion x, but fixing the scaling factor is still important to the analysis. Figure 10-4 shows how the temporal difference curve !'lsM(s,M) depends on the treatment of gE following 10% dissociation of CH2h. The magnitude of the observed signal diminishes by a factor of four if gE is determined individually, by scaling to a particular sM(s) peak at each time step. Furthermore, the !'lsM(s,M) which result from this Chapter Ten: Ultrafast Gas-Phase Electron Diffraction --True Difference --Scaled At 3.84 1/A 0.08 -- 496 0.06 Cl) ::ECl) 0.04 <l 0.02 0 0 3 12 6 15 Figure 10-4: sM(s) difference curves between 90% CHz1 10% CH I and 100% CH l t:i.sM(s) decreases by a factor of four if the amplitude of the original curves are scaled together, as is usually done for ground-state experiments. The post-scaling difference curve corresponds to a system-dependent composition of parent and product. / 2 . 2 2 2 technique are not easily related to the actual structural changes unless x is already known. These problems plagued the early nanosecond CF3I photodissociation study (8.7). The second major modification to data processing followed from these considerations of gE: the focus of the analysis switched from sM(s) to !::,.sM(s,M) curves: (10.7) In Eq. 10.7, tR refers to the negative time step which serves as a reference for ground-state structure, and gE is the scaling factor at tR. There are several advantages to comparing and fitting !::,.sM(s,!::,.t) instead of sM(s). Recall from 7.2 that the total scattered electron intensity during an experiment is: (10.8) where lver(s) depends on the detector and other experimental conditions. Regardless of the photoreaction's progress, the number of scattering centers within the interaction Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 497 region does not change. Long-term fluctuations in laser, electron, and molecular beam fluxes were averaged out in UGED data by cyclically sampling diffraction images from each time step, so in principle /s(s) was temporally invariant. In this ideal case, 11sM(s,11t) curves are automatically background-corrected and there is no need for iterative zeropoint fitting mechanisms. The 11sM(s,11t) can be directly transformed into the change in structure with time, 11f(r,11t). As is discussed in 10.3.1, ls(s) in the UGED experiments did vary with the temporal coordinate, and the analysis could not be simplified as described above. In this case, evaluating 11sM(s,11t) instead of sM(s) still offers a major advantage: the data does not have to be simultaneously fit to the percent completion x of the reaction and the structure of the products at that time step, both of which alter the sM(s) zero points. Consider the half-reaction: A hv B (10.9) where B represents any number of fragment species and their subsequent dynamics. Then: 11sM(s, 11t) = _!__(I(s,t) - I(s,tR)J gE 11sM(s,11t) = _!__([xl(s,B) + (l-x)l(s,A)] - xl(s,A)J gE 11sM(s,11t) liallfbl lialllbl = ~[sM(s,B) - sM(s,A)] (10.10) (10.11) (10.12) gE Eq. 10.12 shows that A and B always have a 1: 1 ratio in 11sM(s,11t), independent of x, and the zero points are only affected by the structure and composition of B. The value of x at that 11t appears in the relative scaling factor, whose adjustment does not shift the zeros. Chapter Ten: Ultrafast Gas-Phase Electron Diffraction Once a fit is found for the curve, x can be calculated using 498 C-I the C-H reference (negative time) gE and the scaling factor determined in I,,, Transformation from the fit. to !if(r,lit) is straightforward. Figure 10-5 !isM(s,!it) ..... CH21 -CH212 Sum · - - - -Zero Line I···I shows explicitly the source of the 1 0 2 3 4 5 Internuclear Separation (A) photodissociation. If the CH2I radical structure is unchanged Figure 10-5: The theoretical b..f(IJ curve following CH2l 2 photodissociation is a 1:1 mixture of f(r) for CH2I and f(r) for CH2l 2 . Assuming that the CH2I structure is unchanged from the parent, then the C-H and H···H peaks are eliminated in the subtraction. from when it was a part of CH2I2, then only negative peaks are found in the !if(r,!it), corresponding to the J.. •I separation and one half of the C-I and H •••I distances. These analysis methods were applied to the first ultrafast structural transients recorded with the UGED instrument. Two such experiments are discussed in the following sections. 10.3.1 CH2l2 Photodissociation: Trial #1 The experimental conditions for time-resolved diffraction studies of diiodomethane were similar to the ground-state investigations (8.5). A round glass bulb half-filled with CH 2li (Aldrich; 99% purity) was attached to the sample inlet system and subjected to several freeze-thaw evacuation cycles to remove dissolved gases. The bulb was heated to Chapter Ten: Ultrafast Gas-Phase Electron Diffraction -30 ps -15 ps Ops 499 +15 ps C en en 200 210 220 230 240 250 260 270 Translation Stage Time Delay (ps) Figure 10-6: Photoionization-induced lensing transient taken to establish time zero for Trial #1 of the UGED CH2l2 studies. The location of the four time steps sampled during the diffraction portion of the experiment are marked. 115 °C, the external tubing of the inlet system was heated to 158 °C, and the temperature 4 of the nozzle tip was 164 °C. The scattering chamber ionization gauge read 2x 10 torr during the experiments, and the laser pulse energy was 90 µJ, with a beam width at the needle tip of 350 µm (0.9 mJ/mm2 ) during diffraction experiments and 50 µm during the time zero measurement. The photoionization-induced lensing transient recorded before the diffraction experiment is shown in Figure 10-6, and time zero was assigned midway along the sharp rise of the transient. Diffraction patterns were taken at four time steps (-30 ps, -15 ps, 0 ps, and + 15 ps). 90-s images were recorded for a total exposure time of 66 min at each point, and the cumulative number of electrons detected per time step was 14 million, an average of 118 scattered electrons per shot. The percent scattering was not measured, but assuming a low value of 5% leads to an electron pulse width of -2 ps. The upper estimate for the total temporal resolution of the experiment, including velocity mismatch (3.4 ps - Chapter Ten: Ultrafast Gas-Phase Electron Diffraction see 9.1.2), was therefore ~5 ps. 500 22 The leveling atoms were a, b = I, a 5-pt boxcar smooth was applied to the sM(s) curve, and an 11-pt boxcar smooth was a.. 21 0 0 O 20 u· • ca LL c, 19 r:: ca 18 () . . (.) applied to the 11sM(s,/1t) curve. simple, and qualitative A quick, method for identifying whether or not a structural change occurred as a function of time was to optimize gE at each time step by scaling the experimental and theoretical I••• I peaks in the radial distribution curves. en 17 16 • ·O I I -30 -15 0 15 Time Delay (ps) Figure 10-7: Scaling factors between experimental and theoretical sM(s) curves as a function of time for Trial #1. The factors were obtained by matching the amplitudes of the experimental and theoretical l•••I peaks in the f(r) curve. Figure 10-7 shows that gE dropped at time zero and + 15 ps relative to negative time. A decrease was expected since the molecular scattering amplitudes of a CH2 h / CH2I mixture decrease as the fraction of CH2I increases. According to Figure 10-7, about 10% of the molecules dissociated. Next the raw 11sM\s,/1t) curves calculated relative to -30 ps were examined to see if ls(s) remained constant with time. Figure 10-8 shows the results of this Trial and three others, and all exhibit the same trends. Negative-time 11sM\s,/1t) were more or less constant within the limits of experimental noise, but beyond time zero the 11sME(s,11t) baselines all drifted at different rates in the same direction, eliminating the possibility of a simple analysis. The magnitude of the drift was on the same scale as the molecular scattering amplitudes. Clearly this effect depended on the arrival of the laser pulse, and the correlation with the laser pulse energy was also strong: the slopes in Trials #3 and #4, Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 501 where E was 250 µJ, were much steeper than the slopes in Trials # 1 -15 0 and #2, where E was 90 µJ. +15 The downward slope of the baseline indicated that the -15 arrival of the laser pulse caused 0 the scattering intensity to increase +15 at smalls relative to large s, which could happen through at least two Trial #3 0 +20 First, the different processes. +40 pump laser excited some fraction of the sample along multiphoton +10 ionization channels (witness the +30 PIL transients), so positive ions +50 were present within the interaction +70 region. The macroscopic effect of these ions on the electron beam was small, and undetectable using the scintillator imaging system. There is a more significant effect at the microscopic level, however. Below -5 the electron 0 2 8 10 Figure 10-8: Raw '1sM(s) curves from four different UGED investigations of the CH2Ii photodissociation process (calculated with Eq. 10.10). The time delay M of each curve is listed on the left with ps units. The time delay of the reference /(s) curves were -30 ps (Trials #1, #2) and -20 ps (Trials #3, #4) . The experimental conditions for Trials #1 and #2 are described in the text. Trials #3 and #4 were recorded by Dr. Jim Cao and Hyotcherl lhee; the 310-nm pump laser in their experiments had a pulse energy of 250 µJ . Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 502 differential scattering cross section for positive ions departs sharply from the values for neutrals, increasing an order of magnitude or more by 1 A- 1 [Pei69], which could cause the observed baseline shift. <I>1 = 9.46 eV for CH2h [Lid92], so ionization is a three-photon process at 310 nm; the question remains as to whether enough ions would be generated from an energy density of 0.9 mJ/mm2 to distort the baseline by such a large amount. A second possibility sterns from the change in the composition of the molecular sample. Chemical binding reduces both atomic and molecular scattering cross sections at small s (2.1.8), so photodissociation should cause the background intensity to shift in that direction. Again, it is unclear whether the magnitude of the observed shift could be due to this effect, since only one bond was broken for every ten molecules. Whatever the source of the baseline drift, the net result was that Afs(s,/),.t) had to be removed from the M E(s,/),.t) difference curves with the same type of zero-point fitting mechanism used for correcting I\s) curves. Figure 10-9 plots the /),.sM(s,M) curves for 15, 0, and +15 ps (calculated relative to -30 ps), and the experimental and theoretical sM(s) curves from -30 ps are also shown to indicate the magnitude of the change. The scaling factor for !),.sM\s,M) at +15 ps was 2.1, which confirmed that the percent completion of the reaction was 10%. gE was then fixed at 2.1 when calculating the two other difference curves. All /),.sME(s,M) were noisy, but at -15 ps there was no agreement between the experimental curve and the theoretical curve corresponding to 10% dissociation. At 0 and + 15 ps, oscillations appear which correlate with the loss of an iodine atom. The difference between the experimental and theoretical sM(s) curves at -30 ps is much noisier than the !),.sME(s,M) curves, at least for s < 6 A- 1. This agrees with some of Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 503 f\ f\ I, ' , ~t = -30 ps \ t I I \ i Experiment Minus Theory At -30 ps (Smoothed) 11sM(s) Relative To -30 ps -15 ps Ops +15 ps 0 2 4 8 10 12 Figure 10-9: Results from Trial #1. (Top) Experimental and theoretical sM(s) curves for M = -30 ps, and their difference. The composition was assumed to be 100% CH21z. (Bottom) Experimental t-,.sM(s) obtained by fitting a background curve to Af(s) using the zero points of a 1:1 mixture of CH21 radical and negated CHJ2 . The theoretical curves correspond to 10% dissociation. Chapter Ten: Ultrafast Gas-Phase Electron Diffraction -30 ps 504 -15 ps ... ..... 3 4 0 5 1 4 Internuclear Separation (A) Internuclear Separation (A) Ops +15 ps 5 ... ... ..... ..... I 0 , ,-, I 5 Internuclear Separation (A) 0 1 2 3 4 5 Internuclear Separation (A) Figure 10-1 0: Experimental and theoretical radial distribution functions from Trial #1. The theoretical f(rj were calculated for 100% CH2Ii in all four snapshots. The decreases of peak amplitudes at 2.2 and 3.6 A for M = 0 and +15 ps in the experimental f(rj correspond to the loss of an iodine atom from -10% of the molecules in the interaction region (see Figure 10-1). the conclusions in Chapter Eight, that the discrepancy was of systematic ongm. Possibilities include non-uniform detector gain, inaccurate theoretical structures, or failure of the scattering theory. Radial distribution functions f(r) were calculated from the sM(s) for each time step using experimental values of s ranging from 1.16 A- 1 to 10.64 A- 1 and a constant scaling factor of 20.5 (see Figure 10-7). The damping constant kd was 0.01 A2 . Figure 10-10 Chapter Ten: Ultrafast Gas-Phase Electron Diffraction shows that the 505 experimental amplitudes of the C-1 and I .. •I peaks dropped at 0 and + 15 ps just as in the theoretical simulation C-1 of CH2Ii dissociation presented -15 ps earlier in Figure 10-1. The !isM(s,lit) curves plotted in Figure 10-9 were also transformed to create !if(r,!it), using an experimental s range of 1.04 A- 1 to 7.00 A- 1. Because the Ops scaling factor was fixed (at 2.1) and PROC5 automatically appended the theoretical curve onto the experimental curve up to Smin, an artificial baseline +15 ps fluctuation was introduced in data preceding + 15 ps. The fluctuation was corrected afterwards 1 2 4 3 Internuclear Separation (A) 5 by subtracting from the tif(r,/it) a theoretical equivalent to !if(r,!it) representing no dissociation. 0 Figure 10-11: The M(r') curves for Trial #1 generated from the ll.sM(s) in Figure 10-9 as described in the text. The theoretical curves correspond to 10% dissociation of the parent. This correction was weighted by the fraction of Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 506 undissociated sample at each time step, and the results are shown in Figure 10-11. The !).j(r,!).t) is flat at negative-time, and at the other time steps increases in agreement with the formation of CH2I radical. All methods of presenting the structural change from Trial #1 showed that the time-zero data was almost identical to the + 15 ps data. Referring back to the PIL transient (Figure 10-6), it appears that assignment of to after the start of the rise was incorrect - the reaction was complete within the temporal resolution of the experiment. The true time zero was probably located at 236 or 237 ps on the translation stage time delay scale; thus the UGED data taken in Trial #1 helped to clarify the interpretation of the PIL transients. 10.3.2 CH2l 2 Photodissociation: Trial #2 The conditions of Trial #2 were very similar to Trial #1. The sample bulb was heated to 128 °C, the external tubing of the inlet system was heated to 165 °C, and the temperature of the nozzle tip was 163 °C (the temperature was ten degrees warmer a few millimeters up from the tip). The scattering chamber ionization gauge read 2.5xl0 4 torr during the experiments, and the laser pulse energy was 90 µJ, with a beam width at the needle tip of 350 µm (0.9 mJ/mm2) during diffraction experiments and 100 µm during the time zero measurement. The photoionization-induced lensing transient recorded before the diffraction experiment is shown in Figure 10-12, and time zero was assigned to the small spike in the 2-ps transient, which coincided with the start of the rise of both transients. Diffraction patterns were taken at four time steps (-30 ps, -15 ps, 0 ps, and +15 ps). 75-s images Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 507 0 -30 ps -15 ps Ops +15 ps I 0 I I I I C en en 0 0 I 0 I I I lo 0 70 80 90 100 110 120 130 140 150 160 Translation Stage Time Delay (ps) Figure 10-12: Photoionization-induced lensing transients taken to establish time zero for Trial #2 of the UGED CHi1 2 studies. The location of the four time steps sampled during the diffraction portion of the experiment are marked. were recorded for a total exposure time of 110 min at each point, and the cumulative number of electrons detected per time step was 88 million, an average of 440 scattered electrons per shot. The percent scattering was not measured, but assuming a low value of 5% leads to an electron pulse width of ~9 83 - i... 0 0 81 0 ps. The upper estimate for the total «I LL 79 C') temporal resolution of the experiment, ·= 77 0 «I 0 en 75 including velocity mismatch, was ~ 10 ps. The leveling atoms were a, b = I, a 5-pt boxcar smooth was applied to the sM(s) curve, and an 11-pt boxcar smooth was applied to the !isM(s,!it) curves. As described in 10.3.1, the relative scaling -0 -30 -15 0 15 Time Delay (ps) Figure 10-13: Scaling factors between experimental and theoretical sM(s) curves as a function of time for Trial #2. The factors were obtained by matching the amplitudes of the experimental and theoretical J... J peaks in the f(!) curve. Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 508 Llt = -30 ps -Cl) :lECl) Experiment Minus Theory At -30 ps (Smoothed) LisM(s) Relative To -30 ps -15 ps 0 ps +15 ps 0 2 4 8 10 12 Figure 10-14: Results from Trial #2. (Top) Experimental and theoretical sM(s) curves for M = -30 ps, and their difference. The composition was assumed to be 100% CH2l 2 . (Bottom) Experimental t.sM(s) obtained by fitting a background curve to Af(s) using the zero points of a 1:1 mixture of CHzl radical and negated CHzl 2. The theoretical curves correspond to 5% dissociation. Chapter Ten: Ultrafast Gas-Phase Electron Diffraction factors at each time step were radial distribution curves, and the gE are plotted in Figure 10-13. The percent completion was less C-1 Theory - - Experiment -- ....a.. than in Trial #1, about 5%. Figure 1···1 -30 ps found using the I••• I peak in the 509 C-H 10-14 plots the I !),.sM(s,/),.t) curves for -15, 0, and 0 1 2 3 4 Internuclear Separation (A) 5 + 15 ps (calculated relative to -30 ps), and the experimental and Figure 10-15: Experimental and theoretical radial distribution functions from Trial #2 at -30 ps. theoretical sM(s) curves from -30 ps are also shown to indicate the magnitude of the change. The radial distribution function at -30 psis presented in Figure 10-15. The scaling factor for !),.sME(s,M) at +15 ps was 4.2, which confirmed that the percent completion of the reaction was 5% (Figure 10-13). Evidently the overlap of the laser, electron, and molecular beams was not as good as in Trial #1. Since six times as many electrons were collected in Trial #2, however, the signal-to-noise ratio was superior, as the /),.sME(s,M) evince. At -15 ps the difference curve is almost perfectly flat; some oscillations start to appear at time zero, and the !),.sME(s,M) at+ 15 ps provides almost a perfect match with theory. Since the magnitude of these oscillations are small on the vertical scale used in Figure 10-14, the quality of the results is much easier to see in the !),.j(r,/),.t) curves shown in Figure 10-16. The data was transformed from an experimental s range of 1.80 A- 1 to 6.24 A- 1 using a constant scaling factor of 4.2 and the baseline corrections discussed in Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 510 10.3.1. The amplitude of the time zero !).j(r,!).t) peaks is about half maximum, which would be expected from a measurement that - - - ·1_,(\ •. - - \C . -I. •. ....<l'- straddled t0 . Identification of t0 in \. :\J••• J " I \/ \ \ -15 ps this data set may not necessarily have been better than in Trial #1, - - - - · ;· - - - - - - - since the effective experimental pulse width was twice as large, 1 ....'- <l offering greater room for error. The results from both Trial 0 ps #1 and Trial #2 offered no more than a cursory examination of the CH2I radical structure. Although the modified molecular scattering -.... '- <l curves for ground-state structures +15 ps have been recorded out beyond 12 A- 1 with UGED, the signal from the change in structure is an order of magnitude less because the percent completion of the reaction was at best 10%. As both the 0 1 2 4 3 Internuclear Separation (A) 5 Figure 10-16: The M(r) curves for Trial #2 generated from the t.sM(s) in Figure 10-14 as described in the text. The theoretical curves correspond to 5% dissociation of the parent. Chapter Ten: Ultrafast Gas-Phase Electron Diffraction 511 theoretical estimate in Figure 5-2 and the experimental 11sM(s,11t) curves in Figure 10-9 and Figure 10-14 have shown, the range of s available for analyzing the structural change was less than 8 A- 1. This was sufficient to demonstrate the formation of CH2I from CH2Ii, but CH2I itself only makes a 15% contribution to the 11sM(s,/1t), according to an estimate that weights scattering terms by nZ;Z/rij, Thus the CH2I molecular scattering signal was just 1% of the total, and no more than the coarsest conclusions could be reached about its structure with the existing electron flux. 512 Chapter Eleven Conclusions and Future Directions 11.1 Summary of Results For the first time, structural transients were obtained by gas-phase electron diffraction with ultrafast temporal resolution (on the order of 10 ps or less). These CH2I 2 photodissociation experiments demonstrated that chemical dynamics could be followed as a function of time by measuring the structural differences between the reactants and products. UGED was thus established as a new method for probing picosecond kinetic processes and rotational coherence. Extending GED to the ps regime required blending state-of-the-art technologies from disparate scientific disciplines into a single experiment. The framework for ultrafast temporal resolution was established with a CPM/PDA laser system set up in a pump/probe configuration. The photoemission electron gun and the pulse width measurement techniques were descendants of streak camera technology; the Chapter Eleven: Conclusions and Future Directions 513 gun's temporal response was 1 ps for every 1,000 electrons per pulse. Single scattered electrons were detected by a novel dual-CCD, two-dimensional imaging system, which provided very high spatial resolution (~ 14 µm) over a small area using direct electron bombardment, and moderate spatial resolution (~80 µm) over a much larger area by the more resilient approach of scintillation and intensification. These components plus a molecular beam source were put together in an otherwise conventional gas-phase electron diffraction arrangement, and the instrument's temporal coordinate was synchronized by observing subtle distortions in the electron beam shape following excitation of the sample with the pump laser. Finally, a software package was developed based on the principles of GED analysis, and the programs were extended to meet new and different needs associated with the ultrafast diffraction experiments. The goal proposed in Chapter One of obtaining R(t) surfaces with femtosecond resolution and then studying coherent processes awaits solutions for a number of technical challenges. At least one other research group, Geiser and Weber, have constructed their own UGED apparatus [Gei95], and ultrafast low-energy electron diffraction experiments have also been proposed [ThJ95]. Ben-Nun et al. have suggested applying time-resolved diffraction methods to the study of excited atomic states [BeM96], and Liu and Lin have conducted rigorous theoretical calculations of UGED from diatomic molecules [LiW97]. UGED research continues in the Zewail group's laboratory as well. The CH2Ii photodissociation experiments reported in Chapter Ten were repeated by Dr. Jianming Cao and Hyotcherl lhee with greater laser power ( ~250 µJ per pulse), and the resulting transients reflected a 15% change in sample composition and showed improved signal-to- Chapter Eleven: Conclusions and Future Directions noise ratios [Wil97]. This publication is reproduced in Appendix F. 514 More recently, UGED has been applied to the study of C2F4Ji and CF2l 2, and a paper discussing the dynamics of Fe(CO)s photodissociation has been submitted [Ihe97]. CH2Ii would be an excellent candidate for generating asymmetric diffraction patterns due to rotational coherence effects, and perhaps such an experiment will be begun soon. 11.2 The Third-Generation UGED Instrument Construction of a third-generation UGED apparatus at Caltech is being considered, and this section suggests some modifications for the new instrument. The two primary goals for any design changes are to increase the signal-to-noise ratio in the experimental sM(s) curve, and to improve the total temporal resolution of the apparatus. 11.2.1 The Laser System Although in principle any gas-phase molecular system can be studied with UGED, in practice the application of the technique is limited by the available pulse energy and wavelength of the excitation laser (10.1). The absorption cross section of the molecule must be high enough such that the photoreaction is initiated in at least ten percent of the sample. With the second-generation instrument, only those molecules with cross sections greater than 1x10· 19 cm2 at the fundamental CPM wavelength of 620 nm (Eq. 10.2), or greater than 2.5x10· 18 cm2 at the second harmonic 310 nm, were considered to be viable candidates. Other wavelengths could be created with methods such as continuum generation (3.1.4), but the resulting pulse energies were too low for UGED, typically less Chapter Eleven: Conclusions and Future Directions than 10 µJ. 515 More chemical systems could be studied with UGED by adding a second To Scattering Chamber s p HWP Nd: YAG laser to the optical table to amplify the energy of these alternative wavelength pulses. For the third-generation UGED BSC Figure 11-1: Optical arrangement for generating a pair of pump laser pulses with orthogonal polarization vectors. M: mirror; BS: beam splitter; HWP: half-wave plate; BSC: polarizing beam splitter cube. instrument, a completely different ultrafast laser system such as the titanium-sapphire might provide greater flexibility. Assuming that photoexcitation takes place along a linear dipole transition moment, and no saturation occurs, the theoretical limit on percent completion of the reaction is 33% because the molecules do not rotate within the time span of the laser pulse (10.1). If the laser system were upgraded to yield pulse energies approaching twice the value estimated from Eq. 10.2, then the percent completion (and the SNR) could be doubled using two excitation pulses with orthogonal polarization vectors. One possible optical arrangement is shown in Figure 11-1. The pump laser is split into two arms of a MachZehnder interferometer, and the polarization vector of one arm is rotated 90° using a zeroorder half-wave plate. The two arms are then recombined with a polarizing beamsplitter cube used as a mixer rather than a separator. One arm of the interferometer must include extra path length, slightly longer than the temporal length of the laser pulse, so that the two beams do not simply recombine to give a polarization vector rotated by 45°. Since temporal broadening due to the electron pulse width and velocity mismatch are large, the total experimental temporal resolution should not be significantly affected if a pair of 300- Chapter Eleven: Conclusions and Future Directions 516 fs laser pulses, separated by ~100 fs, are used to excite the sample. Laser amplifiers with higher repetition rates would improve the signal-to-noise ratio of the experiment by increasing the number of electron pulses per second. For this modification to be truly effective, however, the gain of the scintillator imaging system would have to be lowered in order to keep the ratio of image integration time to CCD readout time (during which no data is collected) large. One option would be to simply lower the image intensifier gain in order to prevent CCD saturation at small s, but this method has limitations: the average number of ADU from a single electron event must still be greater than thermal and dark current noise levels to keep the SNR high at large s, where the scattering intensity is small. A second option would be to reduce the gain only at small s by applying a thin aluminum coating over the central portion of the large fiber optic taper, perhaps out to ~5 A- 1. This would be identical to the installation of a disjointed rotating sector. Flat field image correction would almost certainly be necessary under such circumstances. Alternatively, a laser with a higher repetition rate could be used to improve the total experimental temporal resolution by reducing the number of electrons per pulse while keeping the total electron flux constant. An order-of-magnitude increase in the repetition rate would allow the use of electron pulses 1 ps or less in duration, and the total resolution would be limited instead by velocity mismatch. 11.2.2 The Sample Inlet System The design of the free-jet expansion nozzle system used for the experiments reported in this thesis was simple (3.3.2) and would benefit from an upgrade. After Chapter Eleven: Conclusions and Future Directions 517 working with several low vapor pressure samples, a general observation was made that in order to generate sufficient pressure at the nozzle tip, the UGED inlet system had to be heated to higher temperatures relative to other GED inlet systems described in the literature. One explanation is that the sample pressure in the interaction region of other diffraction instruments can be much less than in UGED because those instruments have orders of magnitude greater higher electron fluxes. In addition, the diameter of the nozzle orifice in UGED is small, 130 to 150 µm, constricting the flow; perhaps shortening the travel distance from sample bulb to orifice (by moving the sample bulb into the scattering chamber) and shortening the length of the nozzle tip would improve the relationship between temperature and pressure. The experiment would also benefit from the installation of a cold trap (LN2 or thermoelectrically-cooled) immediately below the nozzle tip, especially if the trap could be removed from the scattering chamber without breaking vacuum once the experiment was complete. This would greatly reduce the background chamber pressure and the amount of chemicals pumped through the vacuum system. Effort could be spent enhancing the piezoelectric pulsed nozzle (3.3.3) or building a shielded solenoid nozzle like Bartell and French's [Bar89], but the value of a pulsed nozzle (in reducing the background chamber pressure) would be diminished if the laser repetition rate were increased. The third-generation UGED instrument might incorporate a different sample-inlet design using an additional vacuum chamber and differential pumping to create a skimmed molecular beam in the scattering chamber. With a slit-like skimming aperture, it might be possible to create a molecular beam with a rectangular cross-section: ~300-µm wide along the axis matched to the electron beam waist dimension, but very narrow (< 100 µm) along Chapter Eleven: Conclusions and Future Directions 518 the axis matched to the pump laser beam waist. The pump laser would therefore be focused into the interaction region with cylindrical lenses to match its dimensions to both the molecular beam and the electron beam. This design would simultaneously increase the energy density of the pump laser (by allowing tighter focusing along one axis) and reduce the severity of temporal broadening due to velocity mismatch (9.1.2). Using the same method of derivation as in 9.1.1, !itvM for an elliptical molecular beam when pulse CD (the probe) and pulse C2> (the pump) intersect orthogonally (9 = 90°) is: (11.1) where WMi is the molecular beam width along the same direction as w1, and wM2 is likewise measured parallel to w2. ~ is equal to v2/v 1. 11.2.3 The Electron Gun Improving the temporal response of the UGED electron gun can proceed along many different directions. At the outset, a better method should be sought for measuring the accuracy and precision of different electrode voltages. Present measurement methods, using a Keithley High Voltage Probe and a Fluke Multimeter, are limited to 1 or 2% in accuracy and -0.05% in precision (4.3.1). Increasing the kinetic energy of the electrons above 18 ke V would reduce space-charge broadening [Suy88], decrease velocity mismatch with the excitation laser (9.1.2), shorten the transit time to the nozzle tip, and improve the electron beam's lateral coherence (4.3.7). A side effect of this change, however, would be a loss in resolution of the streaking experiment. experiment already needs improvement - (The streaking see 11.2.4.) Shortening the distance from Chapter Eleven: Conclusions and Future Directions 519 electron gun to nozzle tip would decrease transit time broadening due to the electron energy distribution and space-charge, but again the resolution of the streaking experiment would suffer. If higher electron energies were used, L could be increased simply by rotating the scattering chamber top flange 180° since the molecular beam flange connection is off-axis (Figure 3-8). This would simultaneously shorten the electron-gunto-nozzle distance. In the absence of space-charge, the limit of the electron gun's temporal response was found to be ~850 fs, stemming almost entirely from broadening in the photocathodeto-extraction-pinhole region (4.3.6.1). l1tpc could be reduced either by narrowing the initial electron energy distribution, 11£, or increasing the extraction electric field E. The silver photocathode might be better optimized for photoemission at 4.0 eV by studying the dependence of the work function on film thickness. Actual measurements of 11£ as a function of laser energy would reveal whether thermally-assisted photoemission affected the electron pulse width (4.2.1.4), since estimates have placed the incident laser energy density close to the threshold (4.3.5.2). The search for other candidate materials for the photocathode, such as the unidentified substance with a 11£ of 0.1 eV at A = 620 nm [Niu88b], [FiA88], should certainly continue. The extraction electric field in the UGED electron gun can probably be doubled by machining a new photocathode mount and reducing the PC-to-EPH distance (4.3.2). Changing either the PC or EPH voltages is another possibility; Kinoshita and co-workers have suggested pulsing the extraction field to reach E values of 30 kV/mm or more [Kin90]. Under such conditions, with 11£ at a value of 0.4 eV, Eq. 4.17 predicts that the broadening contribution l1tpc would be only 70 fs - an order of magnitude less than in the Chapter Eleven: Conclusions and Future Directions 520 present arrangement (Table 4-9). More elaborate modifications to the apparatus have been proposed. Kinoshita et al. recommend magnetic lensing over electrostatics in ultrafast electron gun optics because with a magnetic lens the electron velocity is never reduced after extraction from the photocathode [Kin87]. Magnetic lenses are often troublesome in vacuum, though. Weber and co-workers have proposed a reflectron design for an ultrafast electron gun [Web95]. Most temporal broadening due to the initial electron energy distribution would be corrected with a reflectron, and the authors briefly suggested that space-charge broadening would be corrected too. This statement requires testing by simulation, however, because space-charge might actually be aggravated and uncorrected in the low velocity region of the reflectron. The most exotic suggestion is from V artak and Lawandy who proposed compensating space-charge effects by accelerating electrons with optical rectification in a crystal [V ar95] . They calculated that attosecond electron pulses could be created at a specific point in space, but the authors apparently ignored the initial distribution of electron kinetic energies. 11.2.4 Streaking Experiments The temporal resolution of the streaking experiment must be improved if the durations of electron pulses shorter than 1 ps are to be measured (4.4). The temporal resolution is determined by Rlvs, where R is the spatial resolution of the detector and Vs is the streak velocity. In order to resolve faster electron pulses, R must decrease and / or Vs must increase. According to Eq. 4.34, the streak velocity can be increased either by speeding up Chapter Eleven: Conclusions and Future Directions 521 the voltage sweep rate ks, or by changing the physical dimensions of the streak plates (increasing their length l, increasing the distance L from the streak plates to the detector, or decreasing the gap spacing d between the streak plates). The sweep rate depends on the temporal response of the photoconductive switch assemblies and the potential difference applied across the PCSs. In principle the simplest method of increasing ks would be to increase the magnitudes of the applied voltages, but it was observed that the switches suffered electrical breakdown if the potential difference was too great. The PCS assembly response time might be improved by installing the switches inside the electron gun chamber, immediately adjacent to the streak plates, thus eliminating about 60 cm of wiring which connected the external PCSs to the streak plates in the second-generation instrument. Other PCS materials such as GaAs might have an intrinsically faster response time than Fe:InP [MoT91]. The spatial resolution R of the streak experiment was limited by the electron beam width (200 to 300 µm) and the resolution of the scintillator imaging system (100 µm). Reducing the electron beam width would require redesigning the electron gun optics, and might be very difficult. An alternative solution, however, would be to switch the electrongenerating laser wavelength from 310 nm to 620 nm just for streaking experiments because the electron beam created with 620 nm could be focused as tight as ~50 µm (4.3.5). Streaking measurements recorded with both wavelengths would have to be compared to ensure that the temporal responses were the same. With a smaller electron beam width, R would instead be limited by the spatial resolution of the detector. The resolution might be improved by installing a third detector system within the apparatus: a linear-diode array (LDA) operating in direct electron Chapter Eleven: Conclusions and Future Directions 522 bombardment mode. The pixel dimensions of a 1,024-pixel LDA used by Ewbank et al. were 25 µmx 2.5 mm, with a total length of25.6 mm [Ewb84]. If the array was oriented with the long axis parallel to the streaking axis, then the resolution along the streaking axis would be 25 µm, and yet each pixel would be wide enough to integrate the streaked profile along the transverse axis, performing the same function as the programs PROFILE (D.6) or STREAK (D.7). 11.2.5 The Imaging System Several relatively simple improvements could be made to the scintillator imaging system in the second-generation UGED instrument. First of all, the aluminum center spot applied to the large fiber optic taper was too thin, and the intense signal of the unscattered electron beam caused blooming to overwhelm some pixels in the small-angle scattering region (see, e. g., Figure 8-2). The first time the detector was constructed, the taper was coated with a 500-A thick Al center spot which transmitted only 0.1 % of the unscattered electron signal. When the detector was assembled a second time, a 725-A coating was applied, but for unknown reasons this coating transmitted 1% of the unscattered electron signal, an order of magnitude more. Most of the diffraction data presented in Chapters Eight and Ten were collected using this second version of the detector. A second improvement would be to extend the range of s over which diffraction data can be recorded. This would be particularly important if a higher repetition rate laser were introduced and the signal-to-noise ratio at large s increased (several ground-state sM(s) curves recorded with this instrument still showed reasonable SNR near 14 A- 1 see Chapter Eight). The value of Smax was limited to~ 14.5 A- 1 by the camera length L, the Chapter Eleven: Conclusions and Future Directions 523 electron kinetic energy KE, and the detector diameter; the easiest way to increase Smax would be to decrease L or increase KE. Either way, spatial resolution of the diffraction patterns would suffer because the electron beam width would correspond to a larger distance ins. As already mentioned in 11.2.1, if both the repetition rate and Smax were increased, then efficient collection of diffraction data would be limited by the dynamic range of the detector. A third improvement to the scintillator imaging system would be the application of a thin aluminum coating over the central portion of the large fiber optic taper to attenuate signal in the small-angle scattering region, much like a rotating sector. Flat field image correction would be needed to gain normalize the scattered electron intensity of images taken after such a modification. Alternatively, the image intensifier gain could be decreased in order to increase the imaging system's dynamic range. To keep the single electron detective quantum efficiency high, however, background noise within the imaging system would probably have to be lowered. Spontaneous emission from the image intensifier could be reduced by thermoelectrically cooling the device, and CCD dark current could perhaps be reduced further with more TEC stages. Reduction of the CCD read out noise would be less straightforward. More substantial changes could be made in the third-generation UGED imaging system. As discussed in 5.4.3, high detective quantum efficiency results only when the gain preceding electron multiplication in the image intensifier is also high. The DQE of the scintillator / fiber optic / image intensifier imaging system could therefore be improved by either increasing the electron kinetic energy (giving a higher gain at the scintillator), using higher quality fiber optics, or decreasing the demagnification of the large fiber optic Chapter Eleven: Conclusions and Future Directions 524 taper. Photocathodes with quantum efficiencies in excess of 40% at 550 nm have also been reported [Edg92], and might eventually replace the S20 photocathode in the image intensifier. If such modifications were made to improve the pre-MCP gain, then the lessefficient single-crystal cerium-doped YAG scintillator might be used instead of the P20 phosphor. The YAG:Ce3+ is much more uniform and has a faster emission decay time than P20 (5.4.1.2). Different imaging systems should also be considered for the third-generation UGED instrument. Direct bombardment of microchannel plates (5.5.3) might be a viable solution if the problems of background pressure and angle-dependent gain can be surmounted. The image intensifier / small taper / CCD assembly might be replaced with electron-bombarded CCDs currently under development [How95], [WiG95]. Finally, the emerging CMOS active pixel sensor (APS) technology developed by Fossum and coworkers may eventually replace charge-coupled devices as the two-dimensional imager of choice [Nix95], [Eid95]. In contrast with CCDs, pixels in APS devices can be addressed individually, so regions of high intensity could be sampled frequently while low-intensity regions were allowed to continue integrating. A "rotating sector" aluminum coating would be unnecessary if the third-generation UGED instrument used an APS detector. 11.2.6 Establishing Time Zero Several options exist for improving the accuracy and precision with which time zero is established during UGED experiments. For example, some of the direct electronphoton cross-correlation measurements proposed in 9.2 could be put to the test. Ponderomotive scattering would be the simplest effect to look for, requiring virtually no Chapter Eleven: Conclusions and Future Directions change in the existing setup (9.2.3). 525 Kapitza-Dirac scattering would be a more challenging experiment, requiring two pump laser pulses separated in time by 6.t, and a mirror mounted inside the scattering chamber which reflects the pump laser back on itself (9.2.4) . The mirror would have to be precisely positioned a distance cD..t/2 from the electron beam center. If neither direct cross-correlation method proves to be fruitful, then photoionization-induced lensing investigations could be continued in the hopes of providing a better explanation for why the PIL "spike" occurs. 11.2.7 Data Analysis Techniques The introduction of more sophisticated least-squares analysis methods into a new version of PROC5 has already begun. These modifications will allow UGED molecular scattering data to be fit with multidimensional functions dependent on composition or structural parameters, just like in traditional GED treatments. Perhaps the next most important addition to UGED analysis is flat field correction of the raw images (7.1.4). With a flat field correction image, variations in gain across the two-dimensional phosphor detector system can be normalized, which may account for some of the systematic differences observed between experimental and theoretical diffraction data (8.8, 10.3.1). The signal-to-noise ratio of experimental data at large s should also improve as gain errors caused by bubbles in the optical coupling interfaces, and other defects, are removed. A flat field image could be created by repeatedly rastering a continuous, low intensity, defocused electron beam across the scintillator, and averaging many such images. The CW electron beam might be generated with the existing photoelectron gun using an ultraviolet line from the argon ion laser. Chapter Eleven: Conclusions and Future Directions 526 If attempts at making a flat field electron image are unsuccessful, one alternative is to level the raw images with pure atomic scattering data, such as from argon gas [Ewb86]. Many diffraction images would have to be recorded to ensure the signal-to-noise ratio at large s was high. An argon scattering image would not be a true flat field correction unless the absolute total scattering intensity (elastic plus inelastic) was well known as a function of s. From a practical standpoint, the absolute scattering intensity would also be very difficult to measure; for example, in order to prevent interatomic multiple scattering (8.7.2), the percent scattering during the argon flat field measurements would have to be at least an order of magnitude lower than in the ground-state diffraction experiments described in Chapter Eight. Even if the true absolute intensity is not measured, an argon scattering pattern is still circularly symmetric and decreases smoothly as a function of s. With such a reference pattern, raw diffraction images could at least be gain normalized about the scattering center as a function of the angle <)>. However, they would not be gain normalized as a function of s. Finally, the power of UGED for analyzing structural changes as a function of time would be greatly enhanced if the experimental background curve /s(s) was the same at each time step. If this were true, then differential modified molecular scattering curves, 11sM(s,11t) would not require any further background correction, and data analysis procedures could focus completely on decomposing the experimental difference curves to understand the chemical dynamics. As discussed in 10.3.1, however, IB(s) does change with time, and the physical source of this shift should be investigated in the hopes of eliminating it from future UGED experiments. 527 Appendix A Derivation of Electron Wavelength A. 1 Introduction The wavelength Ae of the incident electrons must be known in order to express the experimental diffraction intensity as a function of s (Eq. 2.31). In A.2 of this appendix it is shown how to relate Ae to the accelerating voltage V of the electron gun using the de Broglie equation: Ae = h p h = m,v (A.1) When V > 10 kV, the electron velocity calculated from classical equations is in error by more than one percent. A derivation of v which accounts for relativistic effects is presented in A.3. Corrected forms for electron velocity and mass are then used in A.4 to derive the relativistic version of Ae. Appendix A: Derivation of Electron Wavelength 528 A.2 Nonrelativistic Electron Wavelength The kinetic energy imparted to a photoelectron is determined by the accelerating potential of the electron gun: KE = eV (A.2) Once the electron leaves the gun and enters a potential-free region, its classical velocity is: (A.3) According to de Broglie (Eq. A.1), the electron wavelength is therefore: or: Ae = hj,J2meeV Ae = (15~413t (A.4) 0 A (A.5) where V has units of kV. A.3 Relativistic Electron Velocity A common assignment in introductory special relativity textbooks is to calculate the energy necessary for a particle to move at some fraction of the speed of light. The opposite problem is solved in this section: we wish to know the velocity of an electron imparted with a well-defined amount of energy. The total energy of the electron is a sum of mass and kinetic energies [Hel80], [Eis85]: (A.6) The relativistic mass mR of the electron is related to the velocity by: (A.7) Appendix A: Derivation of Electron Wavelength 529 Using Eqs. A.6 and A.7, we can solve for VR: (A.8) Note that in the low velocity limit (when the electron's kinetic energy is much smaller than its mass energy) VR simplifies to the classical form (Eq. A.3): C 1- 2KE 1+-2 me c ( -1 (A.9) J A.4 Relativistic Electron Wavelength The equation for Ae derived in A.2 (Eq. A.4) is in error by more than 0.5% if KE> 10 keV. The relativistic corrections for mass and velocity must be included in de Broglie's equation to correct this error: Ae = h (A.10) Inserting the relativistic mass (Eq. A.7) leads to: (A.11) and using the relativistic velocity (Eq. A.8) yields: le = hc(2mec KE + KE 2 r½ (A.12) or: le = 12.3985/ ✓v (1022.006 + v) A (A.13) or: le = 2 t (1 5~ 413 (1 + 9.78468x 10- vr½ 7 0 A (A.14) Appendix A: Derivation of Electron Wavelength where V is in kV. The relativistic electron 530 Accelerating Potential de Broglie Wavelength (kV) (A) 1.0 10.0 15.0 18.8 20.0 40.0 100.0 0.388 0.122 0.099 0.089 0.086 0.060 0.037 wavelength is plotted as a function of acceleration voltage in Figure A-1 and selected values are presented in Table A-1. Figure A-1 also shows the percentage difference between the classical electron wavelength and the relativistic electron wavelength. Determining Ae by experimental measure- Table A-1: Relativistic de Broglie wavelengths of electrons for selected accelerating potentials. ment of V with a high-voltage probe may not be very accurate. Often Ae is determined by calculating the camera constant LAe for several values of L using the diffraction patterns from thin metal films or highly-symmetric gas molecules. For more details, see the discussion of our experimental approaches in 7.3. 0.4 30 - - Wavelength -- - .~0.3 25 Difference Cl) 20 .c: Cl) 0 C: :i.. Cl) :E C C) 5i 0.2 15 Cl) C) ca Cl) > ca 10 3: 0.1 C: Cl) 0 :i.. 5 Cl) c.. 0 0 1 100 10 Accelerating Potential (kV) 1000 Figure A-1: Electron de Broglie wavelength, including relativistic corrections as a function of electron gun accelerating potential. Also shown is the percentage difference between the relativistic wavelength and the classical wavelength. 531 Appendix B Derivation of Rotational Coherence Diffraction Integrals B.1 Introduction And Preliminary Mathematics As discussed in Chapter Two, calculating the diffraction pattern from a subset of linear, laser-excited molecules requires integration of the following general equation: -j J 1 P(Q., 1/f )exp(ia cosl/f + ibsin 1/f )sinO.dl/fdQ. 4n o o (B.1) where P(Q.,\jl) is typically a product of sines and cosines. Unfortunately, solutions for this class of definite integrals are not found in mathematical tables [Gra80], [Bey82], [Pru86] . This appendix presents the derivation of three integrals referred to in 2.4 for the case of unsaturated, single-photon laser excitation. The details provided here will hopefully serve as a starting point in the event that Eq. B.1 must be solved for other P(Q.,\jf), such as the spatial distribution of molecules excited by ultrafast two-photon absorption. A brief Appendix B: Derivation of Rotational Coherence Diffraction Integrals 532 review of some mathematical formulas used in the derivations appears below. See general mathematical references such as [Abr72], [Swo83], and [Boy92] for more in depth discussion: B.1.1 Series Expansions The exponential function e' is expanded as a power series: (B.2) The binomial product (y + zl can be expressed as the following summation over k: (y+zf = I I n n-k n.y k=O k z (B.3) k!(n-k)! B.1.2 The Double Factorial Notation Appending the double factorial symbol "! !" to an integer n indicates progressive multiplication from 1 to n. "! !" differs from the single factorial symbol "!" in that "! !" is a multiplication of just the even numbers or just the odd numbers, depending on whether n is even or odd. Examples are shown below: Even: (2m)!! Odd: = 2·4·6· ... ·2m = 2mm! (2m-1)!! = 1·3·5· ... ·(2m-1) (B.4) (B.5) B.1.3 The Gamma Function Euler's gamma function r(z) is the following integral: ~ r(z) = Jtz-1e-'dt; z > o 0 (B.6) Appendix B: Derivation of Rotational Coherence Diffraction Integrals 533 In the derivations in this appendix, we will only be interested in r(z) when z is integer or half-integer. I'(z) then has the following properties: = n! (B.7) = ✓n (B.8) r(n + 1) r(½) r(m+ ½) = 1·3·5· ... ·(2m-1) ✓n = (2m-1)!! ✓n 2"' 2"' (B.9) B.1.4 Bessel Functions Of Integer Order The Bessel functions of the first kind, Ja(z), are one set of solutions to the differential equation: z2J"(z) + ef'(z) + (z2 - a 2 )J(z) = 0 (B.10) Ja(z) can be written as a power series: (B.11) When a is an integer n, then Eq. B.7 can be used to rewrite J,,(z) as: (B.12) The recurrence relation between successive Bessel functions of integer order is: (B.13) B.1.5 Bessel Functions Of Fractional Order When a is a half-integer the solutions to Eq. B.10 are denoted j,,(z), and are related to solutions of integer order by: Appendix B: Derivation of Rotational Coherence Diffraction Integrals 534 (B.14) Successive jn(z) are linked by the recurrence relation: • (Z ) = -2n-+Jln• (Z) - ln-1 z • ( ) ln+I Z (B.15) or can be derived according to: J• (z) 1 d )n sinz -_ zn( --- z dz n z (B.16) The first three fractional order Bessel functions of the first kind are: jo(z) = sinz (B.17) z smz cosz z2 z jl (z) = ----- j2(z) = 3 3 1) • ( -z3 - -z smz - -cosz z2 (B .18) (B.19) As derived in 2.4.2, j 0(z) is the scattering function for an isotropic gas sample. B.2 2~ s:lr exp(iacosljl + ibsinlfl)dlfl This type of integral must be solved when P(Q,\j/) has no dependence on \JI, such as for an isotropic sample distribution (2.4.2). The first step in evaluating the integral is to expand the exponential as a series (Eq. B.2): l ~ ,n -f I.:_(acosljl + bsinljlrdlf/ 2rc o n! 2ir (B.20) n=o The summation can be separated into two parts, a sum over even values of n and a sum over odd values of n: Appendix B: Derivation of Rotational Coherence Diffraction Integrals - I - + I- I = n=O n=0,2,.. . 