Sound Velocities and Equation of State of Iron-Rich (Mg,Fe)O Citation Wicks, June Ki (2013) Sound Velocities and Equation of State of Iron-Rich (Mg,Fe)O. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z94B2Z98. https://resolver.caltech.edu/CaltechTHESIS:06102013-152154645 Abstract Ultralow-velocity zones (ULVZs) are small structures at the base of the mantle characterized by sound velocities up to 30% lower than those of surrounding mantle. In this thesis, we propose that iron-rich (Mg,Fe)O plays a key role in the observed sound velocities, and argue that chemically distinct, iron-enriched structures are consistent with both the low sound velocities and the measured shapes of ULVZs. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Sound velocity, high pressure, earth interior Degree Grantor: California Institute of Technology Division: Geological and Planetary Sciences Major Option: Geochemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Jackson, Jennifer M. Thesis Committee: Rossman, George Robert (chair) Gurnis, Michael C. Asimow, Paul David Jackson, Jennifer M. Defense Date: 28 May 2013 Funders: Funding Agency Grant Number NSF EAR-0711542 CAREER EAR-0956166 CSEDI EAR-0855815 Record Number: CaltechTHESIS:06102013-152154645 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:06102013-152154645 DOI: 10.7907/Z94B2Z98 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 7885 Collection: CaltechTHESIS Deposited By: June Wicks Deposited On: 12 Jun 2013 18:40 Last Modified: 04 Oct 2019 00:02 Thesis Files Preview PDF (Wicks Thesis Full Version) - Final Version See Usage Policy. 11MB Preview PDF (Wicks thesis Chapter 1) - Final Version See Usage Policy. 271kB Preview PDF (Wicks Thesis Chapter 2) - Final Version See Usage Policy. 7MB Preview PDF (Wicks Thesis Chapter 3) - Final Version See Usage Policy. 2MB Preview PDF (WIcks Thesis Chapter 4) - Final Version See Usage Policy. 974kB Preview PDF (Wicks Thesis Chapter 5) - Final Version See Usage Policy. 595kB Preview PDF (Wicks Thesis References) - Final Version See Usage Policy. 153kB Preview PDF (Wicks Thesis Appendix) - Final Version See Usage Policy. 994kB Repository Staff Only: item control page

Sound Velocities and Equation of State of iron-rich (Mg,Fe)O Thesis by June K. Wicks In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2013 (Submitted ) ii © 2013 June K. Wicks All Rights Reserved iii iv Acknowledgements First and foremost, I want to thank my advisor Jennifer Jackson. You’ve believed in me through this whole process, and pushed me to become a better version of myself. Under your mentorship I’ve grown both personally and intellectually. I wouldn’t be here without you, and looking back I am amazed at how far we’ve come. I hope that someday I’ll become as innovative and well-respected a scientist as you are today. You’ve been the best role model. I am thankful to Paul Asimow and George Rossman for your friendship and mentorship, for helping me become a better teacher and a better scientist, and for always having your door open for me, even on weekends and holidays. Thank you George, for letting me hang out in the lab with you for hours at a time just for fun. Thank you Paul, for sharing your wife and kids with me, letting them be such an important part of my life. Thank you, Mike Gurnis, for taking the time to be on my committee and including me in the CSEDI discussions. Thanks to you and Dan Bower, I could learn about and appreciate first hand the insight from dynamic models of the deep earth. This collaboration has taught me so much and has given me a different perspective on future projects. I am grateful to Chi Ma, my mentor in the Analytical Facilities. Thanks for letting me putter around to learn the instruments, for letting me teach classes even though it was helping me more than it was helping the students, and for stepping back in and teaching me as well when I was in over my head. Thank you, John Beckett, for teaching me my way around the synthesis lab. Your thoughtful and thorough way of teaching gave me the good habits that I still have today. Thank you, Bin Chen, for the hours in the diamond anvil cell lab, teaching me the tricks you’ve learned along the way to make the successful cells. v I am so thankful to the great friendships that I have made, to those of you that supported me through this experience: Colette Caggiano, Lauren Edgar (roommate of 4+ years! longest relationship yet!), Melanie Channon, Andrew and Kelly Matzen, Danny and Dani Bower, Emily Hamecher, Aaron Wolf, Mike Baker, Dongzhou Zhang, Jeremy Boyce, and Jed Mosenfelder, and to the members of SSRG and secDEC, you know who you are. Thank you Kevin Lewis and John Bagert, for being my number one fans. These measurements were made with the help of graduate students Dongzhou Zhang, Aaron Wolf, and Caitlin Murphy, post-doctorate Bin Chen and post-doctorate Hasan Yavas. At the Advanced Photon Source, thank you to my co-authors from GSECARS: Vitali Prakapenka, Kirill Zhuravlev, and Sergey Tkachev. I am particularly grateful to the nuclear resonant and inelastic X-ray scattering group: Jiyong Zhao, Tom Toellner, Ercan Alp, and especially Wolfgang Sturhahn, who has played a large role in my mentorship as well. Support for this work was provided by the NSF-EAR 0711542 and CAREER EAR-0956166 (both awarded to JMJ) and CSEDI EAR-0855815 (awarded to MCG, DVH and JMJ). The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences(BES), of the U.S. Department of Energy(DOE) under Contract No. DE-AC02-05CH11231. High temperature X-ray diffraction and neon loading was performed at GeoSoilEnviroCARS (Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation Earth Sciences (EAR-1128799) and Department of Energy Geosciences (DE-FG02-94ER14466). Sector 3 operations, where the nuclear resonant experiments were conducted, are partially supported by COMPRES (NSF EAR 06-49658). Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract No. DE-AC02-06CH11357. Sample synthesis was carried out in the petrological facilities at Caltech. Microprobe analyses were carried out at the Caltech GPS Division Analytical Facility (funded in part by the MRSEC Program of the NSF under DMR-0080065). vi Abstract Ultralow-velocity zones (ULVZs) are small structures at the base of the mantle characterized by sound velocities up to 30% lower than those of surrounding mantle. In this thesis, we propose that iron-rich (Mg,Fe)O plays a key role in the observed sound velocities, and argue that chemically distinct, iron-enriched structures are consistent with both the low sound velocities and the measured shapes of ULVZs. We have determined the room temperature Debye sound velocity (VD ) of (Mg0.16 57 Fe0.84 )O up to 121 GPa using nuclear resonant inelastic X-ray scattering. Using an estimate of the equation of state, the seismically relevant compressional (VP ) and shear (VS ) wave velocities were calculated from the VD s. We have also determined the room temperature VD at multiple pressure points of (Mg0.06 57 Fe0.94 )O using nuclear resonant inelastic X-ray scattering and in-situ X-ray diffraction up to 80 GPa. The effect of the electronic environment of the iron sites on the velocities of both of these studies were tracked in-situ using synchrotron Mössbauer spectroscopy. We also present the pressure-volume-temperature equation of state of (Mg0.06 57 Fe0.94 )O determined up to pressures of 120 GPa and temperatures of 2000 K. We combine these studies with a simple Voigt-Reuss-Hill mixing model to predict the properties of a solid ULVZ and show that a small amount of iron-rich (Mg,Fe)O can greatly reduce the average sound velocity of an aggregate assemblage. When combined with a