535 (B.21) n=l,3,... Each sum can be reindexed to have unit step sizes: for the even terms set n = 2m, and for the odd terms set n = 2k + 1: (B.22) k=O m=O n=O Reindexing Eq. B.20 in this way and moving the integrals inside of the summation yields: l - -2m 2,r - I - ( l ) J(acOSlfl + bsinvr)2mdlfl 2'lr m=O 2m ! 0 + (B.23) I - 1i2k+I J (a cos lfl + b sin lf/ )2k+I dlfl 2-n k=O (2k + 1)! 0 According to Eq. 3.661-1 of [Gra80], all odd powers of a cos lfl + b sin lfl evaluate to zero, so the sum over k vanishes. Using Eq. 3.661-2 of [Gra80], the integral in the sum over m yields: ~. .i2m (2m - 1) !! (a 2 + b 2 ) 111 -1L - - ( ..:...----'--2'lr 2-n m=o (2m)! (2m)!! J (B.24) To simplify this and future equations, y is defined as: (B .25) Using Eqs. B.4 and B.5, some of the factorial terms can be condensed: (2m-1)!! = (2m)! 1· 3 •5 •... •(2m - 1) 1•2 •3 •4 •5 •... •(2m - 1) •2m = 1 (2m)!! (B .26) so that Eq. B.24 becomes: L oo m=O ( ( •2m l 2m) !!) 2 Y2m (B.27) Appendix B: Derivation of Rotational Coherence Diffraction Integrals 536 Using the relationship i2 = -1 and Eq. B.4, this sum may be rewritten as: (B.28) Comparing this to Eq. B.12, we see that this is the power series formulation for the zeroth order Bessel function of the first kind. The final solution for the integral of this section is therefore: (B.29) B.3 2~ 2 J:n: cos lfl exp(ia cos lfl + ib sin lf/ )dlfl This type of integral was seen in 2.4.5 for the spatial distribution of molecules selected by single-photon laser excitation. Evaluation of the integral begins with expansion of the exponential (Eq. B.2): (B.30) followed by expansion of the binomial (Eq. B.3): (B.31) The integral is then moved inside both summations: (B.32) Any terms containing sin lfl which result from the integration will go to zero because of Appendix B: Derivation of Rotational Coherence Diffraction Integrals 537 the integration limits. According to 2.512-4 of [Gra80], all integrals with odd k will therefore be zero, and from 2.512-1 the even terms lead to the following integrals over just cos lfl terms: 1 - - £"" . l•n 2,r n=O (k 1) fl - • • - - - f (COSlf/ )n-k+2 d lfl -a- - - - - - - k=o, 2 ,... k!(n-k)! (n+2) ·n· ... ·(n-k+4) 0 n "" £. n-kbk [ 2:rr ] (B.33) By the same reasoning and 2.512-3 of [Gra80], all integrals with odd n are also zero. Using 2.512-2, the even terms integrate to: 1 - •n 2,r n=~.... l n k=~.... (k-1)!! an-kbk 2n(n-k+l)!! 1 k!(n-k)! (n+2) ·n ·... ·(n-k+4) 2 +(n-k)/2 (1+½(n-k))! (B.34) The indices for the summations are reset according to n = 2m and k = 2j such that the indices have unit step sizes: - • ~l 2 111 m a 2(m - j)b 2 j (2m- 2j + 1)! ! (2j- 1)! ! ~(2j)!(2m-2j)! (2m+2)·2m· ... · (2m-2j+4) 2m-i+ 1 (m-j+l)! (B.35) After pulling factors of two from the product in the central denominator and then reorganizing, the summation becomes: X 2m-2j + 1 2m-j+I (m - j + 1)!2i (m + 1) · m ·... · (m - j + 2) (B.36) The identity from Eq. B.26 is then applied to simplify: (B.37) The product in the right-hand side denominator extends the factorial term (m - j + 1) ! out to (m + 1)!: Appendix 8: Derivation of Rotational Coherence Diffraction Integrals ~ - a 2 (m-j)b 2 j m ~ 2m-2j+l (B.38) 2 £_l £..i22m+1 m=O 1=0 ·1(m - }·)1. ] • 538 (m+l)'. This can be further split into a pair of double sums, the first keeping the 2m - 2j part and the second keeping the + 1 part. Terms containing just m are moved out of the j summations in each of the double sums: (B.39) A number of terms in the left-hand side double sum are zero because of them - j factor in the numerator: the summation over j can be shortened to m - 1, and the zeroth term of the summation over m can be eliminated: _ ~2 (-l)"' 2 "' ( m + 1) ! m-1a2(m-j)b2j(m-j) ~ j !(m - j) ! + - ~2 (-l)"' 2 1 "'+ ( m + 1) ! m a2(m- j)b2j ~ j !(m - j) ! (B.40) Then matching factorial terms are inserted into the numerator and denominator of both double sums: (B.41) Comparison with Eq. B.3 reveals that both summations over j are now equivalent to the binomial expansion: (B.42) These are simplified using the y substitution (Eq. B.25). In addition, the left-hand side summation is reindexed to zero by setting m' = m - 1: Appendix B: Derivation of Rotational Coherence Diffraction Integrals 539 (B.43) Factors of y /2 are introduced before each sum: 2 2 2 2 - - - "______;__...,;____ + - - " - - a (Y) = (-1r'r "'' 2 2 2 £..i2 "'' y m'=O m '!( . m '+2)1. 1 (r) = (-1rr "' 2 2 £..i2 "' y m=O m.1(m + 1) 1. (B.44) Each of the summations is now equivalent to an integer-order Bessel function of the first kind (Eq. B.12): (B.45) and therefore the result of the integration is: (B.46) B.4 ½f: (sinnr+l Jn(bsinO)exp(ia cosO)dn The first step in evaluating this integral is to expand the integer-order Bessel function as a power series (Eq. B.12): (B.47) The integral is then moved inside the summation: (B.48) A solution for this definite integral can be found in [Gra80] by conducting a change of Appendix B: Derivation of Rotational Coherence Diffraction Integrals variables. After setting cosQ = z ( sinQ = 540 Fz2; dQ = -dz/.J1 - z 2 ), the integral becomes: (B.49) which evaluates to: (B.50) using 3.387-2 of [Gra80]. After simplifying with Eq. B.7, the fractional order Bessel function is expanded as a power series (Eq. B.11): (B.51) The gamma function is rewritten in terms of a double factorial (Eq. B.9): (B.52) and the double sum condenses to: (B.53) In order to continue the evaluation, the indices of both summations must be changed; we will set l =m + k and j =k. This change replaces two infinite sums by one infinite sum and one finite sum, but all terms are retained as shown in Figure B-1. The double sum now looks like: (B.54) Appendix B: Derivation of Rotational Coherence Diffraction Integrals 541 Next, factors containing just l are moved out of the j summation and an additional l! term is inserted in the numerator and denominator: (B.55) The summation over j is recognizable as the binomial expansion (Eq. B.3). Additional factors of ..fir/i+n+i are inserted in the numerator and denominator: = (-1)1 ..fir I ii+n+I bn " " ' - - = - - - - ( a 2 + b2) i l! i+n+I ..fir (2l + 2n + 1)! ! (B.56) 6 so that the double factorial term may be replaced by Euler's gamma function (Eq. B.9). Substitution of b" y for a + b is also made, and factors of y /2 are introduced: 2 2 l ( r )n+½ = yn+½ 2 21 (-l)I r21 (B.57) ~2 l!r(n+½+l+l) The summation is equivalent to a Bessel function of the first kind (Eq. B.11): (B.58) and has fractional order (Eq. B.14), so the result of the integration is: k m J 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 A B D G K p V 1 C E H L QW 2 F I M R X 3 J N s y 4 0 T z 5 u 6 0 A 1 B C l=m+k .i = k ⇒ 2 D E F l 3 G H I J 4 K L M N 0 5 6 p Q R s T u vw X y z ... ... Figure B-1: Reindexing technique for the double summation in Eq . B.53. Appendix B: Derivation of Rotational Coherence Diffraction Integrals 542 (B.59) Note that by using the identity sin 2 Q + cos 2 Q = 1 , this result can also be applied to some P(Q,\j/) which have even powers of cosQ . Using a mathematical methodology nearly identical to the one presented here for deriving Eq. B.59, it can be shown that: (B.60) 543 Appendix C Interpolating the Scattering Factors Elastic scattering factors were generated for the UGED software package from tabulated data [lbe74] . This data reported the amplitude f and phase Tl as a function of atomic number Z in integral steps of momentum transfer s (from O to 60 A- 1) for four incident electron energies KE (10, 40, 70, and 100 keV). The program PROC5 (D.4), however, required/ and 11 at a particular KE between 10 and 40 keV, and in 0.01 A- 1 steps of s. To meet the software's needs, Mathematica programs were written to conduct a two-stage interpolation. First, a scattering factor table was formed at the desired kinetic energy by fitting cubic polynomials as a function of KE for each of the sixty-one values of s (C.l). Second, the scattering factors were calculated from this new table in 0.01 A- 1 steps of s (out to some Smax) with a sliding, ten-point polynomial fitting scheme (C.2). The resulting files for several elements were combined together with EXCEL to make Appendix C: Interpolating the Scattering Factors 544 PROC5's scattering factor data files (D.4.2.3). Inelastic scattering factors were used in earlier versions of the analysis software, such as PROC4 (D.8). The first stage of interpolation was unnecessary because the scattering factors were reported independent of KE [Ibe74], [Smi94]. In the second stage, the interpolation method had to be altered slightly over the region of O to 1 A- 1 because the S;(s) are divided by s4 in the equation for the electron inelastic scattering amplitude (Eq. 2.43). Coefficients to the s°, s 1, s2, and s3 terms were set to zero in the fitting polynomial to prevent the theoretical /(s) from blowing up at smalls. C. 1 Interpolation Along Energy The Mathematica routine for conducting an energy interpolation of scattering amplitudes f was INTERP_F.MA. As shown in Table C-1, Line 1 read the raw, tabseparated scattering factor data file into table f. The raw file had eight columns of data: the first four columns were f(s) as a function of KE and the last four columns were 11(s) as a function of KE. Line 2 identified the first four columns, the f(s), as the data of interest for this particular routine. (Energy interpolations for the 11(s) factors were carried out in 1 f = ReadList["E:\CHUCK\SCATFACT\IODINE.RAW", {NUmber, NUmber, NUmber, NUmber, NUmber, NUmber, NUmber, NUmber}]; 2 3 flist = Table[i, {i, 4}]; 4 fv = finter[19.4 / 15]; 5 Save["E:\CHUCK\SCATFACT\IODINE.Fl9", fv] finter[x_] = Table[ Fit[ f[[i, {i, 61} ]; flist]], {1, x, x"2, x"3}, x ], Table C-1: Command list in the Mathematica file INTERP_F.MA. This program calculated scattering factors at a particular energy KE from tabulated data. Appendix C: Interpolating the Scattering Factors 545 INTERP_N.MA.) A table of polynomial coefficients, f inter[x_], was created in Line 3 by fitting the energy-dependent scattering factor data at each s to a cubic polynomial, and these functions were evaluated for a particular energy in Line 4 and stored in fv. The relationship between x and KE was: x = (KE + 20)/30 (C.l) so the value 19. 4/15 shown in Line 4 corresponded to 18.8 keV electrons. The energyinterpolated scattering factors in fv were saved to disk with Line 5. C.2 Interpolation Along Momentum Transfer After the energy interpolation was complete, the Mathematica routines FILLIN3F.MA (shown in Table C-2) and FILLIN3N.MA were executed to create amplitude and phase scattering factor data files with 0.01 A- 1 step sizes. First, Line 1 loaded the output file created with INTERP_F.MA, and Line 2 defined a zeroed table outtable for the output array, in this case extending from Oto 18.00 A- 1. A ten-point polynomial fit was recommended in [Ibe74] for the purposes of interpolation. The scattering factor functions exhibit the most curvature in the region of s < 10 A- 1, so four polynomials were fit over adjoining segments of the data. Lines 3 to 6 generated f(s) in 0.01 A- 1 steps from O to 4.00 A- 1. Line 4 created a temporary table m containing only the segment of ten data points over which the fit was to occur, in this case from fv[[O]] (s = 0 A- 1) to fv[[9]] (s = 9 A- 1). A ten-coefficient polynomial function f icurve [x_] was fit to m in Line 5, and then used to fill the first segment of Appendix C: Interpolating the Scattering Factors 1 2 3 4 5 6 546 <<"E:\CHUCK\SCATFACT\IODINE.F19" outtable = Table[0, {x, 1801}]; i = 1; m = Table[{(x-i)/10, fv[ [x]]}, {x, i, i+9}]; ficurve[x_] = Fit[m, {1,x,xA2,xA3,xA4,xAS,xA6,xA7,xA8,xA9}, x]; Do[outtable[[j+l]] = ficurve[j/1000], {j, o, 400}]; 7 i = 4; 8 9 m = Table[{(x-i)/10, fv [ [x]]}, {x, i, i+9}]; 10 Do[outtable[[j+l]] = ficurve[j/1000 11 12 13 14 i = 7; ficurve[x_] = Fit[m, {1,x,xA2,xA3,xA4,xAS,xA6,xA7,xA8,xA9}, x]; - 0.3], {j ~ 401, 900}]; m = Table[{(x-i)/10, fv [ [x]]}, {x, i, i+9}]; ficurve[x_] = Fit[m, {1,x,xA2,xA3,xA4,xAS,xA6,xA7,xA8,xA9}, x]; Do[outtable[[j+l]] = ficurve[j/1000 - 0.6], {j, 901, 1300}]; i = 12; 15 16 17 m = Table [ { (x-i) /10, fv[ [x]]}, {x, i, i+9}]; 18 Do[outtable[[j+l]] = ficurve[j/1000 19 Do [out table [ [i]] >»"E: \CHUCK\SCATFACT\FUL2_IOD.F19", ficurve[x_] = Fit[m, {1,x,xA2,xA3,xA4,xAS,xA6,xA7,xA8,xA9}, x]; - 1.1], {j, 1301, 1800}]; {i, 1801}] Table C-2: Command list in the Mathematica file FILLIN3F.MA. This program calculates 1 scattering factors in 0.01 A steps using the results of INTERP_F.MA. out table in Line 6. Lines 7 to 10, 11 to 14, and 15 to 18 repeated the same process over segments from 4.01 to 9.00 A- 1, 9.01 to 13.00 A- 1, and 13.01 to 18.00 A- 1, respectively. Small slope discontinuities were present at the transitions between segments. Finally, the filled outtable was written to disk with Line 19. 547 Appendix D Software Developed for Ultrafast Gas-Phase Electron Diffraction D. 1 Introduction This thesis has discussed how electrons, photons, and matter can be coerced into a particular interaction (which we call ultrafast gas-phase electron diffraction) using indelicate laboratory materials - metal, glass, and electricity. More sophisticated aspects of the experiment are embodied in the laboratory computer. The computer serves as golem and translator, automating many mundane experimental tasks while providing the all-important interface between instrument and human operator. The Aerotech translation stage, the H20 monochromator, the SR-245 A~D converter, and the CCD camera are all computer-controlled. The computer must process and manipulate CCD images, often in ways that extend beyond the capabilities of the SpectraSource software. Furthermore, subsequent analysis of the experimental data is mathematically complex and involves a Appendix D: Software Developed for Ultrafast GED 548 Functions Program RADAR2 Calculates radial sums and pulse-height distributions from CCD images. Calculates mean and RMS values of regions on CCD image. Converts CCD image to Windows Paintbrush bitmap format. PROC5 Calculates theoretical GED patterns for isotropic samples. Calculates background curve for experimental GED data. Generates experimental and theoretical radial distribution curves. ADDER Sums and averages CCD images. Divides one CCD image by another. Corrects electron diffraction CCD image with radial background curve to make two-dimensional sM(pix) function. PROFILE . Calculate average x-axis and y-axis profiles of CCD image. STREAK Calculates profiles of CCD image at an arbitrary angle. Converts region of CCD image to an output array of text integers. PROC4 Earlier version of PROCS that includes inelastic scattering factors. R-K Generates semi-classical trajectories for B-state iodine ('2) using a RungeKutta integration technique. PROC3 Calculates sM(s) and radial distribution curves from trajectory arrays created with R-K. Calculates theoretical two-dimensional GED patterns for anisotropic samples. CONV Converts binary data file (floating point or unsigned integer) to text data file . CIRC Reads data from SR245 A➔ D converter while scanning computer-controlled translation stage or monochromator. AUTOHOME Returns computer-controlled translation stage to offset position (Windows). AUTOSCAN Moves computer-controlled translation stage a fixed distance (Windows). Table D-1: Summary of the UGED software package. large quantity of recorded information (one UGED session generates several hundred megabytes of data). A multi-faceted software package has been written expressly for UGED and its associated experiments. This appendix introduces the software package and contains detailed manuals for twelve of the programs. The programs fall into three categories: CCD image processing (RADAR2, ADDER, PROFILE, STREAK), gas-phase electron Appendix D: Software Developed for Ultrafast GED 549 diffraction analysis (PROC5, PROC4, R-K, PROC3, CONV), and laboratory instrument control (CIRC, AUTOHOME, AUTOSCAN). A brief summary of the basic program functions is presented in Table D-1. RADAR2 (discussed in D.3) extracts average radial intensities from diffraction patterns and calculates pulse-height distributions, mean count values, and RMS noise within regions of CCD images. ADDER (D.5) conducts pixel-by-pixel addition and division of images, and also converts diffraction patterns from raw scattering intensities into two-dimensional sM(pix) surfaces. Both PROFILE (D.6) and STREAK (D.7) determine average intensity profiles across CCD images, but STREAK is specially designed for analyzing streaked electron beam images. CIRC (D.12) interfaces with the translation stage, monochromator, and A~D converter. AUTOHOME and AUTOSCAN (both discussed in D.13) are Windows programs that either move the translation stage a fixed distance or else to a fixed position. Of all the programs in the UGED software package, the diffraction data analysis routines have been revised and overhauled the most. This reflects growth in understanding of GED over time, and also a gradual recognition of the special treatment that ultrafast GED data requires. The latest version of UGED analysis software, PROC5, is described in D.4. PROC5 calculates theoretical sM(s) curves, corrects raw data for the experimental background, and generates radial distribution functions. A few comments on the previous version, PROC4, are presented in D.8 because PROC4 includes inelastic scattering factors during calculation of the theoretical scattering intensity. Both PROC5 and PROC4 assume that the molecular sample is isotropic; PROC3 (D.10) will calculate theoretical diffraction patterns from anisotropic samples, and also will convert isotropic Appendix D: Software Developed for Ultrafast GED 550 molecular trajectory data (created with the program R-K - see D.9) into sM(s) andf(r) curves as a function of time. The earliest versions of the electron diffraction analysis software, PROCESS and PROC2, are not discussed in this appendix. Most UGED programs are menu-driven, and all share a common C-code structure. Please note, though, that the software has been developed over a five-year period and should still be considered as works-in-progress. Despite thorough testing, there are undoubtedly a few lingering bugs (presumably of no major consequence), as well as idiosyncratic features and inconsistencies. For example, some input data files must be tabseparated while the rest have CSV format; refer to the program manuals for details. In addition, the formats of several types of input files, particularly batch files, have evolved since their inception. An old batch file recovered from the archives probably will no longer work. Only the current generation of formats are presented here, but rewriting an old batch file should not be too difficult because the earlier versions were usually simpler. D.1.1 The Programming Environment The UGED software package is written entirely in C (e.g., [Ker88]) except for a few assembly language routines involved in extended memory access (see D.2). Programs have been linked and compiled using Borland C++ with Options set as follows: Compiler ➔ Code Generation: A "Huge" memory model is selected, except for AUTOHOME and AUTOSCAN which use "Small" memory models. The Instruction Set is 80286 and Floating Point is 80287, with "Fast Floating Point" deselected. Debug information is included in the object files. Compiler ➔ Entry / Exit Code Generation: All programs are DOS Appendix D: Software Developed for Ultrafast GED 551 Standard except for AUTOHOME and AUTOSCAN, which are Windows, All Functions Exportable. Compiler ➔ C++ Options: Compile as C++ only for .CPP extensions. Compiler ➔ Optimizations: Optimize for speed. Linker: For most programs, link as Standard DOS EXE and include the graphics library. For AUTOHOME and AUTOSCAN, link as Windows EXE and do not include the graphics library. Directories: Add the path for the user-written include files (probably the path is E:\INCLUDE). All programs except AUTOHOME and AUTOSCAN require Borland' s graphics driver EGAVGA.BG! to run. The expected path for this file is C:\TOOLS\BORLANDC\BGI, but the software will also check the current directory. This file is easily overlooked when executables and data are transferred to another computer system! D.1.2 General Characteristics Of The Software The UGED software package is menu-driven and based in DOS, with no mouse control. The code has a tree-like structure which follows the bifurcations of the menus. Much of the code is duplicated from program to program; in particular, the menu, keyboard, graphics, and directory interfaces are identical except for minor variations. Each program consists of at least three types of C-code files (* .C) and at least two types of user-written include files (* .H). The complete list of required files is included in the program manual sections, but the general functions are described below: Appendix D: Software Developed for Ultrafast GED 552 D.1.2.1 The Main .C File The main C-code file usually has the same name as the executable file (except for the extension) and is organized as follows: 1. List of requested include files, both user-written and standard C language. 2. Static character list of menus, including the menu title and all menu items. 3. List of text items displayed in the message bar at the bottom of the screen. 4. Far and local subroutine definitions. 5. Global variable definitions. The default values for paths and extensions of different file types (CCD images, batch files, data files, etc.) are defined here in three character arrays called adrive[i], apath[,], and aext[i]. 6. The C-code subroutines; main() is located at the end of the file. The C-code contains all the menu tree routines and the primary analysis routines, including the software for reading and executing batch files. D.1.2.2 The xxxxxxIO.C File Most of the graphical and keyboard interaction code is found in the xxxxxxIO.C file. These routines initialize the screen, display the menus passed from the main .C file, and allow the user to select items with menu the arrow keys. The Subroutine Purpose ...get_long() ......... Enter.an. i.nteger ...................................."-" '.."0 ._.. 9" .............................. . ... get_realO .... .Enter a .real .number............................"-", .".",.. "0._..9" .......................... . ..... get_strO ...... ... Enter.a. text.string ... "0._._.9",. "A .. _.Z", ."a._._.z",. "*",.. "\",.."-",.."-" get_YN() Enter a Yes: "Y", "y", "1" Yes/No answer xxxxxxl O. C file also contains four Active Keys Table D-2: No: "N", "n", "0" Keyboard 1/0 subroutines found in the *1O.C file. routine accepts input for a certain variable type. Each Appendix D: Software Developed for Ultrafast GED 553 subroutines which permit the user to enter data of different variable types: integer, floating point, character, or Yes/No. These subroutines (listed in Table D-2) draw a highlighted entry bar at a chosen screen coordinate, and display characters one at a time as they are typed on the keyboard. Each routine will accept only those characters which conform to the expected data format. D.1.2.3 The xxxxxxDT.C File Utility routines involving data are found in the xx.xxxxDT.C file. This file contains the C-code which reads directories from the disk drive and allows the user to select one or more files. Routines are available for reading and writing data files , including CCD images. The file also allows up to eight data curves to be plotted on the screen at once, under a variety of scaling and graphing conditions. D.1.2.4 The *.H Files Each program in the UGED software package refers to two types of include files. The SETTINGx.H file defines screen colors, graphical parameters like plotting colors and background bitmaps, and constants, such as array dimensions or descriptive selection flags. The DAT A_.xx.x.H file externalizes global variables so that the xxxxxxIO.C, xxxxxxDT.C, and other files have access. The global variables are initially defined in the main .C file. D.1.2.5 Batch Files All CCD image processing programs (RADAR2, ADDER, PROFILE, and STREAK) can be automated with pre-generated batch files. These batch files guide the Appendix D: Software Developed for Ultrafast GED 554 computer in performing the same operations over and over on any number of CCD images specified by a list of filenames. The generic batch file is a tab-delimited text file created in some type of editor, such as a spreadsheet program like EXCEL. The file consists entirely of text strings and integers, usually unsigned.* The first line of the batch file is always a capitalized identification header, e.g., PROFILE-BATCH-VERT. The header serves as low level error protection - the user cannot try to execute the wrong type of batch file. Beyond this the batch file routines are dumb, with virtually no error checking mechanisms. If the user supplies the wrong format, the batch file routine will most likely crash, hanging up the computer. In the worst case it is possible (but unlikely) that an input filename will be misinterpreted as an output filename, and the input file will be overwritten. The bottom line is that double-checking a new batch file never hurts! Detailed batch file formats and examples are presented in each of the program manual sections. D.2 Reading And Writing CCD Images The computer interacts with the CCDs via the SpectraSource camera head and software. Simple mathematical operations can be performed on CCD images using the SpectraSource software (HPC-1 ), and these operations can be automated by writing and running EXCEL macros (see Appendix E). However, the diffraction patterns and other images recorded during UGED experiments must be analyzed with procedures which are beyond the scope of HPC-1; programs like RADAR2, PROFILE, and ADDER have been • There is one exception - the CCD image addition batch file expects a floating point number for the rescaling divisor. See D.5.2 and Table D-23. Appendix D: Software Developed for Ultrafast GED 555 created to fill the gaps. These programs have two special requirements: knowledge of the CCD image file structure, and access to extended memory: D.2.1 The SpectraSource CCD Image File Structure SpectraSource's HPC-1 (Version 1.8) saves each CCD image file with a 2880 byte header, corresponding to 36 lines of text, 80 characters per line. (Later versions of HPC-1 have longer headers). The first eleven lines contain exposure and processing parameters associated with the image, such as the dynamic range and exposure time (Table D-3). The UGED software is only interested in the image dimensions; the x-axis range, for example, is obtained by executing a C-language atoi() command starting at byte 250 of the header (80 characters x 3 lines+ 10 more characters). The header also contains up to 22 lines of notes which the user can enter in HPC-1. Pixel count values follow the header as a stream of two byte (sixteen bit) integers. The stream starts with pixel (0,0) and continues sequentially, first by column and then by row. Pixel count values are stored high byte SIMPLE = T BITPIX = 16 NAXIS = 2 NAXISl 190 NAXIS2 170 OFFSETl = 0 OFFSET2 = 0 PROCESS= 0000 DATETIME= TUe Oct 15 10:21:39 1996 EXPTIME = 1.000 INSTRUME= SpectraSource Instruments HPC-1 END ISTARTNOTESI = = i Up to 22 lines of notes / low byte, which is opposite to J, !ENDNOTES! the convention integer. C-language standard for a two-byte For example, a pixel Table D-3: Sample header from a SpectraSource CCD image file. Each line is 80 characters long, padded with blank spaces as necessary. NAXISl and NAXIS2 are the x- and y-axis ranges, respectively. EXPTIME is the exposure time of the image in seconds. Appendix D: Software Developed for Ultrafast GED 556 with a count value of 1,731 ADU is stored as O6 C3 (hexadecimal notation) in the image file, but gives a value of 49,926 when read in as a two-byte unsigned integer by a C program. To correct this, the high and low bytes are swapped with a _rotl() command during CCD image 1/0. The minimum size of a SpectraSource CCD image file is expected to be: Image Size (bytes) = 2880 + 2x,y, (D.1) but HPC-1 pads the file, saving the data in 32-row chunks (rounding up). As an example, the size of the image corresponding to the header in Table D-3 is actually 75,840 bytes instead of the 67,480 bytes predicted by Eq. D.1. The UGED software always saves images at the minimum size, so a processed image will often take up less disk space than the original raw image. D.2.2 Accessing Extended Memory HPC-1 can expose images with dimensions as large as 1024x1024, which corresponds to 2 Mb of memory (ignoring the header). This quantity of information greatly exceeds the standard 640 kb of RAM usually available for programs and data on the PC, so some other memory system must be exploited. The UGED software stores CCD images in extended memory using subroutines developed by Williams [WiA91]. These routines call on DOS interrupt 15H to allocate extended memory and transfer data between conventional and extended memory. For INT 15H to work, a block of extended memory must be made available by including the following line in the CONFIG.SYS file: DEVICE= C:\DOS\HIMEM.SYS /intlS=x.xxx (D.2) where xx.xx is the memory size in kilobytes. The recommended value of xxxx for the Appendix D: Software Developed for Ultrafast GED Subroutine 557 Purpose ...................... ext_sizeO ....................... ....Returns .the..amount..of. available .extended. memory..in .kb .............. ext_alloc(amnQ Allocates extended memory of size amnt (in kb) for current .................................................................................... program •.................................................................................................................... Copies memory chunk of length amnt (in words) from srce to extmemcpy(dest, srce, amnQ dest. Both srce and dest are 24-bit addresses (long .......................................................................... ......... , poi.nters..LPTR) •.................................................................................................... ext free() Deallocates extended memory. Table D-4: Extended memory subroutines used by the UGED software to store CCD images, scattering factors, and theoretical molecular trajectories. Subroutines are from [WiA91]. present set of UGED programs is 6144 (6 Mb). Software which accesses extended memory must compile and link three of Williams' files: two include files (CEXT.H and COMPAT.H), and one C-code file (CEXT.C). Compiling CEXT.C gives warning messages that nine parameters are not used, but these warning messages can be ignored. Four of the extended memory subroutines are used by the UGED software; their definitions and functions are shown in Table D-4. In addition to CCD images, extended memory is also a buffer for electron scattering factors (PROC5 and PROC4) and molecular trajectory data (R-K). D.3 RADAR2 The primary purpose of this program is to generate raw, one-dimensional scattering intensity curves, l(pix), from experimental diffraction images. RADAR2 will calculate the average radial intensity of an image, with various degrees of sophistication, relative to a user-provided center point. The center point (usually the location of the unscattered electron beam) can be determined by running a batch file utility in RADAR2 which evaluates the x- and y-axis profiles of the electron beam. RADAR2 will calculate Appendix D: Software Developed for Ultrafast GED (RADAR2) 558 the mean and RMS count values over regions on RADAR2.EXE Program Files Include Files the CCD image, which is the standard method for RADAR2.C RADAR2DT.C RADAR210.C CEXT.C determining image background offset values and corrections for thermal drift. The mean and RMS DATA_RD2.H SETTNGR2.H CEXT.H COMPAT.H Table D-5: Program and include files needed to build RADAR2.EXE. measurement process can be automated with a batch file. Finally, there are two additional features which are not directly related to radial intensity profiles. First, RADAR2 will calculate an image's pulse-height distribution. Second, RADAR2 will convert any SpectraSource CCD image into a format compatible with Windows' Paintbrush program (.BMP files). Two color maps are available, and the image can be rescaled before conversion. RADAR2 requests 4 Mb of extended memory from the computer system, enough to store one full 1024x1024 image and a flat-field correction image. Table D-5 lists the files necessary to build RADAR2; a discussion of the seven main menu options follows: D.3.1 RADAR2 Option One: Load CCD Image If the user is analyzing a single CCD image (as opposed to running a batch file), then the image must be selected with this menu option. The user can also change the default path and extension which RADAR2 references when locating any CCD image. Altering the default parameters at this point in the program determines which directory RADAR2 expects to find images listed in the batch files of options three, four and seven. D.3.2 RADAR2 Option Two: Calculate Radial Intensity This menu option is available once a CCD image has been loaded into extended memory. The user must manually enter the parameters RADAR2 requires to calculate a Appendix D: Software Developed for Ultrafast GED {RADAR2) 559 radial intensity profile. These parameters include: 1. The x- and y-axis coordinates for the center of the radial intensity profile. 2. The background offset value (in ADU) at the top of the image and the correction for thermal drift. 3. Change in image gain as a function of row number. 4. The center and radii of the beam stop and exclusion circles. 5. Image regions which should be ignored during the calculation. 6. The name of the flat-field correction image (if any). Once these parameters are specified, the radial sum can be calculated with or without a correction routine that removes "bad" pixels from the sum. Pulse-height distributions can also be calculated. Eleven menu items are displayed: D.3.2.1 Set Beam Stop / Exclusion Radii This menu item leads to a sub-menu where the user enters the central coordinates and radii of the beam stop and the exclusion circle. The beam stop is the aluminum-coated circle on the large fiber optic taper which reduces the unscattered electron beam signal (see 6.3) . Pixels within the beam stop circle are not included in the radial sum. The exclusion circle designates the outer boundary of the detector's active region, apparently as limited by the small fiber optic taper. Pixels outside of the exclusion circle are not included in the radial sum. RADAR2 will create a CCD image file that shows the current setting of these two boundaries. The circle parameters can be optimized by iteratively comparing border images with a sample detector image. Appendix D: Software Developed for Ultrafast GED (RADAR2) 560 D.3.2.1.1 Beam Stop Radius This unsigned integer corresponds to the radius of the beam stop circle. If the distance from a pixel to the beam stop center is less than or equal to this radius, then the pixel's count value will not be included in the summation. Setting the radius to zero will still mean that one pixel (the center) is ignored. D.3.2.1.2 X-Coordinate Of Beam Stop Center This unsigned integer is the x-coordinate of the center of the beam stop circle. D.3.2.1.3 Y-Coordinate Of Beam Stop Center This unsigned integer is the y-coordinate of the center of the beam stop circle. D.3.2.1.4 Exclusion Radius This unsigned integer sets the radius of the exclusion circle. If the distance from a pixel to the exclusion circle center is greater than this radius, then the pixel's count value will not be included in the summation. To deactivate the exclusion circle, choose a large value for the radius (e.g., 500 pixels). D.3.2.1.5 X-Coordinate Of Exclusion Center This unsigned integer is the x-coordinate of the center of the exclusion circle. D.3.2.1.6 Y-Coordinate Of Exclusion Center This unsigned integer is the y-coordinate of the center of the exclusion circle. D.3.2.1.7 Border Image Filename The user enters a standard DOS eight-character name for the border image. The Appendix D: Software Developed for Ultrafast GED (RADAR2) 561 border image will have the same path and extension as input images (see D.3.1). D.3.2.1.8 Generate Border Image This menu item creates a border image, a file in the SpectraSource CCD image format which shows the limits of the beam stop and exclusion circles. Pixels on these rings have count values of 65,000 ADU; the count values of all other pixels in the image are set to 0. Only pixels between (and not including!) the two rings will be considered in a radial sum. (The exclusion circle is drawn with its radius incremented by one.) The border image will have the same header and x-y dimensions as the most recently loaded CCD image, and will overwrite this CCD image in extended memory. An "Image Altered" warning will appear if the user tries to sum after a border image is created. To check the radii and centers of the beam stop and exclusion circles, the user should create a border image, exit RADAR2, and run HPC-1 . After selecting the "Cli~ping" option, the border image is subtracted from a real exposure image. This creates black rings in the real exposure which correspond to the beam stop and exclusion circles, and the user can judge whether the circle parameters should be adjusted. D.3.2.2 CCD Image Background The second item of the Calculate Radial Intensity menu is an unsigned integer with two functions. If the user conducts a radial sum, then the integer is Bwff, corresponding to the background offset value (in ADU) of the input CCD image at the top of the image (the first row) . If the user calculates a pulse-height distribution, however, then this menu item is the starting offset point (in ADU) for the PHD abscissa. Appendix D: Software Developed for Ultrafast GED (RADAR2) 562 D.3.2.3 Background Or PHD Range This unsigned integer is in ADU and has two functions. For radial intensity summations, BRng corresponds to the average increase in the background offset value at the bottom of the image relative to the top. The increase in Baff is due to the linear accumulation of thermal noise during image readout (see 6.6.1.5). RADAR2 assumes that the CCD has 512 rows (like the SITe 502A CCD) and calculates the total offset at Row 512 as BTOtf + BRng• If images from a CCD of different dimensions are being corrected for thermal drift in the background offset, then the measured value of BRng must be interpolated or extrapolated to Row 512. For example, the Texas Instruments TC 211 CCD has 165 rows; the user should therefore enter a range equal to (512/165) x Brng• If a pulse-height distribution is calculated, then BRng corresponds to the sampling range of the PHD in ADU. BRng should have a minimum value of 300 ADU, and the best results are obtained when BRng is an integer multiple of 300 ADU. D.3.2.4 X-Coordinate Of e- Beam This unsigned integer is the x-axis pixel position for the center of the radial sum. In most cases this will correspond to Xeb• D.3.2.5 Y-Coordinate Of e- Beam This unsigned integer is the y-axis pixel position for the center of the radial sum. In most cases this will correspond to Yeb D.3.2.6 Change In Image Gain By studying 2-D sM(pix) curves, we have determined that the gain of the detection Appendix D: Software Developed for Ultrafast GED (RADAR2) 563 apparatus decreases linearly as the CCD image is read out (7.1.4). With this menu item, the user can enter a real number for gv representing the fractional change in gain from the top row of the CCD image down to the bottom row. The usual value is 0.3. The gain as a function of row number is calculated according to Eq. D.3: (D.3) D.3.2.7 Flat Field Image The user selects a flat -field image with the same extension and from the same path as the diffraction images. The flat-field image is stored in extended memory along with the current CCD image. A warning message is displayed if either the x- or y-axis dimension of the flat-field image is smaller then the current CCD image's dimensions, but the user can still perform summations. Contributions from pixels outside of the flat-field image's scope are unpredictable. D.3.2.8 Exclude Regions From Sum With this menu item, the user can view and edit the list of CCD image pixel regions which will be ignored during the summation. A new forbidden region is defined by entering the pixel coordinates of two opposing corners. RADAR2 automatically sorts the region list, first by the lower y-axis coordinate and then by the upper x-axis coordinate. D.3.2.9 Conduct Simple Radial Sum Radial and pulse-height distribution sums are calculated with the subroutine summation() in RADAR2. This subroutine reads the CCD image from extended memory one row at a time and then considers each pixel in the row individually. First, Appendix D: Software Developed for Ultrafast GED (RADAR2) Mode Flag 564 Operation Calculates a radial sum. FLAT_FIELD_RAD Calculates a radial sum, correcting pixel count values with flat-field ................................................ ........... image •.................................................................................................................................................... ..... PULSE_HEIGHT .........Calculates.a pulse-height.distribution.···················································································· ...... RADIAL_SDEV ..........Calculates .the. standard. deviation .of pixel .count. values.for .each..radius ....... . CHECK_PIXELS Checks that a pixel count value is within n standard deviations of the mean. If not, the pixel is removed from the radial sum. RADIAL Table D-6: Modes of operation for subroutine swnmation() in the program RADAR2. swnmation() evaluates whether the pixel is valid: the pixel must be inside the exclusion radius, outside of the beam stop circle, and not located within one of the forbidden regions set in the eighth menu item (D.3.2.8). Pixels with a count value of O ADU are also ignored unless the program is calculating a PHD. If the pixel is valid, then the pixel's count value is corrected for the background offset (but not the range) and RADAR2 calculates r xy, the distance from the current pixel to the center of the sum, is: (D.4) Next, swnmation() acts upon the pixel's count value depending upon the current mode of operation. These modes are summarized in Table D-6. Results are stored in four different arrays, all functions of rxy: (1) total_data[rxy][i] contains average radial sums, pulse-height distributions, and standard deviations; (2) swn_data[rxy][i] contains the total, unnormalized radial sums; (3) tot_count[rxy] contains the number of contributing pixels for the current image, and (4) swn_count[rxy] contains the number of contributing pixels when summing over many images with a batch file (D.3.3). These arrays are summarized in Table D-7. A simple radial sum only uses modes RADIAL and FLAT_FIELD_RAD, depending on whether or not a flat-field correction image has been selected. In both cases Appendix D: Software Developed for Ultrafast GED (RADAR2) Array Name Variable Type 565 Data Stored total_data[rxy][O] Four-Byte Mean radial sum (or pulse-height distribution). Real Standard deviation for mean radial sum. total_data[rxy)[l]_ ................................................ ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••·························· Eight-Byte Total (unnormalized) radial sum from current image. sum_data[rxy)[O] Real ....Total. (unnormalized).. radial_ sum. from. all __images .......... ..... tot_count[rxyJ... ... .four-Byte .Integer ... .... Number.of .contributing _pixels .from _current _image ....... Eight-Byte Integer Number of contributing pixels from all images. sum_count[rxv] ... sum_data[rxy][l] .... •••••••••••••••••••••••••••••••••••••••••••••••• Table D-7: Array names and functions in subroutine swnmation() of program RADAR2. Except for the pulse-height distribution, arrays are a function of rxv, the pixel distance to the center of the radial sum. the pixel count value is corrected for changes in the background offset and the linear gain variation. With a flat-field correction, the count value is divided by the flat-field image count value and rescaled by a factor of 1000. These two calculations are summarized in Eqs. D.5 and D.6: (D.5) (D.6) This contribution is added to sum_data[r.xy][O], and tot_count[r.xy] is incremented by one. After all image pixels have been considered, summation() determines the mean radial sum by calculating: total_data[r.xy][O] = sum_data[r.xy][O] / tot_count[r.xy] (D.7) Next, the subroutine f inish_radial_swn() is called, which finds the minimum and maximum r.xy where tot_count[r.xy] is non-zero. There are no valid, contributing pixels for radii outside of these limits, so the data in total_data[r.xy][O] is shifted by the minimum r.xy such that the first radius with data begins in total_data[O][O]. Finally, a graph of total_data[r.xy][O] is plotted on the screen. Appendix D: Software Developed for Ultrafast GED (RADAR2) 566 D.3.2.10 Conduct Pulse-Height Sum Selecting this menu item runs summation() in the PULSE_HEIGHT mode. A pulse-height distribution plots number of pixels as a function of count value in ADU (see 5.3.2 for an example of a PHD). In summation(), a fixed number of counting bins, 301, are available for calculating the PHD. Each bin corresponds to a range of ADU; if the count value of a pixel falls within this range, the bin is incremented by one. Since a pulseheight distribution is primarily a diagnostic feature for CCD images, pixel count values are not corrected for variations in gain or background. Instead, the background offset and range specify the ADU region (somewhere between O and 65,535) over which the PHD is calculated. The PHD works best when BR11g is an integer multiple of 300 because the number of bins is fixed at 301; bins then correspond to an integral range of ADU. Setting BRng less than 300 is not recommended since a periodic subset of bins will always be zero (their fractional ranges will not encompass one of the integers). As summation() reads in the CCD image, the count values of valid pixels are compared to the ADU range specified by BToff and BR11g• If the count value is within this range, then the appropriate bin (located in total_data[i][O]) is incremented by one. After the entire image has been evaluated, a graph of total_data[i][O] is plotted on the screen. The offset value for the x-axis coordinate of this graph will be correct, but the range may not - RADAR2 assumes that the x-axis range is always 300 ADU in the plotting sequence, regardless of what the user selected. (This bug should be fixed at some point.) Note that the entire graph will be plotted, but the coordinate values may be wrong. The x-axis coordinate values will be correct when the data is saved to disk. On occasion the user may wish to know the pulse-height distribution for a certain Appendix D: Software Developed for Ultrafast GED (RADAR2) 567 distance rxy from the center position (see 7.1.5). This is easily done by removing the comment characters from one line of code in the subroutine summation(): case PULSE_HEIGHT: if (/*r_meas == xxx &&*/value>= 0 && value< disc_range) { temp= 300. * value; temp/= disc_range; where xx.x would be the integer pixel distance rxy• If the user wishes to account for linear gain variation, an extra line can be included which multiplies value by the gain correction factor. D.3.2.11 Conduct Refined Radial Sum Detection noise such as background emission from the image intensifier can cause a few image pixels to register abnormally high intensities. These anomalous pixels dramatically affect the radial sum and experimental sM(s) curve, particularly at large s where the total scattering intensity is already low (7.1.5). Manual evaluation of images, in which each obvious anomaly is removed by specifiying a forbidden region, is imprecise and impractical since one experiment may involve hundreds of images. The refined radial sum provides automated pixel-by-pixel evaluation of the input image, where the count value of each pixel is compared with the mean value at that radius. Pixels with unusually high or low count values are declared "bad" pixels and are not included in the radial sum. The logic flowchart for calculating radial sums is shown in Figure D-1. The refined sum calls summation() many times in different modes of operation; the first call calculates the simple radial sum (mode RADIAL) as described in D.3.2.9. To find the standard deviation of count values as a function of radius, the entire image must be read Appendix D: Software Developed for Ultrafast GED (RADAR2) 568 again using mode RADIAL_SDEV. For each valid pixel, the program finds rxy (Eq. D.4) and subtracts the mean count value at r xy• The square of the difference is added into total_data[rxy][l]: total_data[rxy][l] += (sum_data[rxy][O] - total_data[rxy][O]) 2 (D.8) After iterating across all the image pixels, swnmation() calculates the standard deviation of count value distributions as a function of r xy according to: total_data[rxy][l] = .Jtotal_data[rxy][l] / (tot_count[rxy ] - 1) (D.9) At large radial distances where scattering intensity is low, the calculated standard deviation <Jca1c may be less than the expected standard deviation of single electron events, <Je. If cr Cale < <Je, then cr c ate is redefined as <Je in order to avoid throwing out valid electron signals. A pixel will be thrown out if its count value is more than n standard deviations away from the mean count value. The standard deviations in total_data[rxy][l] are multiplied by n in anticipation of this comparison. At present the values for <Je and n are set at 40 ADU and 4, respectively (see 7.1.5 for justification). These values can be changed by editing RADAR2.C and rebuilding the program. The values are initialized in the routine main(), and the variable names are min_std_dev for <Je and num_std_dev for n. After the modified standard deviations are calculated as a function of rxy , swnmation() is called again in the mode CHECK_PIXELS. As the image is read from extended memory this time, the count value of each valid pixel is compared with the mean and modified standard deviation. If the count value is outside the distribution limits, then the pixel is declared "bad" and several corrections are made: Appendix D: Software Developed for Ultrafast GED (RADAR2) 1. The count value is subtracted from 569 Load CCD Image the sum total in sum_data[rxy][0]. C a:'lcu late?N u'ni""bj~ Contributing P·ix' Suro Qou,Qt V A Fune!"''" ' dius This does not alter the radial mean (stored in total_data[rxy][0]) which will still be used for evaluating other Yes pixels at this rxy. No 2. tot_count[rxy] is decremented by one .• Calculate Standa'rd Dev iation Of Pixel CountValues 'As A FUncliOfl 'Of R~cfius (the pixel is thrown out). 3. The count value in the image array Identify "Bad ' Pixels: A Pixel Is ' Bad ' If Count. Value Is Outside Four Standard, Deviations· Of The Mean is set to zero and the array is saved back to extended memory. As mentioned in D.3.2.9, a pixel with count value of 0 ADU is Correct * Number Of. Contributing Pixels Apd ) Sum Count Values By Removing' "Bad' Pixels Yes not considered valid (except for PHO Include Radial Sum In Total sums). Several pixels along a radius near the center of the diffraction pattern may be saturated by Figure D-1: Flowchart for both the simple and refined radial sums in subroutine swnmation() of the program RADAR2. blooming - enough that the standard deviation becomes too large to discredit the saturated pixels. An explicit upper cutoff limit is needed, and so a pixel is also thrown out if its count value is greater than the variable TOO_HIGH. TOO_HIGH is set to 35,000 ADU at present. After iterating across all the pixels, the mean radial sum is recalculated according to Eq. D.7; summation() does not have to be called again in mode RADIAL. The program iterates between RADIAL_SDEV calls and CHECK_PIXELS calls as Appendix D: Software Developed for Ultrafast GED (RADAR2) 570 long as "bad" pixels are found (Figure D-1 ), or until a maximum number of passes are made. The current limit is 20 passes, which can be changed by editing the subroutine smart_radial_sum() in RADAR2.C. Analysis of a typical diffraction image takes about six passes during which -1500 pixels are thrown out. After the iteration is completed, the program calls f inish_radial_sum() and a graph of the final mean radial sum is plotted on the screen. Note that the refined sum alters the image stored in memory by setting the count values of "bad" pixels to O ADU. Subsequent selection of either the Simple Radial Sum or Refined Radial Sum menu items will produce the exact same curve. If a flat-field image has been selected, summation() is called one last time in mode FLAT_FIELD_RAD before the subroutine finish_radial_sum() is executed. At the present time the flat-field image is not included in the iterative pixel evaluation process because a true flat-field image has not been generated, and appropriate values for n and cre are unknown. Including the flat-field image correction in all aspects of the refined radial sum should be straightforward and is left for future versions of RADAR2. D.3.2.12 Save Radial Sum After calculating a radial sum or pulse-height distribution, the data can be saved to disk with this menu item. The user enters a standard DOS eight-character filename and selects the destination path and output extension. The data is saved in CSV format, starting with a line of text which reports the type of calculation and the source CCD image filename. For radial sums, each subsequent line contains a pixel distance and the corresponding mean radial intensity. For pulse-height distributions, each line in the output Appendix D: Software Developed for Ultrafast GED (RADAR2) 571 file contains a count value x; (in ADU) and the number of pixels which had count values greater than or equal to x; and less than x;+ 1 (found in the next line). D.3.3 RADAR2 Option Three: Automatic Radial Intensity Processor This menu option allows the user to determine the mean radial intensity profile from a collection of CCD images. The user must first create a batch file in the format shown in Table D-8. Following the identification header (RADAR2-BATCH-FILE) is the name of the flat-field correction image without extension. correction then the user enters ''None" instead. If there is no flat-field Below this is the number of 'jobs" RADAR2 will perform, where each job results in the creation of one mean radial intensity file. Each job is further broken down into a number of "sets" so that the average profiles from images with different forbidden region requirements can be combined together. A job starts with the number of these sets, followed by filenames and extensions for the mean radial intensity output file and a statistics file. The statistics file is discussed below. A set begins with the number of forbidden regions, followed by the four coordinates identifying each forbidden region. There are no ill effects if these coordinates extend outside of the CCD image dimensions. Next come the number of input images in the set and the list of image filenames; each filename is accompanied by the electron beam coordinates and the background offsets at the top and bottom of the image. All input images (including the flat-field image) must be located along RADAR2's default CCD image path and must have the default extension; these parameters can be altered with main menu option one (D.3.1). Table D-10 shows a sample mean radial intensity batch file. After selecting the Automatic Radial Intensity Processor, the user is Appendix D: Software Developed for Ultrafast GED (RADAR2) 572 Mean Radial Intensity Batch File Format fiADAR2-BATCH-FILE r- - - - - - - - , - - - - - - - - , -- - - - - - - , -- - - - - - -, I I I I I I r-------.-----r--------,--------.---------,--------7 [Flat Field I I I I I I I Image Name] I I I I I r-------------r--------,--------,--------T--------7 [Number Of Jobs] I I I I I I [Number Of Sets I I I I I Of Job 1] I I I I I r-------------r--------,--------,--------T--------7 [output Filename 1 1 1 , ] 1 I I 1 and Extension 1 1 1 1 1 I I ~[Stats-Filename-~--------T ________ T ________ T ________ 7 I and Extension] I I I I I I I I [Number of F.o rbidden Regions NR ] I I I I I I I I I I I I I I I I 1 I I 1 Upper Offset of • l] Region I I I I I I I I Lower I Lower Offset of I Offset of • , Region 1] I1 Region 1] 1 I I 1 1 I I 1 r-------.-~ --r-----.--+-----.--+-----.--+--------1 [X-Axis I [ Y-Axis I [X-Axis I [ Y-Axis I I Upper Offset of • l] Region r------.: ------r--.----,--~---,--.----T--------7 I : I : I : I I 1 I r-------. ---r-----,--T-----.--,-----,--T--------7 [X-Axis I [ Y-Axis I [X-Axis I [ Y-Axis I I 1 s I Upper I Upper I Lower I Lower 1 1 s t 1I I Offset of I Offset of I Offset of I Offset of I I , I , I , I , I I t ~ __ Region NR~l ___ :-Region N!!iTl+. Region NRg] +Region N!lg! -l---------~ s r-------------r--------T--------~--------,--------~ [Number of Files] I J e I 0 t b 1 1 I 1 I [Input Image Filename 1] I I I I I [X-Axis I [ Y-Axis I [Background I [Background I I Coordinate I Coordinate I Offset I Offset 1 1 (Bottom Of 1 1 Of e- Beam I Of e- Beam 1 (Top Of I I I I I 1 (Image 1)] 1 (Image 1)] 1 Image 1)] 1 Image 1)] 1 r-------------r--------,--------,---------,--------7 I : I : I : I : I : I r-------------r--------,--------~--------T--------~ I [X-Axis I [ Y-Axis I [Background I [Background I I 1 : [Input Image Filename Nrml I 2 I Coordinate I Coordinate I Offset I Offset 1 : Of e- Beam : Of e- Beam : (Top Of : (Bottom Of : I ( Image Nrm> ] I ( Image Nrm> ] 1 Image Nrm) ] 1 Image Nrm> ] 1 [Number of Forbidden Regions] n 1 I 1 d ~------. ------~--I 2 n d I : [Number Of Sets Of Job 2] I .----t--- ~---t--- .----t--- ~---~ : I : I : I : I 1 I I I I I I I ~------. ------~--.----+--~---+--.----+--~---~I I : I : I : I : I : Table D-8: Format of batch file used when calculating mean radial intensity profiles with option three of RADAR2. prompted to choose a batch file. The user can also choose a different default path and extension for the batch file location if necessary. If the batch file has the correct header, a Appendix D: Software Developed for Ultrafast GED {RADAR2) 573 new screen appears displaying the number of jobs, the number of sets in the current job, and other data obtained from the batch file. The program iterates through the jobs, sets, and image lists, calculating refined radial sums on each image. The total radial sum from all images in the current job is stored in sum_data[rxy][l], and sum_count[rxy] contains the total number of contributing pixels (from all job images) at each radial position. Upon completion of a job, the mean radial intensity is determined from these two arrays and written to disk in CSV format under the filename listed in the batch file. The first line of the output file reports the type of calculation; subsequent lines contain radial pixel distances and the corresponding intensity. A statistics file for the current job is also written to disk in CSV format. This file identifies the batch file name, the flat Sample Radial Intensity Batch File field image name, CTe for the refined sum, and all input image filenames. Beside each image filename are its electron beam coordinates, the number of passes required to evaluate the image with the refined radial sum, the number of "bad" pixels, and the total scattering intensity in ADU. The total intensity is the area under the mean radial intensity curve and reflects both the experimental electron Table D-9: Example of a mean radial intensity batch file used with option three of RADAR2. Appendix D: Software Developed for Ultrafast GED (RADAR2) 574 flux and the scattering efficiency of the sample. Both output files will be located in the current directory, most likely the directory in which RADAR2.EXE is located. D.3.4 RADAR2 Option Four: Automatic Beam Center Search To automate radial intensity analysis of diffraction images, the user must include the x-y coordinates of the unscattered electron beam for each image in the batch file. Typically the beam position is determined from a short exposure image in order to avoid saturation problems; there may be dozens of such images at the conclusion of an experiment. This menu option accepts a pre-generated batch file listing these images, and estimates the electron beam coordinates by calculating xand y-axis profiles. The format of the batch file is shown in Table D-10. The batch file starts with the Center Search Batch File Format °cENTER-BATCH-FILE r .- r 1 ~-------.-----~--------+-----~-----1 I [output Filename I I I I 1 and Extension] 1 1 1 1 r-------------,--------T-----,.-----1 I [ X-Axis I [ Y-Axis I [X-Axis I [ Y-Axis I Upper I Upper I Lower I Lower 1 1 1 Offset] Offset] offset] 1offset] 1 [Number of Files] [Input Image [Background 1 1 1 1 1 1 Filename 1] 1 Offset] 1 1 1 1 1 r-------------r--------+-----r-----1 r-------------r--------+-----r-----1 r-------------,--------,-----,-----, I header identification : I : I I I r-------------r--------,-----,-----1 [Input Image [Background 1 I Filename Nrml 1 I 1 Offset] I 1 I 1 I --------------~--------~-----------· (CENTER-BATCH-FILE) Sample File and the name and extension of r--------------r--------.------r-----1 the output file. Next come ~03 03CTR. XLO __ - - ~ - - - - ___ -+-----~-----I 20 25 35 36 the and lower defining the upper f-:CENTER-BATCH-FILE ~ _______ -+- ____ ~ ___ --1 ~-------------~--------+-----~-----1 ~J------------~--------+-----~-----1 S0303E01 3209 ~-------------~--------+-----~-----1 ~J~03E02 - - - - - - - ~ - - 3214 --+-----~-----1 : coordinates region over which RADAR2 should calculate profiles. I : I I Table D-10: (Top) Format of batch file used when determining the electron beam center position in CCD images with option four of RADAR2. (Bottom) Example of a batch file which finds the pixel coordinates of the electron beam center. I Appendix D: Software Developed for Ultrafast GED (RADAR2) 575 These are followed by the number of input images and the list of input image filenames, where each filename is accompanied by the image's average background offset. The location and extension of the input images must match the path parameters set with main menu option one (D.3.1). Once Automatic Beam Center Search is chosen, the user selects a batch file from the list found under the default path and extension. (These parameters can be changed as necessary within this menu option.) If the selected batch file has the correct identification header, then a new screen appears showing the progress of the image analysis. RADAR2 starts by calculating the x- and y-axis profiles across the region defined in the batch file. This region should be small (~ 15x15 pixels) and the electron beam peak should be the most prominent signal. A three-point boxcar smooth is applied to the profiles, and RADAR2 finds the maximum of each curve. The position of the maxima will be returned as the electron beam center position if the variable cs_mode in the subroutine center_batch() is set to zero. Because there are occasional intensity spikes in the electron beam cross-sectional distribution during short exposures, the maxima may not be the best indicator of the beam center. At present a second method is enabled (by setting cs_mode equal to one). For each profile, RADAR2 starts from the maximum position and finds the location of the half-maxima using a two-point interpolation scheme. The halfway point between the two half-maxima is declared to be the beam center. This method is successful as long as RADAR2 is provided with a reasonably accurate background offset value for the image. The results of the center-search analysis are written to disk in CSV format using the filename provided in the batch file. The output file is saved to the current directory, Appendix D: Software Developed for Ultrafast GED (RADAR2) most likely the directory containing RADAR2.EXE. 576 The frrst line of the output file reports the name of the batch file; each subsequent line lists a CCD image filename and the corresponding x-y coordinates of the center position. Note that RADAR2 makes no error checks; if the center search region is outside of the CCD image dimensions, then the results are highly unpredictable. D.3.5 RADAR2 Option Five: Create Bitmap From Image This menu option converts a SpectraSource 16-bit CCD image into a Windows Paintbrush 4-bit bitmap. Although later versions of HPC-1 also make this conversion, RADAR2 allows the user to select an offset and rescale the image, which helps compensate for the loss of twelve information bits per pixel. There are five menu items: D.3.5.1 Create Bitmap This menu item creates the Windows bitmap, presumably after the filename, windowing level (offset Word First and scaling factor), and palette have been chosen. The Windows bitmap starts with a 118-byte header, where the x- and y-axis dimensions are stored in words 10 and 12, Bvte Color ..... High .......... GREEN.... . Word Low BLUE ....................................................................... Second ..... High ..... ......unused .... . Word Low RED Table D-11: Byte assignments for 16-color palette in Windows bitmap. respectively. Words 28 through 59 contain the RGB 16 color palette, two words per color. The map for these colors is shown in Table D-11. Each pixel is represented by a four-bit number which corresponds sequentially to the colors of the palette; the bitmap only has a four-bit dynamic range, although each of the sixteen colors can be selected from 2563 possible colors. Pixels are stored frrst by column, Appendix D: Software Developed for Ultrafast GED (RADAR2) 577 then by row, but unlike the SpectraSource format, the rows in a Windows bitmap start with the last row first. Pixels are stored in four-pixel clumps (four pixels = four nibbles = one word), so a row of 5 pixels uses the same amount of memory as a row of 8 pixels. The conversion process takes each SpectraSource pixel count value and assigns a number between O and 15 based on the offset and range (see D.3.2.4 below): 16 WB(x,y) = Integer[(cI(x,y) - Offset) ] • Range (D.10) Count values below the offset are set to O and values above the range are set to 15. The four-bit number is mapped to another four-bit number using the array scheme[i] (see D.3.2.5), and then inserted into the appropriate nibble of the four-pixel clump. The conversion process does not alter the SpectraSource CCD image stored in memory, so experimentation with the windowing level can be done without reloading the input image. D.3.5.2 Change Filename The user enters a standard DOS eight-character name for the output bitmap file. D.3.5.3 Change Path This item allows the user to alter the default directory path and extension for the output Windows bitmap files. D.3.5.4 Set Windowing Level With this menu item, the user selects the rescaling factors for the conversion process. First the user chooses a range, anywhere from 16 ADU to 65,536 ADU. The ranges are all multiples of sixteen, so each of the sixteen palette colors will correspond to Appendix D: Software Developed for Ultrafast GED (RADAR2) 578 an integral number of ADU (1 ADU out to 4,096 ADU). Next the user chooses an offset value, which must be between O ADU and (65,536 - range) ADU. D.3.5.5 Choose Bitmap Palette Two palettes are currently available: a monochromatic scale which progresses gradually from black to white, and a technicolor scale which uses the light and dark variants of the eight standard video colors (blue, red, green, yellow, magenta, cyan, white, and black). These palettes are part of the bitmap header; two versions of the header are stored in the array BMP _header[2][59] defined in RADAR2DT.C. The actual order in which the colors are assigned to count values depends on the mapping array scheme[16]. Several variants of scheme[i] are commented out in RADAR2DT.C. These variants include going from light-to-dark or from dark-to-light with the greyscale palette, and maps for the technicolor scale when printing the bitmap on a black-and-white printer (a color's relative darkness on the video screen is different on the printed page). To change the selection of scheme[i], RADAR2DT.C must be edited and the executable file rebuilt. D.3.6 RADAR2 Option Six: Calculate Regional Mean And RMS Values Determination of the mean count value from a region of a CCD image is one of the most basic and important functions of RADAR2. The mean value is needed any time RADAR2 and other programs require background offsets for image correction, or when electron beam intensities are requested. The program also returns the root-mean-square deviation of the mean, which is useful for determining the presence of background spikes within a region and for estimating detector noise. There are three menu items: Appendix D: Software Developed for Ultrafast GED (RADAR2) 579 D.3.6.1 Define Regions Of Calculation The user enters a list of regions over which RADAR2 will calculate the mean and . RMS values. A region is identified by entering the coordinates of opposing corners, just like for specifying forbidden regions (D.3.2.8). In this menu item, however, the regions are inclusive (the mean/RMS calculation will be conducted on pixels within the region, including the edge) rather than exclusive, like forbidden regions. D.3.6.2 Treat Data As Signed Integer? The SpectraSource CCD image pixels are stored as unsigned integers, but if the CliE_ping option of HPC-1 is not set then two similar images can be subtracted to effectively create a difference image of signed integers. For some experiments, the user may wish to analyze regions of the difference image; in those cases setting this menu item to "y" will convert all count values according to: Clu(x,y)::;; 32767: CI 5 (x,y) Clu(x,y) > 32767: CI 5 (x,y) = Clu(x,y) CI u (x, y) - 65536 (D.11) and RADAR2 will calculate the mean and RMS values properly. D.3.6.3 Calculate Mean And RMS Values This menu item calculates the mean and RMS values of the selected regions. The results are tabulated on the screen. memory twice - The CCD image is downloaded from extended the first time to calculate the mean and the second time to calculate the sum of the square of the differences relative to the mean. Appendix D: Software Developed for Ultrafast GED (RADAR2) 580 D.3.7 RADAR2 Option Seven: Automatic Mean And RMS Values In many cases, background offsets must be determined for a large collection of CCD images; this menu option automates the calculation of mean and RMS values by allowing the user to run a pre-generated batch file. The format of the batch file is shown in Table D-12. The identification header, RMS-BATCH-FILE, is followed by the number of "jobs" in the batch file. Mean and RMS values are calculated over the same set of regions for each image listed in a job, and one output file is created per job. The job format starts with the name and extension of the output file, and the number of input CCD images. Next comes the number of regions over which the analysis Automatic Mean I RMS Batch File Format ~--------------,----------,----------,----------, RMS-BATCH-FILE 1 1 1 1 r---------------,-----------,----------,----------, [Number of Jobs] I I I I 1 I 1 [output Filename and Extension] : : 1 1 1 1 r---------------,-----------,----------,----------, [Number of Files] I I I I 11 r,---------- .----,-----------,----------,----------, 1 1 1 51 tNwnber of Regions] 1 ti [X-Axis Upper [ Y-Axis Upper [X-Axis Lower [ Y-Axis Lower 1 1 1 1 1 Offset of I Offset of I Offset of I Offset of 1 1 1 1 1 1 Region 1] Region 1] Region 1] Region 1] ,--------------,----------,----------,----------, r--------------+----------r----------r----------i : I : I : I : I r---------------,-----------,----------,----------1 [X-Axis Upper 1 [ Y-Axis Upper 1 [X-Axis Lower 1 [ Y-Axis Lower 1 J1 01 b' Offset of 1 Region N R ] I- - - - - - - - - _ !'g I Offset of I Offset of I Offset of 1 1 1 1 Region NR ] Region N R ] Region NR ] !,2' _ -+- - - - - - - - !,2' - -+- - - - - - - - !,2' _ - ~ I [Signed I I I 1 Image Flag] 1 1 1 1 -+-- - .-- 1 ,-----.-------,---- .-----,----------,----------, - - I [Input Image Filename 1] I : I : I I I I Filename Nrml I Image Flag] I I I 2i [output Filename and Extension] 1 r---------------,---.------,----------,----------, [Input Image I [Signed I I I I 1 n1 1 I I I I r---------------,-----------,----------,----------, [Number of Files] 1 1 1 1 di .r------ .-------,---- .-----,----.-----,---- . -----, : I : I : I : I : Table D-12: Format of batch file used when determining the mean and RMS values from regions in CCD images with option seven of RADAR2. I Appendix D: Software Developed for Ultrafast GED (RADAR2) will be conducted. Each region is identified by 581 Sample Mean I RMS Batch File the x-y coordinates from a pair of opposing corners. The list of CCD image filenames (without extension) follows the coordinate list, and each image filename is accompanied by either a "O" or "1". A "O" indicates the all pixel count values should be treated as unsigned integers, and a "1" indicates signed-integer treatment. RADAR2 expects that the CCD images will be Table D-13: Example of a mean/RMS batch file used with option seven of RADAR2. located along the default image path and have the default extension. These parameters can be altered with main menu option one (D.3.1). A sample mean/RMS batch file is shown in Table D-13. After the user selects Automatic Mean And RMS Values, RADAR2 responds by allowing the user to either choose a batch file or change the default path and extension under which RADAR2 locates batch files. If the selected batch file has the correct identification header, then a new screen is drawn showing the number of jobs, the selected regions for the current job, and other data obtained from the batch file. Calculation of the mean and RMS values should proceed swiftly, limited by the time required to load a CCD image from disk. RADAR2 conducts no error checks during this analysis; if a selected region extends outside of the CCD image dimensions then the results are unpredictable. An output file is created in CSV format using the name and extension provided in the batch file for the current job. This file will be written to the current directory, which is probably the same directory where RADAR2.EXE is located. Each line in the output file Appendix D: Software Developed for Ultrafast GED (RADAR2) 582 contains a CCD image name followed by the mean and RMS values for every selected region. The coordinates of the selected regions are at the column head. RADAR2 automatically orders the selected regions according to the same criteria as forbidden regions (D.3.2.8), so the column order in the output file may be different from how the selected regions were listed in the batch file. D.4 PROC5 The previous section described how the program RADAR2 extracts raw experimental scattering curves !\pix) from CCD images. PROC5 completes the analysis of diffraction data by transforming l(pix) into an experimental modified molecular scattering curve, sM\s). This requires a correction for the experimental background intensity and a conversion from pixels to inverse Angstr0ms (A- 1). The background curve /s(pix) can be loaded from disk or generated from a fit of /£(pix) along zero positions determined from a theoretical modified molecular scattering curve, sMT(s). PROC5 will calculate the sM\s) of any molecular structure for which the user provides a list of internuclear separations and mean amplitudes of vibration. The sMT(s) curve can also be calculated for a mixture of molecules. Iterative fitting procedures are available for determining the camera length L, and for finding what composition of a two-molecule mixture (e.g., CH2Ii and CH21) leads to the best fit with the experimental data. Finally, PROC5 will convert theoretical and experimental sM(s) curves into radial distribution functions,f(r). PROC5 requests 3 Mb of extended memory from the computer in order to store Appendix D: Software Developed for Ultrafast GED (PROCS) 583 atomic scattering factors (less than 1 Mb of PROC5.EXE Program Files Include Files memory is actually used at present). Table D-14 PROC5.C PROC5_DT.C PROC5_10.C PRC5_FIT.C CEXT.C lists the program and include files required to build PROC5.EXE, and the operation of PROC5 is presented in the following sub-sections. Program DATA_PR5.H SETTING5.H CEXT.H COMPAT.H Table D-14: Program and include files needed to build PROC5.EXE. control in most UGED software flows from a main menu down through a menu tree. PROC5 is different; control is centered within two graphical data displays: a modified molecular scattering (MS) screen and a radial distribution (RD) screen. Because the approach to analyzing UED diffraction data is continuously evolving, this particular program manual contains more detail than most other sections in Appendix D. PROC5 variable names are routinely included in the discussion for the user's reference. D.4.1 describes the current method of treating the experimental scattering intensity as the data is transformed from /£(pix) to sM\s) and f(r). The nature and format of all input data files is presented next in D.4.2. Finally, D.4.3 through D.4.21 discuss the eighteen single-keystroke commands which manipulate the graphs and access sub-menus from within the MS and RD screens. D.4.1 PROCS Background Correction Technique PROC5 provides the computational muscle necessary for comparing an experimental modified molecular scattering curve with a theoretical curve. Calculation of the theoretical curve (sMT(pix)) from scattering factors and known structural parameters is straightforward, although some care must be taken to ensure that the theoretical curve duplicates the experimental conditions. Presenting the experimental data in a similar Appendix D: Software Developed for Ultrafast GED {PROC5) Data Arrays Step 584 Data Stored raw_data[MND] corr_raw[MND] Pixel Raw experimental scattering intensity. Pixel Temporary array for rescaling or adding theoretical and • ..................................................................................... experimental .scattering intensities ........................................................ ....theo_raw[MND][2J... . ..... Pixel ..........Theoretical.scattering ..intensity.tor .one .or.two. components ........ background[MND][2] ..... Pixel .......... Experimental .background .data •...................................................................... fifj[MND] Pixel Modified molecular scattering rescaling factor lfallfbl. ••••••••••••••••••••••••••••••••••••••••••••••••••• ••••••••••••••••••••••• ····························x r············································································································· raw_s[MND] Pixel Distance in A. as a function of pixel number. ········~~·~th~~"tt:rrx>f······ Ms::::s·tap· ····ftieoreiicaTs·M(sY·cu·ive··i·n·ierpoiaieCTio··i-eguia·r··i·n·ieivai·s··o1·A· 1 ..................................................................................... •...Only used..when..applying..a. background .tit. to. theory ......... ms_data[MTD][2] MS_step Theoretical and experimental sM(s) curves interpolated to ••••• rd···data[MTD][2f···· ··~0.02 A ····Th;~;e~:~:li~~~=~~~~i!·~~tal· radia(.distribution· curves. ··············· Table D-15: PROC5 data arrays for storing and manipulating scattering data. The 1 coordinates of each array are either in CCD pixels, regular intervals of A· (Ms_step, currently 0.04 A1), or regular intervals of A (set by the user but typically on the order of 0.02 A). MND: static integer MAX_NUM_DATA (current value of 301 ); MTD: static integer MAX_THEO_DATA (set to 401 ); MRD: static integer MAX_RD_DATA (set to 601 ). All static integers are defined in SETTING5.H . format is more challenging because the experimental background must be removed. The background curve, / 8 (pix), is generated by finding the zero positions of the theoretical curve and fitting a spline function to the values of the raw experimental intensity at those points (see 7.2.2 for more details). The raw scattering intensity /E(pix) is then converted to the sM\pix) format using Schafer's normalization [Sch76]: (D.12) Finally, the amplitude of sME(pix) must be matched to the amplitude of sMr(pix). PROC5 accomplishes this by scaling the two curves at the maximum or minimum of one peak (chosen by the user) in the theoretical curve. Alternatively, an absolute scaling factor can be entered by the user, which is often necessary to observe changes in molecular structure when a dominant internuclear separation is broken (see 10.3). During the transition from l(pix) to f(r), theoretical and experimental data are Appendix D: Software Developed for Ultrafast GED (PROCS) 585 c'a l c ___;lf • Cal9~,late ·s As A Function o'f pixel Dist;rnce. _Select Scaling Atoms And Molecule And • ,;>Load Molecular Structure Parameters. . ' select Raw Data Set. °Fill raw_data[I]. . , ; Sel~pt .Backgroun·d Fitting,Method. If Using An Old File.Then ~oa} Expe,rimenta:I Background Pata Into backsrrounc!i[1][1]. calc_theo() >/ Calculate Theoretical Molecular Scattering Intensity As A Function Of Pixel Distance. • - • = · (1j' 'Load /scattering factors from extend.eel memory as: needed. (2) ·Generate theo_raw[i][o] and _fifj[Jl (3) . Boxcar smooth theo_raw[il[o] by electron beam width (n_beam.::.,sz). (4) Reformat theo_r~w[il[o] with sflf811fl (5) Boxcar smooth theo_raw[il[o] by n_pts_fit. ; calc_zeros() ,Calculate Mixture O'f Theoretical sM(s) Intensities And Find Zero Positions. (1) (2) (3) (4) (5) (6) Compute corr_raw[il = a1 theo_raw[l][o] + a2 theo_raw[1l[1]. Interpolate corr_raw[i] from _pixels Jo s. Leaves data in ms_data[tl[o]. , Boxcar smooth 'ms_data[tl[o] with width n_pts_smo. . ", Transfer ms_data[il[o] to ms_theo[tl Find the zero positions in corr_raw[il . Find the scaling peak position and its value in corr_raw{tl ca 1 c _corrected_ exp er() Figure D-2: PROC5 flowchart (1 of 3) for experimental and theoretical ultrafast gas phase electron diffraction data analysis. stored in a number of arrays in the PROC5 routines. These arrays are summarized in Table D-15. Most arrays are indexed by distance in CCD pixels, the data element intrinsic to the UED detection system. Modified molecular scattering curves are functions of s, so the results of PROC5's calculations are interpolated from pixels to regular intervals of A- 1 in order to simplify data presentation and transformation. The interpolated sM(s) curves are stored in ms_data[i]I/]. The radial distribution curves, stored in rd_data[i]U], are indexed by Appendix D: Software Developed for Ultrafast GED (PROC5) 586 regular intervals of A as set by the user (D.4.5.6). Flowcharts depicting the evolution of experimental data from !\pix) to sM(s) and f(r) are shown in Figure D-2, Figure D-4, and Figure D-5. First, PROC5 must generate a conversion table between pixels and A- 1 (Figure D-2). The magnitude of the momentum transfer, s, is related to the electron wavelength Ae and scattering angle 0 by (see the derivations in 2.1.2): s = 4 n sin(0/2) (D.13) A, The conversion from pixels to s is not linear because the detector screen is flat whiles follows a curved surface (Figure D-3). By extending a scattering trajectory to its intersection point with the detector plane, 0 can be rewritten in terms of the camera length L , the effective CCD pixel width at the phosphor scintillator, Wpix, and the distance rxy (in pixels) to the intersection point. Eq. D.13 becomes: • ) s (pix Figure D-3: Scattering geometry. Electron scattered along trajectory k has momentum transfer of magnitude s and intersects the planar detector at pixel position rxy. • [ 1 arctan ( w,,;xr = 4n A, sm L xy ) ] 2 (D.14) The user provides PROC5 with Ae, L, and Wp;x, and the subroutine calc_s() m PROC5_DT.C fills the array raw_s[i] with pixel distances as a function of A-'. Next (Figure D-2) the user selects a set of raw experimental data and a structural model (or mixture of models) of the scattering sample. The experimental data is loaded Appendix D: Software Developed for Ultrafast GED (PROCS) into the array raw_data[i]. 587 PROC5 then calls the subroutine calc_theo() in PROC5.C in order to calculate the theoretical molecular scattering intensity as a function of pixel position. The summation is over all molecules loaded from the molecular structure data file (see Table D-19 for PROC5 variable definitions; n_f is num_found): (D.15) where: Sn = raw_s[n] (D.16) Pm = fract[m] (D.17) N 1s = num_ bonds[m] (D.18) i = bonds[o ][k ][m] (D.19) J = bonds[1][k ][m] (D.20) = bonds[2][k ][m] (D.21) rij = bond_length[k ][m] (D.22) lij = mnamvib[k ][m] (D.23) Nk and: Currently the theoretical curve is calculated out to 15 A- 1, but this can be increased by editing and rebuilding the software if so desired (see D.4.2.3 below). Scattering factors are loaded from extended memory and values at specific s are calculated with a two-point interpolation. The array f ifj [i] is filled at the same time as theo_raw[i][O]. From an experimental standpoint, the entire diffraction pattern is smoothed because the electron beam has a non-zero width Web• The theoretical data accounts for this by applying a boxcar smooth to theo_raw[i][O] of width n_beam_sz, where n_beam_sz is in pixels and set by the user (D.4.4.7) . Note that this smooth occurs on /T(pix), not sM\pix); smoothing under the wrong format will alter the zero positions. Appendix D: Software Developed for Ultrafast GED (PROC5) 588 After applying the electron-beam boxcar smooth, calc_theo() reformats theo_raw[i][0] into sM\pix) with the following equation: theo_raw[i][o] = raw_s[i] theo raw[i][o] f~fj[i] (D.24) Finally, calc_theo() applies a second boxcar smooth of width n__pts_f it, where n__pts_fit is the smoothing width which PROC5 will later apply to the experimental data before finding the zero-position intensities. The user chooses the value of n__pts_f it (D.4.4.5). At this point in the program, PROC5 has generated a theoretical modified molecular scattering intensity based on the structural parameters of the selected molecule, and has smoothed this data twice to mimic treatment which the experimental data has or will receive. As shown in Figure D-2, PROC5 next calls subroutine calc_zeros() in PROC5.C to determine the theoretical zero positions. When fitting experimental data to a two-component mixture (D.4.12), PROC5 will first generate the theoretical scattering intensity for both components individually, storing the second set of data in theo_raw[i][l]. The component ratio is passed to calc_zeros() through variables al and a2 (a2 = 1 - al), and the mixed scattering intensity is put in corr_raw[i]: corr_raw[i] = al·theo_raw[i][o] + a2·theo_raw[i][1] If there is only a single component then al = 1. (D.25) Now corr_raw[i] contains the reference sM\pix) curve, so the data is interpolated to regular intervals of A- 1, boxcarsmoothed with width n__pts_smo (D.4.4.6), and stored in the array ms_theo[i]. The subroutine scans corr_raw[i] for zero positions, identifying them with a two-point interpolation and storing the list of positions in the array zero_list[j]. The location of Appendix D: Software Developed for Ultrafast GED (PROCS) ,, ~ '_ -,,: . :--",::.; ., ' ' 589 '0,;, ,mental Data For Backgro , ·.'· _ '·;'J·· '-t • , :<. ""~ 't' ta[/] t9 c~rr.:.;;raw[i] and reformat w ar smoot corr_raw[i] with width n_pts_fit. ,.•<). + r, , _r~~ [,]\o desired prepa}atfon (Non~. 1/lfallfbl, ,sllf ' . No Warn User If Old , Background Cu rve • Has Fewe.r Points Than ·Raw Pata . < . bapkground_~ i'J:0,. Find Raw .Data Intensities At Zero Positions And Fi!These Values ; • ' With A Smooth,, Segmented C~rve." "", sv • (1) .Determine which zeros are spanned by the faw data . . (2) Determine :Zero -position intensities ,wilh a 1.h ree-pqirt parabolic. Jr interpolation anc:J store values in zero_,;ai[i] . ' ' ' , (~) Fit zero_val[~ using selected j nterpolatiol) method and •''ijeperate background[1][1]. / \ ' . • ;(4) Refo.rmat background[1][1] to raw _data preparation ('None"). calc~corrected_exper() . Wrap Up Background Correction Of Experimental Data:. ·(1) Reformat corr_raw{i] back to raw data preparation ( "None' ) . (2) Generate corr_raw[I] = raw_s[i] (corr_raw[I] - background[/][11) / fifj[/]. (3) Establish the scaling factor and rescale corr_raw[i] to match theory. (4) Interpolate corr_raw[i] from pixels to s. Leaves data in ms_data[i][o].' (5) Boxcar smooth ms_data[i][o] with width n_pts_smo. • (6) Transfer ms_data[l][o] lo ms_data[1][1]. calc_corrected_theory() Figure D-4: PROC5 flowchart (2 of 3) for experimental and theoretical ultrafast gas phase electron diffraction data analysis. the scaling peak is also identified by starting from zero Z;, chosen by the user (D.4.4.1), and stopping at the first local maximum or minimum following this zero. The value of corr_raw[i] at this peak is recorded. With the list of theoretical zero positions, PROCS is ready to correct for the experimental background (Figure D-4). PROCS calls calc_corrected_exper() (located in PROCS.C), which transfers raw_data[i] into corr_raw[i], rescales the Appendix D: Software Developed for Ultrafast GED {PROCS) 590 data with s/ltallthl, and applies a boxcar smooth of width n__pts_fit . The user has the option of generating a new background curve from this set of data or applying an old background curve loaded from disk. When generating a new curve, the user must decide whether to fit the original raw data (!\pix)) or raw data that has been prepared by multiplying with either 1/l!a 11th I or s/lta 11th I (D.4.4.10). Tests indicated that preparation with s/lta11th I led to better fits (7.2.2). PROC5 reformats corr_raw[i] to the desired preparation mode and then calls the subroutine background_£ it(), located in PRC5_FIT.C. This subroutine determines which zeros are spanned by the raw data and then finds the experimental intensities at these zero positions using a three-point parabolic interpolation. The intensities are stored in the array zero_vall/]. A curve is fit to these data points using one of several possible techniques, summarized briefly in D.4.4.11 and 7.2.2. This curve is the experimental background; it is rescaled to the original raw data format (JB(pix)) and stored in the array background[i][l]. Once a background curve has been loaded from disk or generated first-hand, the subroutine calc_corrected_exper() makes the background correction: ·] corr raw [z - - background[i][l]J = raw- s [·]z (corr_raw[i] fifj [] i (D.26) leaving the raw data in sME(pix) format. The experimental amplitude is rescaled, either by matching intensities at the scaling peak (found earlier in calc_zeros()) or by multiplication with a fixed scaling value which the user enters (D.4.4.2, D.4.4.3). Then the data is interpolated to regular intervals of A- 1, boxcar-smoothed with width Appendix D: Software Developed for Ultrafast GED (PROCS) 591 n_pts_smo (D.4.4.6), and stored in the array ms_data[i][l] . As shown in the flowchart (Figure D-5), the final step when generating theoretical and experimental sM(s) curves is to call the subroutine calc_corrected_theory() in PROC5.C. The background correction technique of earlier versions of PROC5 took a different strategy - a background curve was generated for the theoretical data as well. (This is the reason ms_theo[i] exists and background[i][j] has two dimensions.) PROC5 will still do this if the user wishes to test a new background fitting algorithm, but if the algorithm is good then the theoretical data should be unaffected by the whole process. Usually the theoretical data is left as is. The functions. subroutine calc_corrected_theory() performs two additional First of all, the experimental data does not extend to 0.0 k 1; there is a minimum position Smin where the scattering data is obscured by the detector beam stop. To prevent the baseline from wandering in the radial distribution curve, PROC5 appends the low end of the experimental data with theoretical data. PROC5 covers out to the first data point after the first zero position beyond 0.0 k 1, or a position selected by the user (D.4.9). The second additional operation calc_corrected_theory() performs is to transfer the theoretical data from ms_theo[i] into ms_data[i][O]. The calculation is now complete, so PROC5 plots a graph of the theoretical and experimental sM(s) curves, and their difference. Two numerical estimates for the relative discrepancy between experiment and theory are displayed below the right lower corner of the graph. The "RMS" value is simply the point-by-point sum of the square of the differences between the two curves. The "RMSw" value is a weighted SSD, where the weighting term decreases like s2: Appendix D: Software Developed for Ultrafast GED {PROC5) 592 c'~ fb~'3:orrec e _ heo:ry,() App en Th .~ory t>ver Be'ginning Of Experiment. V-N EsfabHsh 'St posilion,:for ~ppending t~eory over exp (2) Append m~~theo[1Jont6 ms_data[1][1]. , :, .(3 )'z-!f requested'. fit'a background cur ve for " • (4), Transfer ms_theo[i] onto m 'e' , ', P - ,,Wi ·,.·. .z_v·; -·'" 0 1 ' b 'i;p1ay'M;ciified M~lecular Scatteri~'g Curves (ms_data['1[/1), . Differen'Ce Curve, And SSD Between ExperimentAnd Theory. , transform() Generate Radial Distri.bution Curves From ms_data[i][JL Fills rd_data[i][JJ. o·isplay Radial Distribution Curves (rd_data[l][/J) , • Differehce Curve, And SSD Between Experiment And Theory. Figure D-5: PROCS flowchart (3 of 3) for experimental and theoretical ultrafast gas phase electron diffraction data analysis. a a = 165.8976 b = 3.888888 (D.27) The constant bis derived from the 104 falloff in scattering intensity between 0.0 and 35.0 A- 1 [Sch76] . The origin of the value of scaling factor a has been forgotten. The user may wish to generate radial distribution functions from this scattering data (Figure D-5). Selecting the ''T" command (D.4.11) starts the transformation. The accepted equation for the transformation is [Har8 8b]: 5 max f(r) JsM(s)sin(sr)exp(-kds2)ds (D.28) o.oA'' where the damping constant kd is included because the experimental data does not extend to infinites. PROC5 approximates this integral with a summation of rectangles: Appendix D: Software Developed for Ultrafast GED (PROC5) 593 MS_end rd_data[i][n] = L (ms_data[j][n]-MS_step)sin(s/1)exp(-kdsJ) (D.29) j=I where: and: j • MS_step sj = r; = i •RDC_step + RDC_start = MS_end· MS_step smax (D.30) (D.31) (D.32) This calculation occurs in the subroutine transform() located in PROC5_DT.C. Note that the default value for MS_end is set by the number of raw experimental data points, but the user can reduce MS_end with the "R" keystroke command (D.4.10). PROC5 plots the f(r) curves and their difference, and the unweighted SSD is displayed below the right lower comer of the graph. D.4.2 PROCS Input Data Files PROC5 reads data from six different types of input files. Three of these file types (DFLT_SET.DAT, ELEMENTS .DAT, and the atomic scattering factor data files) contain default and reference parameters, and are loaded upon start up. A molecular structure data file (.MLS) must be selected before PROC5 can generate theoretical diffraction curves. The remaining two file types contain experimental data - the raw scattering intensity curves generated with RADAR2, and the background intensity curves created with PROC5. The format of each of these input files is discussed below: D.4.2.1 The DFLT_SET.DAT File In an effort to make PROC5 both flexible and portable, most default data parameters are stored externally in a two-column, tab-separated text file called DFLT_SET.DAT. This allows the user to change the default parameters without editing Appendix D: Software Developed for Ultrafast GED (PROC5) File_containing_element_list f_scattering_factor_data_file n_scattering_factor_data_file Raw_scattering_data_file_drive Raw_scattering_data_file_path Raw_scattering_data_file_extension Output_data_file_extension Background_data_file_extension Molecular_data_file_drive Molecular_data_file_path Molecular_data_file_extension Electron_kinetic_energy_{keV) Camera_length_{mm) Pixel_width_at_scintillator_{mm) Electron_beam_FWHM_(pixels) Nwnber_data_points_in_boxcar_smooth Nwnber_data_points_for_fitting_background RD_Curve_starting_position_(A) RD_Curve_ending_position_(A) RD_Curve_step_size_(A) RD_Curve_damping_constant Background_element_l_nwnber Background element 2 nwnber 594 E:\CHUCK\PROCS\ELEMENTS.DAT E:\CHUCK\PROCS\FUL2_Fl9.DAT E:\CHUCK\PROCS\FUL2_Nl9.DAT E: \CHUCK\CCD2\ .XL0 .XL0 .BGD E: \CHUCK\PROC4\ .MLS 18.8 100.1 0.0768 5 1 1 0 5 0.02 0.00 4 11 Table D-16: Example of a default parameter data file (DFLT_SET.DAT) loaded during the initialization of PROC5. PROC5.C and rebuilding the executable file. An example of a current DFLT_SET.DAT file is shown in Table D-16. The first column contains descriptive headers for the user's benefit; PROC5 ignores them. These headers cannot contain blank spaces and have a maximum length of seventy-nine characters. The second column contains the actual data which PROC5 reads. The first eleven items m DFLT_SET.DAT are default filename and directory parameters for input and output data files. The starting three give the complete location of the ELEMENTS.DAT and scattering factor data files. The remaining eight are drive, path, or file extensions for the raw scattering data files, background data files, molecular structure data files, and output data files. The raw data and output file parameters can also be altered within PROC5. The eleven file parameters are followed by twelve calculation parameters. Of these Appendix D: Software Developed for Ultrafast GED (PROC5) 595 twelve, all can be reset while running PROC5 except for the electron kinetic energy, KE, and the pixel width at the scintillator, Wp;x, PROC5 derives the electron de Broglie wavelength from the accelerating potential V (KE= eV) according to Eq. A.13. The parameter Wp;x is used in the conversion from pixels to k' (Eq. D.14). The last two calculation parameters, the background element numbers, indicate the default elements a and b which PROC5 will use in the modified molecular scattering function rescaling factor llallfbl . The number refers to the element list in the file ELEMENTS.DAT, where O is the first element. According to the element list in Table D-17, the background elements selected in Table D-16 are fluorine and iodine. Unfortunately, the default path for DFLT_SET.DAT itself must be hard-coded within PROC5.C. This path is defined in the array def_f ile[i] in the subroutine act_init(). If PROC5 does not find DFLT_SET.DAT under this path, however, the program will also look in the current directory, which is the most likely directory where PROC5.EXE is located. As long as the executable file and default data file are kept together, PROC5 does not need to be rebuilt when it is moved to another computer system or placed in a different directory. D.4.2.2 The ELEMENTS.DAT File This short data file lists the elements according to the order in which they appear in the atomic scattering factor data files. The maximum number of elements PROC5 will consider is set by the static integer MAX_ELEMENTS in the include file SETTING5.H. MAX_ELEMENTS defines the sizes of several small arrays and one large array (the scattering factor buffer chunk[i][j]), so MAX_ELEMENTS may be limited by the amount Appendix D: Software Developed for Ultrafast GED (PROC5) of available conventional memory. 596 ELEMENTS.DAT Format To make r.- - - - - - - , -- - - -r- - - - - , MAX_ELEMENTS even larger, the second dimension I [Number of I I Elements] I I I I I r--------,-----,-----1 of chunk[i]U] (defined by the MAX_CHUNK) can be reduced. static integer If MAX_ELEMENTS I 1 [Element Name 1] I : r-------,-----,-----, off the screen at certain points in the program. To avoid this, the display' s spacing between names can be reduced by editing the routines atom_disp() and atom_disp2() in the file PROCS_DT.C. The format of ELEMENTS .DAT is shown in Table D-17. The file is tab-separated and starts with the number of elements in the scattering factor data files. I : ~ [Element ~[Atomic I I : I f [PROCS : Name N] - I Symbol] I Symbol] I is set greater than seventeen, then the display of element names and abbreviations will begin running I [Atomic I [PROCS I 1Symbol] 1Symbol] 1 Sample File fi2 ' r I !-=Hydrogen-+--ii--+- - -H--I !-=carbon- - -+- -c- -+- - -c- -I ~Ni trogen-+--ii--+---N--1 !-=Oxygen- - -+- -0- -+- - - 0- -I ~Fluorine-+- -F- -+- - -F- -I i-:Sul:fu-r---+--s--+---s--1 !-=Chlorine-+- -Cl--+- - -L- -I firgon- - - -+-Ar--+- - -A- -I i-=Manganese+-Mii--+---li--1 f=rron- - - -+--Fe--+- - -R- -1 f-=Bromine--+--Br--+---B--1 f-:--. ----+-----+------! L.!Odine ___ _L _ _ I __ L _ I __ , Table D-17: (Top) Format of the ELEMENTS.DAT data file which PROC5 loads upon initialization. (Bottom) Example of a twelveatom ELEMENTS.DAT file. Each subsequent line corresponds to one element and contains the element name, atomic symbol, and a single-character abbreviation. These abbreviations are used in the molecular structure data files and for the selection of background elements while running PROC5. D.4.2.3 The Scattering Factor Data Files PROC5 requires atomic elastic scattering factors in order to calculate gas-phase diffraction patterns. As indicated in Table D-16, the scattering factors are stored on disk in two files, one for the amplitudes !fa(s)I and one for the phases T\a(s). Both files have identical, tab-separated formats. The first line of each is a header which PROC5 ignores Appendix D: Software Developed for Ultrafast GED (PROCS) 597 completely; the header can have blank spaces and any length. The second and subsequent lines form an array of scattering factors where the columns are different elements and the rows correspond to 0.01 k 1 steps of s, starting from 0.00 k 1• The column order must correspond to the element order in ELEMENTS.DAT; PROC5 has no way of confirming whether or not the user has prepared these files correctly. Creation of the scattering factor data files is discussed in Appendix C. At present, PROC5 loads 18 k 1 worth of scattering factor data into extended memory. This amount is set by the static integer MAX_PTS in the include file SETTING5.H. MAX_PTS is the number of scattering factor data lines PROC5 will read in, so for s going from 0.00 to 18.00 k 1 in 0.01 k 1 steps, MAX_PTS = 1801. There is plenty of extended memory available for scattering factors, and MAX_PTS can easily be increased if the CCD images extend to larger s. However, two other changes must be made in order to analyze diffraction curves out to larger s. First, a new limit must be set on the calculation of s in the subroutine calc_s() of PROC5_DT.C by editing the following lines: if (raw_s[c] > 15.0) { raw_max_num_pts = ++c; break; } As shown above, the present limit is 15 k 1. Second, the span of the arrays ms_theo[i] and ms_data[i]U] must be greater than the new limit. The span is determined by multiplying the static integer MAX_THEO_DATA (set in SETTING5.H) with the step size MS_step (set in main() of PROC5.C). In the current version, MAX_THEO_DATA = 401 and MS_step = 0.04 k 1, so the span is 16 k 1. If MS_step is changed it may be necessary to edit the graphing routine act_axes() in PROC5_DT.C so that the Appendix D: Software Developed for Ultrafast GED (PROC5) 598 Molecular Structure Data File Format r-----------------,----------r-----------,-----------1 [Number of Molecules] 1 1 I 1I [Name of Molecule 1] I I S i[Numher of Internuclear; [Molecular tI Separations Nzsl I Formula] 1 1 I I 1 I I I I i i 1 1 1 : ~-----------------+----------}-----------h-----------1 [Atom Pair 1] [Number of [Internuclear [Mean Amplitude 1 I Atom 1 l Pair 1] 1 1 Separation] I : 1 1 of Vibration] 1 1 MIr--------.--------,---I I I I .-----r-----. -----,-----. -----1 01 : I : I : I I,r-----------------,----------r-----------r,-----------1 [Atom [Number of 1 [Internuclear 1 [Mean Amplitude 1 1 1 Pair Nzsl e, 2 : [Name of Molecule 2 l I Atom Pair Nzsl I Separation] 1 of Vibration] 1 I I I I 1 1 1 ! I 1 1 n 1r------------------,-----------,-----------,-----------1 [Number of Internuclear 1 [Molecular 1 1 1 I dI Separations Nzsl I Formula] I I I I r------------------,-----------,-----------,-----------1 : I : I : I : I : I Table D-18: Format of the molecular structure data files (.MLS) read by PROCS. horizontal axis tick marks and labels of the sM(s) graphs are correct. D.4.2.4 The Molecular Structure Data Files In order to calculate theoretical sM(s) curves, PROC5 must have access to molecular structure parameters: the molecular formula, number, types and distances of internuclear separations, and mean amplitudes of vibrations. PROC5 loads these parameters from .MLS files, which the user must create in advance. Molecular structure data files are tab-separated text files (the format is shown in Table D-18). The first entry, the number of molecule structures which the .MLS file contains, is stored in the integer variable nwn_found. The maximum number of molecules contained in one .MLS file is limited to ten, and this value is hard-coded into the dimensions of several different arrays (see Table D-19). In retrospect, the limit on nwn_found should have been a static integer defined in the include file SETTING5.H. Each block of structural data starts with the name of the molecule. The name has Appendix D: Software Developed for Ultrafast GED (PROCS) Variable Name Type mun_found Integer 599 Data Stored Number of molecular structures defined in current .MLS file . ....................................................... ......................... ············································································································································· mol_count[ME][lO] Integer Molecular formula array. Identifies the number of atoms of ........................................................................................... each.element.comprising .each..molecular.structure ............ nwn_bonds[lO] Integer Number of different internuclear separations for each structure. ······················••···••••••••••••••••••••••••••••••••••••••••••••••••••••• ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••··························· bonds[O][MB][lO] Element identification number for the first atom in an internuclear separation. bonds[l][MB][lo] Integer Element identification number for the second atom in an internuclear separation. bonds[2][MB][10] Number of these internuclear separations in the structure. ·b~~a:~i~~g.th[MB]TioT ········Reai····· .. ····6fstari·ce..0Teach·i·nte·r·n·uciear·se·p·a·ra:i"fo·;;.. 1i1 A. ••••••••••••••••••••••••••••••• mnamvib[MB][lo] Real Mean amplitude of vibration of each internuclear ....................................................... .................................... separation .in. A.............................................................................................. . fract[lo] Real Fractional contribution (weighting factor) of each molecular ...........................................................................................structure .to .the. total .mixture •...r...fract[1] .=..1.0 •..................... molist[l0][4o] Character Name of each molecule in current .MLS file. Table D-19: Name, type, and purpose of PROC5 variables containing molecular structure data. All variables are for the currently loaded .MLS file only. Element identification numbers are in reference to the order in ELEMENTS.DAT, where O is the first element. ME: static integer MAX_ELEMENTS (current value of 12); MB: static integer MAX_BONDS (set to 40). a maximum length of thirty-nine characters, and all blank spaces in the name must be replaced with the underscore, "_". The next line contains the number of different internuclear separations in the molecule, N1s, and the molecular formula. The maximum number of internuclear separations (currently 40) is set by the static integer MAX_BONDS in the include file SETTING5.H, but PROC5 does not check to see if the values in the .MLS file are over this limit. The molecular formula is a continuous text string of letternumber pairs, where each letter is the single-character abbreviation for an element as defined in ELEMENTS.DAT (see D.4.2.2), and the following number is the number of atoms of that element in the molecule. See the sample molecular structure data file in Table D-20 for an example of how trifluoromethyl iodide's molecular formula (CF3I) is represented. Appendix D: Software Developed for Ultrafast GED (PROC5) There is one line of data per internuclear separation. 600 Sample Molecular Structure Data File r 5 -r ,- T 7 ~----------------+----+----+----~ Trifluoromethyl Iodide ~----------------=+-:----+ ---+-- --~ 4 C1F3Il r----------------+----+----+.----:1 CF 3 1.344 0.0583 r----------------+----+----+.----:1 CI 1 2.101 0.0789 r----------------+----+----+.----:1 FF 3 2.169 0.0678 two-character text string which r----------------+----+----+.----:1 FI 3 2 . 8 7 6 0 . 0 8 21 The first entry in each line is a ~-- - - - - - - - - - - -. - -+-- - -+-- - -+-- - -'.-j defines the atoms of the Carbon Tetrachloride ~----------------+----+----+----~ 2 C1L4 r--------. -------+- .--+--. -+- .--~ I separation using the singlecharacter abbreviations. : I : I : I : I Table D-20: Example of an .MLS data file which shows how the molecule CF3I is represented. elemental The remaining entries are the number of these type of internuclear separations within the molecule, the distance of the separation in A, and the mean amplitude of vibration in A. Both the distance and the mean amplitude are real numbers. Note that PROC5 does not conduct any error checks while loading a structural data file, and the program can crash if the .MLS file has not been written properly or incorrect single-character abbreviations are used. D.4.2.5 The Raw Experimental Data File Raw experimental scattering intensity curves, /£(pix), are the output of the program RADAR2, and the format of these CSV files is discussed in D.3.2.12. To briefly reiterate, the first line of text contains reference information on the file's creation and is completely ignored by PROC5. The reference information can have any length and can contain blank spaces. The remaining lines contain the data: a pixel distance (integer) followed by the mean radial intensity at that pixel distance (real). Actually PROC5 only reads the pixel distance from the first line of data; PROC5 assumes that the pixel distance increases by one in each subsequent line. The raw experimental data file is read until there Appendix D: Software Developed for Ultrafast GED (PROCS) 601 are no more input lines. PROC5 has no way of checking whether the selected file is truly a raw experimental data file, and the program will probably crash if the user mistakenly chooses some foreign file which happens to have the default path and extension. D.4.2.6 The Experimental Background Data File PROC5 both creates and reads experimental background data files (.BGD). These files have CSV format and begin with a text string (maximum of seventy-nine characters, blanks allowed). The text string identifies the raw experimental data file from which the background has been derived. Background intensities are listed as a function of pixel position starting from 0, even though the experimental data typically starts at around 15 pixels. Each line of data contains three real numbers: the value of s at that pixel distance, the background intensity / 8 (pix) in ADU, and the modified molecular scattering function rescaling factor lfa IIJb I- When PROC5 loads a .BGD c - Change Calculation Parameters elements a and b as when N - Select New Raw Data Set M - Select New Molecule S - Scale Experimental Data Relative To Theory A - Append Theoretical Data over Experimental R - Select Range For Sine Transform T - Transform Molecular Scattering Curve B - Get Best Fit To Mixture Composition L - Get Best Fit To Camera Length D - Do MS Calculation On All Molecules F - Save Data To File P - Change Path / - Switch Between MS And RD Screens H - Restrict Horizontal Viewing Range V - Restrict Vertical Viewing Range E - Enlarge To Full Screen ? - Activate Help Screen Q - Quit the Table D-21: PROC5 help screen listing all command keys available in both the MS and RD screens. file, the program reads only the background intensities; PROC5 assumes that the user has chosen the same camera length, electron kinetic energy, and rescaling background intensity was originally derived. The Appendix D: Software Developed for Ultrafast GED (PROC5) 602 program ADDER, however, needs all three columns of data in order to generate twodimensional sM(pix) curves from raw scattering images (D.5.4). D.4.3 "?"- Activate Help Screen This command is available under both the MS and RD screens. The "?" keystroke pulls up a help screen listing all command keys and a brief description of what each key does. The most recent help screen is shown in Table D-21. The help screen is deactivated by pressing "Enter." D.4.4 "C" - Change Calculation Parameters (Molecular Scattering Screen) This menu appears at the very start of PROC5, and also whenever the "C" keystroke is entered under the MS screen. All parameters related to the calculation of modified molecular scattering curves are specified in this menu. There are currently thirteen parameters: D.4.4.1 Nwnber Of Zeros Before Scaling The user identifies an sMT(s) zero with integer Z; to indicate the s position PROC5 should start from when looking for a scaling peak. The zero located at 0.0 A- 1 is considered number zero. PROC5 identifies the scaling peak as the first local maximum or minimum the program finds in the theoretical data following Z;. The variable name for Z; is scale_zero. D.4.4.2 Experiment/Theory Scaling Value This real number (the variable calc_theo_scale) is the scaling factor gE between the theoretical and experimental sM(s) curves. The experimental data is divided Appendix D: Software Developed for Ultrafast GED (PROC5) by gE. 603 Normally PROC5 automatically determines this value within the subroutine calc_corrected_theory() (see D.4.1), but the user can fix gE if desired (D.4.4.3). The scaling value is also displayed in the message bar of the MS graph screen. D.4.4.3 Fix Experiment/Theory Scaling Value? This Yes/No toggle (the variable f ix_scaling) tells PROC5 whether or not to fix the scaling value between theoretical and experimental sM(s) curves. If the setting is "N", then PROC5 determines the scaling value at the first peak following the zero z;. If the setting is "Y", then PROC5 bypasses this calculation and uses the scaling value entered by the user. Generally, the scaling value is only fixed if the user is comparing scattering curves from different time points in a set of time-resolved diffraction data. D.4.4.4 Camera Length The user enters a real number in millimeter units for the camera length L. PROC5 must recalculate the conversion from pixels to A- 1 any time L is changed. PROC5 stores L in the variable cam_dist. D.4.4.5 Nwnber Points To Fit Background The function of the PROC5 integer variable n_pts_f it has evolved and is now perhaps inappropriately named. This integer is the pixel width of the boxcar smooth PROC5 applies to the experimental data (and theoretical data) before determining the background intensities at the zero positions. PROC5 always calculates the intensities with a three-point parabolic interpolation, but if the data is particularly noisy, then the background fit may be better after a little pre-smoothing. When there is minimal noise, Appendix D: Software Developed for Ultrafast GED (PROC5) 604 though, n_pts_fit should be one. D.4.4.6 Nwnber Points In Smooth The integer variable n_pts_smo is the width of the boxcar smooth (in units of MS_step) which PROC5 applies to the interpolated sM(s) data stored in ms_data[i]U]. This smooth only affects the sM(s) curves cosmetically and is usually left at one. If n_pts_smo · is greater than one then the radial distribution curves will be slightly damped, with the amount of damping increasing with r. D.4.4.7 Width Of Electron Beam The user enters an integer value for Web, the FWHM of the unscattered electron beam. The units on this integer are CCD pixels and the variable name is n_beam_sz. D.4.4.8 Data File Directory This menu item is identical to the "P" keystroke command for changing the default input and output paths and extensions- see D.4.16 below. D.4.4.9 Se1ected Data Set This menu item allows the user to select a raw experimental data set located under the default path and extension. The data is automatically loaded once a filename has been selected. This menu item is identical to the "N" keystroke command (D.4.6) except program control returns to the MS "Change Calculation Parameters" menu. Appendix D: Software Developed for Ultrafast GED (PROCS) 605 D.4.4.10 Data Preparation The user chooses the format of the raw experimental data when PROC5 fits the background curve. The options are: 1. "None" - The background curve is fit to IE (pix). 2. "1 /fifj" - The background curve is fit to IE (pix )/Ila Iii,, I3. "s/fifj" - The background curve is fit to sIE (pix)/l!all!bl. Tests indicate that the best fits are achieved with the third format (7.2.2). The preparation format is indexed by the variable prep_mode. D.4.4.11 Background Correction The user can remove the background from raw experimental data with either a previously saved background curve or one of seven fitting algorithms. All fitting subroutines are located in PRC5_FIT.C, and new algorithms are easily added. This section briefly summarizes the different techniques, but a more complete analysis appears in 7.2.2. The basic problem is to fit a curve through the zero points, the intensity of the raw experimental data at the zero positions in sMT(s). The method of background correction is indexed by the variable back_mode. D.4.4.11.1 Load Background Data File This menu item is chosen if the user wishes to correct raw experimental data with a background curve which has already been created. PROC5 presents a list of the background files (described in D.4.2.6) located under the default directory and path with the extension set in DFLT_SET.DAT. The directory and path can be changed using the Appendix D: Software Developed for Ultrafast GED (PROC5) 606 menu item "Data File Directory" (D.4.4.8). After a background file is selected, the data preparation mode is automatically set to ''None" (D.4.4.10). The user is expected to choose from only those background files which were generated from data taken under identical experimental conditions (e.g., Ae, L) as the current set of raw data. A warning is displayed if the range of the loaded background file is less than the range of the current raw data set, but PROC5 will continue to run (smax will be reduced to the background file range). D.4.4.11.2 Exp(A + BsAC) Spline (D'Antonio) This method, taken from [DAn71], fits every segment of three zero points to the function exp(a 1 + a 2·s/\a3). Overlapping segments are merged with linear weighting to generate a background curve with no discontinuities in the slope. D' Antonio's method requires that the slope between successive zero points become increasingly less negative but never zero, so the technique usually only succeeds when the data preparation mode is set to ''None" (D.4.4.10). Even with this constraint, the method still occasionally leads to Out-Of-Range floating point errors which crash the program. D.4.4.11.3 4-pt Cubic Spline (4-pt Spline) This method fits every segment of four zero points to a cubic polynomial. Overlapping segments are merged with linear weighting to generate a background curve with no discontinuities in the slope. D.4.4.11.4 Smoothed 3-pt Cubic Spline ( Smooth 3-pt) This method fits every segment of three zero points to a cubic polynomial Appendix D: Software Developed for Ultrafast GED (PROCS) 607 optimized for smoothness (see [Shi71]). "Smoothness" is defined as minimization of the sum: (D.33) which means that the SSD between successive data points in the background curve is as small as possible. Overlapping segments are merged with linear weighting to generate a background curve with no discontinuities in the slope. D.4.4.11.5 Weighted Slope Fit ( Option 6) This method fits every segment of two zero points to a cubic polynomial. A target slope is determined for every middle zero point by calculating a weighted average of the slopes from the zero point to its surrounding neighbors. The target slopes of terminal zero points are set as the slope between each zero point and its nearest neighbor. Each segment is fit to the pair of zero points and their target slopes. D.4.4.11.6 Piggyback Smooth Slope Fit (Option 7) This method fits every segment of two zero points to a cubic polynomial optimized for smoothness (Eq. D.33). The slope at the second zero point must match the initial slope of the next segment, so the background curve is built up by working backwards. If the data preparation format is ''None" then the last segment is assumed to have a slope of zero at the last zero point. For other formats, the last segment is simply the line connecting the last two zero points. D.4.4.11.7 Weighted Smooth Slope Fit (Option 8) This method duplicates "Option 6" (D.4.4.11.5) except that each two-point Appendix D: Software Developed for Ultrafast GED (PROCS) segment is fit to a quartic polynomial. 608 The additional coefficient 1s determined by optimizing each segment for smoothness (Eq. D.33). D.4.4.11.8 Weighted Slope Fit #2 {Option 9) This method duplicates "Option 6" (D.4.4.11.5) except that the first and last segments are fit to a quadratic equation, which eliminates the need to estimate a target slope for the first and last zero points. As discussed in 7.2.2, "Option 9" has proven to be the most reliable fitting algorithm derived so far. D.4.4.12 Fit Theory With Background Curve Too? This Yes/No toggle (the variable fit_theory) tells PROC5 whether a background curve should be derived for the theoretical data just like the experimental data. As discussed in D.4.1, this toggle setting is almost always ''N" because the theoretical data should be unperturbed if the fitting algorithm is designed properly. D.4.4.13 Select Molecule With this menu item the user can select a molecular structure file and a molecule listed in that file. The modified molecular scattering rescaling elements can also be changed. This menu item is identical to the "M" keystroke command (D.4. 7) except program control returns to the MS "Change Calculation Parameters" menu. D.4.4.14 Calculate Molecular Scattering Curves This menu item calculates both the theoretical and experimental modified molecular scattering curves as described in D.4.1. Program control returns to the MS screen once the calculation is complete. Appendix D: Software Developed for Ultrafast GED (PROC5) D.4.5 "c" - 609 Change Calculation Parameters (Radial Distribution Screen) This menu appears when the "C" keystroke is entered under the RD screen. All parameters related to the transformation of molecular scattering data into radial distribution curves are set in this menu. There are currently seven parameters: D.4.5.1 Damping Constant The user enters a real number (the variable damp_k) for the damping constant kd (see Eq. D.28). With molecular scattering ranges of -13 A- 1, typical values for kd are 0 2 between 0.01 to 0.02 A . D.4.5.2 Scaling Position The user enters a real number to choose a position in A for scaling the experimental radial distribution curve with respect to the theoretical curve. The scaling position is relative to the starting position of the transformation (see D.4.5.4 below) and must be an integer multiple of the step size between radial distribution curve data points. PROC5 will round to the nearest data point position if the user does not enter an integer multiple. This option is available for qualitative comparisons of RD curves; in general the scaling position should be set to 0.0 A so that the curves are not scaled. This menu item performs the same function as the "S" keystroke command (D.4.8). D.4.5.3 Current Directory This menu item is identical to the "P" keystroke command for changing the default input and output paths and extensions - see D.4.16 below. Appendix D: Software Developed for Ultrafast GED (PROCS) 610 D.4.5.4 Starting Position This real number (the variable RDC_start) has units of A and tells PROC5 where to begin calculating the radial distribution transform. Usually this entry is 0.0 A. Unfortunately there is a small bug in the graphing routines, and the horizontal axis tick marks and labels will be incorrect for non-zero starting positions. Vertical illuminated bars (shown, for example, when resizing the graphing region with the "H" command) will display the true position, and the data's abscissa values will be reported correctly in files written to disk. D.4.5.5 Ending Position This real number (the variable RDC_end) has units of A and tells PROC5 where to end the radial distribution function calculation. D.4.5.6 Step Size This real number (the variable RDC_step) has units of A and sets the step size between successive data points in the radial distribution curve. The maximum number of data points is set by the static integer MAX_RD_DATA defined in SETTING5.H, so the user's entry for RDC_step is limited by the equation: RDC_step > RDC_end - RDC_start (D.34) MAX_RD_DATA The current value of MAX RD_DATA is 601. D.4.5.7 Molecular Scattering Range This real number has units of k' and is the upper limit Smax in the radial distribution Appendix D: Software Developed for Ultrafast GED (PROCS) 611 transformation equation (Eq. D.28). If raw experimental data has been loaded, then the value must be within the range of data. This menu item is equivalent to the "R" keystroke command in the MS screen (D.4.10). D.4.5.8 Calculate Radial Distribution Curves This menu item initiates the transformation of both theoretical and experimental scattering data and returns program control to the RD screen. D.4.6 "N'' - Select New Raw Data Set This command is available under both the MS and RD screens. The "N" keystroke brings up a directory listing of all files found using the default path and extension (the default values can be changed with the "P" command - see D.4.16). If a file is selected, PROC5 automatically loads the data, recalculates the modified molecular scattering curves, and returns program control to the MS screen. D.4.7 ''M" - Select New Molecule This command is available under both the MS and RD screens. The "M" keystroke brings up a four-item menu controlling selection of the .MLS file, the molecule or molecular mixture, and the sM(s) rescaling elements. If any menu items are changed then PROC5 will recalculate the molecular scattering curves and return control to the MS screen. D.4.7.1 Molecular Data File Selecting this menu item brings up a directory listing of all molecular structure files located with the path and extension set in DFLT_SET.DAT. PROC5 loads the structural Appendix D: Software Developed for Ultrafast GED {PROCS) 612 data after the user selects a filename. D.4.7.2 Selected Molecule • This menu item displays the names of all molecules found in the current molecular structure file. After the user selects a molecule, PROCS will present a table of the molecule's structural data for reference before returning to the Select New Molecule menu. The user also has the option of choosing ''Molecular Mixture" from the list of molecule names. If this option is selected, weighting factors appear beside the name of each molecule; the user edits these weighting factors to specify the relative population of each molecule within the molecular sample. The option "Clear List" sets all weighting factors to zero. Once the user is satisfied with the weighting distribution, selecting the option "Return" normalizes the weighting factors and displays a list of all selected molecules and their percentage contribution to the mixture. Program control then returns to the Select New Molecule menu. D.4.7.3 Scaling Atom #1 The user selects the first modified molecular scattering curve rescaling element by entering the single-character element abbreviation. These abbreviations are listed on the left side of the screen. D.4.7.4 Scaling Atom #2 The user selects the second modified molecular scattering curve rescaling element with this menu item. Appendix D: Software Developed for Ultrafast GED (PROCS) 613 D.4.8 "S" - Scale Experimental Data Relative To Theory This command is available under both the MS and RD screens once raw experimental data has been loaded. The "S" keystroke rescales experimental data to match the theoretical data at a position specified by the user. For the molecular scattering curves, the interpolated data stored in ms_data[i]U] (see Table D-15) will be temporarily rescaled. This affects the radial distribution transformation and the data saved to disk, but the scaling factor in the message bar will not change because it is the scaling factor calculated during the background fitting procedure. The temporary rescaling position is lost once the molecular scattering curves are recalculated. For the radial distribution curves, the experimental data in rd_data[i]U] is rescaled at the userspecified scaling position. This scaling position is remembered the next time data is transformed; the true experimental RD amplitude can only be recovered by setting the scaling position to 0.0 A in the RD "Change Calculation Parameters" menu (D.4.5). Once "S" is pressed, a vertical illuminated bar appears somewhere in the graphing region. The user Shrrt 71Down/Left By 100 Divisions ,,<,'c'., ' ~ Shrrt Down/Left By10 Divisions can move this bar horizontally with the numeric keypad (see assignments shown in Figure D-6). In the MS screen, the smallest movement division is the plotting step size MS_step (currently 0.04 A- 1; see D.4.2.3). In the RD screen, the smallest division is set by the user in either DFLT_SET.DAT (see D.4.2.1) or under ./ S ' ' Shrrt iDown/Left By1 Division ' ,, □ □ □ Shift ®Up/Right By100 Divisions , ~;;:;. ' ,·'"<'~ Shift ®Up/Right ' By 10 Divisions ' ' ;: Shift ~ Up/Right ' By1 Division ' Figure 0-6: Numeric keypad functions when shifting illuminated bars in PROCS. Appendix D: Software Developed for Ultrafast GED (PROCS) 614 the "C" command menu options (D.4.5). PROC5 automatically rescales the experimental curve as the user repositions the illuminated bar. Pressing "Enter" fixes the bar's position. Selecting a plot coordinate with the numeric keypad and an illuminated bar is a common operation in PROC5. D.4.9 "A" - Append Theoretical Data Over Experimental This command is available only under the MS screen once raw experimental data has been loaded. The "A" keystroke identifies the current appending position for sME(s) with a vertical illuminated bar; theoretical data has been superimposed on the experimental curve for all points to the left of the illuminated bar. The default appending position is the first data point following the first zero, not counting the zero at 0.0 A- 1. This position can be reassigned by shifting the illuminated bar (using the numeric keypad assignment shown in Figure D-6) and pressing "Enter" once the bar is at the desired point. The appending position is now fixed until "A" is pressed again, regardless of whether the user loads a new raw data set or selects a new molecule. To return the append feature back to the default "first zero" mode, the illuminated bar must be moved to 0.0 A-'. D.4.10 "R" -Select Range For Sine Transform This command is available only under the MS screen. The "R" keystroke sets Smax for the radial distribution transformation. A vertical illuminated bar appears at the right edge of the graph; this bar can be moved left and right using the numeric keypad assignment shown in Figure D-6. Once the illuminated bar is placed at the desired position, the user presses "Enter" and a grey, cross-hatched pattern will cover the plotting region from the bar's position to the right edge to indicate the cutoff region. The Smax Appendix D: Software Developed for Ultrafast GED (PROCS) 615 position can also be set within the RD "Change Calculation Parameters" menu (D.4.5.7) . D.4.11 "T" - Transform Molecular Scattering Curve This command is available only under the MS screen. The ''T" keystroke initiates the transformation of displayed sM(s) data into radial distribution curves as described in D.4.1. Program control is left in the RD screen, but the user can quickly swap between RD and MS screens with the "f' keystroke command (D.4.17). D.4.12 "B" - Get Best Fit To Mixture Composition This command is available under both the MS and RD screens once raw experimental data has been loaded. PROC5 will systematically vary the composition of a molecular mixture and identify the best fit by looking for a local minimum in the SSD between experiment and theory. The structural model must be a molecular mixture in which all components have the same molecular formula (e.g., the iodomethylene photofragment CH2I should be stored in the .MLS file with the formula CH2l 2 to include the lost iodine atom). Originally this constraint was necessary for the background correction method used in PROC4, but it is not really required anymore and the formulachecking loop in main() of PROC5.C can be commented out if desired. The "B" keystroke pulls up a sub-menu of six items which allow the user to set fitting parameters: D.4.12.1 Varied Component This menu item lists all components in the molecular mixture. The user selects one component whose presence in the mixture will be varied with respect to all the rest. The relative proportion of unvaried components will be kept the same. Appendix D: Software Developed for Ultrafast GED (PROCS) 616 D.4.12.2 Initial Percentage The user enters a real number to identify the fitting loop's starting percentage of the varied component in the molecular mixture. This percentage can be zero. D.4.12.3 Final Percentage The user enters a real number to identify the fitting loop's final percentage of the varied component in the molecular mixture. This value can be 100%. D.4.12.4 Number Of Zeros Before Scaling The user enters an integer Z; to indicate which sM\s) zero PROC5 should start from when looking for a scaling peak. This menu item is also found in the MS "Change Calculation Parameters" menu (D.4.4.1). D.4.12.5 RMS Weighting Factor PROC5 judges the quality of a fit for a mixture composition based on the sum of the square of the differences between the theoretical curve and the experimental curve. The user can choose an unweighted SSD ("Constant") or an SSD in which the weighting decreases like s2 (''Weight By s"2"). The latter weighting system is intended to diminish the influence of experimental noise, which increases withs (5.1.2). D.4.12.6 Conduct The Fit Selecting this menu item starts the fitting loop. First the program calculates one sM\s) curve for the varied component and one curve for all the remaining components. These two data sets are stored in theo_raw[i][0] and theo_raw[i][l], respectively. Appendix D: Software Developed for Ultrafast GED (PROCS) 617 A new screen appears tabulating the iteration number, the percentage of the varied component, the RMS value, the number of zero points in the theoretical curve, and the position of the scaling peak in A- 1• The number of zero points are included because the loss (or addition) of zero points as an sM(s) peak dips below (or rises above) the zero line can dramatically affect the fit. This table is filled out after each step of the iteration. First PROC5 calculates the RMS value in steps of 10%. A local minimum is identified and PROC5 narrows down the search to a range of 20% and uses 1% steps. This is repeated over a 2% range with an 0.1 % step size search. Control returns to the MS screen with a display of the best fit for composition. The user has the option of saving the fit iteration history to a CSV text file. D.4.13 "L" - Get Best Fit To Camera Length This command is available under both the MS and RD screens once raw experimental data has been loaded. PROC5 will systematically vary the camera length and search for a local minimum in the SSD between experiment and theory. In principle this optimization should be performed on scattering data from a highly symmetric, wellcharacterized molecule like CCLi. Still, there can be variations of 1 mm or more in the optimum L determined by scattering from different molecules under identical experimental conditions. An alternative method for establishing L is to record scattering patterns from metal foils (7.3). The "L" keystroke pulls up a sub-menu of five items which allow the user to set fitting parameters: Appendix D: Software Developed for Ultrafast GED (PROC5) 618 D.4.13.1 Initial Camera Length The user enters a real number to identify the fitting loop's starting camera length (in millimeters). D.4.13.2 Final Camera Length The user enters a real number to identify the fitting loop's ending camera length (in millimeters). The difference between the starting and ending camera length must not be more than 10.0 mm. D.4.13.3 Number Of Zeros Before Scaling The user enters an integer Z; to indicate which sMT(s) zero PROC5 should start from when looking for a scaling peak. This menu item is also found in the MS "Change Calculation Parameters" menu (D.4.4.1). D.4.13.4 RMS Weighting Factor PROC5 judges the quality of a fit for camera length based on the sum of the square of the differences between the theoretical curve and the experimental curve. The user can choose an unweighted SSD ("Constant") or an SSD in which the weighting decreases like s2 (''weight By s"2"). The latter weighting system is intended to diminish the influence of experimental noise, which increases withs (5.1.2). D.4.13.5 Conduct The Fit Selecting this menu item starts the fitting loop. A new screen appears tabulating the iteration number, the camera length, the RMS value, and the position of the scaling Appendix D: Software Developed for Ultrafast GED (PROC5) peak in A- 1. 619 PROC5 calculates theoretical and experimental sM(s) curves from the starting camera length to the ending camera length in 0.1 mm steps, updating the table as it goes. The sM(s) curves must be recalculated each time because the pixels-to-A-' conversion changes as L changes; as a result the camera length fitting loop usually takes longer than the mixture composition fitting loop. Control returns to the MS screen with a display of the best fit for camera length as identified by the local minimum in the RMS values. The user has the option of saving the fit iteration history to a CSV text file. D.4.14 "D" -Do MS Calculation On All Molecules This command is available only under the MS screen once raw experimental data has been loaded. The "D" keystroke tells PROC5 to calculate theoretical and experimental sM(s) curves for all molecules listed in the current molecular structure data file. The program graphs the data, updates the RMS values, displays the current scaling factor, and waits for the user to press "Enter" before proceeding to the next molecule. After data for all molecules have been shown, PROC5 recalculates the sM(s) curves for the molecule which was displayed before "D" was pressed. This command is particularly useful for finding the best experimental fit when the molecular structure is not well known. Molecular data files containing different structural variations of the same molecule can be created and quickly tested for goodness of the fit. D.4.15 "F" - Save Data To File This command is available under both the MS and RD screens. The "F' keystroke allows the user to save the data displayed in the current screen to disk. Four menu items are available: Appendix D: Software Developed for Ultrafast GED (PROCS) 620 D.4.15.1 Change Filename The user enters a standard DOS eight-character name for the output file. This does not save any data to disk; one of the next two menu items must be chosen as well. D.4.15.2 Save Data This menu item writes the data displayed in the current screen (either MS or RD) to a CSV format text file located under the default path and extension. The output file begins with a header which lists the source of raw experimental data (if any) and the name of the molecule whose structural parameters have been used to generate the theoretical curve. If a mixture were selected, all components and their percent contribution are included. A radial distribution data file lists three more pieces of information: ( 1) the starting position Smin of the experimental molecular scattering data as set by default or with the Append command ("A"; see D.4.9), (2) the ending position Srnax for transforming the molecular scattering data as set by default or with the Range command ("R"; see D.4.10), Sample Modified Molecular Scattering Output File ,-----------,::---------~ f;ource: ------~one Selected I ~olecule -----~ercentage --I ~rans-Stilbene ~5. 000 ___ _ __ 1 ~is-Stilbene --1.;5. 000 ______ 1 1-:-----------~heory -----I 0 0 ~-- ------ --~7.36038 - ------ - --1 0 . 04 ~-------~---------1 0.08 14.3215 ~-----------~---------~ 0.12 20.866 ~-----------~---------~ I : I : I Sample Radial Distribution Output File r---------'---------------------1 i;ource: - - - ~ : \CHUCK\CCD~A0930RD4 .XL0 4 ~olecule: -~iiodomethan~---------4 i;>ata Range:~.16 ------~2.56 _____ 4 1-k Value---~. 015 ------+.:--- .-----4 ~- _______ +fheory____ -~xperiment _ 4 0 0 0 0.02 -0.0646649 -0.0648184 0.04 -0.126528 -0.125218 0.06 -0.182956 -0.177051 ~--------+---------+---------4 ~--------+---------+---------4 ~--------+:---------+---------4 ~--------+---------+---------4 I • I : I : I Table D-22: PROC5 output files. (Left) Example of a modified molecular scattering output file with a molecular mixture and no raw experimental data. (Right) Example of a radial distribution output file with a fit to experimental data. Appendix D: Software Developed for Ultrafast GED (PROC5) 621 and (3) the damping constant kd. Note that the transform always starts from O A-', not Smin• After the header, both the MS and RD output files have a line of column descriptors followed by the data. Molecular scattering data occurs in increments of MS_step (at present 0.04 A- 1) and extend out to the full range of raw experimental data regardless of the current value of Smax• The user sets the step size and range of radial distribution data in the RD "Change Calculation Parameters" menu (D.4.5). Examples of both types of output files are shown in Table D-22. D.4.15.3 Create Background File This menu option creates an experimental background data file as described in D.4.2.6. The output file will be located under the default path and will have the extension loaded in from DFLT_SET.DAT. Sometimes the user may wish to generate an output file containing theoretical scattering intensities as a function of pixel position rather than s (for example, when creating a theoretical 2-D scattering image - see D.5.4.12). This menu item can create such a file if the user edits one line of the subroutine act_save_back() located in PROC5_DT.C: for (s = O; s < back_nwn_pts; s++) { sprintf(path,"%G, %10.lOlG, %10.lOlG\n", raw_s[s], background[s] [1], fifj[s]); /* fifj [s], theo_raw[s] [O]); */ fwrite(path, 1, strlen(path), outs); } In this program, the sprintf() command writes the s coordinate, the experimental background curve, and f if j [ i] to the output file. If the comment brackets are moved up Appendix D: Software Developed for Ultrafast GED (PROC5) 622 one line, then the sprint£() command will instead write the s coordinate, f if j [i], and the raw theoretical curve stored in theo_raw[i][O]. Note that theo_raw[i][O] has been smoothed twice with widths of n_beam_sz and n_pts_fit . D.4.15.4 Change Path This menu item is identical to the "P" keystroke command- see D.4.16 below. D.4.16 "P" - Change Path This command is available under both the MS and RD screens. The "P" keystroke produces a menu which allows the user to change the default path and extensions for both raw scattering intensity input files and PROC5 output files (e.g., molecular scattering and radial distribution data). PROC5 also uses this path to search and save experimental background files, but the extension of these files can only be changed by editing DFLT_SET.DAT. D.4.17 "/"- Switch Between MS And RD Screens This command is available under both the MS and RD screens once the scattering data has been transformed into a radial distribution curve. The "/" keystroke simply toggles between the MS and RD screens. D.4.18 "H" - Restrict Horizontal Viewing Range This command is available under both the MS and RD screens. The "H'' keystroke allows the user to zoom in on some horizontal region of the graph by changing the lefthand and right-hand plotting limits using the numeric keypad (see key assignments in Figure D-6 and a discussion in D.4.8). After "H" is pressed, a vertical illuminated bar Appendix D: Software Developed for Ultrafast GED (PROC5) 623 appears on the left edge of the graph. This bar will be the new left-hand limit, and the user can reposition it with the numeric keypad. Pressing "Enter" fixes the bar's position, and then the process is repeated with the right-hand limit. Pressing "Enter" a second time rescales the graph. D.4.19 '~' - Restrict Vertical Viewing Range This command is available under both the MS and RD screens. The "V" keystroke allows the user to zoom in on some vertical region of the graph by changing the upper and lower plotting limits using the numeric keypad (again, see key assignments in Figure D-6). In both the MS and RD screens, the smallest division is ~ 11270th of the vertical range. This division corresponds approximately to the height of one screen pixel. After "V" is pressed, a horizontal illuminated bar appears on the bottom of the graph. This bar will be the new lower limit, and the user can reposition it with the numeric keypad. Pressing "Enter" fixes the bar's position, and then the process is repeated with the upper limit. Pressing "Enter" a second time rescales the graph. D.4.20 "E" - Enlarge To Full Screen This command is available under both the MS and RD screens. The "E" keystroke removes any horizontal or vertical viewing restrictions on the current screen. The x-axis is rescaled to include the full horizontal range, and the y-axis is rescaled to include the highest maximum and lowest minimum of the theoretical and experimental curves (but not the difference curve). Appendix D: Software Developed for Ultrafast GED (PROCS) D.4.21 "Q" - 624 Quit This command is available under both the MS and RD screens. The "Q" keystroke initiates a small thermonuclear reaction within Intel's Pentium processor, eliminating everything within a one meter radius and poisoning the soil within two meters. Or maybe PROC5 just stops and returns control to DOS. D.5 ADDER Three types of mathematical operations can be performed on CCD images with this program. First, ADDER will conduct pixel-by-pixel addition of images chosen by the user. Input images are either selected from a current directory listing or specified in a batch file. ADDER.EXE Program Files Include Files ADDER.C ADDER_DT.C ADDER_IO.C CEXT.C DATA_ADD.H SETTINGA.H CEXT.H COMPAT.H Table D-22: Program and include files needed to build ADDER.EXE. Before the composite image is saved to disk, the image can be rescaled and corrected for background offset and drift. Second, ADDER will do a pixel-by-pixel division of one image by another, which is useful for flat-field image correction. Third, ADDER allows radial background correction of a sum of CCD images. This operation can create a composite two-dimensional experimental sM(pix) image from a set of raw diffraction images using a background file generated in PROC5. Some of these features (addition, division, offset correction) are available in the SpectraSource software, but ADDER is faster and better suited to handling large numbers of images. In order to retain as many significant figures as possible, ADDER stores each pixel Appendix D: Software Developed for Ultrafast GED (ADDER) of a summed image as a long integer - 625 32 bits (SpectraSource images are 16-bit). One full 1024x1024 image requires 4 Mb of memory, so ADDER requests 5 Mb of extended memory upon startup. The files needed to compile ADDER are listed in Table D-22. Operation of the software is described in the next few sections: D.5.1 ADDER Option One: Sum Or Average CCD Images Selecting this option allows the user to add up to sixteen CCD images (pixel-bypixel) chosen from a current directory listing. The sum can be corrected for background offset and drift (due to accumulation of thermal noise during readout), and can be rescaled by a multiplicative constant. Eight menu items are displayed: D.5.1.1 Change Path This item allows the user to alter the default directory path for CCD images. Changing the image path here also changes the default paths for the second (D.5.2) and fourth (D.5.4) main menu options of ADDER. D.5.1.2 Select CCD Images The user may select up to sixteen images; the same image can be chosen more than once. After selecting N1111 images, the user highlights "[RETURN TO MAIN MENU]" and presses return. The computer then reads all images from disk, adding the 16-bit pixel values to long integers stored in extended memory. A warning message is displayed if an image's x-y dimensions differ from previous images, but the summation continues. If the y-dimension is different, only the last rows of the image will be affected because pixels are stored first by column and then by row. If the x-dimension is different, however, Appendix D: Software Developed for Ultrafast GED (ADDER) 626 mismatch in row length will affect the entire summed image. The SpectraSource software will add images of different dimensions correctly. D.5.1.3 Change Output Filename The user enters a standard DOS eight-character name for the output image. The extension of the input image filenames is appended to the output filename. For a different output filename extension, the Change Path menu item can be selected after the input images are loaded into memory. D.5.1.4 CCD Image Background Offset This unsigned integer corresponds to the average background offset value of the input CCD images at the top of the images (the first row). BTOff is in ADU. D.5.1.5 CCD Image Background Range This unsigned integer is in ADU and corresponds to the average increase in the background offset value at the bottom of the image relative to the top. because thermal noise accumulates linearly during image readout. BR11g is nonzero ADDER treats the background offset correction just like RADAR2 (see D.3.2.3). D.5.1.6 Rescaling Divisor After background offset correction, the summed image is rescaled by dividing the value at each pixel with gs, a real number. The default mathematical operation of this menu is to calculate an average of the input images, so gs is initially set to Nim , Appendix D: Software Developed for Ultrafast GED (ADDER) 627 D.5.1. 7 Replace Final Zeros With Ones When creating a denominator image (such as a flat-field correction), each pixel should have a positive count value to avoid division by zero. This Yes/No toggle changes all O ADU values in the output image to 1 ADU. Note that the image division calculation described in D.5.3 also makes this correction. D.5.1.8 Add CCD Images Once values for BTOff, BRng, and gs are entered, executing this menu item downloads the summed image from memory, recalculates pixel values according to Eq. D.35, and saves the final image under the user-provided filename . The image is in SpectraSource format and has the same header as that read in from the most recently loaded CCD image. Negative count values are set to O (or 1), and count values greater than 65,535 are set equal to 65,535. = - 1 ( CI s,,,,,(x,y) - gs BTO!f - y --1) BRng - 511 (D.35) Note that the actual summation process takes place as the input images are loaded from the hard drive (D.5.1.2), and not as a result of selecting this menu item. Furthermore, generation of an output image does not alter the summed image Clsum(x,y) stored in extended memory. As a result, any number of output images with various values of BTOff, BRng, or gs can be created without reloading the input images. D.5.2 ADDER Option Two: Swn Or Average With Batch File If many images must be summed or averaged, then manually selecting files from directory listings is tedious. This menu option allows the user to expedite the summing Appendix D: Software Developed for Ultrafast GED (ADDER) 628 Image Addition Batch File Format Sample File ~----------------r--------------,1 1 r----------------,--------------, 1 1 I I r.-----------,--, 2 ADD-BATCH-FILE 1 [NWnber of Jobs] 1 1 [Output Image Name] 1i [NWnber of Files] 1 1 r----------------,--------------1 1 1 r----------------,--------------1 [Rescaling Divisor] 1 f-- Can Be Real! 1 51 ti [Background Offset f[Background Offset: 1 (Top of Image)] 1 (Bottom of Image)] 1 Ji [Input Image Name 1] 1 1 r----------------r--------------, r----------------,--------------, 01 : I I r.----------------,--------------1 bi [Input Image Name Nrml 1 1 : [Output Image Name] : ! r----------------,--------------, 2i [NWnber of Files] 1 1 r----------------,--------------1 ni [Rescaling Divisor] If-- Can Be Real! 1 di [Background Offset f[Background Offset: (Top of Image)] 1 (Bottom of Image)] 1 [Input Image Name 1] 1 1 1 1 r----------------,--------------1 .r------.--------r------.-------, : I : I : I r.;-IADD-BATCH--=FILE'--7 1 I I ~-----------,--, S0303AV1 1 I 1 r.-----------,--7 3 1 13 I I r.-----------,--, I I r.-----------..--~ 12900 129121 I I I ~o3o3Al-----i--i r------------,--, I I I E0303B1 r.-----------,--7 I E0303Cl 1 1 r,----------T--7 S0303ALL I 110 1 1 r.-----------,--, I I r.-----------,--7 I I r.-----------..--~ 12 • 5 13013 I 3025 I I I I r.-----------,--, IE0303A0 1 1 r-----.-----,-.-7 I : I : I Table D-23: (Left) Format of batch file used when adding or averaging CCD images with option two of ADDER. (Right) Example of an image-addition batch file. process with a pre-generated batch file. The format of the batch file is shown in Table D23. The user enters the batch file identification header (ADD-BATCH-FILE) followed by the number of 'jobs" that ADDER must perform; each job corresponds to the creation of one output image from a set of input images. All jobs have the same format, and contain almost all the same parameters as those entered manually with option one of ADDER (D.5.1): 1. Standard DOS name of the output image (up to eight characters) for this job. 2. Number of input image files in this job. There is no limit on Mm when using a batch file. 3. The rescaling divisor. This value may be a real number. To create an averaged image, the rescaling divisor should equal the number of input images. Appendix D: Software Developed for Ultrafast GED {ADDER) 629 4. The average background offset values at the top and bottom of the CCD images. This matches the format for batch files of other programs (e.g., RADAR2), but differs from the manual-entry menu option for summing images. In that method, the background offset range is entered instead of the value at the bottom of the CCD image (D.5.1.5). 5. The list of input CCD image filenames for this job. All input files must be located along ADDER's default CCD image path and must have the default extension. These defaults can be changed using the Change Path menu item in the first option (D.5.1.1). The output files will be placed in the same directory and have the same extension. After choosing option two of ADDER, the user is prompted to select a batch file. The batch file must be located in the same directory as ADDER.EXE, although the path can be changed by editing ADDER.C and rebuilding the executable file. If the batch file has the correct header, then a new screen appears displaying the number of jobs and other data read in from the batch file. The input image filenames for the current job are listed on the right-hand side of the screen, thirty at a time. The filenames are color-coded to indicate any errors found during the preliminary scan of each CCD image (see Table D24). An image is not included in the sum if its x-y dimensions differ from the dimensions of the first image in the job, or if the count value of any pixel exceeds an upper limit set within the program. The latter error check was initially included for analyzing electron beam images taken during lensing experiments. If the CCD was saturated by the electron beam, then the image was thrown out of the average. At present, however, this error check has been disabled by setting the upper limit to zero. To reactivate the error check, Appendix D: Software Developed for Ultrafast GED (ADDER) the variable blimit in subroutine add_batch() of ADDER.C must be assigned a value within 1 and 65,535. The only indication the user Color 630 Meaning ............ Blue ............... Image .awaiting..analysis .............................. . .......... White ............. current.image .being analyzed:................ ..... .Dark..Blue......... Image .was .successfully analyzed ........ . ......Dark. Grey ...... Image. not .found •............................................... ..........Yellow ............ Image. x-y dimensions .different.............. . Red Pixel count value in image over limit. Table D-24: Color-code scheme of image filenames as displayed when adding or averaging with ADDER's batch file option. receives of a problem with an image is by a change in the color of its filename; ADDER does not summarize the errors found during execution of the batch file. The filenames can flash by quickly if the CCD images are small. If all files are "bad," then an output image is not created. Note that the colors listed in Table D-24 may be different if the default color settings in SETTINGA.H are changed. D.5.3 ADDER Option Three: Divide One CCD Image By Another By selecting this option, the user can divide one CCD image by another, pixel by pixel. The numerator and the denominator images are stored simultaneously in extended memory using the standard 16-bit format. Any background offset corrections for the images must already be made, but the user can rescale the output by choosing a multiplicative constant. Six menu items are displayed: D.5.3.1 Change Path This item allows the user to alter the default directory path for the CCD images. D.5.3.2 Numerator Image The user selects a CCD image for the numerator using the current directory listing. Appendix D: Software Developed for Ultrafast GED (ADDER) 631 The output image will have the same x-y dimensions. D.5.3.3 Denominator Image The user selects a CCD image for the denominator using the current directory listing. The numerator and denominator images must have the same x-y dimensions, but this is not checked until the Divide Images menu item (D.5.3.6) is selected. D.5.3.4 Scaling Factor To maintain the number of significant figures, ADDER stores the pixel count values as real variables before dividing. If the scales of the numerator and denominator images have both been optimized for 16-bit dynamic range, then the pixel values after division will be concentrated between 0.1 and 10.0. The image must be rescaled with a real multiplicative factor gs on the order of 1000 to make full use of the 16-bit dynamic range of the output image. D.5.3.5 Output Filename The user enters a standard DOS eight-character name for the output image. If the user wants the output image to have a path or extension different from the input images, then the Change Path menu item can be selected after the numerator and denominator images are loaded into memory. D.5.3.6 Divide Images Executing this menu item downloads the numerator and denominator images from memory and processes them according to Eq. D.36: Appendix D: Software Developed for Ultrafast GED (ADDER) C!Out(x, y) = CJ Num (x, Y) gs C/Dnm(x,y) The images must have the same x-y dimensions. 632 (D.36) Pixel count values of O in the denominator are automatically set to 1 before division. The final image is saved in SpectraSource format under the user-provided filename, and the image has either the numerator's or the denominator's header, depending on which was selected last. Count values greater than 65,535 in the output image are set equal to 65,535. The input images do not have to be reloaded if the user wants to save several output images with different values of gs. D.5.4 ADDER Option Four: Correct CCD Images With Backgrnd Curve Transforming a gas-phase electron diffraction image from the raw experimental scattering intensity into a two-dimensional sM(pix) curve provides diagnostic details about asymmetries in the scattering and detection processes, and the final image has aesthetic appeal as well. With this main menu option, a set of diffraction images are averaged in extended memory and converted into a 2-D sM(pix) image using a background curve generated earlier with PROC5. The final image can be rescaled to accommodate different presentation methods. Twelve menu items are displayed after selecting this option: D.5.4.1 Change Path This item allows the user to alter the default directory path for the backgroundcorrection data file (* .BGD). Appendix D: Software Developed for Ultrafast GED (ADDER) Image Radial Division Batch File Format 633 Sample File f'i>IV-BATCH-FILE , - - - - - - - - , - - - - - - - - , fi>IV-BATCH-FILE r---r---, f-----------r--------+--------1 I [Number of I I I Fa-----------r---+---i ISO I I I I Images Nzml I I I 1 Name 1] 1 1 I 1S0504A1 I I I I I I I I I i [Input Image fCBackgroundi[Backgroundi I I Offset 1 (Top)] 1 I Offset 1 (Bottom)] r-----.-----~--.----r--~---1 I ; I ; I : I i [Input Image f[Background'f[Backgroundi I Name Nzml I Offset Nzm I Offset Nzm I IL ___________ L I ________ (Top)] (Bottom)] JI LI ________ I I I r-----------r---r---, I 2973 I 2981 1 r-----.: -----r-.-r-.-1 I I ; I : I r-----------r---,---, I I I I 1S0504H0 I 2968 I 2975 I IL _ _ _ _ _ _ _ _ _ _ _ LI _ _ _ LI _ _ _ JI Table 0-25: (Left) Format of batch file used with option four of ADDER when loading CCD images for radial division. (Right) Example of a radial-division batch file. D.5.4.2 Load Raw Images The scattering intensity falls off as s5 along the radial cross section of an isotropic diffraction pattern,* so many two-dimensional diffraction images must be averaged to bring the interference fringes at large s above the noise level. This menu item loads the diffraction images into memory using a pre-generated batch file (the format is shown in Table D-25). The batch file begins with an identification header (DIV-BATCH-FILE) followed by the number of images. The filename of each input image is accompanied by the background offset values at the top and the bottom of the image. After choosing option four of ADDER, the user is prompted to select a batch file of the correct type. ADDER reads through the batch file twice. On the first pass, ADDER reads the image headers and makes sure all images listed in the batch file have the same x-y dimensions; if any image does not, then ADDER displays an error message and aborts execution of the batch file. On the second pass, the images are read from the hard drive and summed in extended memory (just like in options one and two). If the batch file • The total scattering intensity across the two-dimensional detector falls off as s4. Appendix D: Software Developed for Ultrafast GED (ADDER) 634 lists a large number of images, then the loading process can take several minutes to complete. All CCD images must have ADDER's default extension, and the images must be located along the default path. These defaults can be changed using the Change Path menu item in the first option (D.5.1.1). D.5.4.3 x-coordinate of e- Beam This unsigned integer (xeb) is the average x-axis pixel position of the unscattered electron beam in the diffraction images. ADDER needs the electron beam coordinates in order to calculate the radial position of each pixel and convert the pixel's count value from raw scattering intensity into the sM(pix) format. Typically the electron beam position varies by one or two pixels along either axis during the course of an experiment; these fluctuations do not detract significantly from the final corrected image. D.5.4.4 Y-Coordinate of e- Beam This unsigned integer (yeb) is the average y-axis pixel position of the unscattered electron beam in the diffraction images. D.5.4.5 Background Filename By selecting this item, the user can choose a background data file meeting the path and extension parameters set in the Change Path menu item (D.5.4.1). Background files are created with PROC5 (see D.4.2.6 for a discussion of the format) and contain three columns of data: the conversion between pixels and A- 1, the background correction intensity curve /s(pix), and the scattering function product !fal!fbl. ADDER needs these data in order to convert the diffraction pattern from raw scattered intensity as registered Appendix D: Software Developed for Ultrafast GED (ADDER) 635 on the CCD into a two-dimensional sM(pix) curve. D.5.4.6 Flat-Field Image The user selects a flat-field image with the same extension and from the same path as the diffraction images. The flat-field image is not stored in extended memory; instead, the image is read from the hard drive as needed during the creation of an output image. A warning message is displayed at this time if the x-y dimensions of the flat-field image are smaller than the dimensions of the diffraction images, but the calculation continues. No message is displayed if the flat-field image dimensions are larger than the diffraction image dimensions because this portion of ADDER reads and writes images one row at a time. Under such circumstances the I/O is slower but ADDER can easily account for differences in row length and column height. If the flat-field image is smaller than the diffraction images, then the output image will be correct within the dimensions of the flat-field image; the output image is not mangled, as when ADDER sums two images of different dimensions (D.5.1.2). D.5.4.7 Cutoff Radius This unsigned integer places an upper limit on the distance a pixel can be from the electron beam and still be converted to sM(pix). Pixels beyond the cutoff radius have their count values set to zero in the output image. The maximum value for the cutoff radius is set by the length of the background data file; the user may wish to set a smaller value if the diffraction data at large s is too noisy. Appendix D: Software Developed for Ultrafast GED (ADDER) 636 D.5.4.8 Change In Image Gain This menu item is the real number gv, corresponding to the fractional change in CCD image gain from the top to the bottom of the image. The usual value is 0.3. The corrected gain is calculated just like in RADAR2 (D.3.2.6). D.5.4.9 Output Offset Value The modified molecular scattering function oscillates above and below zero, but a 2-D sM(pix) output image from this program must be an array of 16-bit unsigned integers (SpectraSource format). To make this conversion, the zero level is shifted by adding an unsigned integer offset Cfoff to all pixel count values. Recommended values for Cloff depend on the method used to assign a color scale to the output image. If the image is viewed or printed using a linear color scale, such as with Adobe Photoshop or other commercial image manipulation software, then the full 16-bit dynamic range can be exploited. Cloff should be set to the halfway point of the dynamic range, +32,767. If the image is viewed using a logarithmic color scale, such as with the SpectraSource software, then better results are obtained with Cfoff equal to + 10,000. D.5.4.10 Output Scaling Factor In addition to offsetting the zero level of the 2-D sM(pix) curve, the user must rescale the amplitude with a real number scaling factor gs, The scaling factor is chosen such that the lowest peak of the sM(pix) curve corresponds to 0 ADU, the minimum of the output image dynamic range. The optimum choice for gs depends on the experimental conditions and the molecular system; gs is usually refined by trial and error starting with values between 20.0 and 100.0 (assuming no flat-field correction). Appendix D: Software Developed for Ultrafast GED (ADDER) 637 D.5.4.11 Output Filename The user enters a standard DOS eight-character name for the output image. The output image will have the same path and extension as the input images. D.5.4.12 Divide Images Selection of this menu item pulls the summed diffraction image from memory one row at a time, and each pixel is considered individually. First, the distance from the current pixel to the unscattered electron beam is calculated according to: (D.37) If r xy is less than or equal to the cutoff radius, then a flat-field correction is made (if selected) and the count value is converted to rescaled sM(pix) using Eq. D.38: (D.38) Negative count values are set to 0, and count values greater than 65,535 are set equal to 65,535. The output image is saved in SpectraSource format under the user-provided filename, and the image's header is the same as that of the last diffraction image loaded with the radial-division batch file. Generation of an output image does not perturb the summed image in extended memory, so many output images can be created (e.g., using different values of gs) without reloading the diffraction images. Creation of a 2-D sM(pix) curve will be successful only if the background file has been generated under the exact same conditions as the file is used in ADDER. The following criteria must be met: 1. The diffraction images loaded into memory with the radial-division batch file Appendix D: Software Developed for Ultrafast GED (ADDER) 638 (D.5.4.2) must be the same images which RADAR2 analyzed when the raw scattering intensity curve was calculated. The background offset values of the CCD images must also be the same. 2. If flat-field image correction was used in RADAR2, then the same correction image must be used here. 3. The change of image gain must be the same here (D.5.4.8) as in RADAR2. At the present time, the change of image gain in RADAR2 is fixed at 0.3. 4. The one-dimensional raw scattering intensity curve created by RADAR2 cannot be rescaled or corrected in any way prior to generating the background file with PROC5. If these criteria are not satisfied, then the two-dimensional output image will most likely have a wandering baseline: the zero positions of the sM(pix) curve will not have identical count values. Although this option of ADDER was designed for the specific purpose of generating two-dimensional sM(pix) images from experimental data, the software can be applied in other ways. Background File As Radial Filter Pixel# 0 1 At the simplest level, the background file can be edited to create a radial which are between 100 and 200 pixels of 1 I Q I O I l I I : I : I : I I l I Q I l I I l I Q I l I I : I : : I I l I Q I l I r- - - - - :- - - - - - ,- -:- -r-:- -, r-----------r--r-7 Q I O I l I r-----------r--r-7 99 100 101 r- - - - - - - - - - -,- - -r- -, 199 of all pixels to Cloff except for those regions 1 r-----------r--r-7 I O I O I l I r- - - - - - - - - - -r- -r- -, I image filter. For example, the background file shown in Table D-26 will set the count value r------------r--r-7 1source: E:\xxxx 1 200 r-----:------r-:--r-;-7 I r-- - - - - - - - - - - - -i- - -r-- - -1 I l I Q I l I r- - - - - - - - - - -,- - -r- -, Table D-26: Example of an edited background file prepared to set all image pixel count values to Gloff except those pixels within 100 and 200 pixels of the center. Appendix D: Software Developed for Ultrafast GED (ADDER) 639 whatever the user chooses as the center. Another useful application is to create a theoretical 2-D sM(pix) image which can be compared with a corresponding experimental image. The user starts by editing the experimental background file. The sand !fal!fbl columns stay the same, but the / 8 column is replaced with - g E I~ (pix), where gE is the PROC5 scaling factor between theoretical and experimental sM(s) curves. (See D.4.15.3 for how /~(pix) can be obtained from PROC5). The user then writes a radial-division batch file which will load just one blank image into extended memory. With all Clsum(x,y) equal to zero, Eq. D.38 generates an sM\pix) image scaled to match the experimental image. D.6 PROFILE PROFILE calculates the average x-axis and y-axis intensity distributions within a user-specified region of a CCD image. This software is most commonly applied to studies of the electron beam shape, such as streaking experiments (4.4.2) and time-zero measurements (9.3.2). One set of profiles can be calculated at a time, or the process can be automated with a pre-generated batch file. This program also has an alignment option in which the user can shift individual profiles relative to each other before an average profile is calculated. PROFILE does not make corrections for background offset values, thermal drift, or image gain variation. Although the SpectraSource software will show intensity profiles of either a single row or column, it has no output features and cannot calculate the average profile of a two-dimensional region. Appendix D: Software Developed for Ultrafast GED (PROFILE) PROFILE asks the computer for 3 Mb of PROFILE.EXE Program Files Include Files extended memory, enough memory to store one PROFILE.C PROFI_DT.C PROFI_IO.C CEXT.C full 1024xl024 image in standard 16-bit format. The program is compiled from the files listed in 640 DATA_PRF.H SETTINGF.H CEXT.H COMPAT.H Table D-27: Program and include files needed to build PROFILE.EXE. Table D-27. Details of PROFILE's function and operation are presented in the following pages: D.6.1 PROFILE Option One: Load CCD Image The user selects the CCD image which will be analyzed with option two of PROFILE. The user can also change the default path and extension which PROFILE references when locating any CCD image. Altering the default parameters at this point in the program determines which directory PROFILE expects to find the images listed in the batch files of options three and four. D.6.2 PROFILE Option Two: Create x and Y Profiles After a CCD image has been loaded into memory, this option can be selected for manually generating x- and y-axis profiles. The user chooses a region of the image for analysis, and the program will display the average profiles along both axes. The profiles can be saved individually to the hard drive. Six menu items are displayed under this option: D.6.2.1 Generate Profiles When this menu item is selected, the program calculates the average horizontal and vertical intensities over the user-specified profile region using Eqs. D.39 and D.40: Appendix D: Software Developed for Ultrafast GED (PROFILE) 641 (D.39) (D.40) Both profiles are displayed simultaneously. The curves are normalized to have identical minimum and maximum values for presentation purposes only; the true, unadjusted profiles will be saved to the hard drive. D.6.2.2 Save Profiles This menu item allows the user to save individual profiles, choosing the filename, path, and extension of the output. A profile is written to the hard drive in CSV format as a list of pixel positions and the corresponding averaged intensity. D.6.2.3 X Offset This unsigned integer (xu) is the x-coordinate of the profile region's left side. D.6.2.4 Y Offset This unsigned integer (yu) is they-coordinate of the profile region's top side. The pixel position (xu, Yu) corresponds to the upper left corner of the profile region. D.6.2.5 X Range This unsigned integer (xr) is the width of the profile region along the x-axis. If x1 corresponds to the x-coordinate of the profile region's right side, then: (D.41) The maximum value for Xr is currently set at 351 pixels. Appendix D: Software Developed for Ultrafast GED (PROFILE) 642 D.6.2.6 Y Range This unsigned integer (yr) is the height of the profile region along the y-axis. The maximum value for Yr is currently set at 351 pixels. D.6.3 PROFILE Option Three: Simple Batch File Processor With this option, automated profile calculations can be carried out over multiple regions and multiple images. The user must first write a batch file which follows the format shown in Table D-28. The identification header (PROFILE-BATCH-BOTH) indicates that profiles will be calculated for both axes and that profiles from different images will not be aligned. The header is followed by the number of ')obs" in the batch file, where one job involves the calculation of x- and y-axis profiles over one region. Each job begins with two standard DOS names and extensions for the output files, one for the horizontal (x-axis) profiles and one for the vertical (y-axis) profiles. These are followed by the number of input images (a maximum of ten) and then the offsets and ranges for the profile region. * The x- and y-axis ranges may each be a maximum of 351 pixels. Each job concludes with a list of the input image filenames (no extensions). PROFILE expects that the input CCD images will have the default image extension and be located along the default image path. The user may change these default parameters using option one (see D.6.1). The destination of the output files is the current directory, most likely the directory in which PROFILE.EXE is located. • Unfortunately the formatting of regions in PROFILE and STREAK batch files is different from the formatting in RADAR2 batch files. Regions in RADAR2 batch files are identified by upper and lower coordinate (xu, Yu) and (x1, y 1). Regions in PROFILE and STREAK batch files are identified by the upper coordinates (xu, Yu) and the ranges x, and y, along the two axes. Appendix D: Software Developed for Ultrafast GED (PROFILE) Once option three has been chosen, the user must select a valid batch file. 643 Simple Profile Batch File Format [PROFILE-BATCH-BOTH i _____ T_____ T_____ i r--------------,-------,------,------7 1 [Number of Jobs] 1 1 1 1 i [output Filename i I and Extension of 1 1 1 : IHorizntal Profiles] I 1 1 1 i--------- . -----t--------t--------t-------i 11 [OUtput Filename I I I 1 1 and Extension of 1 1 1 1 S1 Vertical Profiles] 1 I 1 1 ti I I 1 I 1 Batch files must be located in the same directory as f---------------+-----+-----+------4 PROFILE.EXE although the location can be changed by editing PROFILE.C. A new screen displays information about the automated profile analysis obtained from the batch file (number of jobs, profile region, etc.). A list of the input image filenames 1 [Number of Images] 1 1 1 1 r--------------,-----,------,-----7 J, [X-Axis 1 [ Y-Axis 1 [X-Axis I [ Y-Axis I 1 Offset] 1 Offset] 1 Range] 1 Range] 1 0I 1 1 I 1 r--------------,-----,-----,------7 bi [Input Image 1 1 1 1 1 Filename 1] 1 1 1 1 r------ .-------,-----,------,-----7 1 : 1 1 1 1 r--------------,-----,------,-----7 1 [Input Image 1 1 1 1 1 Filename Nrml 1 1 1 1 1 [OUtput Filename 1 1 1 1 1 and Extension of 1 1 1 1 1 1 1 Horizntal Profiles] 1 I 2 f--------.------+-----+-----+------, [output Filename 1 1 1 1 1 1 and Extension of 1 1 1 1 n1 Vertical Profiles] 1 1 1 1 cf. I I I 1 f---------------+-----+-----+------4 1 1 1 1 [Number of Images] 1 r--------------,-----,------,-----7 J1 ex-Axis [ Y-Axis I [X-Axis I [ Y-Axis I 1 1 Offset] 1 Offset] 1 Range] 1 Range] 1 0I I 1 1 I r--------------,-----,-----,------7 bi [ Input Image 1 1 1 1 1 Name 1] 1 I 1 1 . r------ .-------,--. --,---. --,--. - - 7 :I : I : I : 1 : I in the current job appears on Sample File the right side of the screen. The status of each image is indicated by the color of the filename (see Table D-29); unlike ADDER's batch file routine (D.5.2), PROFILE does not check the input 7 li,ROFILE-BATCH-BOTH ,-' ' !i--------------+-----+-----+------4 ~1201"i~xLO-------+-----+- ----+-----"1 ~1207A~XL0-------+-----+-----+------4 ~--------------+-----+-----+------4 S.oo------------+--so--+--s1--+--2-1---4 ~1201"ii---------+-----+-----+------4 ~1201"i.2- - - - - - - - -+-- - - -+-- - - -+-- - - -"1 f;--------------+-----+-----+------4 ~1207A3 _________ _L _ _ _ _ _ .l_ _ _ _ _ _ ..L _____ _j Table D-28: (Top) Format of batch file used when creating horizontal and vertical profiles f ram CCD images with option three of PROFILE. (Bottom) Example of a simple profilegeneration batch file. Appendix D: Software Developed for Ultrafast GED (PROFILE) CCD images for matching x-y dimensions or saturation, so an image is "bad" only if PROFILE does not find it under the default path and extension. Color 644 Meaning .............Blue .............. Image _ awaiting. analysis ......................... ...........White .............current .image. being. analyzed ........... .......Dark.Blue ...... __Image was. successfully.analyzed .... Dark Grev lmaae not found. Table D-29: Color-code scheme of image filenames as displayed when calculating profiles with PROFILE's batch file options. If no images in a job are found, then the output files are not created. As in ADDER, the color assignment listed in Table D-29 may be different if the color settings in SETTINGF.H are altered. After an input filename listed in the current job is read, PROFILE loads the CCD image and calculates the average horizontal and vertical profiles. PROFILE does not check to see that the profile region defined by the batch file is within the dimensions of the CCD image. The results are unpredictable if the profile region is out of range. All x-axis (horizontal) profiles of the current job are collected into one output file (CSV format), and all y-axis (vertical) profiles are collected into another. The first column of an output file is a list of pixel positions, and each remaining column is the profile from one input image. The first row of each column contains the filename of the input image. D.6.4 PROFILE Option Four: Aligned Batch File Processor The general application of this menu option is to a collection of sets of images, where the experimental conditions are the same for all images in a given set, but some experimental parameter (e.g., delay time, voltage, etc.) varies across the collection. This menu option will automate the measurement of change in the average profiles from the sets of images. The average profile from the first set of images is assumed to be the .. reference profile; if the imaged signal is unaffected by varying the experimental parameter, Appendix D: Software Developed for Ultrafast GED (PROFILE) then the average profile from each subsequent 645 START #1 set will be identical to the reference profile. •• User" This portion of PROFILE has an additional level of sophistication: • Pre-4~ ·B ; (Format profile Rre sAI alignment. In some experiments, the change in the imaged signal profile is smaller than the shot-to-shot jitter in the position of the imaged signal on the CCD. PROFILE allows the user (8,qrizo In Wind PROF! An In Ba >Align . (Ve rtie Refere a to correct for jitter by aligning the input images in three different ways: 1. Pre-align a set of images along the axis orthogonal to the direction of the output profile. This alignment .:., A!ign (Vertical Job Align Average· (:refile Of ·Job n With Average Profile Of • ' Reference linage :'r'. step can enhance changes in the Write Output Profiles imaged signal: the range of the profile region along the orthogonal axis is narrowed down to window Figure D-7: Flowchart of aligned profile calculation process. just the region of the image that changes. 2. Align the profiles of a set of images before calculating the average profile. This alignment step corrects for jitter along the profile axis. 3. Align the average profile from each set relative to the reference profile. The program has been written such that the user can include all three methods in the analysis, or just the second and third. To run the first method (pre-alignment), the user Appendix D: Software Developed for Ultrafast GED (PROFILE) 646 must prepare a batch file (see D.6.4.2). As shown in the flowchart (Figure D-7), the computer produces an intermediate batch file after the pre-alignment phase is executed; this batch file runs the second and third methods. In order to bypass the pre-alignment step, the user writes the intermediate batch file instead. The menu structure of option four has three items: D.6.4.1 Set Pre-Alignment Window Width The unsigned integer in this menu item is the pre-alignment window width wp. The purpose of pre-alignment is to narrow the width of the profile region (along the axis orthogonal to the profile) in order to enhance any changes in the imaged signal's profile. If, for example, the final output is a profile along the x-axis, then pre-alignment should lead to a smaller Yr• PROFILE will use Wp as the new value for Yr in the intermediate batch file unless Wp is greater than the original Yr• D.6.4.2 Pre-Align Vertical and Calculate Horizontal This menu item is for calculating averaged, aligned, x-axis profiles from a collection of images. The user can pre-align the vertical profiles with a batch file, and the computer will create an intermediate batch file in which the y-axis range is reduced to Wp. An average horizontal profile is made either with this computer-generated batch file, or, if the pre-alignment phase is skipped, with a batch file written by the user. A more detailed discussion of these procedures is presented in the following list of sub-menu items: D.6.4.2.1 Pre-Align Vertical Profiles The same pre-alignment batch file can be used for pre-aligning vertical profiles and Appendix D: Software Developed for Ultrafast GED (PROFILE) 647 horizontal profiles (D.6.4.3). The format of this type of batch file is shown in Table D-30. The identification header (PROFILE-BATCH-ALIGN) is followed by a standard DOS eight-character name for the intermediate batch file. PROFILE will give the intermediate batch file the same path and extension as the pre-alignment batch file. The next item in the batch file is the name and extension of the final output file. This file is generated by running the intermediate batch file (see D.6.4.2.2). Under the output filename is the number of "jobs," where each job processes one set of CCD images. Ideally, all the images in a set would be the same, having been taken under identical conditions. The images are different because of experimental noise and jitter; the purpose of PROFILE' s option four is to correct for the jitter and average out the noise when making the profile. All jobs begin with a descriptive text string (up to forty characters with no blank spaces). This header identifies the images in the job (e.g., "Time_Step :_SO_ps") and will appear in the final output file as a row label. Below the header are the offsets and ranges which delineate the profile region. The initial value of Yr should be large (maximum of 351) because it is the purpose of pre-alignment to reduce Yr, replacing it by the window width wp and adjusting for an optimum y-axis offset in the process. PROFILE conducts no error checks on the size of the profile region and the dimensions of the CCD images. The final entries in each job are the number of images and the list of the image filenames (no extensions). PROFILE will look for the CCD images under the default image path and extension, which can be changed using option one (D.6.1). Appendix D: Software Developed for Ultrafast GED (PROFILE) Once 648 Pre-Align Profile Pre-Alignment Batch File Format vertical Profiles has been selected, the user a batch file r::--------------:,------,-------,-------7 1PROFILE-BATCH-ALIGN 1 1 1 1 I [Intermediate Batchl I File Name] I I I I I I I r.--------------,------,-------,------, r- - - - - - - chooses identified by the path and extension set in the Change item Path menu (D.6.4.2.3). A new screen appears, showing details about the batch file and the current job being processed. The image filenames are .- - - - - -,- - - - - - , - - - - - , -- - - -7 [output Filename I I I I and Extension] 1 1 1 1 r--------------,------,-------,-------7 I [Number of Jobs] I I I I I 1 : [Header of Job 1] 11 [X-Axis Offset] : 1 1 1 r--------------,------,------,------7 I I [ Y-Axis I [X-Axis I [ Y-Axis I I Offset] I Range] I Range] I I I I I S1r--------------,------,------,------7 [Number of Images] 1 1 t, 1 1 r--------------,------,-------,-------7 [Input Image Filename 1] I I I I 1 I I 1 I I 1 I I 1 I J r------ .-------,------,------,-----7 01 : I I I I r--------------,------,-------,-------7 bi [Input Image 1 1 1 1 I Filename Nrml I I I I 1 [Header of Job 2] 1 1 1 1 r--------------,-------,-------,-----7 I 1 I [X-Axis Offset] I [ Y-Axis I [X-Axis I [ Y-Axis I 1 Offset] 1 Range] 1 Range] 1 I I I I 2 ,--------------,------,------,-----7 [Number of Images] di-[Input Image __ i _____ i _____ ; _____ i ni I I I I 1 1 1 1 Filename 1] 1 : I : I r--------------,------,-------,-------7 : I : I : I listed on the right and colorSample File coded according to Table D29. The vertical profiles are aligned in groups of eight. CCD images belonging to the first group are loaded into extended memory and their vertical profiles are calculated. All profiles are plotted on the screen, each 1 1 7 fpROFILE-BATCH-ALIGN1 ~--------------+-----+-----+------! HRZ0709 f;;--------------+-----+-----+------l H0709PRF.XL0 !-:;--------------+-----+-----+------! 11 f-=--------------+-----+-----+------l Background ~--------------+-----+-----+------! 55 80 31 35 ~--------------+-----+-----+------! 3 f-=--------------+-----+-----+------l E0709BK1 F---------------+-----+-----+------l E0709BK2 F---------------+-----+-----+------l E0709BK3 F-. -------------+-----+-----+------! i,'.f::me__:-Step-1 ______ +-----+-----+------l 55 80 31 35 ~--------------+-----+-----+------! 3 f-=--------------+-----+-----+------l E0709A1 f=--------------+-----+-----+------l I : I : I : I : Table D-30: (Top) Format of batch file used when prealigning vertical or horizontal profiles with option four of PROFILE. (Bottom) Example of a pre-alignment batch file. I Appendix D: Software Developed for Ultrafast GED {PROFILE) in a different color. The pre-alignment window width 71 Shnt Profile 1o Pixels Left is marked off by two vertical red bars, centered in the - 649 Cycle Forward One Profile Shnt Profile 10 Pixels Right ~'-#:l: <v~ E .- ,,~:;;]§~ z ' ii.%4'' ® Shnt"' ~ plotting region (assuming that Wp < Yr). The user can Shift Profile 1 Pixel Left :;,( shift the profiles left or right, one at a time, with Profile 1 Pixel Rig ' h~t. : '- ·~= ~ commands entered on the numeric keypad (see Figure Shnt Profile 0.1 Pixels Left D-8; the 0.1 pixel shift options are not available during pre-alignment). Once each profile is positioned as desired within the pre-alignment window, the user presses "Enter" and confirms that he or she is done "' ,, '\:. ~~~~~ ~ Cycle Shnt · Backward Profile 0.1 One Profile , Pixels Right : ,._ _ ,,.,,, '% ' Figure D-8: Numeric keypad functions when aligning profiles. The 0.1 pixel shifts (keys "1" and "3") are not available in the prealignment phase. aligning this group. The computer then writes the new values of Yu and Yr for each image to the intermediate batch file. PROFILE continues with the next group of eight images in the current job until all images are aligned. The pre-alignment process is shown schematically in Figure D-9. In this example, the imaged signal occupies 12 pixels within a 12xll profile region relative to offset (xu, Yu), and wp has been chosen to be 6 pixels. Several other pixels, unrelated to the imaged (x,,, Yul r - - Xr ~ r Jj ~:o : ---~·~ ________________ _ ,, Y,r l· , <4- ' , " Wi:lth ~ :t ~ro;~ Up2Pixels * Profile Region In Pre-Alignment Batch File Vertical Profile - ~ ~ - WP l r--X,~ ,, ,. ~ Profile Region In lnterm ediate Batch File Figure D-9: Example of CCD image pre-alignment. The vertical profile is shifted by two pixels such that the profile peak is centered within the pre-alignment window (dashed lines). The new profile region has a y-axis offset of Yu + 4 and a y-axis range of Wp. Appendix D: Software Developed for Ultrafast GED (PROFILE) 650 signal, have also been exposed and are to be removed from the profile region by prealignment. The user shifts the vertical profile by two pixels, such that the imaged signal will be centered within the pre-alignment window. PROFILE writes a new profile region for this image to the intermediate batch file. The y-axis range is now wp and the y-axis offset has become Yu + 4; the x-axis offset and range are not changed. Once all images in all jobs have been aligned, PROFILE closes the intermediate batch file and returns control to the menu. Now the user can proceed with the second phase of analysis, in which the averaged horizontal profile from each set of images (each job) is calculated. D.6.4.2.2 Calculate Horizontal Profiles With this menu item, the x-axis profiles from a set of CCD images are aligned before creating an average horizontal profile. The resulting profile is then normalized by area and aligned relative to a reference profile (the average profile from the first set of images). Executing this process requires a batch file created either by the computer, as a result of pre-alignment, or by the user. The intermediate batch file (Table D-31) starts with an identification header (PROFILE-BATCH-HORIZ), followed by the name and extension of the output file and the number of jobs. As in the pre-alignment batch file, each job in this batch file processes one set of CCD images, all taken under identical experimental conditions. The output from each job is a single horizontal profile, an average of the x-axis profiles from all the images in the set. The very first job generates the reference profile, presumably corresponding to the control set of CCD images. The average profile from all other jobs will be aligned relative Appendix D: Software Developed for Ultrafast GED (PROFILE) to the reference profile. Intermediate Aligned Profile Batch File Format Each job in the batch file starts with a forty- character text 651 string (no blank spaces) which will be included at the beginning of r.:--------------,-----,-----,-----7 PROFILE-BATCH-HORIZ [Output Filename and Extension] 1 I 1 1 I I 1 I 1 I [Number of Jobs] I I I I ; [Header of Job 1] ; ; ; ; 1 r - - - - - - - -. - - - - - , - - - - - - , - - - - - - , - - - - - I 1 1 I 1 -7 r--------------,-----,-----,-----7 r--------------,-----,-----,-----7 1 [Number of Images] 1 1 1 1 r--------------,-----,-----,-----7 11 [X-Axis I [ Y-Axis I [X-Axis I [ Y-Axis I I Offset 1] I Off 1] I Rng 1] 1 Rng 1] 1 SI I I I I r--------------,-----,-----,-----7 t, [Input Image I I I I 1 Filename 1] 1 1 1 1 r--------------,------,------,------7 the corresponding data row in the output file. Next comes the number of input images in the job. This is J1 : I : I : I : I r--------------,-----,-----,-----7 01 [X-Axis 1 [ Y-Axis 1 [X-Axis 1 [ Y-Axis 1 l Offset Nrml I Off Nrml I Rng Nrml I Rng Nrml I b r--------------,------,------,------7 I I I I I I [Input Image I I I I I Filename Nrml I I I I 1 1 [Header of Job 2] 1 1 1 r--------------,-----,-----,-----7 2, [Number of Images] 1 1 1 1 r--------------,-----,-----,-----7 n, [X-Axis Offset 1] followed by two rows of I [ Y-Axis I [X-Axis I [ Y-Axis I 1 Off 1] 1 Rng 1] 1 Rng 1] 1 U1 I I I I ,--------------,-----,-----,-----7 I [Input Image I I I I 1 Filename 1] 1 1 1 1 information for each image: :I _,i r--------------,------,------,------7 : I : I : I : I the offset and range of the Sample File image's profile region, and ~--------------+-----+-----+------1 H0709PRF.XL0 f-:;--------------+-----+-----+------1 11 1-=--------------+-----+-----+------l Background ~--------------+·-----+-----+------1 3 f-;--------------+-----+-----+------1 55 84 31 25 f-=--------------+-----+-----+------1 E0709BK1 ~--------------+-----+-----+------1 55 83 31 25 f-=--------------+-----+-----+------1 E0709BK2 ~--------------+-----+-----+------1 55 84 31 25 f-=--------------+-----+-----+------1 E0709BK3 F-. -------------+-----+-----+------1 Time-Step-1 ~--------------+-----+-----+------1 3 ~------ .-------+--. ---1 the image filename. If the intermediate batch file was created from a pre-alignment batch file, then the values of Yu will probably vary from image to image. The values of Xu, Xr, and Yr will most likely not change, though, f°pROFILE-BATCH-HORIZ' I : I ' : ' 7 --+--. --+-.: I : I Table D-31: (Top) Format of batch file used when calculating and aligning horizontal profiles with option four of PROFILE. If calculating and aligning vertical profiles, the identification header changes to PROFILE-BATCH-VERT. (Bottom) Example of an intermediate batch file for finding averaged horizontal profiles. I Appendix D: Software Developed for Ultrafast GED (PROFILE) 652 and if the batch file were created by the user, then Yu will be constant too. The image filenames should not have extensions; PROFILE will use default values for the path and extension, which the user can alter (D.6.1). After selecting Calculate Horizontal Profiles, the user picks an appropriate batch file and the program begins to run it. The batch file screen display and its conventions are the same as those described earlier (D.6.3, D.6.4.2.1). In the prealignment phase, vertical profiles were aligned relative to the window width. In this part of the program, however, all horizontal profiles should be aligned relative to each other. The horizontal profile from the first image is arbitrarily assigned as the standard, and the remaining profiles are then aligned, in groups of seven, relative to the first profile. The first profile is always plotted in red and each of the other profiles has a different color. The amplitudes of all profiles are normalized to have the same minimum and maximum values. Profiles can be shifted left or right using the numeric keypad (see Figure D-8 for key assignments), and fractional shifts of 0.1 pixel are allowed. Fractional shifts are estimated with a cyclic two-point interpolation scheme: for an 0.3 pixel shift to the left, PROFILE interpolates values of the profile 0.3 pixels to the right of each original pixel. These new values are then inserted as temporary values for the original pixels. subsequent shifts, PROFILE interpolates again from the original pixel values - On never the new temporary values. After all seven profiles in a group are aligned relative to the profile from the first image of the job, the user presses "Enter" followed by a "Y" to confirm the user' s satisfaction with the alignment. The remaining groups within the job are aligned in a similar fashion. Once all profiles in a set are aligned, the average horizontal profile is calculated using the original amplitudes of the image profiles (not the normalized curves Appendix D: Software Developed for Ultrafast GED (PROFILE) used when aligning). A three-point boxcar smooth is applied to the average profile. An example of this process is shown for three simplistic sample nnages in Figure D-10. First, the horizontal profiles are calculated for Image #1 653 Image #2 Image #3 ~ Ill ½ . D . . Ll ......... Ll . ~ Align AmplitudeNormalized Profiles t l-;!/:1, ~ I t :'I\ ,, ,k,,,s.. , ,, each of the three images. Next, these profiles are amplitude-normalized and aligned: #1 is the standard, #2 is shifted 2.5 pixels to the right, and #3 is shifted 1 pixel to the left. Restore Original Amplitudes And Average Profiles ,,,6,,, Average Aligned Profile Figure D-10: Alignment and calculation of averaged profiles. Image #2 is shifted 2.5 pixels to the right; Image #3 is shifted 1 pixel to the left. The profiles are restored to their original amplitudes and the average horizontal profile is calculated. The smoothed, averaged profile is normalized to have a total area of 100,000 ADU. If this profile does not come from the first job in the batch file, then the normalized profile must be aligned relative to the reference profile, again using the numeric keypad. The difference curve is also plotted on the screen, and the sum of the square of the differences (SSD) is shown in the message bar. The SSD is divided by 106 . After all jobs in the batch file are complete, PROFILE writes the output file to the current directory, which is probably the directory containing PROFILE.EXE. The output file is in CSV format, and each row contains one average horizontal profile. (Note that this is different from the simple profile batch file processor (D.6.3) which writes profiles Appendix D: Software Developed for Ultrafast GED (PROFILE) 654 out as a column of data.) The rows are written in the order the jobs were processed, so the first profile is the reference profile. Each row begins with the descriptive text string followed by the SSD/106, and the profile curve fills out the remainder of the row. D.6.4.2.3 Change Path This item allows the user to alter the default directory path for both types of alignment batch files. D.6.4.3 Pre-Align Horizontal and Calculate Vertical The operation of this menu item is almost identical to Pre-Align Vertical and Calculate Horizontal (D.6.4.2). Averaged, aligned, y-axis profiles are calculated from a collection of images. The horizontal profiles can be pre-aligned with the exact same batch file created for pre-aligning vertical profiles (Table D-30 in D.6.4.2.1). The output is an intermediate batch file where the x-axis range has been reduced to the pre-alignment window width wp. Averaged vertical profiles are calculated with this computer-generated batch file, or with a batch file written by the user. The format of the vertical intermediate batch file is also identical to its horizontal variant (Table D-31 in D.6.4.2.2) except the identification header should read PROFILE-BATCH-VERT instead ofPROFILE-BATCH-HORIZ. D.7 STREAK Streaking experiment data comprise CCD images of electron beam spot pairs. The temporal widths of the electron pulses are calculated by measuring the beam profiles and Appendix D: Software Developed for Ultrafast GED {STREAK) 655 separation of each pair along the streaking axis (4.4.2). Unfortunately, the streaking axis may not necessarily line up with the x- or y-axes of the CCD detector because neither the electron gun nor the CCD can be installed with high angular accuracy in the present apparatus. If the alignment is not perfect, then the program PROFILE provides only an estimate of the true streaked electron pulse shape, and the temporal widths obtained with PROFILE must be corrected for angle. STREAK is a slower but more sophisticated version of PROFILE in which the average profile across a CCD image can be calculated for an arbitrary rotational angle. In addition to the profiles, STREAK automatically reports the intensity, center position, and FWHM of each peak it finds along the streaking axis, as well as the separation distance between different peaks. The program can be run one image at a time or with a batch file. Later versions of STREAK might incorporate a Lorentzian fitting routine as an additional method for analyzing peak shapes. STREAK has an additional feature which is not directly related to streaking experiments: the program will convert any region of a CCD image into an output file containing a two-dimensional array of count values. The array can be loaded directly into graphing programs for creating two- and threedimensional intensity plots. STREAK requests 3 Mb of extended memory from the computer in order to store one full CCD image. Table D-32 lists the program and include files required to build STREAK.EXE. The program has three main menu options: STREAK.EXE Program Files Include Files STREAK.C STRK_DT.C STRK_IO.C CEXT.C DATA_STR.H SETTINGE.H CEXT.H COMPAT.H Table 0-32: Program and include files needed to build STREAK.EXE. Appendix D: Software Developed for Ultrafast GED (STREAK) 656 D.7.1 STREAK Option One: Load A CCD Image If the user is manually evaluating angular profiles or creating an output array of pixel count values, then this menu option must be selected first in order to load a CCD image into extended memory. Under this option, the user can change the default path and extension for locating CCD images; the batch file processor (option three) locates images with these parameters as well. D.7.2 STREAK Option Two: Analyze Single CCD Image Once a CCD image has been loaded into memory, the user can select this menu option in order to manually generate image profiles along axes making an angle 0 relative to the CCD x- and y-axes. The user must identify two image regions using x- and yoffsets and ranges: (1) the foreground region over which STREAK will calculate profiles, and (2) the background region from which an average background offset value will be determined. The results of the profile analysis are written in a text file to disk. The user can also convert the pixel count values within the foreground region into either a binary or text format output file. D.7.2.1 Output Filename With this menu item the user enters a standard DOS eight-character filename for the output file . The output file will contain either the results of the streak image profile analysis or the 2-D surface of the foreground region. D.7.2.2 Change Path The user can change the default path and extension for the streak analysis output Appendix D: Software Developed for Ultrafast GED {STREAK) 657 file with this menu item. Surface output files will be located along the same path, but their extension cannot be altered from the default value ".XLF" without editing STREAK.C. D.7.2.3 Foreground X Offset This unsigned integer is the x-coordinate of the foreground region's left side. The size of the foreground region is limited by the image dimensions. Only those pixels located within the foreground region will be used to calculate the streak profiles, so if 0 is near ±45°, then the intensity of the output profile at its edges will result from an average of just a few pixels (see D.7.2.13 below for more details). The foreground region also specifies the area over which a surface is generated from the CCD image. D. 7.2.4 Foreground Y Off set This unsigned integer is they-coordinate of the foreground region's top side. D. 7.2.5 Foreground X Range This unsigned integer is the width of the foreground region along the x-axis. D.7.2.6 Foreground Y Range This unsigned integer is the width of the foreground region along the y-axis. D.7.2.7 Background X Offset This unsigned integer is the x-coordinate of the background region's left side. STREAK averages the count values of all pixels in the background region in order to calculate the background offset for the profiles. This method of estimating the background offset is most accurate when the background region covers the same rows as Appendix D: Software Developed for Ultrafast GED (STREAK) 658 the foreground region (thus avoiding differences due to thermal drift). The accuracy of the background value directly determines the accuracy of reported peak intensities, FWHM, and center positions determined from the FWHM. The size of the background region is limited only by the image dimensions. D.7.2.8 Background Y Offset This unsigned integer is they-coordinate of the background region's top side. D. 7.2.9 Background X Range This unsigned integer is the width of the background region along the x-axis. D.7.2.10 Background Y Range This unsigned integer is the width of the background region along the y-axis. D.7.2.11 Streak Angle This signed integer is the angle 0 between the streak axis and the CCD y-axis. The angle can be between -90° and +90°, where positive 0 refers to a counterclockwise rotation of the y-axis. The user must estimate this angle from CCD images, presumably by finding the electron beam coordinates at the outer limits of the streak. D.7.2.12 Discriminator The discriminator is an unsigned integer (pd) representing a percentage between 0 and 99%. STREAK uses the discriminator during the identification of peaks across the streak axis profile. As explained in D.7.2.13, a region of the streak profile is isolated for independent analysis (as a "peak") if the region contains a local maximum whose Appendix D: Software Developed for Ultrafast GED (STREAK) 659 amplitude is within Pd percent of the absolute profile maximum. The amplitudes are taken relative to the local minima flanking the local maximum. Furthermore, the local minima must have amplitudes less than Pd percent of the absolute profile maximum. D.7.2.13 Analyze Streak Image A streak profile analysis of the foreground region proceeds in four steps. First, the image background offset is calculated by averaging the count values of all pixels located within the background region. Second, profiles at angle 0 relative to the x- and y-axes are calculated across the entire foreground region. The rotated y-axis should be the streak axis in the CCD images. STREAK examines the profile along this axis, breaking the profile into one or more segments corresponding to the peaks it identifies as described below. Third, profiles at angle 0 are calculated individually for each peak region. The program determines the center position and FWHM of each peak using two different techniques, both very simple. Finally, STREAK creates an output file summary of the peaks and their profiles. Determining the average intensities along a CCD image's x- or y-axes is an easy calculation (see Eqs. D.39 and D.4O in D.6.2); this is not so along other trajectories, although the basic principle is the same. STREAK calculates angular profiles by mathematically overlaying a rotated coordinate frame on the foreground region (see Figure D-11). In this figure, the original axes are unprimed and border the top (x-axis) and left (y-axis) edges of a 4x3 pixel region. Rotation takes place about the upper left corner of the foreground region, the origin of both frames. The new foreground region in the rotated (primed) frame must completely cover the original foreground region, and Appendix D: Software Developed for Ultrafast GED (STREAK) 660 therefore the dimensions of the new region will be the same or larger (5x4 in the example of Figure DI 11) than the dimensions of the original region. X I i I I Furthermore, the origin will not be located at the \ -1 I I upper left corner of the new foreground region. If 0 --E. ... is positive (counterclockwise rotation), then the new foreground region will extend into negative x'. If 0 is negative (clockwise rotation), then the region will extend into negative y'. After establishing the primed Figure D-11: Rotation of coordinate frame to find the profiles along an angle e relative to the CCD x-y axes. In the example shown here, the 4x3 pixel array must be mapped onto a rotated 5x4 pixel array. frame, STREAK calculates the average x' - and y' -axis profiles by taking each pixel in the original foreground region and dividing its total count value amongst the columns and rows of the primed frame. For example, columns C and D of the x' -axis in Figure D-11 would each receive roughly half the total count value of the dark pixel at (2, 1). Row B of the y'-axis would receive a little less than half the count value, and row C would receive the remainder. The totals are weighted appropriately in order to calculate the correct average profiles; in Figure D-11, columns A and E receive count value contributions from smaller areas of the original foreground region than columns B, C, and D. A single pixel in the original foreground region can overlap anywhere from one to three rows and columns in the rotated frame, depending on pixel position and 0. A boxcar smooth is applied to the average profiles, although the smoothing process will increase the true peak FWHM. The width of the smooth is hard-coded into STREAK, but can be adjusted by altering the variable boxcar_width in the subroutine Appendix D: Software Developed for Ultrafast GED (STREAK) 661 streak_analyze() of STREAK.C. Currently, boxcar_width is set to 3 pixels. As mentioned earlier, STREAK generates angular profiles across the entire foreground region and uses the y' profile to determine the number of peaks. This profile is rescaled such that the minimum count value is set to O ADU, and the maximum count value CPMax is noted. The entire profile is then broken up into at most ten segments, where each segment meets two criteria dependent on the discriminator dp. First, the ends of the segment must be local minima with count values less than dpxCPMax• (The end of a segment can also be one of the profile boundaries, in which case the count value 1s unconstrained). Second, the segment must have a local maximum CPLocMax such that: CPLocMax - CPLocMin ~ d p ( CPMax - CPLocMin) (D.42) where CPLocMin is the larger of the two local minima. STREAK then redetermines angular profiles for each segment and corrects the profiles with the background offset. The FWHM of a segment profile is estimated by interpolating the pixel position of half intensity on either side of the maximum. Two peak center positions are found, one corresponding to the profile maxima and one corresponding to the FWHM centers Uust like in RADAR2's center search procedure - D.3.4). At the end of the analysis, STREAK creates a CSV file under the user-supplied output name. The output file contains the following information: 1. The source CCD image, background offset, streak angle, discriminator value, and number of peaks. 2. Two tables of distances between peak center positions, one for centers found from peak maxima and one for centers estimated from peak FWHM. Appendix D: Software Developed for Ultrafast GED (STREAK) 662 3. Total peak intensities (corrected with the background offset). 4. Peak center positions, both from the profile maxima and FWHM. 5. The offset and ranges used to calculate each peak's profiles. The offsets have been transformed from the primed frame into the unprimed frame, and will most likely be located outside of the original foreground region. 6. The FWHM for both the x and y' profiles of each peak. 7. Tables of average profile intensities as a function of distance (in pixels) in the primed frame. This output file will be located under the path and extension set with the Change Path menu item (D.7.2.2). D.7.2.14 Generate Surface (Text) Recent versions of SpectraSource's HPC-1 program allow the user to export CCD images in various picture formats, but not as tables of raw data. This menu item converts a CCD image into a text array of pixel count values, suitable for loading by commercial spreadsheet programs and other analysis software. Moreover, the entire CCD image does not have to be converted; the user can extract just a rectangular subset of the image pixels. The conversion area is defined by the foreground region offsets and ranges. STREAK then creates a CSV output file listing pixel count values first by column and then by row. The x- and y-axis pixel coordinates head each column and row, respectively, and the path and filename of the source CCD image are also included in the output. The output file is saved under the name and path selected by the user (menu items one and two) and under the extension ".XLF'. STREAK does not use the background region, streak angle, or discriminator values when generating a surface. Appendix D: Software Developed for Ultrafast GED {STREAK) 663 D.7.2.15 Generate Surface {Binary) This menu item also generates an array of pixel count values, but the output file is more compact. (Typically, a binary surface file will be one-third to one-half the size of a corresponding text surface file.) The binary output file begins with the x- and y-axis ranges of the foreground region, written as two long integers (four bytes each). Then the count values are written as unsigned integers (two bytes), first by column and then by row. The output file does not contain the coordinates of the foreground region or the name of the source CCD image. The binary file can be converted into a CSV format text array using option five of the program CONY (D.11.5). D.7.3 STREAK Option Three: Batch File Processor In the standard streaking experiment, many CCD exposures are recorded in order to span a wide range of electron beam intensities. With this menu option, the user can run a pre-generated batch file in order to automate analysis of the streak images. The batch file (format shown in Table D-34) starts with an identification header (PROFILEBATCH-STREAK) and the number of ')obs" in the batch file. Each job lists the offsets and ranges for the foreground region, the offsets and ranges for the background region, the streak angle, and the discriminator percentage. These values are followed by the number of input CCD images the job will examine and the list of their filenames and corresponding output filenames (without extensions). The CCD images should be located along the default image path under the default extension, although these parameters can be changed beforehand with main menu option one (D.7.1). A sample streak profile batch file is presented in Table D-33. Appendix D: Software Developed for Ultrafast GED (STREAK) 664 Streak Profile Batch File Format ~---------------,-----------r-----------r-----------1 PROFILE-BATCH-STREAK 1 1 1 r----------------,-----------r-----------,-----------, I [Number of Jobs] I I I I 1 1 I 1 I [Foreground X-Axis Offset] [Background X-Axis Offset] I I [Foreground 1 1 I Y-Axis Offset] I [Foreground X-Axis Range] [Background [Background 1 1 I Y-Axis Offset] I X-Axis Range] I I 1 I 1 I [Foreground Y-Axis Range] [Background 1 I Y-Axis Range] r---------------;--------------r-----------r-----------11 1i I S1 I I I I I t,r---------------Ti-----------r-----------r-----------, [Rotation Angle] [Discriminator] 1 1 1 1 r----------------,-----------r-----------,-----------, [Number of Images] 1 1 1 1 1 J,r---------------,-----------r-----------,-----------, [Input Image I [Output I I I 1 Filename 1] 1 Filename 1] 1 1 1 01 I I I I r----- ----------,-----------r-----------,-----------, b1 : I : I : I : I r---------------,-----------r-----------,-----------, I [Input Image I [Output I I I I Filename Nrml I 2: [Foreground X-Axis Offset] : 1 di _______ n1 = _______ Filename Nrml I [Foreground Offset] 1 Y-Axis I I [Foreground X -Axis Range] I [Foreground Y-Axis Range] I 1 1 I T _____ -----r----- =-----:-----=-----~ = I I Table D-34: Format of batch file used with option three of STREAK to analyze a collection of streaked electron beam images. Once Batch File Processor is selected, the user can either choose a batch file or change the default path and extension under which STREAK searches for the batch file. If the chosen batch file has the correct header, then the analysis begins immediately. No new screen is displayed; instead a simple line of text appears indicating the job number and the current input CCD image and output filename . The output files will have the path and extension set using the Change Path item of main menu option two (D.7.2.2). STREAK conducts no error checks during the analysis; the results are Sample Streak Profile Batch File Appendix D: Software Developed for Ultrafast GED (STREAK) 665 unpredictable if the batch file contains a foreground or background region extending outside of the limits of a CCD image. D.8 PROC4 PROC4 is the immediate predecessor to PROC5, and the two programs are quite similar in several ways. Both have control structures centered on graphical displays, the MS and RD screens, and most of the same keystroke commands. Both use the same ELEMENTS.DAT, the same molecular structure data files, and the same scattering factor data files. PROC4 does require one additional set of data, the electron inelastic scattering factors Sa(s), but the format of this file is identical to the other scattering factor files. The PROC4 version of DFLT_SET.DAT file is slightly different. PROC4 was mothballed because the background correction method is inadequate: only the D' Antonio fitting method is available (D.4.4.11.2), with no preparation of the raw experimental data. Furthermore, the theoretical data is not treated in a way that ensures a perfect match of experimental and theoretical zero positions. Background curves cannot be saved, loaded, or used on other experimental data sets, and the amplitude scaling factor between sME(s) and sMT(s) cannot be fixed. Finally, PROC4 was written when the UED laboratory still used a 1024x1024 CCD detector, so the data arrays have larger dimensions than in PROC5. Consequently there are fewer data arrays in PROC4 than in PROC5 because of memory limitations, and the program code is harder to understand since the same arrays must be used to store different data during different steps in the calculation. A description of PROC4 is included in this appendix because PROC4 loads the Appendix D: Software Developed for Ultrafast GED (PROC4) 666 inelastic scattering factors, whereas PROC5 does not. Although PROC4 should not be used anymore for fitting experimental data, the program will still generate I\) or 1: () correctly for an arbitrary molecule. Either curve can be created as a function of pixel position or regular intervals of s, but minor editing of PROC4 routines is required. As with PROC5, the theoretical scattering curves are initially calculated in the subroutine calc_theo() and then manipulated further in calc_zeros() (both subroutines are found in PROC4.C). The theoretical atomic and inelastic scattering curve defined in Eq. D.43 is stored in atomic[i] as a function of pixels, and the array background[i] (D.43) When PROC4 runs through calc_zeros(), raw_data[i] is filled with sM\pix), but output files of either IT(s or pix) or I: ( s or pix) can be created by editing the following lines from calc_zeros(): raw_data[fx] = s*molecular/background[fx] /*atomic[fx]*/; /* raw_data[fx] =molecular+ atomic[fx]; */ /* background[fx] =molecular+ atomic[fx]; */ To generate {(pix) or 1: (pix), remove the comment brackets from around the definition of background[fx]. (The example shown here puts {(pix) in background[fx].) To generate l(s) or 1: (s), the data must be interpolated to regular intervals of s. This is the destiny for data stored in raw_data[i], so the comment brackets around the second definition of raw_data[fx] ought to be removed. The interpolated data will be placed in the array ms_data[i][O]. Several lines from the subroutine which creates the output file (act_save() in Appendix D: Software Developed for Ultrafast GED (PROC4) 667 PROC4_DT.C) must also be edited depending on whether the output data is a function of s or of pixels: for (s = O; s < snum_pts /* raw_num_pts */; s++) { if (proc_mode) else { if (load_flag) else sprintf(path,"%G, %G\n", raw_s[s], background[s]);*/ sprintf(path,"%G, %G\n", (s*MS_step), ms_data[s] [0]); /* } fwrite(path, 1, strlen(path), outs); } The code shown here is currently prepared to write ms_data[i][O], which is a function of s. Two changes must be made to write data as a function of pixel position. First the upper limit on the for() loop must be changed from snum__pts to raw_num__pts. Second, the comment brackets must be moved from the upper sprint£() statement to the lower sprint£() statement so that the array background[s] is written instead. As a final note, it is worthwhile to doublecheck the values for both Ae and L. Also, make sure the boxcar-smoothing widths n_beam_sz and n__pts_smo are reset to desired values. The array atomic[i] is smoothed once with width n_beam_sz, and the array raw_data[i] is smoothed twice: once with width n_beam_sz and once with width n__pts_smo. No arrays are smoothed with width n__pts_fit; n__pts_fit is used in a slightly different manner in PROC4. PROC4 requests 3 Mb of extended memory from the computer in order to store PROC4.EXE Program Files Include Files PROC4.C PROC4_DT.C PROC4_10.C PRC4_FIT.C CEXT.C DATA_PR4.H SETTING4.H CEXT.H COMPAT.H Table D-35: Program and include files needed to build PROC4.EXE. Appendix D: Software Developed for Ultrafast GED (PROC4) 668 atomic scattering factors (less than 1 Mb of memory is actually needed). Table D-35 lists the program and include files required to rebuild PROC4.EXE. D.9 R-K As part of the theoretical investigation into UGED, classical trajectories of photoexcited iodine molecules on the B state were calculated for a range of excitation energies (2.5.2) using the program R-K. R-K is essentially an ordinary-differential- equation integrator ensconced in the trappings of a molecular dynamics simulator. The program uses an embedded Runge-Kutta integration scheme with Cash-Karp parameters (adapted from Numerical Recipes [Pre92]), and could easily be modified to accommodate other theoretical problems involving ODEs. All integration variables are double precision floating point (eight byte), affording roughly 15 significant figures. In its present form RK integrates just two ODEs, the equations of motion for a one-dimensional system: ✓~(E-V(r)) r = V V 1 d = a = ---V(r) µ dr (D.44) (D.45) where r (in this case) is the internuclear separation between two atoms, and V(r) is the potential energy function. Actually, R-K is written to simulate the photoexcitation dynamics of a specific system, molecular iodine, generating trajectories along the B-state surface during a time interval of -0.75 ps to +2.75 ps. As a result, R-K is not as userfriendly as most other programs in the UGED software package. R-K certainly can be modified to model other systems over different time intervals, but some programming will Appendix D: Software Developed for Ultrafast GED (R-K) 669 be involved. The X- and B-state potential energy surfaces are approximated with HulburtHirschfelder equations [Hul41], [Hul61] using Gerstenkorn and Luc's Dunham coefficients [Ger85] (see 2.5.2 for more details). After seeding the random number generator with the clock, R-K establishes the initial conditions and integrates the trajectory's path in time steps of at most 1 fs. The zero of time corresponds to the arrival of the fs laser excitation pulse. Energy variables have units of cm·1, the position coordinate has units of A, time is in ps, and velocity has units of Alps. R-K is designed to keep errors below one part in 105 (including energy conservation errors), and in practice the error estimates are much less than this. The trajectories are stored as a probability array, T(r;, tj), in time intervals of 5 fs over a range of -0.75 to +2.75 ps. Position is recorded to the nearest 0.01 Aover a range of 0.0 to 14.0 A. R-K both reads and writes raw trajectory data files . The program also creates a second type of trajectory data file (write-only) with the same position coordinates, but spanning a smaller time range of 0.0 to +2.0 ps. This files accounts for the temporal width of a probing electron pulse by convoluting T(r, t) with the electron pulse-shape over the temporal coordinate, creating a new array, Te(r, t). The Te(r, t) files serve as input for the program PROC3 (see D.10). R-K requests 4 Mb of extended memory from the computer, enough memory to store one set of raw trajectory data. (The data is stored as four-byte floating point numbers, and 4 bytes x 1401 position intervals x 701 time intervals = 3.75 R-K.EXE Program Files Include Files R-K.C R-K_DT.C R-K_IO.C CEXT.C DATA_R-K.H SETTINGK.H CEXT.H COMPAT.H Table 0-36: Program and include files needed to build R-K.EXE. Appendix D: Software Developed for Ultrafast GED (R-K) 670 Mb.) The program and include files required to build R-K.EXE are listed in Table D-36. D.9.1 R-K Option One: Calculate Vibrational Trajectories This menu option generates iodine vibrational trajectories along the ground (X) state or the B-state. These trajectories can be saved into a new raw data file or added into an old raw trajectory file if option three of R-K has been selected first (D.9.3). Although there are nine menu items, the first three items (involving the integration time and range) probably should not be changed from their default settings. R-K has no error checks and, as discussed below, the program has been tuned to a specific time interval and step size. D.9.1.1 Start Time This floating point number has units of ps and tells R-K where in time to start recording the trajectory. The zero of time for excitation to the B state has been hardcoded as 0.75 ps in the initial-condition routine, and the default value of the start time (0 ps) actually refers to -0.75 ps. At present, the excitation time for a given B-state trajectory will be to± 64 fs, so the start time should never be greater than 0.686 ps. D.9.1.2 End Time This floating point number has units of ps and tells R-K where in time to stop recording the trajectory. The default value of 3.5 ps actually refers to +2.75 ps on the time scale of the B-state dynamics. The end time should be greater than the largest possible initial excitation time for a B-state trajectory (0.814 ps). Several arrays are hardcoded to a dimension of 701, however, so the end time should not become too big such that there are more than 700 temporal steps. Appendix D: Software Developed for Ultrafast GED (R-K) 671 D.9.1.3 Step Time This floating point number has units of ps and sets the size of the temporal intervals in T(r, t). The default value for the step size is 5 fs. Although R-K does not conduct an error check, the program will run into trouble (and probably crash) if an interval size is chosen which leads to more than 700 steps between the start time and the end time of the integration (see D.9.1.2 above). D.9.1.4 Number Of Trajectories The user chooses the number of trajectories (NT, stored as a long integer) which RK will calculate upon selection of either of the integration menu items (D.9.1.8 and D.9.1.9). A single set of raw data can store a very large number of trajectories; the ultimate limit is set by the greatest possible value of a four-byte floating point variable. D.9.1.5 Initial Energy For integration along the B-state, this floating point menu item is the average excess energy E0 (in cm- 1) of the excitation laser relative to the bottom of the potential energy well. The actual excitation energies of trajectories will be distributed about this value. For integration along the X-state, the initial energy is again relative to the bottom of the well, but there will be no distribution of trajectory energies (see D.9.1.8 below). D.9.1.6 Output Filename The user enters a standard DOS eight-character name for the next raw trajectory data file to be generated by one of the integration menu items. The file will be saved along the default path with the default extension, both of which can be changed with main menu Appendix D: Software Developed for Ultrafast GED (R-K) 672 option four (D.9.4). D.9.1.7 Clear Memory Of Trajectories This menu item clears the section of extended memory in which R-K stores the raw trajectory data set. D.9.1.8 Integrate - X State Integration along the X state is included in R-K to test the Runge-Kutta integrator. The technique is a bit different from the method for generating iodine trajectories on the B-state (see D.9.1.9 below) because the goal is simply to simulate ground-state classical behavior, so the energy and pulse width of the excitation laser do not come into play. All trajectories start with the same initial energy relative to the bottom of the X-state potential well. For each trajectory, R-K calculates a value for the starting internuclear separation by completing the following steps: 1. Finding the inner turning point for energy Ea. 2. Choosing a random time t between O fs and h, where h is the vibrational period of iodine at energy Ea. The value for his hard-coded into the program get_X_init_cond() of R-K_DT.C, and must be determined by the user in advance. One method of finding his to edit R-K so that the program simply evolves a trajectory from the inner turning point for several periods. Currently, 1 h= 157.86 fs for Ea= 308.96 cm· . This energy corresponds to the average '2 energy of the Boltzmann distribution at 150 °C. 3. Find the starting internuclear separation by evolving a trajectory from the inner turning point for time t. Appendix D: Software Developed for Ultrafast GED {R-K) 673 After this initialization sequence, R-K resets the time and evolves the trajectory from the Start Time to the End Time, as chosen in this menu. The program has now created a list of internuclear separations r as a function of time. R-K stores this trajectory by pulling T(r, t) from extended memory, finding the r; coordinate nearest to the calculated r for each time step fj, and incrementing T(r;, fj) by one. Once R-K has accumulated all NT trajectories, the program saves the raw trajectory array to disk under the name chosen with the Output Filename menu item (D.9.1.6). (Note that pressing the ESC key will interrupt the integration before R-K has reached NT, but the program will save the results of all completed trajectories.) The output file is binary and starts with two long integers: the number of position elements (1401) and the total number of trajectories. This is followed by the array of four-byte floating point numbers comprising T(r, t), written first by row (position) and then by column (time). The raw trajectory data files can only be read with main menu option three of R-K (D.9.3). The files are not in the proper format for either PROC3 or CONV; they must be convolved with the electron pulse width first (D.9.2). The trajectory data is still in memory even though an output file has been created, so more trajectories can be added in as desired (including B-state trajectories). Unfortunately, at the present time different X-state energies cannot be mixed without exiting the program, changing TE, rebuilding R-K.EXE, and then reloading an old trajectory into memory. D.9.1.9 Integrate - B State When this menu item is selected, R-K begins calculating NT trajectories of iodine Appendix D: Software Developed for Ultrafast GED (R-K) photoexcited to energy E0 above the bottom of the B-state potential well. 674 For each trajectory, R-K must establish a set of initial conditions, and the program makes three main assumptions: ( 1) iodine is photoexcited from the lowest vibrational level of the ground state, (2) the excitation laser pulse has a gaussian temporal distribution with a FWHM of 50 fs, and (3) the laser pulse is transform-limited. R-K uses the Monte Carlo technique to choose random values for the initial position, energy, and excitation time of each trajectory. The starting internuclear separation rn of trajectory n must belong under the probability distribution of ground-state iodine's lowest vibrational level, modeled as a harmonic oscillator. This gaussian function has a standard deviation of: a = Ii -- ✓2µme = o.0352 A (D.46) By assuming the laser pulse is transform-limited, the initial energy En must fall under a gaussian distribution of energies centered on E 0 . This distribution will have a FWHM given by [Gre74], [Fle86]: l:1E fwhm Kh = -- (D.47) /j.f fwhm where K is the time-bandwidth product. For gaussian pulses, K = 0.441. The FWHM is related to cr by: a = fwhm/Js In 2 (D.48) If a particular combination of rn and En lie outside of the B-state PES, then new values are found. The initial velocity is determined from rn , En, and the PES, and a direction is randomly assigned. The last initial condition R-K must pick is the zero of time to,n for this Appendix D: Software Developed for Ultrafast GED (R-K) 675 trajectory; to,n is assumed to lie under a gaussian probability distribution with FWHM of 50 fs centered on t0 . Once all the initial conditions are established, R-K evolves the trajectory on the Estate from to,n to the End Time. The resulting list r(t) is stored in T(r, t) as described for the X-state integration, but with one difference. The probability distribution for the lowest vibrational level of the X-state is added into all time steps tj before to,n in order to represent the molecule's pre-excitation history. This probability distribution is normalized to have unit area. After all NT trajectories have been calculated, a new raw trajectory data output file is created with the same method as under the Integrate - X State menu item (D.9.1.8). D.9.2 R-K Option Two: Convolve Electron Pulse Time Molecular trajectory arrays T(r, t) created with option one of R-K only account for temporal broadening due to the initiating laser pulse width. The detection process has not been incorporated; that is the purpose of this menu option, which allows the user to test the effects of different detector resolutions on the same set of trajectory data. R-K assumes that the detection pulse (referred to as an electron pulse to keep in the spirit of UGED) has a gaussian temporal distribution with standard deviation aeb• R-K convolutes the current T(r, t) loaded in extended memory with this probability distribution out to 3aeb• The resulting trajectory array Te(r, t), which covers a temporal range extending from to out to to+ 2 ps, is written directly to a new file on disk, and T(r, t) in extended memory remains unaffected. Appendix D: Software Developed for Ultrafast GED (R-K) 676 D.9.2.1 Electron Pulse FWHM This floating point number is the FWHM of the electron beam temporal profile in fs (not ps). The maximum value is 585 fs, which corresponds to a <Jeb = 248.4 fs according to Eq. D.48. With this limit, 3aeb is always less than the 0.75 ps of trajectory history extending before and beyond the 0.0 to +2.0 ps range of the output file Te(r, t). (Recall from D.9.1.1 that to is actually located at +0.75 ps.) The electron beam pulse width may be set to zero. D.9.2.2 Output Filename The user enters a standard DOS eight-character name for the electron-pulse-widthconvolved trajectory data file. The file will be saved along the default path with the default extension, both of which can be changed with main menu option four (D.9.4). D.9.2.3 Convolve In Electron Pulse Time Selecting this menu item tells R-K to convolute the trajectory array in extended memory with a gaussian temporal pulse with standard deviation <Jeb• The general form of a convolution integral is: F(r) = f J(t)g(r-t)dt (D.49) but in this application the functions f and g are actually discrete arrays and a summation must be performed instead. The normalized equation is: R-K writes the results of this calculation directly to a binary data file under the name Appendix D: Software Developed for Ultrafast GED (R-K) 677 selected with the Output Filename menu item (D.9.2.2). The binary file starts with two long integers (eight bytes): the number of position elements (1401) and the number of temporal elements (701). The array of four-byte floating point numbers making up Te(r, t) then follows, written first by row (position) and then by column (time). The new binary file will be accepted as input by the program PROC3 (D.10), which uses Te(r, t) to create time-dependent sM(s) andf(r) functions. The binary file can also be converted into a CSV format text file of floating-point numbers with the program CONY (D.11). D.9.3 R-K Option Three: Load Old Trajectories This menu option allows the user to choose a raw trajectory data set located under the default path and extension. The data is automatically loaded once a filename has been selected, and any old data still present in extended memory will be overwritten. R-K makes no error checks when loading trajectory data. The user should not try to load files containing Te(r, t) trajectory data. D.9.4 R-K Option Four: Change Path This menu option allows the user to alter the directory path for all trajectory input and output data files. The default extensions for the raw data files (.TRJ) and electronpulse-width-convolved data files (.CNV) can also be changed. D.9.5 R-K Option Five: Test Initial Conditions The user may wish to check that the trajectory initialization routine does indeed produce the desired random distributions of position, energy, and time for the reaction. Selecting this menu option tells R-K to run the initialization routine 1000 times and write Appendix D: Software Developed for Ultrafast GED (R-K) 678 the results to a CSV text file called INITTEST.XL0. R-K requires an initial excitation energy; this value is hard-coded as the variable init_energy into the subroutine test_init_cond() of R-K.C. For each trajectory, INITTEST.XL0 lists the actual excitation energy (cm- 1), the internuclear coordinate (A), the relative velocity (Alps), and the reaction start time (ps). INITTEST.XL0 will be located in the current directory; the file's name and path can only be changed by editing test_init_cond() and then rebuilding R-K.EXE. D.9.6 R-K Option Six: Check The Total Count Another method for doublechecking the integration program is to demonstrate "trajectory conservation." For every time step tj the following equation should be true: (D.51) The inequality occurs only if the initial excitation energy is above the dissociation energy; in this case it is possible for the total count to decrease over time as individual trajectories pass outside of the array dimensions. Executing this menu option causes R-K to download the trajectory array stored in extended memory and sum the population at each time step. A single column text file called TOT ALCHK.XL0 is created which lists these populations (the temporal coordinate is not present). TOT ALCHK.XL0 will be located in the current directory; the file's name and path can only be changed by editing the subroutine total_check() in R-K.C and rebuilding R-K.EXE. Appendix D: Software Developed for Ultrafast GED (PROC3) 679 D.10 PROC3 The primary purpose of PROC5 and most of its predecessors is to remove the background function from experimental isotropic GED patterns, and then compare the results with theoretical simulations. PROC3, however, was written with a different goal in mind. PROC3 generates theoretical sM(s) and f(r) curves for two sets of scattering conditions unique to ultrafast GED. The first case is vibrational coherence, where the total experimental resolution MT01 is comparable to or less than the time scale of internuclear motion. A description of the molecular dynamics simulation program, R-K, has already been provided (D.9); PROC3 takes the trajectory arrays produced by R-K and calculates time-dependent molecular scattering and radial distribution curves from them. The second case is rotational coherence, where MTo1 is comparable to or less than the time scale of molecular rotation. In a UGED experiment, the excitation laser changes the molecular sample from an isotropic distribution into an orientationally anisotropic mixture of excited and unexcited molecules (2.4). This anisotropy appears in the diffraction pattern whenever the excited or unexcited molecules undergo a rotational recurrence, and PROC3 will simulate the anisotropy. Like R-K, PROC3 is not particularly user-friendly because the program was written at a time when the theoretical ramifications of ultrafast GED were first being developed. In fact, PROC3 assisted in showing that the integral: 2 2 -f f sin Ocos l/f -f exp(is • )da sinOdlfldQ 4n 2n 1 ir ir O O 2 2 [ 1 ir ] r;j 0 had an analytical solution (see 2.4.7 for angular dependences of sand rab): (D.52) Appendix D: Software Developed for Ultrafast GED (PROC3) 680 (D.53) Table D-37 lists the files required to build PROC3.EXE. PROC3 does not require extended PROC3.EXE Program Files Include Files memory because trajectory arrays are read one line PROC3.C PROC3_DT.C PROC3 10.C at a time and all other data can be stored in conventional memory. PROC3 loads only two data DATA_PR3.H SETTING3.H Table D-37: Program and include files needed to build PROC3.EXE. files, BESSEL.DAT and HCFI18KV.DAT, during the program's initialization phase. Both files should be located in the same directory as PROC3; the paths and filenames are hard-coded into arrays bes_buf[i] and sf_buf[i] in the subroutine act_init() of PROC3.C. BESSEL.DAT is a text file which contains values of the zeroth order Bessel function, J0(z), over a range of0 ~ z ~ 25. The file has one datum per line in steps of0.01, or 2501 lines total. The data in BESSEL.DAT is used only by main menu option nine, the twodimensional anisotropic molecular scattering calculation for CF3I (D.10.9), which numerically integrates Eq. D.52 over Q and \j/. The other 2-D scattering calculations use the analytical solutions. The second file, HCFI18KV.DAT, contains electron scattering factors !f;(s)I and ll;(s) for the elements hydrogen, carbon, fluorine, and iodine. The format of this file is similar to the scattering factor data files for PROC5 (D.4.2.3) except there is no header line and the amplitudes and phases are combined into one file. The data starts at 0.00 A- 1 and continues in 0.01 A- 1 steps, one value of s per line, out to at least 15.00 A- 1 (PROC3 stops reading HCFI18KV.DAT then). Each CSV line lists the four amplitudes followed Appendix D: Software Developed for Ultrafast GED (PROC3) 681 by the four phases. PROC3 actually only needs the scattering factors in 0.02 A- 1 steps, so the program skips over every other data line. This approach seemed easiest; HCFI18KV.DAT can be created simply by copying columns from existing scattering 1 factor data files (stored in 0.01 A- steps) without removing every other line. The scattering factors must correspond to the same electron kinetic energy as the Ae used in PROC3. The de Broglie wavelength appears in the definition of the floating point variable wave_constant in the file PROC3.C. The twelve main menu options in PROC3 are listed below. Six of the first seven options control the transformation of R-K's Ii dynamics trajectory arrays into sM(s, t) and J(r, t) surfaces. The last five options calculate 2-D sM(s) and J(r) surfaces for various anisotropic sample distributions of Ii, CF3l, and CH2Iz. Option five, which defines the value of the damping constant kd, affects both sets of calculations. D.10.1 PROC3 Option One: Change Path With this menu option, the user alters the default drive and path specifications for input and output files related to time-dependent vibrational coherence scattering calculations. The extension for input trajectory arrays (.CNV) can also be changed. D.10.2 PROC3 Option Two: Select Input Position Array This menu option allows the user to select a trajectory array located under the default path and extension set in option one (D.10.1). The trajectory array must have been convoluted with the electron beam temporal pulse width (i.e., the array cannot be one of R-K's "raw" trajectory arrays). The format of the input array is described in D.9.2.3. The selected array is not immediately loaded, but rather read as needed during Appendix D: Software Developed for Ultrafast GED (PROC3) 682 the calculation of sM(s, t) andf(r, t). D.10.3 PROC3 Option Three: Molecular Scattering Filename The user enters a standard DOS eight-character name for the output file which will contain sM(s, t) . The default destination path can be changed with main menu option one (D.10.1), but the output extension .MS is hard-coded in the character array ext_MS[i] defined in PROC3.C. D.10.4 PROC3 Option Four: Radial Distribution Filename The user enters a standard DOS eight-character name for the output file which will contain f(r, t). The default destination path can be changed with main menu option one (D.10.1), but the output extension .RD is hard-coded in the character array ext_RD[i] defined in PROC3.C. D.10.5 PROC3 Option Five: Damping Constant The user enters a real number for the radial distribution transformation damping constant kd (see Eq. D.28 in D.4.1). The damping constant has units of A.2. D.10.6 PROC3 Option Six: Calculate Scattering When this menu option is chosen, PROC3 converts the Te(r, t) data from the selected trajectory file into two, two-dimensional output arrays - sM(s, t) and f(r, t). PROC3 makes several assumptions about Te(r, t): 1. The trajectory data depict the internuclear motion of homonuclear diatomic molecules (not necessarily 12). There is only one internuclear coordinate. 2. Each trajectory contributing to Te(r, t) actually represents not one but a set of Appendix D: Software Developed for Ultrafast GED (PROC3) 683 molecules with isotropic spatial orientations undergoing identical motion. In 3. The r-axis (with 1,401 elements) stores the population density in 0.01 Asteps. 4. Successive rows along the temporal coordinate are separated by 5 fs, but the number of these rows is unrestricted. The 12 Te(r, t) arrays generated with R-K have 1401x401 = -600,000 values. Most PCbased graphics packages struggle with this quantity of data, so the output arrays PROC3 creates are reduced to dimensions on the order of lO0xlO0. This particular menu option condenses the temporal coordinate by converting only every fourth data row (the three intervening rows are ignored), so rows in the output arrays sM(s, t) andf(r, t) occur every 20 fs. The modified molecular scattering data is calculated from 0.0 to 15.0 A- 1 in 0.1 A- 1 steps, so the sM(s, t) output array converted from R-K's 12 Te(r, t) data will have dimensions of 15lxl01. Thef(r, t) output array reports radial distribution data from 0.0 to 10.0 Ain 0.1 A steps, so the dimensions off(r, t) will be lOlxlOl. The trajectory array Te(r1, tk) records the fraction of homonuclear diatomic molecules having internuclear separation r1 at time tk, PROC3 calculates the s;M(s;, tk) array by summing the scattering contributions at different r1 as weighted by Te(r1, tk): (D.54) Electron scattering factors are not needed for this calculation; there is no phase difference between the atoms of a homonuclear diatomic, and the amplitudes cancel out in the Norwegian formulation of the modified molecular scattering curve. The exponential term containing the mean amplitude of vibration is also absent from Eq. D.54 because each Appendix D: Software Developed for Ultrafast GED (PROC3) 684 trajectory in Te(r, t) corresponds to a subset of molecules in perfect phase with each other. If NT is sufficiently large (~ 1000) then the sM(s) curve will reflect the average motion of the diatomic molecule. The oscillations will be damped just as if the sM(s) curve had been calculated at the average internuclear separation using the exp(-s2z2/2) term. PROC3 actually calculates the sM(s) curve in 0.02 A- 1 steps for each time element tk, but only every fifth value is inserted into sM(s, tk). The high resolution sM(s) curve is generated for transformation into the radial distribution curve. PROC3 calculates f(r) in 0.1 A steps and saves the results to f(r, tk)- The mathematics of the transformation is the same as in the program PROC5 (see D.4.1) although some of the variable names are different. PROC3 creates the two output files time-step by time-step as the analysis progresses. The files are binary and start with the array dimensions saved as two long integers (first the s- or r-dimension, then the t-dimension). The floating point values follow, written first by scattering or position coordinate and then by temporal coordinate. These files can be converted into CSV text arrays with the program CONY (D.11). D.10.7 PROC3 Option Seven: Calculate Scattering For Specific Times This menu option is very similar to its predecessor, Calculate Scattering, except the output files are CSV text format and the sM(s, fk) and f(r, tk) curves are saved with higher resolution (0.02 A-' and 0.02 A intervals, respectively). PROC3 calculates these curves for up to ten time steps tk. The values of k are hard-coded into the array when[i] in the subroutine spec_traj_to_scat() of PROC3.C, and the number of time steps PROC3 should convert is stored in the integer variable num_when. Note that when[i] lists the row number k, referring to Te(r, tk), and not actual times! Appendix D: Software Developed for Ultrafast GED {PROC3) 685 The mathematics of the sM(s, fk) andf(r, tk) calculation is identical to D.10.6. The first column of each output file identifies the s- or r-coordinate, and each remaining column contains sM(s) or f(r) at the specific time tk. The value of h in femtoseconds (assuming 5 fs per division in Te(r, t)) appears at the top of each column. D.10.8 PROC3 Option Eight: Calculate 2-D Scattering (IODINE) As mentioned in the introduction, this menu option and the remaining four generate two-dimensional sM(s) and f(r) arrays for GED from orientationally anisotropic sample distributions. These distributions emerge during the rotational recurrences of laser-excited (and -unexcited) molecules. Option eight calculates 2-D sM(s) surfaces for six sample mixtures of X-state and B-state molecular iodine with different spatial orientation distributions (see Table D-38). PROC3 uses the following equation: (D.55) As with the 12 trajectory conversions (D.10.6), electron scattering factors are not needed in Eq. D.55. Values for ri-1 and l,_, correspond to the lowest vibrational level of each electronic state. The implied scattering geometry is the same as Figure 2-11 in 2.4.2, and the functional forms of Fab(s) are listed in Table 2-5. The user should also refer to the analytical forms of the fractional order Bessel Output X-State 8-State Filename Distribution Distribution .MSl2A.XL0. .........Isotropic ........ .................-................. MS12B.XL0 PPU ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• •••••••••••••••••••••••••••••••••••• MSI2C.XL0 PPU PPE MSl2D.XL0_....2/3 .Isotropic .... ....1/3 ..lsotropic.... .MSl2E.XL0.............. PPU .................1/3__Isotropic.... MSl2F.XL0 1/3 Isotropic PPE + PLE Table D-38: X-state and B-state '2 spatial orientation distributions in the 2-D sM(s) output files created with option eight of PROC3. Isotropic: an isotropic molecular sample; PPU: excitation laser polarization vector perpendicular to ko and consider just the unexcited subset of molecules (X-state); PPE: perpendicular/ excited (B-state); PLE: parallel/ excited (B-state). Appendix D: Software Developed for Ultrafast GED (PROC3) 686 functionsj;(z) listed in Eqs. B.17 through B.19 when reading the C-code. The names of the six output files which PROC3 creates are hard-coded in the array rot[i] of the subroutine calc_2D_I2() in PROC3.C. These CSV format text files are written to the current directory. PROC3 calculates sM(s) in 0.2 A- 1 steps along both the x- and y-axes; since each axis spans a range from -10.0 A- to+ 10.0 A- , the output arrays 1 1 have dimensions of lOlxlOl. The data is written out first by x-coordinate and then by ycoordinate, and each column and row is headed by the value of s x or Sy, respectively. D.10.9 PROC3 Option Nine: Calculate 2-D Scattering {CF3I) This menu option calculates the sM(s) surfaces of ground-state CF3I for the five different spatial orientation distributions listed in Table D-39. The transition dipole moment is assumed to be along the C-1 axis. PROC3 uses Eq. D.56 to generate sM(s): (D.56) where Fu(s) is the triple integral shown earlier in Eq. D.52. The integral over a can be done analytically yielding a complicated expression involving the zeroth Bessel function of zeroth order, J0(z) (see 2.4.7 and Eq. 2.164). This menu option calculates the remaining double integral numerically, breaking the Q and 'JI integrals into summations with step sizes of rr/50. The values for J0(z) are obtained from two Output Spatial Filename Distribution .CF31A.XL0 .......... Isotropic ........ CF31B.XL0 PPE ................................................................. CF31C.XL0 PPU ···•••······•••••·••••••••••• •••••••••••••••••••••••••••••••••••• CF31D.XL0 PLE ................................................................. CF31E.XL0 PLU Table D-39: Ground state CF 31 spatial orientation distributions in the 2-D sM(s) output files created with option nine of PROC3. sources: (1) when O ~ z ~ 25, J0(z) is interpolated from data provided by BESSEL.DAT, and (2) when z > 25, J0(z) is calculated using the first few Appendix D: Software Developed for Ultrafast GED (PROC3) 687 terms of the asymptotic expansion [Abr72]. Option nine is the only portion of PROC3 which uses BESSEL.DAT. Amplitude and phase scattering factors are interpolated from data provided by HCFI18KV.DAT. The format of the output files is identical to the 2-D sM(s) output from option eight. D.10.10 PROC3 Option Ten: Calculate 2-D Scattering {CH2I2} When this menu option is selected, PROC3 creates the 2-D sM(s) scattering surface from a PPE distribution of ground-state CH2h molecules. The parallel transition dipole moment is assumed to lie along the I·· •I axis, and PROC3 calculates sM(s) using Eq. D.56 with the !fFl!fil denominator term replaced by !fil 2 . Instead of integrating over Q and \jf as in the previous menu option, PROC3 employs the analytical solution shown in Eq. D.53. Scattering factors are estimated using the data read from HCFI18KV.DAT. The output file, CH2l2_PE.DAT, has the same format as the output files in options eight and nine, and the file will be located in the current directory. D.10.11 PROC3 Option Eleven: Calculate 2-D Transform {IODINE} Although PROC3 generates the 2-D sM(s) surfaces across a rectangular coordinate system (sx, Sy), Figure 2-11 shows that the scattering symmetry lends itself more appropriately to polar coordinates (s, <!> ). The diffraction pattern is symmetric about the x- and y-axes, so the program need only create a surface for one quadrant of the detection plane. PROC3 calculates individual radial distribution functions for specific angles <\>;, where O ::;:; <\>; ::;:; rc/2 and successive <\>; are separated by rc/60 (3°). The program must first, though, generate the associated sM(s) curves along radial lines, and PROC3 Appendix D: Software Developed for Ultrafast GED (PROC3) 688 does this over a range of 0.0 to 15.0 A- 1 in 0.02 A- 1 steps. Output Spatial Filename Distribution The mathematics of the transform is the same as in PROC5 12RDA.XL0 •••••••••••••••••••••••••••• ........Isotropic ........ _12RDB.XL0_ •••••• ••••••••••••••••••••u PPE •••••••• 12RDC.XL0 PPU (D.4.1), and the f(r) curves are created in 0.1 A steps. Table D-40: This particular menu option calculated 2-D f(r, <1>) surfaces for three spatial orientation distributions (Table D40) of 1z in the X-state (v = 0). Ground state spatial orientation distribu-tions in the 2-D f(r') output files created with option eleven of PROC3. 12 The sM(s) curves are calculated as in D.10.8 with Eq. D.55 (except no B-state molecules are included) and the f(r) curves span a range of 1.0 to 4.0 A. The CSV text output files are formatted for the graphing program PSPlot because PSPlot is one of the few software packages which will plot in cylindrical coordinates (r, <1>, f(r, <1>)). The output file has no headers; each line contains an internuclear separation, the radial angle, and finally f(r, <1> ). The data varies first by r and then by <1>, so all data for a specific <l>i are grouped together. The output files will be found in the current directory. D.10.12 PROC3 Option Twelve: Calculate 2-D Transform (CF3I) When this menu option is selected, PROC3 creates 2-D f(r, <1>) surfaces of groundstate CF3I using the same technique as in option eleven. Two surfaces are generated, one corresponding to an isotropic sample distribution (CF3IA.XL0) and one corresponding to a PPU distribution (CF3IB.XL0). The sM(s) PPU distribution is not numerically integrated as in D.10.9; instead PROC3 calculates the PPE distribution with Eqs. D.53 and D.56 (just like for the 2-D sM(s) CH21z surface in D.10.10) and then makes use of the fact that PPU = Isotropic - PPE. The f(r) curves span a range of 0.5 to 3.5 A in 0.1 A steps. The output files have the same PSPlot format as the l2RDx.XL0 files described Appendix D: Software Developed for Ultrafast GED (PROC3) above (D.10.11). CONV.EXE Program Files Include Files CONV.C CONV_DT.C CONV 1O.C D.11 CONV 689 DATA_CNV.H SETTINGC.H Table D-41: Program and include files needed to compile CONV.EXE. CONY is a utility program which converts binary floating point and unsigned integer data files into CSY format text files. This program was originally written to transform the output files from R-K, PROC3, and STREAK, but CONY has general applications. CONY is compiled from the files listed in Table D-41, and does not access extended memory. Operation of CONY is straightforward: D.11.1 CONV Option One: Change Path This menu option allows the user to select the directory path and extension of the input data file. The output file will be located along the same path unless this menu option is executed again after the input file is chosen. D.11.2 CONV Option Two: Select Binary File This menu option allows the user to choose an input binary data file found with the path and extension set in the first main menu option. CONY does not load the data file at this time since the file could be very large; the data is loaded in segments as needed during the conversion process. CONY has no means for checking whether the selected file is truly a binary data file, or whether the file contains floating point or unsigned integer data. The user must keep track. Appendix D: Software Developed for Ultrafast GED (CONV) 690 D.11.3 CONV Option Three: ASCII Filename The user enters a standard DOS eight-character filename for the output file. The default extension appended to the file name (.XL0) cannot be changed without editing CONY.C and rebuilding. D.11.4 CONV Option Four: Convert Floating Point Data Selecting this option starts the floating point conversion process. The first eight bytes of the input file are read as two long integers, and correspond to the x- and y-axis dimensions of the data array. CONY will halt the conversion process if the input file is too big (> 10 Mb) as estimated by the dimensions. The dimensions are immediately followed by the data, read in as four-byte floating point values. The data are stored sequentially, first by column (along the x-axis) and then by row (the y-axis). CONY reads the data in 20 kilobyte chunks, and extended memory is not needed. Floating point values are converted to text strings and written to the output file as an x-y array in CSY format. The output file will be several times larger than the input file. D.11.S CONV Option Five: Convert Unsigned Integer Data Unsigned integer binary data files are converted to text with this menu option. The binary files begin with the x- and y-axis dimensions (four-byte integers) and are followed by the unsigned integer data (two byte) stored first by column and then by row. The unsigned integers are converted to ASCII text strings and written to the output file in CSY format as an x-y array. Appendix D: Software Developed for Ultrafast GED (CIRC) CIRC.EXE Program Files Include Files D.12 CIRC CIRC is a data-collection program which interacts with several instruments in the UGED laboratory. The 691 program uses National CIRCSCAN.C DATA_MNP.C SCRNIO.C ACT_TALK.C U14TOOLS.C TCIB.OBJ DATA_SET.H SETTINGS.H CMDLIST.H UNIDEX.H DECL.H Table D-42: Program and include files needed to build CIRC.EXE. Instruments NI-488 GPIB interface software to control an Instruments SA H20 monochromator and to "talk" with a Stanford Research Systems SR245 A➔D converter. Other GPIB-compatible instruments can easily be added to CIRC's communication list. The program also contains the command sequences for operating an Aerotech precision translation stage via a Unidex 14 controller. The translation stage usually serves as an optical delay line, varying the path length of one interferometer arm relative to the second (fixed) arm. CIRC can scan for data by varying the translation stage position, changing the transmission wavelength of the monochromator, or counting time with the computer's internal clock. After each step of the scan, CIRC will collect data from one or two channels of the A➔D converter and display the values graphically in real time. Scans can be repeated, and the averaged signal from all scans will be plotted as well. The final averaged data set can be saved to disk as a CSV format text file. CIRC has the distinction of being the first program written for the UGED software package, and the C and include files which comprise CIRC are listed in Table D-42. Some of these files are required for the instrument interfaces, and therefore have not been discussed yet in this appendix. First of all, DATA_MNP.C and SCRNIO.C are the forebears of the xxxxxxDT.C and x.xxxxxIO.C files found in other programs, and likewise Appendix D: Software Developed for Ultrafast GED (CIRC) i gplst[i] 692 Function .. o... .......MA\x0D ...... ... SR245:. Set .asynchronous .mode (respond. immediately) . ............................................. .. 1.... ...MS;T1\x0D... ....SR245: ..Set .synchronous. mode..and .trigger.off.every pulse .at .bi!:J.?.!Y.POrt .1.-.... ..2... ...... __?1\x0D ....... ... SR245: ..Return _voltage.value.of.analogport. 1........................................................................ ..3...........?2\x0D ....... ... SR245: ..Return _voltage. value.of. analog.port.2 •..................................................................... 4 MR\x0D SR245: Master reset to default values. ········································ ................................................................................................................................................................................... . 5 ........................................ ···················································································································································································· 6 J. ......... H0\x0D ...........H20:. Retrieve. current .gratingposition ......................................................................................... .. a......Go 1%1i\x0D.......H20:.Setgrating position.during. calibration..sequence ..................................................... .. 9... ... F0, %Ii\x0D .......H20: .Rotate .grating..position. a..relative .number. of. steps ................................................. .10 ............... E.............. ....H20:. Check. if..motor. is..busy. _H20.returns .a 'q' _for busy.and.'z'.for. not .busy .. .1.1.... blank.space ......H20:.Test .GPIB .communications.with. H20 .... Should .return .a.'B'..or _'F'_. ................ 12 A H20: Initialize motor. H20 should return an 'o'. ········································ ................................................................................................................................................................................... . 13 O2000\x00 H20: Transfer control of monochromator to main oroaram. Table D-43: List of GPIB command strings in array gplst[i] . converter; 5,6: unused; 7 to 13: H20 monochromator. o to 4: SR245 A➔ D no additional explanation is required for DATA_SET.H and SETTINGS.H. Most of the routines with simple interface requests (i.e., ''Translation stage: please find the Home Position") are located in ACT_TALK. C. TCIB. OBJ and DECL.H contain fundamental GPIB command programs and definitions, and were both supplied by National Instruments. The routines in U14TOOLS.C (a modified version of Aerotech's program Ul4_INTR.C) establish communication with the U14 controller and translation stage, and UNIDEX.H is an associated include file. CIRC has no extended memory requirements. The last unfamiliar name appearing in Table D-42 is CMDLIST.H. This include file collects in one place all text string commands which may be issued to the laboratory instruments. GPIB commands for the SR245 A➔D converter and H20 monochromator are stored in the character array gplst[i] (Table D-43), and the lengths of each command (in characters) are stored in the integer array gpcnt[i] . Note that "\x.hh" corresponds to a single ASCII character whose hexadecimal index is hh. The GPIB device names appear in the character array dvlst[i] . The device names are sent as Appendix D: Software Developed for Ultrafast GED (CIRC) i cmlst[i] 693 Function .. 0................... RQ;················· .... Request .input..bit. status_(no. longer.used) •....................................................................... 1 LF;VL%li;HM0; Turn off limit switches; set velocity; home stage in the positive direction and calibrate to 0 . .. 2... .......HH;VL 1000;······· .... set."Home".flag.active.high;.set_velocity to..1000.encoder pulses per.s..... 3 HL;MA0;GO;ID; Set "Home" flag active low; move to absolute position 0; activate ............................................................. "Done" .flag at .end.of .travel •............................................................................................... 4 VL%Ii;MA%li; Set velocity; move to absolute position; activate "Done" flag at end of ........ ............ GO;ID;············· ........... travel •................................................................................................................................................. .. s... ................ OAi.....................Check.axis .status.without.clearing.flags •.......................................................................... .. 6....................LN;················· ....Turn.on. limit.switches •................................................................................................................... .. 7... ................ RP;················· ....Request .axis..position •.................................................................................................................... ..B.................... IC;·················· ....Clear .interrupt flags •........................................................................................................................ 9 AX;EF;ST;HL; Activate x-axis; disable echo; stop all motion; set "Home" flag active low. ··········••••••••·••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••······························ .10 ....... BH12;BH1.3;······· .... set. output. bits (local .control.and ..resetting home. cycle) high ............................. .1.1 ....... AC%li;VL%Ii;······ .... set. stage. acceleration. and. velocity . ................................................................................... .12 ................. BX;················· .... Return .status .of..input. bits .for fault .check•........................................................................ .13 ..... MA%Ii;GO;.ID;····· .... Move.stage. to. absolute .Position;.activate. "Done".flag at.end. of.travel. ...... .14 ................ WY; ················ ....Ask."Who.are.you?" .. controller. must. respond."Pc3s ...ver ...1 •. 60-4E" ...... .15 . ...............HR0; ...................Home.stage .in. the. negative. direction..and .calibrate.to. 0....................................... .16 ................. RE;················· ....Request .encoder position •........................................................................................................... 17 MR%li;GO;ID; Move to relative position ; activate "Done" flag at end (no longer used). Table 0-44: List of Aerotech translation stage command strings in array cmlst[1]. parameters of the ibf ind() call during the device initialization sequences in the subroutine act_init() of CIRCSCAN.C. The names in dvlst[i] must match the configuration values set externally by running National Instrument's IBCONF.EXE program, or else CIRC will be unable to find the devices. Also, the GPIB interface will fail unless the CONFIG.SYS file has a line similar to the following: DEVICE= D:\AT-GPIB\GPIB . COM (D.57) Command strings for the Aerotech translation stage are stored in the character array cmlst[i] (Table D-44). When CIRC is started, the program will attempt to establish contact with all instruments, starting first with the Aerotech translation stage and then with the GPIB devices. The results of CIRC's attempts are displayed on the screen, but the program may Appendix D: Software Developed for Ultrafast GED (CIRC) crash if there is some sort of configuration error. 694 After the initialization sequence is complete, the user presses "Enter" and the translation stage begins a homing sequence. The six options of the main menu are presented, and at the top of the screen are four status windows. The first two windows show the progression of a scan, displaying (from left to right) the current point in the scan, the number of total points in the scan, the current scan number, and the number of total scans in the measurement. The third window shows the Aerotech translation stage status and will display either a number (the stage position in units of 0.1 µm), the word "HOMING" if the stage is currently seeking the Home Position, or the word "Lost" if the translation stage was not found during the initialization sequence. The last window shows the H20 monochromator status and will display either a number (the transmission wavelength in units of 0.05 nm), the phrase ''UNCAL" if the monochromator dial position has not yet been calibrated, or the word "Lost" if the monochromator was not found during the initialization sequence. D.12.1 CIRC Option One: Conduct A Translation Stage Scan This method of data collection advances the Aerotech translation stage by a fixed amount after every data point. At the end of each scan, the stage recalibrates itself by finding the Home Position again (D.12.5.2) before moving to the starting offset position for the next scan. The Aerotech stage is optically encoded, with each encoder pulse corresponding to a distance of 0.1 µm. The absolute position of the stage is always referred to in these units, where 0 e-p is the Home Position next to the motor, and 2,000,000 e-p is the end of travel (the stage is 20 cm long). Because the laser makes two passes along the delay line, 1.0 ps of time delay is equal to 1498.9 e-p of stage motion, Appendix D: Software Developed for Ultrafast GED (CIRC) 695 and 1000 e-p is equal to 667 fs of delay. Internally, Aerotech's software refers to the end of travel as -2,000,000 e-p, with the Home Position lying in the positive direction; CIRC, however, negates stage position values so the user can always enter positive numbers. Programming the stage with Aerotech's U14 utilities was frustrating because their software contained bugs and fluky behavior. One side effect of this is that sometimes CIRC must pause to avoid confusing the Unidex. This pause occurs in the wait() subroutine of ACT_TALK. C, and is unfortunately based on a dummy for() loop rather than the computer's internal clock. As a result, the ending parameter of this loop might have to be increased if CIRC is transferred to a faster computer. The four items in main menu option one are described below. Note that when this option is selected, CIRC actually bypasses the first three items and bumps program control immediately to the fourth one, "Set Stage Scan Parameters." D.12.1.1 Stage Scan Selecting this menu item initiates data collection under the current set of scan parameters (D.12.1.4). CIRC starts by clearing the data arrays. A graphing window appears showing stage position (in e-p) along the x-axis and voltage (assuming signal comes from the SR245) on the y-axis. During the first scan, the y-axis limits will be ±11.0 V, corresponding to the maximum output voltage from the SR245 A➔D converter, but on subsequent scans the graph is rescaled to the absolute minimum and maximum values of the averaged data. New data points from the first source are plotted in yellow, and the averaged data is drawn as a red line. New data points from the second source are plotted in cyan, and the averaged data is drawn as a blue line. These colors can change if the Appendix D: Software Developed for Ultrafast GED (CIRC) 696 default values in SETTINGS.Hare altered. CIRC homes the translation stage at the start of each scan. A scan can be interrupted at any point by pressing the ESC key, and the averaged data from all completed scans may still be saved. D.12.1.2 View Scan Results This menu item simply replots the most recently taken data set. D.12.1.3 Save Data To Disk This menu item allows the user to save the most recently taken data set to disk. D.12.1.3.1 Save Data Scanned data is saved in CSV text format. The header line is "pos s" for reasons which date back to the fitting of autocorrelation curves with the program MINSQ. (MINSQ is an ancestor of SCIENTIST.) Each subsequent output line lists a stage position in units of 0.1 µm, the averaged data from channel one for that stage position, and, if the channel is used, the averaged data from channel two. D.12.1.3.2 Change Filename The user enters a standard DOS eight-character filename under which to save the data set. Note that selection of a filename does not save the data - the user must select the "Save Data" menu item above. D.12.1.3.3 Change Path The user changes the default path and extension for the output file with this item. Appendix D: Software Developed for Ultrafast GED (CIRC) 697 D.12.1.4 Set Stage Scan Parameters The user establishes translation stage scanning parameters with this menu item. There are nine items to be considered: D.12.1.4.1 Stage Offset Position The user enters a long integer for the absolute offset position of the translation stage at the beginning of each scan. This value (in e-p) also specifies the offset position to which CIRC automatically returns the translation stage after seeking the Home Position (D.12.5.2). D.12.1.4.2 Stepsize Between Points The user enters a long integer to set the distance (in e-p) which the translation stage should be advanced after each data point is recorded. D.12.1.4.3 Number Of Points The user enters an integer to specify the number of data points in the scan. The maximum number of points is 1450, although the user cannot choose a value which would extend the scan out beyond the limits of the translation stage (2,000,000 e-p). D.12.1 .4.4 Number Of Reads Per Point The user enters an integer for the number of times CIRC should poll the data sources at each time point. All values will be averaged together. Values greater than one may help increase the scan efficiency if the scan speed is strongly limited by the time required to reposition the translation stage. Appendix D: Software Developed for Ultrafast GED (CfRC) 698 D.12.1.4.5 Number Of Scans The user enters an integer for the number of scans CIRC should complete for the current data set. Overestimation is okay because scans can always be interrupted (without losing data) by pressing the ESC key. D.12.1.4.6 Wait For A Trigger To Scan? This Yes/No toggle tells CIRC whether or not to synchronize data collection. If the toggle is ''N," then CIRC immediately reads data from the source(s). If the toggle is "Y," CIRC waits for the first binary (TTL) input channel of the SR245 to activate before reading from the analog channels. The trigger signal might come from a boxcar integrator or the Nd:YAG laser timing pulses. D.12.1.4.7 Pause Between Points? If the user sets this Yes/No toggle to ''y," then CIRC will pause the scan after every data point and wait for the user to press "Enter." D.12.1.4.8 First Data Source CIRC reads either one or two channels of input while conducting a scan. The source for the first channel can be selected from amongst the first three menu items listed in Table D-45. D.12.1.4.9 Second Data Source The source for the second data channel can be set to any of the five menu items listed in Table D-45. Appendix D: Software Developed for Ultrafast GED {CIRC) Data Source Menu Items Description 699 CIRC Channel? SR245 A-> D (Analog Channel 1) Reads a voltage from the first analog channel of 1 and 2 the SR245. SR245 A -> D Reads a voltage from the second analog channel 1 and 2 (Analog Channel 2) of the SR245. Random Nwnber Generator Provides a random number betwen -0.5 and +0.5. 1 and 2 SR245 A -> D (Normalize Divides the voltage from the first analog channel Only 2 ............. ch ... 1 ...with .. ch ... 2 >............. .......... by.the _voltage.of.the .second. analog. channel ................................. None Source is off. Only 2 Table D-45: List of possible data sources available during translation stage, monochromator transmission wavelength, or temporal scans. D.12.2 CIRC Option Two: Conduct A Monochromator Scan The menus for data collection via H20 monochromator wavelength transmission scans are nearly identical to those for translation stage scans (D.12.1). The monochromator' s grating is rotated after every data point such that the transmission wavelength changes by a fixed amount. For the H20, one encoder pulse corresponds to 1120th of a nm. Unfortunately, this part of CIRC's software has not been refined and the program expects all monochromator position values to be in e-p; users must make the conversion on their own. At the completion of each scan, CIRC merely rotates the grating back to the offset wavelength. The H20 has no Home Position, and the recalibration sequence is too time-consuming (D.12.6.2). In order to avoid backlash, CIRC always instructs the H20 to approach new positions from smaller encoder values. If the H20 is moving to a smaller encoder value, CIRC tells the H20 to overshoot by 200 e-p and then come back in the correct direction. D.12.3 CIRC Option Three: Conduct A Time Scan The menus for a temporal scan are also similar to translation stage scans (D.12.1). Appendix D: Software Developed for Ultrafast GED (CfRC) 700 After every data point the computer simply waits for a fixed amount of time (in hundredths of a second) measured relative to the computer's internal clock. D.12.4 CIRC Option Four: View Scanned Data This menu option allows the user to view the graphs of up to seven data sets at one time. There are four menu items: D.12.4.1 View Data After choosing data sets with the second menu item (D.12.4.2), selection of ''View Data" generates a graph which plots all curves simultaneously. Units along the x- axis are only displayed if all data sets have the same offset, step size, and number of data points; otherwise the axis label reads ''Normalized," meaning that all differing step sizes are rescaled to be equal, and all plots start from the same x-coordinate. The ending x-coordinate of each plot is determined by the number of data points in the set. D.12.4.2 Load Data The user may select up to seven data sets from amongst those located under the current path and extension parameters. To be eligible, a file must have the format described in D.12.1.3, including the header line "pos s". After some files have been loaded from one directory, the user can change the path parameter and select additional files from other directories. D.12.4.3 Normalize Data? If the user sets this Yes/No toggle to ''y," then the y-axis of the graph will be normalized. The data sets will be rescaled for plotting such that they all have common Appendix D: Software Developed for Ultrafast GED (CIRC) 701 absolute maxima and minima. D.12.4.4 Change Path The search path and extension for valid data sets can be changed with this menu item. These parameters also determine the destination of any new data sets which are subsequently saved to disk (just like in D.12.1.3.3). D.12.S CIRC Option Five: Control The Translation Stage This menu option provides the user with simple control of the Aerotech translation stage. There are three items in this menu: D.12.5.1 Move Stage To A New Position The user enters a long integer value for the new absolute position of the translation stage. This value must be between 10,000 and 2,000,000 (the stage limits). D.12.5.2 Home Stage To Offset Position Selecting this menu item instructs the translation stage to find the Home Position in the encoder. The homing sequence takes several steps and involves different commands (Table D-44). First, CIRC executes cmlst[l] under the assumption that the stage is on the negative side of the Home Position. This command moves the stage in the positive direction towards the motor at maximum velocity (200,000 e-p/s), and overshoots the Home Position. Next CIRC resets the "Home" flag, lowers the stage velocity to 1,000 ep/s (cmlst[2]) and searches for the Home Position in the negative direction (cmlst[lS]). The Home Position is calibrated as zero e-p. After making this identification, CIRC resets the "Home" flag again and moves the stage to the absolute Appendix D: Software Developed for Ultrafast GED (CfRC) 702 zero position (cmlst[3]). Finally, CIRC executes cmlst[ 4] which resets the velocity to the default value and moves the stage to the offset position chosen in "Set Stage Scan Parameters" (D.12.1.4.1). D.12.5.3 Move Stage To Opposite End When this item is selected, CIRC looks at the current stage position and then moves the stage as far away as possible, either to 10,000 e-p or 2,000,000 e-p. This item is especially useful when tweaking the pump laser through the delay line mirrors to minimize beam walk during a translation stage scan. D.12.6 CIRC Option Six: Control The Monochromator This menu option provides the user with basic control of the H20 monochromator: it can be moved to a new transmission wavelength or recalibrated relative to the dial position. Upon start up of CIRC, the monochromator must be calibrated before the user may either reposition or scan with it. D.12.6.1 Move Monochromator To A New Position With this menu item the user can instruct the H20 monochromator to rotate the grating such that a different wavelength is transmitted. The user enters an integer value for the new wavelength; the value has units of 0.05 nm. D.12.6.2 Recalibrate The Monochromator This menu item is selected whenever the user wishes to calibrate the motor encoder position with the value of the wavelength counter dial (located on the side of the monochromator). The user enters the dial's value (multiplied by twenty) and CIRC Appendix D: Software Developed for Ultrafast GED (C/RC) 703 compares this value with the encoder position. If they disagree, then CIRC moves the monochromator grating to the zero position with reference to the dial's value. The user is prompted for the new dial position, and should enter a negative number if the dial has rotated past zero into the 900 region. CIRC will continue tweaking the grating position until both the dial and the encoder agree that the grating is rotated to zero. D.13 AUTOHOME And AUTOSCAN Operation of the CCD camera has been automated by writing and executing EXCEL macros (see Appendix E). For repetitive experiments, the macros can conveniently run SpectraSource's HPC-1 program by passing it keystroke commands and output image filenames from a list. Some experiments also require continuous repositioning of the Aerotech translation stage, but unfortunately CIRC.EXE is a DOSbased program which cannot be controlled by an EXCEL macro. Actually only two of CIRC's many functions are needed - homing the translation stage and advancing the stage a set amount. These needs are instead met by two, single-purpose Windows-based programs, AUTOHOME and AUTOSCAN. Unlike their brethren in the UGED software package, AUTOHOME and AUTOSCAN are not menu driven and, in fact, have no userinterface. AUTOHOME simply returns the translation stage to the Home Position and then advances it to a hard-coded offset position, while AUTOSCAN moves the translation stage a fixed distance from its current position. As mentioned in D.1.1, these programs are compiled and linked as Windows EXE files with the "Small" memory model and no graphics library. (Under Borland's Options Appendix D: Software for Ultrafast GED (AUTOHOME and AUTOSCAN) menu, simply select Application... choose Windows App.) and The program and include files required to build AUTOHOME and AUTOSCAN are listed in Table D-46 and Table D-47 respectively. 704 AUTOHOME.EXE Program Files Include Files AUTOHOME.C ACT_AUTO.C U14TOOLS.C CMDLIST.H UNIDEX.H AUTOHOME.DEF Table D-46: Program and include files needed to build AUTOHOME.EXE. Neither program needs a .xx.xx.xxlO.C or SETTINGx.H file because there is AUTOSCAN.EXE Program Files Include Files no user-interface; a DATA_xxx.H file is not AUTOSCAN.C ACT_AUTO.C U14TOOLS.C needed either because the programs require very little data. CMDLIST.H and UNIDEX.H are the CMDLIST.H UNIDEX.H AUTOSCAN.DEF Table D-47: Program and include files needed to build AUTOSCAN.EXE. same include files requested by CIRC (Table D-42) for controlling the translation stage, but the U14TOOLS.C file is slightly different and, unfortunately, has not been renamed. Unlike the other UGED software, AUTOHOME and AUTOSCAN also require a .DEF file to build them as Windows EXE programs. Four "Unused Parameter" warnings appear when the executable files are built, but these warnings can be ignored. After finding the Home Position as described in D.12.5.2, AUTOHOME advances the translation stage to a fixed offset position. This offset position is stored in the long variable off_pos of the subroutine go_home() in AUTOHOME.C. The value of off_pos should be a positive number between 10,000 and 2,000,000, the translation stage limits. (The translation stage actually references negative positions, but the subroutines called by go_home() will negate the value of of f_pos.) One stage position unit corresponds to 0.1 µm, or 0.667 fs of laser travel time in the standard double-pass arrangement. Appendix D: Software for Ultrafast GED {AUTOHOME and AUTOSCAN) 705 AUTOSCAN advances the translation stage by the value of the variable place. This long variable is initialized in the subroutine go_scan() of AUTOSCAN.C. The sign convention in AUTOSCAN is different (oops ... ) from AUTOHOME: a negative value for place moves the stage away from the motor, towards what would be a larger positive offset position in AUTOHOME. 706 Appendix E EXCEL Macros for Automating UGED Experiments E. 1 Introduction Recording and analyzing the various types of UGED data involves a great deal of repetition. As described in Appendix D, all programs which evaluate CCD images can be controlled with one or more batch files so that the user is freed from manually performing every mundane task. The UGED software package cannot help, however, in automating the data collection process because CCD images must be generated by running SpectraSource's Windows-based HPC-1 program. Furthermore, most UGED experiments require alternating between CCD exposures and movement of the Aerotech translation stage, so even the Script Files found in later versions of HPC are of no help. Fortunately experimental control can be relinquished to a "higher power" of sorts - a poor man's version of LabView. Microsoft EXCEL's macro language is quite powerful, Appendix E: EXCEL Macros for Automating UGED Experiments 707 extending beyond the scope of EXCEL itself out into the Windows environment. An EXCEL macro can run other software, sending pre-orchestrated keystroke commands and then waiting for responses. Controlling HPC-1 with this language is straightforward, and EXCEL can also execute the programs AUTOHOME and AUTOSCAN (D.13) which move the translation stage. This appendix presents three examples of EXCEL macros currently employed in the UGED laboratory. EXAMINE.XLM (E.2) parses rapidly through a list of CCD images, allowing the user to quickly scan each image for gross aberrations. UGED_EXP.XLM (E.3) is a macro designed for recording actual time-resolved diffraction data. Scattering images are exposed at different time steps, and a test image of the electron beam position is taken too. Finally, TIMEZERO.XLM (E.4) controls the exposure of electron beam lensing images when establishing the location of time zero. All these macros were created with EXCEL 4.0. EXCEL 5.0 will run them too, but Microsoft is shifting the macro language towards VirtualBasic, and at some point the macros listed here will have to be rewritten. E.2 Macro For Examination Of CCD Images Before analyzing a new set of time-resolved diffraction images with RADAR2, each image in the set ought to be checked for obvious defects. Occasional arcing within the electron gun can saturate exposures, significantly distorting the final, averaged /E(pix) profile churned out by RADAR2. Such problems can be avoided in advance by glancing briefly at the raw data before running RADAR2. The macro EXAMINE.XLM listed in Appendix E: EXCEL Macros for Automating UGED Experiments A B ------t 708 C f--=APP.MINIMIZE() C930E001 Set ouput directo/}'.' ___ r=DIRECTORY("C:\TOOLS\CCD") C930E002-~ Run HPC-1 -------r=EXEC("C:\TOOLS\CCD\HPC.EXE",1) ____ t- C930E003 Pass cooler mess~e =SEND.KEYS("~",TRUE) C930E004 7 Char1..9~ color scheme __ ~=SEND.KEYS("%AF6-",TRUE)________ C930E005 ~ 1 2 3 t 4 5 6 -------------~------------------------t--C~~~E~Q.6_ 1 Loqps,n filename list --~=FOR.CELL("CurrentCell'',C1 :C10,TRUE) --t- C930E007 1 Open the CCD im~e __ ~=SEND.KEYS("f'()") ______________ +- C930E008 1 -------------f--=SEND.KEYS(CurrentCell) __________ C930E009 7 8 g t- 4 -------------r="§~~~~~§t~I~~~-----------+--c~~~~~-, 11 Char1..9e windowin[_ ___ f-=SEND.KEYS("%AW{PGDN}-",TRUE) ____ t---------l 10 12 13 14 15 Pause =WAIT{NOW()+"00:00:03") C/oseffleimage-----~=SEND.KEYS("0/oFC",TRUE)---------+---------I 1s 11 ExftHPc-1-------~SEND.KEYsf"0<1--------------+---------l -------------f-==APP.MAXIMIZE(f--------------+---------l 1a =============~RETURNO==================t=======j --~----------~NExnf-------------------+---------1 -------------~------------------------t---------l Table E-1: EXCEL 4.0 macro EXAMINE.XLM for briefly displaying CCD images. Table E-1 automates a quick check of images. Column B contains the actual macro; column A is commentary, and column C lists the filenames of the CCD images which will be examined. To run the macro, the user clicks on cell B1, selects !ools and ~aero . .. , and then presses a carriage return. This same sequence runs UGED_EXP.XLM and TIMEZERO.XLM as well. The first five commands of EXAMINE initialize HPC-1. Cell B 1 minimizes EXCEL, cell B2 sets the default directory and path for the CCD images, and cell B3 starts HPC-1. The macro then bypasses the "Camera cooler has been turned off" message with cell B4 by sending HPC-1 a carriage return.• In cell B5, the false color setting is changed to Color Scheme ~The eight commands in cells B7 through B14 load and display each of the images • In the SEND.KEYS() command, "-" is a carriage return, ""'' is the Control key, and "%" is the Alt key. The TRUE parameter tells EXCEL to wait for the receiving program to process the keystroke sequence. Appendix E: EXCEL Macros for Automating UGED Experiments 709 listed in column C. The user must enter the cell coordinates for the filename list in the second parameter of the FOR.CELL command. On each iteration of the loop, EXCEL first tells HPC-1 to open an image (88) and then passes HPC-1 the filename in the cell pointed to by the loop index (89). Cell 811 moves the CCD image color scheme windowing level half way down the logarithmic scale, and then cell 812 tells EXCEL to pause (in this case for three seconds) so that the user can examine the CCD image. The CCD image is closed by executing cell 813. The final three lines of the macro wrap up loose ends: cell 815 exits the HPC-1 program, cell 816 maximizes EXCEL, and cell 817 passes control back to the normal interface. The user can now change the filenames in column C to the next subset of images and then run the macro again. E.3 Macro For The UGED Experiment In a time-resolved gas-phase electron diffraction experiment, scattering patterns are recorded at two or more positions of the laser delay line. The standard approach is to change the time delay after every image so that long-term fluctuations in laser, electron, and molecular beam intensities are averaged out across the temporal scan. UGED_EXP.XLM (Table E-2) is a macro which executes one temporal scan, collecting a single diffraction image at each time point. The scan is preceded by a short exposure of the central image region to record an unsaturated image of the unscattered electron beam. This image will be used to monitor the position of the electron beam (and the center of the diffraction pattern - see D.3.4) throughout the course of the experiment. Column 8 in Appendix E: EXCEL Macros for Automating UGED Experiments A B 710 C D E t 1 2 3 4 5 6 =APP.MINIMIZE() E051701 T1 1 Home translation stc!f}f! i-=EXEC("C:\TOOLS\CCD\AUTOHOME.EXE", 1[ t A051701 X1 I- 21 o I Set ou!Pyt directofjl +=DIRECTORY("C:\TOOLS\CCD")_ _______ +-8051701 +.Y1 t 250-: Run HPC-1 ------+-=EXEC("C:\TOOLS\CCD\HPC.EXE",1) _____ +-~Q?.!_~.!.+~1_1-_§Q_I Pass cooler mess~ft +=SEND.KEYS("~",TRUE) ------------t-g_051701 +H1 L 60 -I Chaf!.9!! color scheme t-=SEND.KEYS("%AF6~",TRUE) _________ t------+--~---I 7 8 9 10 + T2 f- 75 I X2 o of electron beam test -+:SEND.KEYS($E$1) --------------+------tv2 f- o _I im~!! ·--------+:'SEND.KEYS("{TAB 4}") ------------+------+W2 t 525_: 13 14 15 16 17 10 ------------+-:~~~~:~~~~~!{~!~}") -------------+------+H2 I- 520I ------------+.-==SEND.KEYS($E$3) --------------+------+--1----1 ------------f=SEND.KEYS("{TAB}") -------------f------+--~---1 - - - - - - - - ----t-=SEND.KEYS($E$4) - - - - - - - - - - ----t- - - - - - + - -f- ---1 ------------t-==SEND.KEYS("{TAB}") -------------t------+--f----1 ------------t-==SEND.KEYS($E$5) --------------t------+--f----1 - - - - - - - - - - - -t-==SEND.KEYSf°.7' ;=fRUE)- - - - - - - - - - - -t- - - - - - + - -1- - - -I 19 20 21 22 Exe_ose e- beam imc!f]!! j~SEND.KEYS("%ES~",TRUE) - - - - - - - - - t - - - - - t - - t - - - 1 Save im~ft ·-----+-=SEND.KEYS("%FS") -------------+------+--1----I Send im~ft filename -t-=SEND.KEYS($C$1) __________ _ and carriag_e return =SEND.KEYS("~",TRUE) + ~ ~~ ~! t- t- Setexe_osure values -+:SEND.KEYS("%EC") ____________ - t- +- I Close e-beam imc!f}ft .t=SEND.KEYS("%FC",TRUE) ----------t-----+--~---1 t-=SEND.KEYS("%EC") +- --+--f----1 25 Set exe_osure values 26 21 ofdiffractioritmaies-=t=SEND.KEYS($E$7)==============t=====t==t===I ------------+..:".§~~~'S.f:Y.§{'.JI~~~·1 ____________ +------+--l----l ~: 30 31 32 33 34 35 ------------+-:~~~~:~~~~~!{~!~}") -------------+------+--1----1 ------------f=SEND.KEYS($E$9) --------------f------+--~---1 ------------t-=SEND.KEYSf°{TABl'1-------------t------+ - -f----l ------------t-==SEND.KEYS($E$10) -------------t------+--f----1 ------------t-==SEND.KEYS("{TAB}") -------------t------+--1----1 ------------t-==SEND.KEYS($E$11T-------------t------+--I----I ------------t-==SEND.KEYS("~",TRUE) ------------+------+--1----1 36 37 38 39 40 Exe_ose 1st diffraction _t=SEND.KEYS("%ES-",TRUE) ---------t-----t==t===I : Save im~ft ·-----t-=SEND.KEYS("%FS") -------------f------+--~---1 Send im~ft filename -t-=SEND.KEYS($C$2) --------------t------+--f----l and carriag_e return --t-=SEND.KEYS("~",TRUE) ------------t------+--f----l Close imaf}!J -----t-=SEND.KEYS("%FC",TRUE) ----------t------+--f----l ------------+--------------------------+------+--1---~ 43 44 45 46 47 48 :~ 51 52 53 Start looe_ _______ t-=FOR.CELL("CurrentCell'',C3:C5,TRUE) ____ +------+--I----I St£PJranslation stag~ 4-=EXEC("C:\TOOLS\CCD\AUTOSCAN. EXE", 1) _ t- ____ - + - -1- __ -I Exe_ose next diffraction +-=SEND.KEYS("%ES~",TRUE) ---------+------+--!----! Save im~gft -------VSEND.KEYS("%FS") -------------f------+--~---1 Send im<!_gft filename -t-=SEND.KEYS(CurrentCell) __________ -t- ____ - + - -f- ___ 1 and carriag_e return --t-=SEND.KEYS("~",TRUE) ------------t------+--f----l Close imaf}!J -----t-=SEND.KEYS("%FC",TRUE) ----------t------+--f----l ------------t-=~~~T_i)_____________________ t------+--1----1 Ex7iHPC-t------+-=SEND.KEYSf°"X1---------------+------+--I----I - - - - - - - - - - - -t-=~PP.MAXIMIZE()- - - - - - - - - - - - - - -+- - - - - - + - -1- - - -I ------------t-=-------------------------+------+--1----1 ____________ eRETURN() ___________________ L _____ _i_ __ L ___ I Table E-2: EXCEL 4.0 macro UGED_EXP.XLM for taking time-resolved diffraction data. Appendix E: EXCEL Macros for Automating UGED Experiments 711 Table E-2 contains the macro; column A contains brief commentary, column C lists the output filenames, and column D labels the exposure parameters in column E. As in the macro EXAMINE (E.2), the first few lines of UGED_EXP minimize EXCEL and initialize HPC-1. There is one additional command: cell B2, which executes the program AUTOHOME.EXE. This causes the Aerotech translation stage to find the Home Position and move from there to a fixed offset position (D.13). The offset position will be the first time point in the temporal scan. Exposure parameters for the unsaturated electron beam image are usually different from those of the diffraction images. Cells B8 through B18 set the electron beam image parameters using data listed in cells E1 through E5. First the macro sends HPC-1 an exposure time in seconds (B9). UGED_EXP skips over the three Auto-Adjust items (B10) and then sends the offset and dimensions of the Sub-Frame (B11 to B17). The values shown in Table E-2 correspond to a one second, 60x60 exposure starting at pixel coordinates (210, 250). In cells B19 through B23, the macro causes HPC-1 to take the exposure, save the CCD image under the filename listed in cell C 1, and close the image. Next UGED_EXP resets the exposure parameters to those for diffraction images, in this case a 75 second, 525x520 image starting at the origin (cells B25 to B35). Cells B36 to B40 instruct HPC-1 to expose, save, and close the diffraction image for the first time point. The macro then starts a FOR.CELL loop (B42) over the remaining time points (three in this example), with the location of the output filename list entered in the second parameter of the FOR.CELL command. Of course the translation stage must be advanced between each time point, so cell B43 runs the program AUTOSCAN.EXE to do this (D.13). The exposures are taken, saved, and closed with cells B44 to B48. Once Appendix E: EXCEL Macros for Automating UGED Experiments 712 the temporal scan is complete, cells 851 through 853 return control to EXCEL. E.4 Macro For Determination Of Time Zero The establishment of time zero requires many exposures of electron beam lensing images over a range of time delay. Like UGED experiments, these measurements benefit from averaging successive, complete scans, as opposed to recording all images at one time point before moving on to the next time point. Still, the dimensions of lensing images are generally small and the exposures are short, so creating one lensing image may take only one or two seconds. If the translation stage's motion is the slowest part of the experiment, then the user may wish to take two or three lensing images at each time step during a scan. TIMEZERO.XLM (Table E-3) gives the user the freedom to choose not only the number of time steps in a scan, but also the number of images to record at each time step during one scan. The macro recognizes that sometimes the user wishes to change the width of the step size during the scan, e.g., start with three 10 ps steps, then take ten 2 ps steps, and conclude with five more 10 ps steps. This level of complexity has also been incorporated into TIMEZERO. The number of exposures taken at each time step during a scan is set in cell F1 of Table E-3. Column 8 contains the macro commands, column A is commentary, column C is blank, column D repeats the row numbers for clarity, and filenames are listed in column E and beyond, depending on the value of cell F1. The initialization routine in cells 81 through 86 is identical to UGED_EXP: EXCEL is minimized, the translation stage finds the Home Position and moves a fixed distance away, and HPC-1 is started. Appendix E: EXCEL Macros for Automating UGED Experiments 713 A B CD E F 1 =APP.MINIMIZE() # Shots: 2 2 Home translation sta!l~=EXEC("C:\TOOLS\CCD\AUTOHOME.EXE", 1) BCKG£1~~ = = = = 3 Set oute_ut direct£~-+=DIRECTORY("C:\TOOLS\CCD") -------1-+3 I- A070~~-f!'_Q~0~Q._Z--l 4 R}!_'!_fiP_2.:_1_ _____ +=:_E~~<2_CC~.Y:!:.q_~L_§~~Q'.tl!:<2.-~~~ ...!)_____l-+-l-------+--------l 5 Pass cooler messa.9.e +=SEND.KEYS("~",TRUE)____________ _ 1ST IMAGE 6 Chan!le color scheme +=SEND.KEYS("%AF6-",TRUE) --------~+6 A07060A=t~f9~~~ 7 TAKE BACKGROUND =FOR("Count",1,$F$1) 8 E~p!)Se back9.!ound _ +=SEND.KEYS("%ES-",TRUE) --===----f-+=f-BEG LOOPt-- - ---j 9 Save bacj<g,Iound __ +=SEND.KEYS("%FS") ______ _ ______ f-+9 ~ A07060B-~07060B7 10 Send ima.9.e filename t=SEND.KEYS(OFFSET($D$3, 0, Count)) ---~~O~ A07060C-}o7060C~ 11 and carri?9!1 return - +=SEND.KEYS("~" ,TRUE) ___________ -1-~ 11- ______ -1-- ___ ---l 12 Close imf!ge -----+=SEND.KEYS("%FC",TRUE) __________ l-~2 l--------l--------l 13 +=NEXT() 13 14 TAKE FIRST IMAGE =FOR("Count" ,1,$F$1) -------------t-fi4t------t-----4 -----------+-------------------------f-+.-f-------t------j 15 E~p!)Se firstim?9!3 --+=SEND.KEYS("%ES-",TRUE) ---------f-~5f-- - ----t------j ~ t-~ t ~ ~ ---~i~~------t----~ ~~ ~=~:~::;~;f~ame t=~~~~:~~~~~i~~•~T($D$6, 0, Count)) 18 and carri?9!1 return -+=SEND.KEYS("~",TRUE) ____________l-~81-------f---- - --l 19 Close first image ---+=SEND.KEYS("%FC",TRUE) __________l-+-l-------f-------l 20 +=NEXT() 21 BEGINNING LOOP - =FOR.CELL("CurrentCell",D9:D10,TRUE) ---1-+-I-MID LOOP -1--------l 22 Stee_ translation Stf!ge =EXEC("C:\TOOLS\CCD\AUTOSCAN.EXE",1) ~2 A07060D ~07060~~ 23 Loop On # Of Shots =FOR("Count", 1,$F$1) 23 A07060E A07060E 24 E~p!)se imf!ge ----t=SEND.KEYS("%ES-",TRUE) ---------~~4~ A07060F t.A07060~~ 25 Save imafl_e -----+=SEND.KEYS("%FS") -------------1-~51- A07060G A07060G 26 Send imafJ_e filename +=SEND.KEYS(OFFSET(CurrentCell, 0, Count)) l-~61- A07060H ~07060H~ 27 and carri?9!1 return -+=SEND.KEYS("-",TRUE) _______ _ ____ l-~71- A07060I_-I--A07060I--l 28 Close imf!ge - - - - - +=SEND.KEYS("%FC",TRUE) __________l-~8l--------l--------l t ~~ ~ ~ -----------+;~{~~~--------------------t~it------t-----4 31 MIDDLE LOOP ---+=FOR.CELL("CurrentCell",D22:D27,TRUE) --f-~1 f-------t------j t 32 Stee_ translation st~ge =EXEC("C:\TOOLS\CCD\AUTOSCN2.EXE" ,1) ~ t - ~ _____ - t - ___ ~ 33 Loop On# Of Shots _+=FOR("Count", 1,$F$1) -------------l-+-1--------1--------l 34 E_xp!)Se im~ge ____ +=SEND.KEYS("%ES-",TRUE) ---------1-+-~------+-------l 35 Save imafl_e -----+=SEND.KEYS("%FS") -------------1-+:-I-END LOOP -1------:-l 36 Send imafJ_e filename + =SEND.KEYS(OFFSET(CurrentCell, 0, Count)) l-~61- A07060J -t-:A07060J;-J 37 and carri?9!1 return -+=SEND.KEYS("~",TRUE) ____________ t47 A07060K ~07060K 4 38 Close im~ge _____ +=SEND.KEYS("%FC",TRUE) __________ f-~8f- A07060L t;;A07060L,i 39 __________ -+=_Ni~TIL ___________________ -f-+-3~f- ~Q.7_Q~o~_ ¢,Q~~o-~ 40 =NEXT() 40 A07060N A07060N7 41 END LOOP -----t=FOR.CELL("CurrentCell",D36:D41,TRUE) --~~1 A07060O }070600~ 42 Stee_ translation stage+=EXEC("C:\TOOLS\CCD\AUTOSCAN.EXE",1) I- ~21- _____ -+- ___ ---l t ~ 43 Loop On# Of Shots _+=FOR("Count" ,1,$F$1) -------------1-~3l-------f- - -----l 44 E_xp!)se im~ge __ --+=SEND.KEYS("%ES-",TRUE) ________ -1--¢41- _____ --1--- _ ----l 5 filename +=~~~~:~~~~~i~~•~T(CurrentCell, 0, Count)) ~-- - - - - t - - - - ~ 47 and carriag!} return -+=SEND.KEYS("~",TRUE) ____________ f-+-f-------t------j 48 Close image _____ +=SEND.KEYS("%FC",TRUE) __________ f-+-f-------t------j :: ~=~:~: ~: ~! :~ -----------+;~{~~~--------------------1-+-l-------t------l 51 ExitHPc-:1------+=-sEN□.i<fvsr·Ai;f--------------1-+-1-------+------1 52 -----------+,;-APP.MAXIMIZE0---------------1-+-l-------+-------l -----------+-------------------------1-+-l-------+--------l 53 ___________ ...1..=RETURN() __________________ L..L_L ______ L ____ .J Table E-3: EXCEL 4.0 macro TIMEZERO.XLM for recording time-zero lensing transients. Appendix E: EXCEL Macros for Automating UGED Experiments 714 The first set of images TIMEZERO exposes are intended to be background images (cells B7 through B 13). During this time, the user usually blocks the pump laser beam so that snapshots of the unperturbed electron beam can be recorded. The list of background image filenames begins in cell E3 and continues out horizantally, through as many columns as specified by the value of F1. The macro identifies the location of the current background filename in B10 using the OFFSET command referenced to the FOR.CELL loop counter. Lensing images at the first time point are recorded with the commands in cells B 13 through B19, and the filenames of these images start in cell E6. In order to allow the user to change translation stage step sizes mid-scan, TIMEZERO takes images with three identically structured double loops (B21 to B30, B31 to B40, and B41 to B50). Each of the outer loops is a FOR.CELL command, where the second parameter in the command identifies the cell range of the first image filename at each time point. The translation stage is advanced before the start of each inner loop (B22, B32, and B42), and the inner loops take as many exposures at each of these time points as set by the cell F1 . The program AUTOSCN2, found in cell B32 of the middle loop, is identical to AUTOSCAN except it advances the stage by a different amount (the value of the variable place is different - see D.13). Putting these steps together, the macro in Table E-3 has the following function: 1. Records two background images and two regular images (the first time point). 2. Beginning Loop: Advances the translation stage twice by distance x and records two images while at each of the two positions. 3. Middle Loop: Advances the translation stage six times by distance y and Appendix E: EXCEL Macros for Automating UGED Experiments 715 records two images while at each of the six positions. 4. End Loop: Advances the translation stage six times, again by distance x, and records two images while at each of the six positions. Once the end loop is complete, TIMEZERO exits HPC-1 (B51) and returns control to EXCEL (B52, B53). 716 Appendix F Clocking Transient Chemical Changes By Ultrafast Gas-Phase Electron Diffraction letters to nature Clocking transient chemical changes by ultrafast electron diffraction J. Charles Williamson, Jianmlng Cao, Hyotcherl lhee, Hans Frey & Ahmed H. Zewail Artht1r Amos Noyes Laboratory of Chemilal Physics, California /nsricure of Tech110/agy, Pasadena, California 91125. USA With the advent of femtosecond (fs) time resolution in spectroscopic experiments, it is now possible to study the evolution of nuclear motions in chemical and photobiochemical reactions. In general, the reaction is docked by an initial fs laser pulse (which establishes a zero of time) and the dynamics are probed by a second fs pulse; the detection methods include conventional and photoelectron spectroscopy and mass spectrometry•-•. Replacing the probe laser with electron pulses offers a means for imaging ultrafast structural changes with diffraction techniques;-•, which should permit the study of molecular systems of greater complexity (such as biomolecules). On such timescales, observation of chemical changes using electron scattering is non-trivial, because space-charge effects broaden the electron pulse width and because temporal overlap of the (clocking) photon pulse and the (probe) electron pulse must be established. Here we report the detection of transient chemical change during molecular dissociation using ultrafast electron diffraction. We are able to detect a change in the scattered electron beam with the zero of time established unambiguously and the timing of the changes clocked in situ. This ability to clock changes in scattering is essential to studies of the dynamics of molecular structures. Diffraction methods, generally utilizing X-rays or electrons, are direct approaches for determining complex structures at microscopic dimensions•-". Techniques for creating ultrashort, coherent and collimated X-ray pulses are still in their infancy, and at present the X-ray flux from most sources is relatively low. For gas-phase ultrafast electron diffraction ( UED) to succeed, major challenges must be surmounted. First, because the number densities of gas samples are orders of magnitude lower than solids and surfaces, gasphase diffraction intensities are very weak. Second, there is no longrange order to enhance coherent interferences, and thus the incoherent background scattering from gases is orders of magnitude greater. Last , there has not previously been a way to determine i11 situ the zero of time in UED experiments. In gas-phase electron diffraction (GED) the scattering intensity decreases as the fourth power of the momentum transfer s = (41r/A)sin(0/2), where A is the de Broglie wavelength of the electrons and 0 is the scattering angle. Conventional GED experiments require a high electron flux ( of the order of microamperes) to yield internuclear separations with precision on the order of0.001 A (ref. 15). Over the past two decades, the speed of GED experiments has improved to the micro- and nanosecond timescale. :-..licrosecond studies include time-of-flight investigations of molecular clusters". and photodissociation experiments where the electron beam is electromagnetically chopped"·". A temporal resolution of 15 ns has been achieved with a pulsed laser dri ven electron source''-'. In order to probe ps and sub-ps changes and the associated orienuiional anisotropy'° with l'ED, three basic experiments must be incorporated into our apparatus: measurement of the ekctron pulsew idth, accurate clocking of the reaction, and detection of single electrons ( necessary to reduce the electron flux and minimize space-charge broadening). To this end we have developed the new apparatus shown in Fig. I, represen tative of a second generation of Appendix F: Clocking Transient Chemical Changes Bv UGED 717 letters to nature diffraction experiments in our laboratories'·'. The apparatus is composed of a fs laser, an ultrafast ele.:tron gun, a free-jet expansion source, and a newly designed two-dimensional single-electron detection system. Femtosecond laser pul ses were created from a colliding-pulse mode-locked ring dye laser. The output from this laser was directed through a four-stage pulsed dye amplifier with no pulse compression (620 nm, 2-3 mf. 30 Hz, 300 fs). For initiation of the reaction, 95% of this beam was doubl ed ( 310 nm, - 250 µ.f) . The remainder (also doubled) was focused onto a back-illuminated, negatively-biased photocathode to generate the electron pulse via the photoelectric effect. The ejected photoelectrons were a.:celerated into a series of electrostatic lenses that collimate and focus the electron beam; for I 9 keV, 1' is 0.088 A. The position of the electron beam was controlled with horizontal and vertical deflectors. Two closely spaced metal plates were used for streaking experiments. The vacuum system was divided into two chambers and differentially pumped (Fig. I) . The sample molecules entered the vacuum chamber in a free-jet expansion mounted on an xyz positioning stage. The scattering chamber background pressure with gas flow was -2 X 10-• torr. Both chambers were shielded with µ.-metal to reduce the effects of the Earth's magnetic field. The component most critical to the success of UED is the detection system. The electron flux must be very low in order to keep the temporal resolution ultrafast. Early on we recognized that all of the scattered electrons must be detected for the experiment to succeed', and we introduced the two-dimensional charge-coupled Electron gun device (CCD) as a detector in a direct electron bombardment mode'. To increase the longevity and flexibility of the singleelectron detection system, our second-generat ion apparatus now employs two CCDs: one is a small, direct-bombardment device installed in the scattering chamber, and the other is a large, scientific-grade device mounted in a separate chamber at the end of a phosphor scintillator/fibre optic/image intensifier chain. Details will be published elsewhere. To confirm the time resolution of the apparatus, we have measured the electron pulse duration in situ as a function of the number of electrons per pulse using the high-speed deflection technique in a streak camera arrangement. Streak velocities (which measure the conversion from temporal to spatial resolution, as shown in Fig. 2) attained with this setup are on the order of 1.6 X IO' ms - 1 , or -2 pixels per ps on the detector. The resolution of the streak experiment is therefore :=0.5 ps. Steak images spanning three orders of magnitude of electron number are shown in Fig. 2. a 0 1ttract1on chamber b Mb~i~lar ~ -;;;- Detector .e 15 .c ti -~ 10 Q) S 5 Cl. 10 fs laser 100 10,000 1,000 100,000 Number of electrons -A ► C l f• . . . Thermoelectric cooler ! -~ ;~~,-: " .: ,-,_: CCD I I' ' -150 .~ 0 ' I I I I 50 100 150 200 Time delay (ps) CCD • P20 scintillator '-100 " ' ' -50' c• ~ ·[-Ii ~. 1 Fibre -optic taper Figure 2 a, Surtace contour plots of low- and high-intensity streaked electron pulse pairs. Ea ch pair comes from two incident light pulses. one of wh ich is delayed by 66.7 ps. The horizontal coord inate is the steaking axis . The temporal durations of pulses with high electron numbers (top trace: 7.400e • . 6.6 ps: 3,790 e - , 4.3 ps) are broadened by space-charge effects. Fo, 10w electron numbers (bonom trace: 295e · , 0.5ps: 15Qe · , 0.5ps). measurement of the pulse width is limited br tne resolution of the streak experimen~. The electron Figure 1 Top. second-generation ultrafast electron diffraction apparatus. pulse width was obtaineC by subtracting the width of the unstrea<ed electron consisting of an electron gun chamber, a diffraction chamber and a detector beam (4 pixels) from the width of the streaked pulses (lorentz1a": orotiles). b, chamber. Two fs laser pulses are used: the first initiates the chemical change and Measured electron pulse widths as a function of the number o' e:ectrons. The the second generates the electron pulse . Bonam, detection scheme. Incident streak velocity was 2.1 pixe ls per ps, or 1.6 x 10~ ms - electrons either directly bombard a small CCD or stnke a phosphor-coated fused -1 k.V ns - •. c. Experimema l photoionization-induced lensing trans1e:"lt. The ordi- fibre-opt1c window. Light emined from the phosphor is amplified by an image nate renects the relative difference between the average protite o' the electron The swsep voltage is intensifier and brought to a scientific-grade CCD. Both CCDs are thermoelec- beam spot in the presence of the excitatmn laser and a referer.:::e profile (no trically cooled. laser). 160 t<ATURE \'OL 386 I! \!ARCH 1997 Appendix F: Clocking Transient Chemical Changes By UGED 718 letters to nature For electron intensities on the order of 10' electrons per pulse, the width is typically - 10 ps. The laser and electron beam waists at overlap was measured to be 450 :!: 50 µm, so the velocity mismatch contribution' to the total experimental temporal resolution is -4ps. To clock chemical changes, we must establish the zero of time (10 ) . A streak camera' or photo-triggered deflection plates' 1 can give to to within 10-20 ps, but these methods require some extrapolation and do not duplicate the design of crossed-beam experiments. Another approach is to rely on changes in the diffraction pattern of the i e- beam pulse width= 15 ps e- beam pulse width = 30 ps f\ t \ -20ps = :'\ •20ps !I!. '-~--1--"--J--'-.,_..__~.,._ f--,......,-,,---i-1-+-"r-,l-\-,J-"1 RHldual: (fM&Ur off)• (fH&Mr on: -20 ps) Ruldu.i: (fs•l ... r off)• (t ...._., on; •20 pa) ..... ~ ,J~ i ··~-~ ~ -- ~~~ .... '.~ .~ ·--~ ~ 10 10 system under investigation, but this is not an independent means of finding to, More importantly, this method is simply not practical for gas-phase work because of the long integration times required to obtain a single data point. In the clocking technique developed here for UED, we use the crossed-beam geometry of the actual diffraction experiment, rather than relying on scattered electrons. The idea is to let the initiation laser pulse create a coulombic field (by ionization), which deflects the unscattered electron beam only during and after the laser pulse passes through. The· phenomenon, termed lensing, occurs because the field focuses the charged electron beam. Fig. 2 shows the degree of lensing versus time; the lensing is a maximum when the laser and electron pulses are temporally overlapped. The results accurately show the precise t 0 (to -2 ps) and hence allow a direct clocking of changes in the diffraction experiment with ps resolution. We recorded lensing transients as a function of the position, polarization and diameter of the pump laser, and conducted control experiments where no gas was flowing and where the sample source tip was far removed from or close to the interaction region. After successfully establishing to, we conducted the first timeresolved gas-phase electron diffraction experiment with picosecond resolution. Diiodomethane (CH 2l 2) was selected as our prototype system because the loss of an iodine atom after dissociation at 310 nm is a major structural change which occurs in less time than the rotational period (- 10 ps)"·". To clock the change, diffraction images were recorded on the CCD at delays of - 20 ps, 0 ps, and up to +70 ps {Figs 3 and 4) . The experimental modified molecular scattering intensity, sM(s), was obtained at each time point ·"( ·) _ . l,0 ,(s) - I,".(s) ,,v, ' - ' Figure 3 Experimental moditied molecular scattering curves for two sets of data taken with t5-ps (leh panel) and 30-ps (right panel) electron pulses. The delay times between the fs laser pulse and the ps electron pulse are shown. Theoretical calculations of sM(s) at - 20 ps are presented (see text). If. 11 f ,I (I) where [10 1 is the total scattering intensity, lb"' is the background (including atomic ) scattering intensity, and J; and fi, are atomic scattering amplitudes 15•1'. Typical sM(s) raw data taken at - 20 ps e- beam pulse width = 30 ps e- beam pulse width= 15 ps .::- "=' -. ----- - -- 10 ps 1:ps ~1~ I 0 70 P• ~ ops -~t: ::~~ :::::=~ : ~ ~ 2 3 4 5 r(A) Figure 4 Radial distribution functions l (r) and .ll(r ) obtained from me sM(s) and ~ M(sl curves of Fig. 3. also for 1wo sets of data I t5-ps and 30-ps electron pulse width. left and rig ht panel, respectively ). The correspo nding theoretical f{r) cu rve for the - 20ps data is shown . The ch ang es obtained are in the region of the C-1 and I- .. 1internuclear separations tse~ tex t). Note that in /(r) th e peak corres pond· ing to the 1... 1distance should ha1.- e about tvvice the area of the hrst :::ea k. {C- 1and H-• -1): the peak area scales approximately as n, Z,Z/ r,1 (where Z :s the atomic 0 2 3 4 I 5 r (A) numbe- a--c :i is th e multiplicity for nuclear pai rs ). HtJwever. because of damping 1n eqL;a :: i: r. i2L th e peaks appear to be of equal areas. ar. d this is evident in our simuia: : ---s ;or different va lues oi f< . The theoretical simulations shown in the hgure 3·e oased on the structural Cata of re f. 24. We have a1s0 used more recent data 'r:"· <. ""1€dberg ·s and co-wcrk.ers (personal commun1cation) and obtained ve ry s1,... ::a~ ";n curves (data not s11own). within the reportea reso lution. 161 Appendix F: Clocking Transient Chemical Changes By UGED 719 letters to nature are shown in Fig. 3. The theoretical fits, calculated from structural parameters" (see also Fig. 4 legend) ofCH 2l2, are superimposed on the experimental data. To unambiguously establish the magnitude of the change with time, we also recorded the sM( s) in the absence of the fs initiation laser and obtained the residual of that sM( s) minus the sM(s) taken at - 20ps. This residual is essentially flat (Fig. 3), indicating that the two are identical. Thus, the sM(s) at - 20 psis a calibration point in time, independent of any theoretical fit. The change in the diffraction pattern as a function of time is shown in two sets of data having differing temporal resolutions ( 15 ps and 30 ps) ; the t!i.sM( s) curves are relative to the - 20 ps data. Radial distribution curves were obtained from the sM(s) curves according to the standard GED equation: f(r) = f~ sM(s)sin(sr)exp( - ks')ds (2) where the constant k is a damping coefficient included for the limited s range. Figure 4 shows the experimental and theoretical fl r) obtained from the - 20 ps sM(s) curves of Fig. 3. The timeevolution of D.fi r) is also presented for the two sets of data. At positive time the amplitudes of the dominating C-1 and J••-I peaks decrease, corresponding to the loss of an iodine atom. Both the sM( s) and fl r) representations of our diffraction data clearly show a chemical change occurring as the delay between the fs laser pulse and the ps electron pulse sweeps from negative, to zero, and to positive times. From the fir) data, we obtained the standard deviation for more than 100 diffraction images for each data set, and established that the signal-to-noise ratio is better than 60. Thus, we could detect a change as small as 3%, which is a factor of 5 less than the changes reported here. Breakage of one C-1 bond reduces the[ . .. I peak twice as quickly as the C-1 peak because CH 212 has two C-1 bonds and one [ .. . J internuclear separation. This is observed in our data, corroborated by theoretical simulations of fir) (not shown) which account for the percentage change of CH 2 l 2 to CH 21 and I. Similar time-resolved studies were made for C 2 F,1 2 and CHI 3. Quantitative analysis in the future should yield the changes due to the second C-1 bond breakage, and elucidate the structure of the intermediate. Last, ground-state diffraction patterns of three other molecules (CF 31, CCI, and SF6 ) were recorded with our new UED apparatus (data not shown). As mentioned earlier, the diffraction patterns were converted to experimental sM(s) curves and radial distribution functions. The experimental and theoretical agreement is very good. From the results presented here, it is now evident that ultrafast electron diffraction has achieved the temporal resolution and detection sensitivity necessary for picosecond and subpicosecond studies of complex molecular systems. In future work, utilizing modulation and difference detection techniques, efforts will be directed toward the suppression of background scattering from unreactive species so that molecular structural changes can be analysed with precision. 0 11. Kim. K.-J., Chauopadhyay, S. & Shank. C. V. Gcncmio n of femtos«ond X-rays by 90-dcg.rcts Thomson sc.Jttcring. .\fuel. Instr. ,\,feth. Phys. Rn. A 341, 351-354 (1994), 12. Williamson, S.. Mo urou. G. & Li, f. C. M. Time-resolved laser-induced ph~ tr.lnsform.ition in .llumi num. Phys. R....,. Utt. S2, 2364-2367 (1984). • 1J. Els.ayt'd-Ali. H. E. Timc-re-solvcJ reflection high-cnc-rgy electron diffraction ol metal surfaces. Proc. SP/£ 2521, 92-102 Cl99.S). 14. A~hlimann. M. tt al. A picosccond electron gun for surface analysis. Rev. Sci. lnstru m. 66.. 10001009 l(995). 15. Hargiuai, I. & Hargiuai, M. (eds ) Sttrtocht!mic11I AppliwionsO{Gas-PhaH Elutron Diffraction CVCH, N~ York. 1988). 16. Dibble. T. S. & 8.Jndl, LS. Electron diffraction studies of the k.incticsofphasc changes in molecular dusters. J. Solid-st.Uc phase 1ransformations in S.::F. and (C H,lJCCI. /.Phys.Chem. 96., $603-8610 (1992}. 17. tschenko, A. A. t t 1,1L A stroboscopical gas-electron diffraction mtthod for the in~ tigation of shonlivcd mol«ul.u spccio:s. AppL Phy!. 8 32, 161-163 I 1983 1. 18. Rood, A. P. & Milledge, J. Combined flash-photolysis .ind ga.s- phuc demon diffra.:tion studies of small molecules./. Chtm. Sot. Faraday Trans. 1 80, 1145- 1153 (1984). 19. lschenko. A. A., Schafer, L. Luo, J. Y. & Ewbank. J. D. Structural and vibrational kinetics by stroboscopic gas de.::tron diffuc1ion: the 193 nm photodis.sociation ofCSi. /.Phys.Chem. 98, 8673ll6iS (1994). 20. Williamson, J.C. & Zewail, A. H. Ultrafast dcctron diffraction. 4. Molecular structures ,md coherent dynamics./. Phys. Chem. 98, 2766-2i81 (1994). 21. Williamson, S.. ~lourou, G. & Lctzring, S. Picosccond d ectron diffrmio n. PrO!. SPIE 348, 313-317 (1983). 22. Kawasaki, M. , L«. S. J. & Busohn, R. Photodiuo,.:iation of molecular ~.ims of methylene iodide and iodofo rm. /. Clztm. Ph,•$. 63, 8<W- 8 14 {1975). 23. Baughcum, S. L. & Leone, S. R. Photofrag.mcntation infrared emission studies of vibr.uionally C"xci1ed free radicals CH 1 ,1nd CH!ll· /.Chem.Phy$. 72, 6531 -65-1 5 ( 1980). 24. Hassel, 0. & Vicrvoll, H. Electron diffrac1ion investigation of molecular structurt II, results obtained by the rotating s«tor method. Alfa Chem. ScanJ. I, 1-19-168 (1947). Acknowledgements. We 1hank S. Preuss fo r his help in the construction .ind testing of the expcrimen1al apparatus, and H. Els.iyed-Ali for providing us with pan of the design of the electron gun. Corrtsponden..:c , hould b< ,1ddresscd to A.H.Z. I. t:hcrgui. ~1. ltd.; frmt~·hm1istry: l'ffraf-.Ut Chtmic<ll ,m,I Ph1·$h·<ll Proc,;ue$ in ,\ l.,fw,Wr S_ v$ftms tWor1J Sdentili.:. Sing,1 por,:. 19%). ~l.1nz. I. & Wilstc. l. 1,:Jsl F,·mt,Htcoml Clrtmistry(\'CH. ~tw York. 1995) . .\ . Zcw.1il, :\. H. Ftmr.,,:horu.rry: Ultri1jiw Dyn.im,.-s <.If 1/r.• Ch.-mit·,1/ &m,I I World Sdent11i..:. Sing;ipme:. l'l'I-IJ . 4. ~l.rnz, I. & C.1)tll.'m.1n , A.\\'. Fcnmxhe:mi)try. /. Plrys. (1,.-,11. tsri:.:. iss. J 97(4~). l!-C3-1:b4'1 t J•NJl. Willi.1mson, I. C. & Zt•w.1il. .-\ . t-1. Stru..:tur.il IL·mto.:htmim-y: cx~rimc-n1.1I mC'lh,)dolo~·- Pr,,c. .'l,11/ :\.-,td. St·i. USA 88, :-0.:1-~u.:s 11991 l. h. \Villi,mmm , I. C.. D,1ntus, \I., Kim, S. 8. & Zcwail. A. H. l"11r.1t',bt Jitfra.:1ion .ind mok.:ul,1r stru.:t un:. Cli.·m. PIM. L.-rr. 196. ~.:'1-53-1 I I~.:). Willi.imsun, J.C. & Zi:w,1il. A. H. Uhraf,1)1 d.·.:tron J in"r.1,;tion. \'dod1y mism.11.:h ,1nJ IC'mr-,ral r.:wlu1ion in (ro,~,:J -hi:jn, ,·xpcrimi:nts. C/rc111. Php. Lm. !09, 10- lh ( l<NJI. ~- l),1111us, :O.L J.:im. :,.. B.. Williamson. I. C. & Z,:w.111.. \ . H. L"ltr.ifasl dl".:tron Jitfr.1.:1ion. 5. Exrcrm1t·111.1I 11m,: rt!w lution .mJ .1pplk.11ion:.. /. P/11·~. c...·1,,-111. 98, :;N.?-.?7% 11994 l. "· l(.1k~i. Erl ,1/. L'l!rJl'. hl ); -r.1~· .1h'iorp1ion prnhing uf .i ..:h.:mt(.1] r,:,1.::1ion. /. Clz.•m. Pin-!. 104, oOM t•Ofl'l t lY':lh ). 1n. fon111v, I. V.,t:hl"n . P. & R,:nt1t·pis. P. ~1. Pi.:oK.::unJ lim.:-r,:~•lwJ x- r,1ydiffr.1,;tion Junn~ IJKr-pulsc h,·.11in~ uf .111 :\u< I ! I ..:n ·~t.11. /. A.pp/. C:rn1,1//,,gr. 28, .>.>:-- .>r,: l 1~'13 1. 162 ~ATURE : VOL 386 ! U M ARCH 199; 720 References [Abr72] M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions, Dover Publications, Inc.: New York, 1972. [Ade92] G. A. Adegboyega, J. Phys. lII (Fra.) 2, 1749-1755 (1992). [Aes95a] M. Aeschlimann, E. Hull, J. Cao, C. A. Schmuttenmaer, L. G. Jahn, Y. Gao, H. E. ElsayedAli, D. A. Mantell, and M. R. Scheinfein, Rev. Sci. lnstrum. 66(2), 1000-1009 (1995). [Aes95b] M. Aeschlimann, E. Hull, C. A. Schmuttenmaer, J. Cao, Y. Gao, D. A. Mantell, and H. E. Elsayed-Ali, Proc. SPIE 2521, 103-112 (1995). [Alm61] A. Almenningen, 0. Bastiansen, and M . Trretteberg, Acta Chem. Scand. 15, 1557-1562 (1961). [Alm59] A. Almenningen, 0. Bastiansen, and M. Trretteberg, Acta Chem. Scand. 13, 1699-1702 (1959). [AnA72] A. L. Andreassen and S. H. Bauer, J. Chem. Phys. 56(8), 3802-3811 (1972). [AnB69] B. Andersen, H. M. Seip, T. G. Strand, and R. Styjlevik, Acta Chem. Scand. 23(9), 3224-3234 (1969). [AnB66a] B. Andersen and P. Andersen, Acta Chem. Scand. 20(10), 2728-2736 (1966). [AnB66b] B. Andersen and P. Andersen, Trans. Am. Cryst. Assoc. 2, 193-196 (1966). [And93] T. Anderson, I. V. Tomov, and P. M. Rentzepis, J. Chem. Phys. 99(2), 869-875 (1993). [Ani77] S. I. Anisimov, V. A. Benderskii, and Gy. Farkas, Sov. Phys. Usp. 20(6), 467-488 (1977). [AnK71] K. W. Andrews, D. J. Dyson, and S. R. Keown, Interpretation of Electron Diffraction Patterns, 2nd. Ed., Plenum Press: New York, 1971. References 721 [AnP65] P. Andersen, Acta Chem. Scand. 19(3), 629-637 (1965). [Aru63] F. R. Arutyunian and V. A. Tumanian, Phys. Lett. 4(3), 176-178 (1963). [Arv79] M. M. Arvedson and D. A. Kohl, Chem. Phys. Lett. 64(1), 119-121 (1979). [AuA76] A. Authinarayanan and R. W. Dudding, Adv. Electr. Electr. Phys. 40A, 167-181 (1976). [Aut83] R. Autrata, P. Schauer, Jo. Kvapil, and J. Kvapil, Scan. Elec. Microsc., II, 489-500 (1983). [Aut78] R. Autrata, P. Schauer, Jo. Kvapil, and J. Kvapil, J. Phys. E 11, 707-708 (1978). [Bab92] A. V. Babushkin, G. I. Bryunkhnevitch, V. P. Degtyareva, S. A. Kaidalov, B. B. Moskalev, V. E. Postovalov, A. M. Prokhorov, E. I. Titkov, V. I. Fedotov, and M. Ya. Schelev, Proc. SPIE 1801, 218-225 (1992). [Bac77] G. E. Bacon, Neutron Scattering in Chemistry, Butterworths: Boston, 1977. [BaD91] D. Barlett, C. W. Snyder, B. G. Orr, and R. Clarke, Rev. Sci. lnstrum. 62(5), 1263-1269 (1991). [Bak94] R. J. Baker and B. P. Johnson, Meas. Sci. Technol. 5, 408-411 (1994). [BaL80] S. L. Baughcum and S. R. Leone, J. Chem. Phys. 72(12), 6531-6545 (1980). [BaM95] M . Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, (eds.), Handbook of Optics, 2nd. Ed., McGraw-Hill, Inc.: New York, 1995. [BaO60] 0. Bastiansen and M. Trretteberg, Acta Cryst. 13, 1108 (1960). [Bar90] L. S. Bartell and T. S. Dibble, J. Am. Chem. Soc. 112, 890-891 (1990). [Bar89] L. S. Bartell and R. J. French, Rev. Sci. Instrum. 60(7), 1223-1227 (1989). [Bar84a] L. S. Bartell and M.A. Kacner, J. Phys. Chem. 88(16), 3485-3489 (1984). [Bar84b] L. S. Bartell and M.A. Kacner, J. Chem. Phys. 81(1), 280-287 (1984). [Bar81a] L. S. Bartell, M. A. Kacner, and S. R. Goates, J. Chem. Phys. 75(6), 2730-2735 (1981). [Bar81b] L. S. Bartell, M. A. Kacner, and S. R. Goates, J. Chem. Phys. 75(6), 2736-2741 (1981). [Bar80] L. S. Bartell, S. R. Goates, and M. A. Kacner, Chem. Phys. Lett. 76(2), 245-248 (1980). [Bar78] L. S. Bartell and S. K. Doun, J. Mot. Struct. 43, 245-249 (1978). [Bar72] L. S. Bartell and T. C. Wong, J. Chem. Phys. 56(5), 2364-2367 (1972). [Bar68] L. S. Bartell, Phys. Lett. 27A(4), 236-237 (1968). [Bar65a] L. S. Bartell, D. A. Kohl, B. L. Carroll, and R. M. Gavin, J. Chem. Phys. 42(9), 3079-3084 (1965). [Bar65b] L. S. Bartell, H.B . Thompson, and R.R. Roskos, Phys. Rev. Lett. 14(21), 851-852 (1965). [Bar55a] L. S. Bartell, J. Chem. Phys. 23(7), 1219-1222 (1955). [Bar55b] L. S. Bartell, L. 0 . Brockway, and R.H. Schwendeman, J. Chem. Phys. 23(10), 1854-1859 (1955). [BaS77] S. C. Barnes and K. E. Singer, J. Phys. E 10, 737-740 (1977). [Bas94] J. S. Baskin and A.H. Zewail, J. Phys. Chem. 98(13), 3337-3351 (1994). [Bas89] J. S. Baskin and A. H. Zewail, J. Phys. Chem. 93(15), 5701-5717 (1989). [Bas87] J. S. Baskin, P. M. Felker, and A. H. Zewail, J. Chem. Phys. 86(5), 2483-2499 (1987). References [Bas86] J. S. Baskin, P. M. Felker, and A.H. Zewail, J. Chem. Phys. 84(8), 4708-4710 (1986). [Bau50] S. H. Bauer, J. Chem. Phys. 18(1), 27-41 (1950). 722 [BaW8la] W. Baumann and L. Reimer, Scanning 4(3), 141-151 (1981). [BaW8lb] W. Baumann, A. Niemietz, L. Reimer, and B. Volbert, J. Microsc. 122(2), 181-186 (1981). [Bea78] B. Beagley, A. Foord, and V. Ulbrecht, J. Phys. E 11, 357-360 (1978). [Bec75] J. H. Bechtel, W. L. Smith, and N. Bloembergen, Opt. Comm. 13(1), 56-59 (1975). [BeL88] L. Bergonzi, M. Lemonier, and M. Petit, Adv. Electr. Electr. Phys. 74, 165-172 (1988). [BeM96] M. Ben-Nun, T. J. Martfnez, P. M. Weber, and K. R. Wilson, Chem. Phys. Lett. 262, 405-414 (1996). [Ben84] 0. J. Benston, J. D. Ewbank, D. W. Paul, V. J. Klimkowski, and L. Schafer, Appl. Spec. 38(2), 204-208 (1984). [BeR89] R. B. Bernstein and A.H. Zewail, J. Chem. Phys. 90(2), 829-842 (1989). [Ber86] J. P. Bergsma, M. H. Coladonato, P. M. Edelsten, J. D. Kahn, K. R. Wilson, and D.R. Fredkin, J. Chem. Phys. 84(11), 6151-6159 (1986). [BeW88] W. Becker, J. K. Mciver, and R.R. Schlicher, Phys. Rev. A 38(9), 4891-4894 (1988). [Bey82] W. H. Beyer (ed.), CRC Standard Mathematical Tables, 26th Ed., CRC Press, Inc.: Boca Raton, 1982. [Bij69] J. M. Bijvoet, W. G. Burgers, and G. Hagg, Early Papers on Diffraction of X-Rays by Crystals, International Union of Crystallography: Utrecht, 1969. [Blo87] M . M . Blouke, B. Corrie, D. L. Heidtmann, F. H. Yang, M. Winzenread, M. L. Lust, H. H. Marsh, and J. R. Janesick, Opt. Eng. 26(9), 837-843 (1987). [Boh67] R. K. Bohn and S. H. Bauer, lnorg. Chem. 6(2), 304-309 (1967). [Bon74] R. A. Bonham and M. Fink, High Energy Electron Scattering , Van Nostrand Reinhold Co.: New York, 1974. [Bon69] R. A. Bonham, M. Fink, and D. A. Kohl, Chem. Phys. Lett. 4(6), 349-351 (1969). [Bon65a] R. A. Bonham and T. Iijima, J. Chem. Phys. 42, 2612-2614 (1965). [Bon65b] R. A. Bonham, J. Chem. Phys. 43(4), 1103-1109 (1965). [Bon65c] R. A. Bonham, J. Chem. Phys. 43(6), 1933-1940 (1965). [Bon63a] R. A. Bonham and J. L. Peacher, J. Chem. Phys. 38(10), 2319-2325 (1963). [Bon63b] R. A. Bonham and T. Iijima, J. Phys. Chem. 67(11), 2266-2272 (1963). [Bon62] R. A. Bonham, J. Chem. Phys. 36(12), 3260-3269 (1962). [Bon59] R. A. Bonham and L. S. Bartell, J. Chem. Phys. 31(3), 702-708 (1959). [Bor95] G.D. Boreman and S. Yang, Optics and Photonics News 6(2), Eng. and Lab. Notes (1995). [Bow89] R. M. Bowman, M. Dantus, and A.H. Zewail, Chem. Phys. Lett. 161(4,5), 297-302 (1989). [Bow95] N. Bowering, M. Volkmer, Ch. Meier, J. Lieschke, R. Dreier, J. Mol. Struct. 348, 49-52 (1995). [Bow94] N. Bowering, M. Volkmer, C. Meier, J. Lieschke, M. Fink, Z. Phys. D 30, 177-182 (1994). References 723 [Boy92] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 5th Ed., John Wiley and Sons: New York, 1992. [Bra75] D. J. Bradley and W. Sibbett, Appl. Phys. Lett. 27(7), 382-384 (1975). [Bra71] D. J. Bradley, B. Liddy, and W. E. Sleat, Opt. Comm. 2(8), 391-395 (1971). [Bre55] E. Breitenberger, Prog. Nucl. Phys. 4, 56-94 (1955). [Bri62] A. Bril in Luminescence of Organic and Inorganic Materials, H.P. Kallmann and G. M. Spruch (eds.), Wiley: New York, pp. 479-493, 1962. [BrL25] L. de Broglie, Ann. d. Phys. 3, 22+ (1925). [Bro36] L. 0 . Brockway, Rev. Mod. Phys. 8(3), 231-266 (1936). [BrS64] L. S. Brown and T. W. B. Kibble, Phys. Rev. 133(3A), A705-A719 (1964). [Bru91] A. Brun, P. Georges, G. Le Saux, and F. Salin, J. Phys. D 24, 1225-1233 (1991). [BrW12] W. L. Bragg, Proc. Cambridge Phil. Soc. 17, 43-57 (1912). [Bry92] G. I. Bryukhnevich, S. A. Kaidalov, B. B. Moskalev, V. E. Postovalov, A. M. Prokhorov, A. V. Srnirnov, and M. Ya. Schelev, Proc. SPIE 1801, 115-118 (1992). [Buc88] P.H. Bucksbaum, D. W. Schumacher, and M. Bashkansky, Phys. Rev. Lett. 61(10), 11821185 (1988). [Buc87] P.H. Bucksbaum, M. Bashkansky, and T. J. Mcilrath, Phys. Rev. Lett. 58(4), 349-352 (1987). [CaM78] M. Cardona and L. Ley (eds.), Topics In Applied Physics: Photoemission In Solids I, Vol. 26, Springer-Verlag: Berlin, 1978. [Car74] J. L. Carlos, R.R. Karl, and S. H. Bauer, J. Chem. Doc. Far. Trans. 2, 177-187 (1974). [Cha89] D. Charalambidis, E. Hontzopoulos, C. Fotakis, Gy. Farkas, and Cs. T6th, J. Appl. Phys. 65(7), 2843-2846 (1989). [ChE94] E. Chevallay, J. Durand, S. Hutchins, G. Suberlucq, and M. Wurgel, Nucl. Instrum. Meth. A340, 146-156 (1994). [Che96] M. Chergui (ed.), Femtochemistry: Ultrafast Chemical and Physical Processes in Molecular Systems, World Scientific: Singapore, 1996. [ChJ94] J. Chen, K. Imasaki, M. Fujita, C. Yamanaka, M. Asakawa, S. Nakai, and T. Asakuma, Nucl. Instrum. Meth. A341, 346-350 (1994). [ChK69] K. L. Chopra, Thin Film Phenomena , McGraw-Hill Book Co.: New York, 1969. [Cho86] S. E. Choi and R. B. Bernstein, J. Chem. Phys. 85(1), 150-161 (1986). [ChP87] P. Chen, Particle Accelerators 20, 171-182 (1987). [ChW64] W. N. Charman, Photog. Sci. Eng. 8, 253-259 (1964). [ChY79] Y. W. Chan and W. L. Tsui, Phys. Rev. A 20(1), 294-303 (1979). [Cla89] R. Clauberg and A. Blacha, J. Appl. Phys. 65(11), 4095-4106 (1989). [CoD83] D. M. Considine (ed.), Van Nostrand's Scientific Encyclopedia, 6th Ed., Van Nostrand Reinhold Co. : New York, 1983. [CoH89] Collimated Holes, Inc., Fiber Optic Scintillating Screens , (1989). [Col54] J. W. Coltman, J. Opt. Soc. Am. 44(6), 468-471 (1954). References 724 [Con96] P. Cong, G. Roberts, J. L. Herek, A. Mokhtari, and A.H. Zewail, J. Phys. Chem. 100(19), 7832-7848 (1996). [Cos66] C. C. Costain, Trans. Am. Cryst. Assoc. 2, 157-164 (1966). [Cou85] E. A. Coutsias and J. K. Mciver, Phys. Rev. A 31(5), 3155-3168 (1985). [Cow90] J.M. Cowley, Diffraction Physics, 2nd Ed., North-Holland: Amsterdam, 1990. [CrS92] Crystal Semiconductor Corporation, Volume I Data Book: AID Conversion ]C's, (1992). [Dab96] I. Daberkow, K.-H. Herrmann, L. Liu, W. D. Rau, and H. Tietz, Ultramicroscopy 64, 35-48 (1996). [Dab93] I. Daberkow, K.-H. Herrmann, and F. Lenz, Ultramicroscopy 50, 75-82 (1993). [Dab91] I. Daberkow, K.-H. Herrmann, L. Liu, and W. D. Rau, Ultramicroscopy 38, 215-223 (1991). [Dac78] H. bachs (ed.), Neutron Diffraction, Springer-Verlag: Berlin, 1978. [Dai74] J.C. Dainty and R. Shaw, Image Science: Principles, Analysis, and Evaluation of Photographic-Type Imaging Processes, Academic Press: London, 1974. [DAn71] P. D' Antonio, C. George, A.H. Lowery, and J. Karle, J. Chem. Phys. 55(3), 1071-1075 (1971). [Dan94] M. Dantus, S. B. Kim, J.C. Williamson, and A. H. Zewail, J. Phys. Chem. 98(11), 27822796 (1994). [Dan9la] M. Dantus, M. H. M. Janssen, and A.H. Zewail, Chem. Phys. Lett. 181(4), 281-287 (1991). [Dan91b] M. Dantus, Ph.D. Dissertation, California Institute of Technology, 1991. [Dan90] M. Dantus, R. M . Bowman, and A.H. Zewail, Nature 343, 737-739 (1990). [Dan88] M. Dantus, M. J. Rosker, and A.H. Zewail, J. Chem. Phys. 89(10), 6128-6140 (1988). [Dan87] M. Dantus, M. J. Rosker, and A.H. Zewail, J. Chem. Phys. 87(4), 2395-2397 (1987). [Dar75] E. H. Darlington, J. Phys. D 8, 85-93 (1975). [Dar72] E. H. Darlington and V. E. Cosslett, J. Phys. D 5, 1969-1981 (1972). [Dau87] T. Daud, J. R. Janesick, K. Evans, and T. Elliot, Opt. Eng. 26(8), 686-691 (1987). [Dav27] C. Davisson and L. H. Germer, Phys. Rev. 30(6), 705-740 (1927). [Deb88] P. J. W. Debye, The Collected Papers of Peter J. W. Debye, Ox Bow Press: Woodbridge, 1988. [Deb41] P. Debye, J. Chem. Phys. 9, 55-60 (1941). [Deb30] P. Debye, Physik. Zeitschr. 31, 419-428 (1930). [Deb29] P. Debye, L. Bewilogua, and F. Ehrhardt, Physik. Zeitschr. 30, 84-87 (1929). [Deb16] P. Debye and P. Scherrer, Physik. Zeitschr. 17, 277-283 (1916). [Deb 15] P. De bye, Ann. d. Phys. 46, 809-823 (1915). [Deg37] Ch. Degard, Bull. Soc. Roy. Sci. Liege 12, 383+ (1937). [Deg35] Ch. Degard, J. Pierard, and W. van der Grinten, Nature 136, 142-143 (1935). [Den86] P. N. J. Dennis, Photodetectors: An Introduction To Current Technology, Plenum Press: New York, 1986. References 725 [Dha94] L. Dhar, J. T. Fourkas, and K. A. Nelson, Opt. Lett. 19(9), 643-645 (1994). [Dib92] T. S. Dibble and L. S. Bartell, J. Phys. Chem. 96(21), 8603-8610 (1992). [Dom92] A. Domenicano and I. Hargittai (eds.), Accurate Molecular Structures: Their Determination and Importance, Oxford University Press: London, 1992. [Dow82] K. H. Downing and D. A. Grano, Ultramicroscopy 7, 381-404 (1982). [DuB33] L.A. DuBridge, Phys. Rev. 43, 727-741 (1933). [DuB32] L.A. DuBridge, Phys. Rev. 39, 108-118 (1932). [Dvo89] M. I. Dvorkin, S. L. Dobychin, S. N. Nekhoroshkov, and A. V. Seryakov, Opt. Spec. (USSR) 67(3), 343-346 (1989). [Dwe75] A. W. Dweydari and C.H. B. Mee, Phys. Stat. Sol. A 27, 223-230 (1975). [EaR73] R. M. Eastment and C.H. B. Mee, J. Phys. F 3, 1738-1745 (1973). [Eas70] D. E. Eastman, Phys. Rev. B 2(1), 1-2 (1970). [Ebe68] E. H. Eberhardt, Appl. Opt. 7(10), 2037-2047 (1968). [Edg92] J.P. Edgecumbe, V. W. Aebi, and G. A. Davis, Proc. SPIE 1655, 204-210 (1992). [Ehl87] F. Ehlotzky, J. Phys. B 20, 2619-2626 (1987). [Eid95] E.-S. Eid, A. G. Dickinson, D. A. Inglis, B. D. Ackland, and E. R. Fossum, Proc. SPIE 2415, 265-275 (1995). [Eis85] R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd Ed., John Wiley and Sons: New York, 1985. [Els95] H. E. Elsayed-Ali, Proc. SPIE 2521, 92-102 (1995). [Els90] H. E. Elsayed-Ali and J. W. Herman, Rev. Sci. lnstrum. 61(6), 1636-1647 (1990). [Els88] H. E. Elsayed-Ali and G. A. Mourou, Appl. Phys. Lett. 52(2), 103-104 (1988). [End71] J. G. Endriz and W. E. Spicer, Phys. Rev. B 4(12), 4159-4184 (1971). [Eng83] T. J. Englert and E. A. Rinehart, Phys. Rev. A 28(3), 1539-1545 (1983). [Eps77] J. Epstein and R. F. Stewart, J. Chem. Phys. 66(9), 4057-4064 (1977). [Eve71] T. E. Everhart and P.H. Hoff, J. Appl. Phys. 42(13), 5837-5846 (1971). [Ewb94] J. D. Ewbank, L. Schafer, and A. A. Ischenko, J. Mol. Struct. 321, 265-278 (1994). [Ewb93] J. D. Ewbank, J. Y. Luo, J. T. English, R. Liu, W. L. Faust, and L. Schafer, J. Phys. Chem. 97(34), 8745-8751 (1993). [Ewb92] J. D. Ewbank, W. L. Faust, J. Y. Luo, J. T. English, D. L. Monts, D. W. Paul, Q. Dou, and L. Schafer, Rev. Sci. lnstrum. 63(6), 3352-3358 (1992). [Ewb90] J. D. Ewbank, W. L. Faust, D. L. Monts, D. W. Paul, L. Schafer, R. Bakhtiar, and Q. Dou, Mol. Cryst. Liq. Cryst. 187, 351-356 (1990). [Ewb89] J. D. Ewbank, D. W. Paul, L. Schafer, and R. Bakhtiar, Appl. Spec. 43(3), 415-419 (1989). [Ewb86] J. D. Ewbank, L. Schafer, D. W. Paul, D. L. Monts, and W. L. Faust, Rev. Sci. Jnstrum. 57(5), 967-972 (1986). [Ewb84] J. D. Ewbank, L. Schafer, D. W. Paul, 0 . J. Benston, and J. C. Lennox, Rev. Sci. Jnstrum. 55(10), 1598-1603 (1984). References 726 [Ewb81] J. D. Ewbank, P. Bowers, J. Pinegar, and L. Schafer, Appl. Spec. 35(6), 540-543 (1981). [Fan94] G. Y. Fan, D. G. Dunkelberger, and M. H. Ellisman, Ultramicroscopy 55, 7-14 (1994). [Fan93a] G. Y. Fan and M. H. Ellisman, Ultramicroscopy 52, 21-29 (1993). [Fan93b] G. Y. Fan, C. Bueno, D. Dunkelberger, and M. H. Ellisman, J. Electr. Microsc. 42, 419-423 (1993). [FaR69] R. W. Fane and W. E. J. Neal, J. Opt. Soc. Am. 60(6), 790-793 (1969). [Far93] Gy. Farkas and C. T6th, Opt. Eng. 32(10), 2469-2474 (1993). [Far90] Gy. Farkas and Cs. T6th, Phys. Rev. A 41(7), 4123-4126 (1990). [Far87] Gy. Farkas, Z. Gy. Horvath, Cs. T6th, C. Fotakis, and E. Hontzopoulos, J. Appl. Phys. 62(11), 4545-4547 (1987). [Far85] Gy. Farkas and S. L. Chin, Appl. Phys. B 37, 141-143 (1985). [Far84] Gy. Farkas and S. L. Chin in Multiphoton Processes, P. Lambropoulos and S. J. Smith (eds.), Springer Series On Atoms And Plasmas, Vol. 2, Springer-Verlag: Berlin, pp. 191-199 1984. [Far83] Gy. Farkas, S. L. Chin, P. Galarneau, and F. Yergeau, Opt. Comm. 48(4), 275-278 (1983). [Far78] Gy. Farkas in Multiphoton Processes, J. H. Eberly and P. Lambropoulos (eds.), John Wiley and Sons: New York, pp. 81-100, 1978. [FaU47] U. Fano, Phys. Rev. 72(1), 26-29 (1947). [Fax27] H. Faxen and J. Holtsmark, Z. Physik 45, 307-324 (1927). [FaW92a] W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. Lett. 68(18), 2834-2837 (1992). [FaW92b] W. S. Fann, R. Storz, H. W. K. Tom, and J. Bokor, Phys. Rev. B 46(20), 13592-13595 (1992). [Fed97] M. V. Fedorov, S. P. Goreslavsky, and V. S. Letokhov, Phys. Rev. E 55(1), 1015-1027 (1997). [Fed91] M. V. Fedorov, Interaction of Intense Laser Light with Free Electrons, Harwood Academic Publishers: Chur, 1991. [Fed81] M. V. Fedorov, Prag. Quant. Electr. 7, 73-116 (1981). [Fed67] M. V. Fedorov, Sov. Phys. JETP 25(5), 952-959 (1967). [Fel87] P. M. Felker and A.H. Zewail, J. Chem. Phys. 86(5), 2460-2482 (1987). [FeP92] P. Felder, Chem. Phys. Lett. 197(4,5), 425-432 (1992). [FeP91] P. Felder, Chem. Phys. 155, 435-445 (1991). [FiA88] A. Finch, Y. Liu, H. Niu, W. Sibbett, W. E. Sleat, D.R. Walker, Q. L. Yang, and H. Zhang, Proc. SPIE 1032, 622-626 (1988). [Fie72] J. R. Fiebiger and R. S. Muller, J. Appl. Phys. 43(7), 3202-3207 (1972). [Fin89] M. Fink, A. W. Ross, and R. J. Fink, Z. Phys. D 11, 231-238 (1989). [Fin88] M. Fink and D. A. Kohl in Chapter Five of [Har88a]. [Fin79] M. Fink, P. G. Moore, and D. Gregory, J. Chem. Phys. 71(12), 5227-5237 (1979). References 727 [Fin70a] M. Fink, D. A. Kohl, and R. A. Bonham, J. Chem. Phys. 52, 5487-5489 (1970). [Fin70b] M. Fink and R. A. Bonham, Rev. Sci. lnstrum. 41(3), 389-396 (1970). [Fio63] G. Fiocco and E. Thompson, Phys. Rev. Lett. 10(3), 89-91 (1963). [Fle86] G. R. Fleming, Chemical Applications of Ultrafast Spectroscopy, Oxford University Press: New York, 1986. [FoH70] H. R. Foster, J. Appl. Phys. 41, 5344-5346 (1970). [Fom66] V. S. Fomenko, Handbook Of Thermionic Properties, G. V. Samsonov (ed.), Plenum Press Data Division: New York, 1966. [For84] R. L. Fork, 0. E. Martinez, and J.P. Gordon, Opt. Lett. 9(5), 150-152 (1984). [For83] R. L. Fork, C. V. Shank, R. Yen, and C. A. Hirlimann, IEEE J. Quant. Elec. QE-19(4), 500.506 (1983). [For82] R. L. Fork, C. V. Shank, and R. T. Yen, Appl. Phys. Lett. 41(3), 223-225 (1982). [For81] R. L. Fork, B. I. Greene, and C. V. Shank, Appl. Phys. Lett. 38, 671-672 (1981). [Fos94] E. R. Fossum, Proc. SPIE 2172, 1-16 (1994). [Fou95] J. T. Fourkas, L. Dhar, K. A. Nelson, and R. Trebino, J. Opt. Soc. Am. B 12(1), 155-165 (1995). [Fow31] R.H. Fowler, Phys. Rev. 38, 45-56 (1931). [Foy84] A.G. Foyt and F. J. Leonberger in Picosecond Optoelectronic Devices, C.H. Lee (ed.), Academic Press: Orlando, pp. 271-31 I, 1984. [Fra83] G. W. Fraser, Nucl. lnstrum. Meth. 206, 445-449 (1983). [Fre86] R.R. Freeman, T. J. Mcilrath, P.H. Bucksbaum, and M. Bashkansky, Phys. Rev. Lett. 57(25), 3156-3159 (1986). [Fril 2] W. Friedrich, P. Knipping, and M. von Laue, Ann. Physik 41, 971+ (1912). [Fry28] T. C. Fry and H. E. Ives, Phys. Rev. 32, 44-56 (1928). [Fuj84] J. G. Fujimoto, J. M. Liu, E. P. lppen, and N. Bloembergen, Phys. Rev. Lett. 53(19), 18371840 (1984). [Gal90a] Galileo Electro-Optics Corp., Spectral Response of Typical Photosensitive Devices, (1990). [Gal90b] Galileo Electro-Optics Corp., Detector Assemblies and also About Galileo Long-Life Microchannel Plates, (1990). [GaM71] M. Galanti, R. Gott, and J. F. Renaud, Rev. Sci. lnstrum. 42(12) , 1818-1822 (1971). [GeA81] A. G. Gershikov, Teor. i Eksper. Khim. 17(4), 463-468 (1981). [Gei95] J. D. Geiser and P. M. Weber, Proc. SPIE 2521, 136-144 (1995). [Ger85] S. Gerstenkorn and P. Luc, J. Physique 46(6), 867-881 (1985). [Gho82] C. Ghosh, Proc. SPIE 346, 62-68 (1982). [Gir95a] J. P. Girardeau-Montaut, C. Girardeau-Montaut, and S. D. Moustaizis, J. Phys. D 28, 212215 (1995). [Gir95b] J.-P. Girardeau-Montaut, M. Afif, A. Perez, C. Girardeau-Montaut, and C. Tomas, Proc. SPIE 2521, 32-43 (1995). References 728 [Gir93] J. P. Girardeau-Montaut, C. Girardeau-Montat, S. D. Moustaizis, and C. Fotakis, Appl. Phys. Lett. 63(5), 699-701 (1993). [Gla58] R. J. Glauber, Lectures in Theoretical Physics 1, 315-414 (1958). [Gla53] R. Glauber and V. Schomaker, Phys. Rev. 89(4), 667-671 (1953). [Glu94] J. P. Glusker, M. Lewis, and M. Rossi, Crystal Structure Analysis for Chemists and Biologists, VCH Publishers: New York, 1994. [Gol83] V. V. Golubkov, A. V. Zgurskii, A. A. lschenko, and V. I. Petrov, /zv. Akad. Nauk SSSR, Ser. Fiz. 47(6), 1115-1118 (1983). [Gom61] R. Gomer, Field Emission and Field Ionization, Harvard University Press: Cambridge, 1961. [Gra80] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press: . New York, 1980. [Gre74] R. C. Greenhaw and A. J. Schmidt, Adv. Quant. Elec. 2, 157-286 (1974). [Gru93] M. Gruebele and A.H. Zewail, J. Chem. Phys. 98(2), 883-902 (1993). [Gru90] M. Gruebele, G. Roberts, M. Dantus, R. M. Bowman, and A. H. Zewail, Chem. Phys. Lett. 166(5,6), 459-469 (1990). [GuD96] D.-S. Guo, Phys. Rev. A 53(6), 4311-4319 (1996). [GuD92] D.-S . Guo and G. W. F. Drake, Phys. Rev. A 45(9), 6622-6635 (1992). [Gui95] V. Guidi and A. V. Novokhatsky, Meas. Sci. Technol. 6, 1555-1556 (1995). [Gus71] R. Gush and H. P. Gush, Phys. Rev. D 3(8), 1712-1721 (1971). [Guo94] H. Guo and A.H. Zewail, Can. J. Chem. 72, 947-957 (1994). [Haa70a] J. Haase, Z. Naturforschung A 25, 1219-1235 (1970). [Haa70b] J. Haase, Z. Naturforschung A 25, 936-945 (1970). [HaB91a] B. D. Hall, D. Reinhard, J.-P. Borel, and R. Monot, Z. Phys. D 20, 457-459 (1991). [HaB91b] B. D. Hall, M. Fliieli, D. Reinhard, J.-P. Borel, and R. Monot, Rev. Sci. /nstrum. 62(6), 14811488 (1991). [HaF95] F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, Phys. Rev. E 51(5), 4833-4843 (1995). [Hag95] T. Hager, Force of Nature: The Life of Linus Pauling , Simon and Schuster: New York, 1995. [HaH36] H. Halban and P. Preiswork, C. R. Acad. Sci. Paris 203, 73+ (1936). [HaJ75] H.-J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65(6), 742-744 (1975). Values of n, k, and Rare tabulated in [Wea81]. [Hal78] D. Halliday and R. Resnick, Physics, J. Wiley and Sons: New York (1978). [HaM79] M. D. Harmony, V. W. Laurie, R. L. Kuczkowski , R.H. Schwendeman, D. A. Ramsay, F. J. Lovas, W. J. Lafferty, and A.G. Maki, J. Phys. Chem. Ref Data 8(3), 619-722 (1979). [Ham67] J. F. Hamilton and J.C. Marchant, J. Opt. Soc. Am. 57(2), 232-239 (1967). [Har92] I. Hargittai in Chapter Five of [Dom92] . [Har88a] I. Hargittai and M. Hargittai (eds.), Stereochemical Applications of Gas-Phase Electron Diffraction, VCH Publishers: New York, 1988. References 729 [Har88b] I. Hargittai in Chapter One of [Har88a]. [Has61] G. Hass and J.E. Waylonis, J. Opt. Soc. Am. 51(7), 719-722 (1961). [Hay70] J. G. Hayes (ed.), Numerical Approximation to Functions and Data, Oxford University Press, Inc.: New York, 1970. [HeC49] C. Herring and M. H. Nichols, Rev. Mod. Phys. 21(2), 185-270 (1949). [Hec87] E. Hecht and A. Zajac, Optics, 2nd Ed., Addison-Wesley Publishing Co.: Reading, 1987. [Hel80] T. M. Helliwell, Introduction to Special Relativity, Harvey Mudd College: Claremont, 1980. [Her95] K.-H. Herrmann and R. Sikeler, Optik 98(3), 119-124 (1995). [Her92] K.-H. Herrmann and L. Liu, Optik 92(1), 48-50 (1992). [Her87] K.-H. Herrmann and M . Korn, J. Phys. E 20, 177-181 (1987). [Her84] K.-H. Herrmann and D. Krahl, Adv. Opt. Electr. Microsc. 9, 1-64 (1984). [Her82] K.-H. Herrmann and D. Krah!, J. Microsc. 127(1), 17-28 (1982). [Hib92] M. Hibino, K. Irie, R. Autrata, and P. Schauer, J. Electr. Microsc. 41, 453-457 (1992). [HiE83] E. Hirota, J. Phys. Chem. 87, 3375-3383 (1983). [Hie79] R. G. Hier, E. A. Beaver, G. W. Schmidt, and G.D. Schmidt, Adv. Electr. Electr. Phys. 52, 463-480 (1979). [Hi176] G. E. Hill, Adv. Electr. Electr. Phys. 40A, 153-165 (1976). [Hir77] P. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan, Electron Microscopy of Thin Crystals, 2nd Ed., R. E. Krieger Publishing Co.: Malabar, 1977. [Hmt92] Hamamatsu Photonics K. K., Image Intensifiers, (1992). [Hoe53] J. A. Hoerni and J. A. Ibers, Phys. Rev. 91(5), 1182-1185 (1953). [HoG96] G. C. Holst, CCD Arrays, Cameras, and Displays, SPIE Optical Engineering Press: Bellingham, 1996. [Ho166] A. A. Holscher, Surf Sci. 4, 89-102 (1966). [Hol79] J. Holz] and F. K. Schulte, Springer Tracts In Modern Physics 85, 1-150 (1979). [Hop64] B. J. Hopkins and J.C. Riviere, Brit. J. Appl. Phys. 15, 941-946 (1964). [Hor96] H. Hora, W. Scheid, B. W. Boreham, R. Hopf!, P. R. Bolton, and Y.-K. Ho, Opt. Comm. 130, 283-287 (1996). [How95] N. E. Howard, Proc. SPIE 2415, 188-198 (1995). [Hra93] V. P. Hradil, T. Suzuki, S. A. Hewitt, P. L. Houston, and B. J. Whitaker, J. Chem. Phys. 99(6), 4455-4463 (1993). [HuA17] A. W. Hull, Phys. Rev. 9(1 ), 84-87 (1917). [Hub80] J. H. Hubbell, H. A. Gimm, and I. 0verb0, J. Phys. Chem. Ref Data 9(4), 1023-1147 (1980). [Hub79] J. H. Hubbell and I. 0verb0, J. Phys. Chem. Ref Data 8(1), 69-105 (1979). [Hul61] H. M. Hulburt and J. 0 . Hirschfelder, J. Chem. Phys. 35, 1901 (1961). [Hul41] H. M. Hulburt and J. 0. Hirschfelder, J. Chem. Phys. 9, 61-69 (1941). [Hun82] T. F. Hunter and K. S. Kristjansson, Chem. Phys. Lett. 90(1 ), 35-40 (1982). References 730 [Hwa92] H.J. Hwang and M.A. El-Sayed, J. Phys. Chem. 96(22), 8728-8735 (1992). [Ibe74] J. A. lbers and W. C. Hamilton (eds.), International Tables For X-Ray Crystallography, Vol. 4, Kynoch Press: Birmingham, pp. 176-269, 1974. See corrections in [Sel78]. [lhe97] H. Ihee, J. Cao, and A. H. Zewail, submitted to Chem. Phys. Lett.. [Ipp75] E. P. lppen and C. V. Shank, Appl. Phys. Lett. 27(9), 488-490 (1975). [lsc96a] A. A. Ischenko, L. Schafer, and J. D. Ewbank, J. Mot. Struct. 376, 157-171 (1996). [Isc96b] A. A. lschenko, V. A. Lobastov, L. Schafer, and J. D. Ewbank, J. Mot. Struct. 377, 261-269 (1996). [lsc95] A. A. Ischenko, J. D. Ewbank, and L. Schafer, J. Phys. Chem. 99(43), 15790-15797 (1995). [Isc94a] A. A. lschenko, J. D. Ewbank, and L. Schafer, J. Mot. Struct. 320, 147-158 (1994). [Isc94b] A. A.. Ischenko, J. D. Ewbank, and L. Schafer, J. Phys. Chem. 98(16), 4287-4300 (1994). [Isc94c] A. A. Ischenko, L. Schafer, J. Y. Luo, and J. D. Ewbank, J. Phys. Chem. 98(35), 8673-8678 (1994). [lsc93] A. A. Ischenko, V. P. Spiridonov, L. Schafer, and J. D. Ewbank, J. Mot. Struct. 300, 115-140 (1993). [lsc90] A. A. Ischenko, V. P. Spiridonov, and Yu. I. Tarasov, Sov. J. Chem. Phys. 6(1), 48-59 (1990). [lsc89] A. A. Ischenko, B. G. Sartakov, V. P. Spiridonov, and Yu. I. Tarasov, Sov. J. Chem. Phys. 5(3), 427-443 (1989). [lsc88] A. A. Ischenko, V. P. Spiridonov, Yu. I. Tarasov, and A. A. Stuchebryukhov, J. Mot. Struct. 172, 255-273 (1988). [Isc83] A. A. Ischenko, V. V. Golubkov, V. P. Spiridonov, A. V. Zgurskii, A. S. Akhmanov, M. G. Vabischevich, and V. N. Bagratashvili, Appl. Phys. B 32, 161-163 (1983). [lsh93] K. lshizuka, Ultramicroscopy 52, 7-20 (1993). [Iti90] Y. ltikawa and A. Ichimura, J. Phys. Chem. Ref Data 19(3), 637-651 (1990). [IvA87] A. E. Iverson, D. L. Smith, N. G. Paulter, and R. B. Hammond, J. Appl. Phys. 61(1), 234-239 (1987). [Ive74] R. C. Ivey, P. D. Schulze, T. L. Leggett, and D. A. Kohl, J. Chem. Phys. 60(8), 3174-3177 (1974). [IvH28] H. E. Ives, A. R. Olpin, and A. L. Johnsrud, Phys. Rev. 32, 57-80 (1928). [Jac70] E. J. Jacob and L. S. Bartell, J. Chem. Phys. 53(6), 2231-2235 (1970). [Jaf75] M. Jafarpour, Ph. D. Dissertation, University of Wyoming, 1975. [JaJ87] J. R. Janesick, T. Elliot, S. Collins, M. M. Blouke, and J. Freeman, Opt. Eng. 26(8), 692-714 (1987). [JaJ85] J. Janesick, K. Klaasen, and T. Elliot, Proc. SPIE 570, 7-19 (1985). [JaM86] M. C. Jackson, R. D. Long, D. Lee, and N. J. Freeman, Laser and Particle Beams 4(1), 145156 (1986). [Jan93] M. H. M. Janssen, M. Dantus, H. Guo, and A.H. Zewail, Chem. Phys. Lett. 214(3,4), 281289 (1993). References 731 [Jon68] R. C. Jones, Sci. Amer. 219(3), 110-117 (1968). [Jor48] T. Jorgensen, Am. J. Phys. 16, 285-289 (1948). [Jos89] N. V. Joshi, J. C. Sanchez, and J. M. Martin, J. Phys. Chem. Sol. 50(6), 629-632 (1989). [KaM75] M. Kawasaki, S. J. Lee, and R. Bersohn, J. Chem. Phys. 63(2), 809-814 (1975). [Kan93] D. J. Kane and R. Trebino, IEEE J. Quant. Electro. 29(2), 571-578 (1993). [Kap33] P. L. Kapitza and P.A. M. Dirac, Proc. Cambridge Phil. Soc. 29, 297-300 (1933). [KaJ50] J. Karle and I. L. Karle, J. Chem. Phys. 18(7), 957-962 (1950). [Kar50] I. L. Karle and J. Karle, J. Chem. Phys. 18(7), 963-971 (1950). [Kar49] I. L. Karle and J. Karle, J. Chem. Phys. 17(11), 1052-1058 (1949). [Kar47] I. L. Karle, D. Hoober, and J. Karle, J. Chem. Phys. 15(10), 765 (1947). [Kat92] T. Katsouleas, Am. J. Phys. 60(6), 568-569 (1992). [Kaw95] H. Kawashima, M. M. Wefers, and K. A. Nelson, Ann. Rev. Phys. Chem. 46, 627-656 (1995). [KaY84] Y. Kawamura, K. Toyoda, and M. Kawai, Appl. Phys. Lett. 45(4), 307-309 (1984). [KeD65] D. H. Kelly, Appl. Opt. 4(4), 435-437 (1965). [Kel65] L. V. Keldysh, Sov. Phys. JETP 20(5), 1307-1314 (1965). [Ker88] B. W. Kernighan and D. M. Ritchie, The C Programming Language, 2nd Ed., Prentice Hall PTR: Englewood Cliffs, 1988. [Khu90] L. R. Khundkar and A. H. Zewail, J. Chem. Phys. 92(1), 231-242 (1990). [Kib66a] T. W. B. Kibble, Phys. Rev. Lett. 16(23), 1054-1056 (1966) and erratum in Phys. Rev. Lett. 16(26), 1233 (1966). [Kib66b] T. W. B. Kibble, Phys. Rev. 150(4), 1060-1069 (1966). [KiM67] M. Kimura, S. Konaka, and M. Ogasawara, J. Chem. Phys. 46(7), 2599-2603 (1967). [Kim94] K.-J. Kim, S. Chattopadhyay, and C. V. Shank, Nucl. Instrum. Meth. A341, 351-354 (1994). [Kin90] K. Kinoshita, M. Suyama, Y. Inagaki, Y. Ishihara, and M. Ito, Proc. SPIE 1358, 490-496 (1990). [Kin88] K. Kinoshita, M. Ito, and M. Suyama, Proc. SPIE 1032, 441-447 (1988). [Kin87] K. Kinoshita, M. Ito, and Y. Suzuki, Rev. Sci. Instrum. 58(6), 932-938 (1987). [KiS82] S.S. Kim and G.D. Stein, Rev. Sci. Instrum. 53(6), 838-844 (1982). [Kit93] D. Kitriotis and Y. Aoyagi, Jpn. J. Appl. Phys. 32, Pt. 2 (3B), L441-L443 (1993). [Kle29] 0. Klein and Y. Nishina, Z. Physik 52, 853-868 (1929). [Klu74] H. P. Klug and L. E. Alexander, X-Ray Diffraction Procedures For Polycrystalline and Amorphous Materials, 2nd Ed., John Wiley and Sons: New York, 1974. [Kne85] J. L. Knee, L. R. Khundkar, and A.H. Zewail, J. Chem. Phys. 83(4), 1996-1998 (1985). [Kno79] G. F. Knoll, Radiation Detection and Measurement, John Wiley and Sons: New York, 1979. [Kof81] J.B. Koffend and S. R. Leone, Chem. Phys. Lett. 81(1), 136-141 (1981). [Koh92a] D. A. Kohl and E. J. Shipsey, Z. Phys. D 24, 33-38 (1992). References 732 [Koh92b] D. A. Kohl and E. J. Shipsey, Z. Phys. D 24, 39-45 (1992). [Koh80] D. A. Kohl and M. M. Arvedson, J. Chem. Phys. 72(3), 1922-1927 (1980). [Koh67] D. A. Kohl and R. A. Bonham, J. Chem. Phys. 47(5), 1634-1646 (1967). [Kon88] S. Konaka in Chapter Three of [Har88a]. [Kon72] S. Konaka, Japan. J. Appl. Phys. 11(8), 1199-1204 (1972). [Kor69] V. V. Korobkin, A. A. Maljutin, and M. Ya. Schelev, J. Photog. Sci. 17, 179-182 (1969). [Kra53] J. Kraitchman, Am. J. Phys. 21(1), 17-24 (1953). [Kri93] 0. L. Krivanek and P. E. Mooney, Ultramicroscopy 49, 95-108 (1993). [Kro76] P. M. Kroger, P. C. Demou, and S. J. Riley, J. Chem. Phys. 65(5), 1823-1834 (1976). [Kub62] R. Kubo, J. Phys. Soc. Japan 17, 110- (1962). [Kuc92] K. Kuchitsu in Chapter Two of [Dom92]. [Kuc88] K. Kuchitsu, M. Nakata, and S. Yamamoto in Chapter Seven of [Har88a]. [Kuc72a] K. Kuchitsu in Molecular Structures and Vibrations, S. J. Cyvin (ed.), Elsevier Publishing Co.: Amsterdam, pp. 148-170, 1972. [Kuc72b] K. Kuchitsu and S. J. Cyvin in Molecular Structures and Vibrations, S. J. Cyvin (ed.), Elsevier Publishing Co.: Amsterdam, pp. 183-211, 1972. [Kuc67] K. Kuchitsu, Bull. Chem. Soc. Japan 40(3), 498-504 (1967). [Kuc65] K. Kuchitsu and Y. Morino, Bull. Chem. Soc. Japan 38(5), 805-813 (1965). [Kuc61] K. Kuchitsu and L. S. Bartell, J, Chem. Phys. 35(6), 1945-1949 (1961). [Kuj92] S. Kujawa and D. Krah!, Ultramicroscopy 46, 395-403 (1992). [Laa60] J. van Laar and J. J. Scheer, Phil. Res. Rep. 15(1 ), 1-6 (1960). [Lad93] M. F. C. Ladd and R. A. Palmer, Structure Determination by X-Ray Crystallography, Plenum Press: New York, 1993. [Lea69] C. Lea, B. H. Blott, and C.H. B. Mee, Appl. Opt. 8(1), 203-204 (1969). [Leg74] T. L. Leggett, R. E. Kennerly, and D. A. Kohl, J. Chem. Phys. 60(8), 3264-3267 (1974). [Leg73] T. L. Leggett and D. A. Kohl, J. Chem. Phys. 59(2), 611-616 (1973). [Lei73] W. Leiser and K. H. Gankler, Optik 38(2), 177-186 (1973). [Ley90] Leybold Vacuum Products Inc. , Product and Vacuum Technology Reference Book, 1990. [Lid92] D. R. Lide (ed.), CRC Handbook of Chemistry and Physics, 73rd Ed., CRC Press, Inc.: Boca Raton, 1992. [Lie93] Ch. Lienau, J.C. Williamson, and A.H. Zewail, Chem. Phys. Lett. 213(3,4), 289-296 (1993). [Lin83] J.-T. Lin and T. F. George, J. Appl. Phys. 54(1), 382-387 (1983). [Liu90] Y. Liu and W. Sibbett, Proc. SPIE 1358, 503-510 (1990). [LiW97] W.-K. Liu and S. H. Lin, Phys. Rev. A 55(1), 641-647 (1997). [Log69] E. M. Logothetis and P. L. Hartman, Phys. Rev. 187(2), 460-474 (1969). [Lom78] L.A. Lompre, G. Mainfray, C. Manus, J. Thebault, Gy. Farkas, and Z. Horvath, Appl. Phys. Lett. 33(2), 124-126 (1978). References 733 [Loo83] J. F. Van Loock, L. Van den Enden, and H.J. Geise, J. Phys. E 16, 255-257 (1983). [Lov84] S. W. Lovesey, Theory of Neutron Scattering From Condensed Matter, Clarendon Press: Oxford, 1984. [Luc80] P. Luc, J. Mot. Spec. 80, 41-55 (1980). [MaB69] B. W. Manley, A. Guest, and R. T. Holmshaw, Adv. Electr. Electr. Phys. 28A, 471-486 (1969). [Mac76] J. P. Macau, J. Jamar, and S. Gardier, IEEE Trans. Nucl. Sci. NS-23(6), 2049-2055 (1976). [MaH32] H. S. W. Massey and C. B. 0. Mohr, Proc. Royal Soc. London Al35, 258-275 (1932). [MaL59] L. Mandel, Brit. J. Appl. Phys. 10, 233-234 (1959). [Man95] J. Manz and L. Woste (eds.), Femtosecond Chemistry, VCH Publishers: New York, 1995. [Man93] J. Manz and A. W. Castleman, J. Phys. Chem. 97(48), 12423-12649 (1993). [MaP87] P. J. Martin, P. L. Gould, B. G. Oldaker, A.H. Miklich, and D. E. Pritchard, Phys. Rev. A 36(5), 2495-2498 (1987). [Mar88] H. F. Mark in Introduction of [Har88a]. [Mar30] H. Mark and R. Wierl, Naturwis. 18, 205 (1930). [Mas91] V. S. Mastryukov, Moscow Univ. Chem. Bull. 46(3), 30-33 (1991). [Mat71] A.G. Mathewson and H.P. Myers, Phys. Scripta 4, 291-292 (1971). [MaU96] U. Marvet and M. Dantus, Chem. Phys. Lett. 256, 57-62 (1996). [McC72] G. H. McCall, Rev. Sci. Instrum. 43(6), 865-866 (1972). [McP94] A. McPherson, B. D. Thompson, A. B. Borisov, K. Boyer, and C. K. Rhodes, Nature 370, 631-634 (1994). [Mei94] C. Meier, M. Volkmer, J. Lieschke, M. Fink, and N. Bowering, Z. Phys. D 30, 183-187 (1994). [Men92a] A. Mens, D. Gontier, J.C. Huilizen, R. Sauneuf, D. Schirmann, R. Verrecchia, P. Audebert, J. C. Gauthier, J. P. Geindre, A. Antonetti, J. P. Chhambaret, G. Hamoniaux, and A. Mysyrowicz, Proc. SPIE 1801, 502-513 (1992). [Men92b] A. Mens, Endeavour, New Series 16(2), 74-79 (1992). [Mih89] A. Mihill and M. Fink, Z. Phys. D 14, 77-83 (1989). [MiJ92] J. D. Miller and M. Fink, J. Chem. Phys. 97(11), 8197-8200 (1992). [Mij75] F. C. Mijlhoff, J. Mot. Struct. 27,447 (1975). [Mil81] B. R. Miller and M. Fink, J. Chem. Phys. 75(11), 5326-5328 (1981). [Mi180] B. R. Miller and L. S. Bartell, J. Chem. Phys. 72(2), 800-807 (1980). [MiP95] P. Millier and M.A. Darizcuren, Proc. SPIE 2415, 160-171 (1995). [Mit36] D. P. Mitchell and P. N. Powers, Phys. Rev. 50, 486-487 (1936). [MoC95] C. I. Moore, J.P. Knauer, and D. D. Meyerhofer, Phys. Rev. Lett. 74(13), 2439-2442 (1995). [Moc86] J. Moc, Z. Latajka, and H. Ratajczak, Chem. Phys. Lett. 130(6), 541-544 (1986). [Mok90] A. Mokhtari, P. Cong, J. L. Herek, and A.H. Zewail, Nature 348, 225-227 (1990). References 734 [MoM93] M. D. Morris, (ed.), Microscopic and Spectroscopic Imaging of the Chemical State, Marcel Dekker, Inc.: New York, 1993. [Mon87] D. L. Monts, J. D. Ewbank, K. Siam, W. L. Faust, D. W. Paul, and L. Schafer, Appl. Spec. 41(4), 631-635 (1987). [Moo89] J. H. Moore, C. C. Davis, and M. A. Coplan, Building Scientific Apparatus, 2nd. Ed., Addison-Wesley Publishing Company: Reading, 1989. [MoR80] R. Moutran, B. Beagley, D. W. J. Cruickshank, A. Foord, and R. G. Pritchard, J. Phys. E 13, 1189-1192 (1980). [Mor65] Y. Morino and Y. Murata, Bull. Chem. Soc. Japan 38(1), 114-119 (1965). [Mor60a] Y. Morino, Y. Nakamura, and T. Iijima, J. Chem. Phys. 32(3), 643-652 (1960). [Mor60b] Y. Morino, Acta Cryst. 13, 1107 (1960). [MoT91] T. Motet, J. Nees, S. Williamson, and G. Mourou, Appl. Phys. Lett. 59(12), 1455-1457 (1991). [Mot65] N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd. Ed., Oxford University Press: London, 1965. [Mou82] G. Mourou and S. Williamson, Appl. Phys. Lett. 41(1), 44-45 (1982). [MuD79] D. K. Murti, J. Vac. Sci. Tech. 16(2), 226-229 (1979). [Mur94] M. M. Murnane, H. C. Kapteyn, S. P. Gordon, and R. W. Falcone, Appl. Phys. B 58(3), 261- 266 (1994). [Mur89] M . M. Murnane, H. C. Kapteyn, and R. W. Falcone, Phys. Rev. Lett. 62(2), 155-158 (1989). [Nag82] M. Nagashima, S. Konaka, and M. Kimura, Bull. Chem. Soc. Japan 55(1), 28-32 (1982). [Nag73] M. Nagashima, S. Konaka, T. Iijima, and M. Kimura, Bull. Chem. Soc. Japan 46(11), 33483352 (1973). [Nak91] H. Nakanishi, Y. Yoshida, T. Ueda, T. Kozawa, H. Shibata, K. Nakajima, T. Kurihara, N. Yugami, Y. Nishida, T. Kobayashi, A. Enomoto, T. Oogoe, H. Kobayashi, B. S. Newberger, S. Tagawa, K. Miya, and A. Ogata, Phys. Rev. Lett. 66(14), 1870-1873 (1991). [Nea70] W. E. J. Neal, R. W. Fane, and N. W. Grimes, Philos. Mag. 21, 167-175 (1970). [New86] D. E. Newbury, D. C. Joy, P. Echlin, C. E. Fiori, and J. I. Goldstein, Advanced Scanning Electron Microscopy and X-Ray Microanalysis, Plenum Press: New York, 1986. [Nit63] H.F. Nitka, Photog. Sci. Eng. 7, 188-195 (1963). [Niu92] H. Niu, H. Zhang, Q. L. Yang, B. P. Guo, Z. X. Song, J. L. Zhou, Y. A. Ren, and H.J. Zhao, Proc. SPIE 1801, 1035-1041 (1992). [Niu88a] H. Niu, V. P. Degtyareva, V. N. Platonov, A. M. Prokhorov, and M. Ya. Schelev, Proc. SPIE 1032, 79-85 (1988). [Niu88b] H. Niu, H. Zhang, Q. L. Yang, Y. P. Liu, Y. C. Wang, Y. A. Reng, and J. L. Zhou, Proc. SPIE 1032, 472-479 (1988). [Niu81] H. Niu and W. Sibbett, Rev. Sci. lnstrum. 52(12), 1830-1836 (1981). [Nix95] R.H. Nixon, S. E. Kemeny, C. 0. Staller, and E. R. Fossum, Proc. SPIE 2415, 117-123 (1995). [Not56] W. B. Nottingham in Encyclopedia Of Physics: Electron-Emission Gas Discharges I, Vol. 21, S. Fliigge (ed.), Springer-Verlag: Berlin, pp. 1-175, 1956. References 735 [Nov79] V. P. Novikov, J. Mot. Struct. 55, 215-221 (1979). [Oat85] C. W. Oatley, J. Microsc. 139(2), 153-166 (1985). [Ogu77] I. Ya. Ogurtsov, L.A. Kazantseva, and A. A. lschenko, J. Mot. Struct. 41, 243-251 (1977). [Ost85] D. E. Osten, Proc. SPIE 570, 89-94 (1985). [PaD83] D. W. Paul, J. D. Ewbank, 0 . J. Benston, and L. Schafer, Appl. Spec. 37(2), 127-130 (1983). [Par89] D. H. Parker and R. B. Bernstein, Ann. Rev. Phys. Chem. 40, 561-595 (1989). [Pau95] L. Pauling, Linus Pauling In His Own Words: Selected Writings, Speeches, and Interviews, B. Marinacci (ed.), Simon and Schuster: New York, 1995. [Pau35] L. Pauling and L. 0. Brockway, J. Am. Chem. Soc. 57, 2684-2692 (1935). [Pau34] L. Pauling and L. 0. Brockway, J. Chem. Phys. 2, 867-881 (1934). [Paw74] J. Pawley, Scan. Elec. Microsc., 28-34 (1974). [Ped94] S. Pedersen, J. L. Herek, and A. H. Zewail, Science 266, 1359-1364 (1994). [Pei69] E. M. A. Peixoto, Phys. Rev. 177(1), 204-211 (1969). [Pen81] W. H. Pence, S. L. Baughcum, and S. R. Leone, J. Phys. Chem. 85(25), 3844-3851 (1981). [Per91] M. D. Person, P. W. Kash, and L. J. Butler, J. Chem. Phys. 94(4), 2557-2563 (1991). [Pos71] J. Pospisil and V. Bumba, Optik 34(2), 136-152 (1971). [Pre92] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd Ed., Cambridge University Press: Cambridge, 1992. [Pro91] A. M. Prokhorov, M . Ya. Schelev, and S. J. Nebeker, Laser Focus World, December, 125-128 (1991). [PrS95] S. Preuss, A. Demchuk, and M. Stuke, Appl. Phys. A 61, 33-37 (1995). [Pru86] A. P. Prudnikov, Yu. A. Brychkov, and 0 . I. Marizhov, Integrals and Series , N . M . Queen, trans., Gordon and Breech Science Publishers: New York, 1986. [Pul83] P. Pulay, R. Mawhorter, D. A. Kohl, and M. Fink, J. Chem. Phys. 79(1), 185-191 (1983). [Pun90] A. K. Puntajer and C. Leubner, J. Appl. Phys. 67(3), 1606-1609 (1990). [Pus88] D. Puseljic, B. Baumbaugh, J. Bishop, J. Busenitz, N. Cason, J. Cunningham, R. Gardner, C. Kennedy, E. Manne!, R. J. Mountain, R. Ruchti , W. Shephard, M . Zanabria, A. Baumbaugh, K. Knickerbocker, A. Rogers, B. Kinchen, C. G. A. Hill, IEEE Trans. Nucl. Sci. NS-35(1), 475-476 (1988). [Rak96] F. Raksi, K. R. Wilson, Z. Jiang, A. Ikhlef, C. Y. Cote, and J.-C. Kieffer, J. Chem. Phys. 104(15), 6066-6069 (1996). [Ran80] L. M. Rangarajan and G. K . Bhide, Vacuum 30(11,12), 515-522 (1980). Portions of this article were plagiarized from [SpW64]. [ReC67] C. Reinsch, Numer. Mathe. 10, 177-183 (1967). [Rei91] S. E. Reichenbach, S. K. Park, and R. Narayanswamy, Opt. Eng. 30(2), 170-177 (1991). [ReL85] L. Reimer, Scanning Electron Microscopy, Springer-Verlag: Berlin, 1985. [Ren45] H. C. Rentschler and D. E. Henry, Trans. Electrochem. Soc. 87, 289-298 (1945). [Rid78] G. H. N. Riddle, J. Vac. Sci. Tech. 15(3), 857-860 (1978). References 736 [Rif93] D. M. Riffe, X. Y. Wang, M. C. Downer, D. L. Fisher, T. Tajima, J. L. Erskine, and R. M. More, J. Opt. Soc. Am. B 10(8), 1424-1435 (1993). [Riv69] J.C. Riviere, Sol. Sta. Surf. Sci. 1, 179-289 (1969). [RoA92] A. W. Ross, M. Fink, and R. Hilderbrandt in International Tables For Crystallography, Vol. C, A. J.C. Wilson (ed.), Kluwer Academic Publishers: Dordrecht, pp. 245-338, 1992. [RoA88] A. W. Ross and M. Fink, Phys. Rev. A 38(12), 6055-6058 (1988). [RoB87] B. W. Rossiter and J. F. Hamilton, Physical Methods of Chemistry, 2nd Ed., Vol. IIIA, John Wiley and Sons: New York, 1987. [Roe92] B. P. Roe, Probability and Statistics in Experimental Physics, Springer-Verlag: New York, 1992. [RoL94] L. Rosenberg, Phys. Rev. A 49(2), 1122-1130 (1994). [RoM88] M. J. Rosker, M. Dantus, and A.H. Zewail, J. Chem. Phys. 89(10), 6113-6127 (1988). [Roo84] A. P. Rood and J. Milledge, J. Chem. Soc. Faraday Trans. 2 80, 1145-1153 (1984). [RoP92] P. W. Roehrenbeck, Laser Focus World, November, 169-171 (1992). [Ros48] A. Rose, J. Opt. Soc. Am. 38(2), 196-208 (1948). [Ros46] A. Rose, J. Soc. Motion Picture Engineers 47(4), 273-294 (1946). [RoT89] T. S. Rose, M. J. Rosker, and A.H. Zewail, J. Chem. Phys. 91(12), 7415-7436 (1989). [RoW65] W. van Roosbroeck, Phys. Rev. 139(5A), Al702-Al716 (1965). [Ruc86] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, J. Busenitz, N. Cason, J. Cunningham, R. Gardner, S. Grenquist, V. Kenney, E. Manne!, R. Mountain, W. Shephard, A. Baumbaugh, K. Knickerbocker, C. Wegner, R. Yarema, A. Rogers, B. Kinchen, J. Ellis, R. Mead, and D. Swanson, IEEE Trans. Nucl. Sci. NS-33(1), 151-154 (1986). [Ruc85] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, N. Cason, J. Cunningham, R. Erichsen, S. Grenquist, V. Kenney, E. Manne!, R. Mountain, W. Shephard, P. Wilkins, A. Baumbaugh, K. Knickerbocker, A. Kreymer, J. Simanton, C. Wegner, R. Yarema, A. Rogers, R. Mead, and D. Swanson, IEEE Trans. Nucl. Sci. NS-32(1), 590-594 (1985). [Ruc84] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, N. Cason, R. Erichsen, V. Kenney, A. Kreymer, R. Mountain, W. Shephard, and A. Rogers, IEEE Trans. Nucl. Sci. NS-31(1), 69-73 (1984). [Ruc83] R. Ruchti, B. Baumbaugh, J. Bishop, N. Biswas, N. Cason, L. Dauwe, R. Erichsen, V. Kenney, A. Kreymer, W. Shephard, D. Potter, and A. Rogers, IEEE Trans. Nucl. Sci. NS-30(1), 40-43 (1983). [Rui92] W. J. de Ruijter and J. K. Weiss, Rev. Sci. Instrum. 63(10), 4314-4321 (1992). [Sai88] N. A. Sainov, Sov. Tech. Phys. Lett. 14(9), 731-732 (1988). [Sa!80] K. L. Sala, G. A. Kenney-Wallace, and G. E. Hall, IEEE J. Quant. Elec. QE-16(9), 990-996 (1980). [Sas92] Y. Sasaki, H. Takeuchi, S. Konaka, and M. Kimura, Int. J. Quant. Chem. 43, 701-712 (1992). [Sav85] E. D. Savoye, Proc. SPIE 570, 95-97 (1985). [ScE83] E. Schmied!, P. Wissmann, and E. Wittmann, Surf. Sci. 135, 341-352 (1983). [ScF95] Schott Fiber Optics Inc., Fused Fiber Optic Tapers, (1995). References 737 [ScG80] G. Schmitt and F. J. Comes, J. Photochem. 14, 107-123 (1980). [ScH73] H. Schwarz, Phys. Lett. 43A(5), 457-458 (1973). [ScH65] H. Schwarz, H. A. Tourtellotte, and W.W. Gaertner, Phys. Lett. 19(3), 202-203 (1965). [Sch76] L. Schafer, Appl. Spec. 30(2), 123-149 (1976). [Sch71] L. Schafer, A. C. Yates, and R. A. Bonham, J. Chem. Phys. 55(6), 3055-3056 (1971). [Sch68] L. Schafer, J. Am. Chem. Soc. 90(15), 3919-3925 (1968). [ScJ94] J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73(16), 2180-2183 (1994). [ScL54] L. G. Schulz, J. Opt. Soc. Am. 44(5), 357-362 (1954). [ScM71] M. Ya. Schelev, M. C. Richardson, and A. J. Alcock, Appl. Phys. Lett. 18(8), 354-357 (1971). [Sco88] G. Scoles (ed.), Atomic and Molecular Beam Methods, Oxford University Press: New York, 1988. [ScR96] R. W. Schoenlein, W. P. Leemans, A.H. Chin, P. Voltbeyn, T. E. Glover, P. Balling, M. Zolotorev, K.-J. Kim, S. Chattopadhyay, and C. V. Shank, Science 274, 236-238 (1996). [ScV52] V. Schomaker and R. Glauber, Nature 170, 290-291 (1952). [ScW23] W. Schottky, Z. Physik 14, 63-106 (1923). [Sei73] H. M. Seip in Chapter One of [Sim73]. [Sei67] H. M. Seip in Selected Topics in Structure Chemistry, P. Andersen, 0. Bastiansen, and S. Forberg (eds.), Universitetsforlaget: Oslo, pp. 25-68, 1967. [Sel78] H. L. Sellers, L. Schafer, and R. A. Bonham, J. Mol. Struct. 49, 125-130 (1978). [Sha59] M. H. Shamos, Great Experiments in Physics, Henry-Holt and Co.: New York, 1959. [ShE80] E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22(4), 1612-1628 (1980). [She93] M. H. Sher, U. Mohideen, H. W. K. Tom, 0. R. Wood, G. D. Aumiller, R.R. Freeman, and T. J. Mcilrath, Opt. Lett. 18(8), 646-648 (1993). [Shi72] S. Shibata, Bull. Chem. Soc. Japan 45(6), 1631-1634 (1972). [Shi71] S. Shibata and L. S. Bartell, J. Mol. Struct. 9, 1-9 (1971). [Shi64] S. Shibata, L. S. Bartell, and R. M. Gavin, J. Chem. Phys. 41(3), 717-722 (1964). [Sho38] W. Shockley and J. R. Pierce, Proc. Inst. Radio Eng. 26, 321-332 (1938). [ShP46] P. Shaffer, V. Schomaker, and L. Pauling, J. Chem. Phys. 14(11), 659-664 (1946). [Sib82] W. Sibbett, H. Niu, and M. R. Baggs, Rev. Sci. Instrum. 53(6), 758-761 (1982). [Sim73] G. A. Sim and L. E. Sutton (eds.), Molecular Structure by Diffraction Methods, Vol. 1, The Chemical Society: London, 1973. [SIT95] Scientific Imaging Technologies, Inc., S/Te 5I2x5/2 Scientific-Grade CCD, (1995). [SIT94] Scientific Imaging Technologies, Inc., An Introduction to Scientific Imaging Charge-Coupled Devices, (1994). [Sit87a] G. 0 . Sitz, A. C. Kummel, and R. N. Zare, J. Chem. Phys. 87(5), 3247-3249 (1987). [Sit87b] G. 0. Sitz, A. C. Kummel, and R. N. Zare, J. Vac. Sci. Tech. A 5(4), 513-517 (1987). References 738 [SmD73] D. W. Smith and L. Andrews, J. Chem. Phys. 58(12), 5222-5229 (1973). [Smi94] V. Smith, 1994. Personal communication from M. Fink. [Som68] A.H. Sommer, Photoemissive Materials, J. Wiley and Sons: New York, 1968. [Spe88] J.C. H. Spence and J. M. Zuo, Rev. Sci. Instrum. 59(9), 2102-2105 (1988). [Spi81] V. P. Spiridonov, A. A. Ischenko, and L. S. Ivashkevich, J. Mo!. Struct. 72, 153-164 (1981). [Spi79] V. P. Spiridonov, A. Ya. Prikhod'ko, and B. S. Butayev, Chem. Phys. Lett. 65(3), 605-609 (1979). [SpW64] W. E. Spicer and C. N. Berglund, Rev. Sci. Instrum. 35(12), 1665-1667 (1964). [Sri91] T. Srinivasan-Rao, J. Fischer, and T. Tsang, J. Appl. Phys. 69(5), 3291-3296 (1991). [StE54] E. J. Sternglass, Phys. Rev. 95(2), 345-358 (1954). [Ste89] D. G. Stearns and J. D. Wiedwald, Rev. Sci. Instrum. 60(6), 1095-1103 (1989). [SuJ90] J. J. Su, T. Katsouleas, J.M. Dawson, and R. Fedele, Phys. Rev. A 41(6), 3321-3331 (1990). [Suy88] M. Suyama and K. Kinoshita, Proc. SPIE 1032, 448-452 (1988). [Swo83] E.W. Swokowski, Calculus with Analytic Geometry, Prindle, Wever, and Schmidt: Boston, 1983. [Tag84] M. Taguchi and T. Iijima, Japan. J. Appl. Phys. 23(11), 1509-1517 (1984). [Tak86] M. Takeuchi, M . Nagashima, K. Tanaka, S. Konaka, and M. Kimura, Int. J. Quant. Chem. 30, 821-830 (1986). [Tan71] K. Tanaka and F. Sasaki, Int. J. Quant. Chem. 5, 157-175 (1971). [Tav67] C. Tavard, D. Nicolas, and M. Rouault, J. Chim. Phys. 64, 540-554 (1967). [Tav66] C. Tavard, Cahiers. Phys. 20, 397- (1966). [Tav65a] C. Tavard, M. Rouault, and M. Roux, J. Chim. Phys. 62, 1410-1417 (1965). [Tav65b] C. Tavard and M. Roux, C. R. Acad. Sci. Paris. 260, 4933- (1965). [Tek92] Tektronix, Inc., The Imaging CCD Array: Introduction and Operating Information, (1992). [Tek91a] Tektronix, Inc., Thinned, Back Illuminated CCDs for Short Wavelength Applications, ( 1991 ). [Tek91b] Tektronix, Inc., Quantum Efficiency Measurements on Charge Coupled Devices (CCDs) , (1991). [Tek91c] Tektronix, Inc., MPP Operation of CCDs, (1991). [Tex94] Texas Instruments, Inc., Area Array Image Sensor Products Data Book, ( 1994). [Tha75] A. Thanailakis, J. Phys. C 8, 655-668 (1975). [ThH96] H. Thomassen and K. Hedberg, 1996. Personal communication. [ThH92] H. Thomassen, S. Samdal, and K. Hedberg, J. Am. Chem. Soc. 114(8), 2810-2815 (1992). [ThJ95] J. R. Thompson, P. M. Weber, and P. J. Estrup, Proc. SPIE 2521, 113-122 (1995). [Tho28a] G. P. Thomson, Proc. Royal Soc. A 117, 600-609 (1928). [Tho28b] G. P. Thomson, Proc. Royal Soc. A 119, 651-663 (1928). [Tho27] G. P. Thomson and A. Reid, Nature 119, 890 (1927). References 739 [ThS90] S. W. Thomas, R. L. Griffith, and A. T. Teruya, Proc. SPIE 1358, 578-588 (1990). [Tom95a] I. V. Tomov, P. Chen, and P. M. Rentzepis, J. Appl. Cryst. 28, 358-362 (1995). [Tom95b] I. V. Tomov, P. Chen, and P. M. Rentzepis, Proc. SPIE 2521, 13-22 (1995). [Ton93] A. Tonomura, Electron Holography, Springer-Verlag: Berlin, 1993. [T6t91] C. T6th, Gy. Farkas, and K. L. Vodopyanov, Appl. Phys. B 53, 221-225 (1991). [Toy64] M . Toyama, T. Oka, and Y. Morino, J. Molec. Spec. 13, 193-213 (1964). [Tre88] J. Tremmel and I. Hargittai in Chapter Six of [Har88a]. [TrF33] F. Trendelenburg, Naturwis. 21, 173-177 (1933). [Tsa93] T. Tsang, Appl. Phys. Lett. 63(7), 871-873 (1993). [Tsa92] T. Tsang, T. Srinivasan-Rao, and J. Fischer, Nucl. lnstrum. Meth. A318, 270-274 (1992). [Tsa91] T. Tsang, T. Srinivasan-Rao, and J. Fischer, Phys. Rev. B 43(11), 8870-8878 (1991). [Typ78] V. Typke, M . Dakkouri, and H. Oberhammer, J. Mot. Struct. 44, 85-96 (1978). [Uga94] E. Ugaz, Phys. Rev. A 50(1), 34-38 (1994). [Vac62] Vachaspati, Phys. Rev. 128(2), 664-666 (1962) and erratum in Phys. Rev. 130(6), 2598 (1963). [VaJ86] J. A. Valdmanis and R. L. Fork, IEEE J. Quant. Elec. QE-22(1), 112-118 (1986). [Val66] R. C. Valentine, Adv. Opt. Electr. Microsc. 1, 180-203 (1966). [Val64] R. C. Valentine and N. G. Wrigley, Nature 203, 713-715 (1964). [Var95] S. D. Vartak and N. M. Lawandy, Opt. Comm. 120, 184-188 (1995). [Vie47] H. Viervoll, Acta Chem. Scand. 1, 120-132 (1947). [Vod89] K. L. Vodopyanov, L.A. Kulevskii, Cs. T6th, Gy. Farkas, and Z. Gy. Horvath, Appl. Phys. B 48, 485-488 (1989). [Vol96] M. Volkmer, Ch. Meier, J. Lieschke, A. Mihill, M. Fink, and N. Bowering, Phys. Rev. A 53(3), 1457-1468 (1996). [Vol92] M. Volkmer, Ch. Meier, A. Mihill, M. Fink, and N. Bowering, Phys. Rev. Lett. 68(15), 22892292 (1992). [War93] W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581-1589 (1993). [Wea81] J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Physics Data 18, Mathematik GmbH: Karlsruhe, 1981. [Web95] P. M. Weber, S. D. Carpenter, and T. Lucza, Proc. SPIE 2521, 23-30 (1995). [Whe59] P. J. Wheatley, The Determination of Molecular Structure, Oxford University Press: London, 1959. [WiA91] A. Williams, DOS 5: A Developer's Guide, M&T Books: Redwood City, 1991. [Wie31] R. Wierl, Ann. d. Phys. 8(5), 521-564 (1931). [WiG95] G. M. Williams, A. L. Reinheimer, V. W. Aebi, and K. A. Costello, Proc. SPIE 2415, 211235 (1995). [Wij80] R. W. Wijnaendts van Resandt, J. Phys. E 13, 1162-1164 (1980). References 740 [Wil97] J.C. Williamson, J. Cao, H. Ihee, H. Frey, and A.H. Zewail, Nature 386, 159-162 (1997). [Wil94] J.C. Williamson and A.H. Zewail, J. Phys. Chem. 98(11), 2766-2781 (1994). [Wil93] J.C. Williamson and A.H. Zewail, Chem. Phys. Lett. 209(1,2), 10-16 (1993). [Wil92] J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, Chem. Phys. Lett. 196(6), 529534 (1992). [Wil91] J.C. Williamson and A.H. Zewail, Proc. Natl. Acad. Sci. USA 88, 5021-5025 (1991). [WiO88] S. 0. Williams and D. G. Imre, J. Phys. Chem. 92(23), 6648-6654 (1988). [WiS84] S. Williamson, G. Mourou, and J.C. M. Li, Phys. Rev. Lett. 52(26), 2364-2367 (1984). [WiS82] S. Williamson, G. Mourou, and S. Letzring, Proc. SPIE 348, 313-317 (1982). [WiS--] S. Williamson, G. Mourou, P. Bado, C. G. Dupuy, and K. R. Wilson (unpublished). [WiT68] T. J. Williamson and R. W. Albrecht, Nucl. Sci. Eng. 33, 141-143 (1968). [Wiz79] J. L. Wiza, Nucl. lnstrum. Meth. 162, 587-601 (1979). [Won73] T. C. Wong and L. S. Bartell, J. Chem. Phys. 58(12), 5654-5660 (1973). [Wor73] J. Wormald, Diffraction Methods, Clarendon Press: Oxford, 1973. [WuT62] T.-Y. Wu, and T. Ohmura, Quantum Theory of Scattering, Prentice-Hall, Inc.: Englewood, 1962. [Yam85] T. Yamazaki, T. Noguchi, S. Sugiyama, T. Mikado, M. Chiwaki, and T. Tomimasu, IEEE Trans. Nucl. Sci. NS-32(5), 3406-3408 (1985). [Yan94] Q. L. Yang, H.J. Zhao, Z. X. Song, M. Z. Pan, B. P. Guo, and H . Niu, Proc. SPIE 2513, 112118 (1994). [Yat72] A. C. Yates and A. Tenney, Phys. Rev. A 5(6), 2474-2481 (1972). [Yat69] A. C. Yates and R. A. Bonham, J. Chem. Phys. 50(3), 1056-1058 (1969). [Yat68] A. C. Yates and T. G. Strand, Phys. Rev. 170(1), 184-189 (1968). [Yen80] R. Yen, J. Liu, and N. Bloembergen, Opt. Comm. 35(2), 277-288 (1980). [Yen79] R. Yen, P. Liu, M. Dagenais, and N. Bloembergen, Opt. Comm. 31(3), 334-339 (1979). [Zav95] A. Zavriyev, I. Fischer, D. M. Villeneuve, and A. Stolow, Chem. Phys. Lett. 234(4,5,6), 281288 (1995). [Zew96] A.H. Zewail, J. Phys. Chem. 100(31), 12701-12724 (1996). [Zew94] A.H. Zewail, Femtochemistry: Ultrafast Dynamics of the Chemical Bond, World Scientific: Singapore, 1994. [Zew91] A.H. Zewail, Faraday Disc. Chem. Soc. 91(), 207-237 (1991). [ZhA96] A. A. Zholents and M. S. Zolotorev, Phys. Rev. Lett. 76(6), 912-915 (1996). [Zha88a] J. Zhang and D. G. Imre, J. Chem. Phys. 89(1), 309-313 (1988). [Zha88b] J. Zhang, E. J. Heller, D. Huber, D. G. Imre, and D. Tannor, J. Chem. Phys. 89(6), 36023611 (1988). [Zho97] D. Zhong, S. Ahmad, and A.H. Zewail, J. Am. Chem. Soc. 119(25), 5978-5979 (1997).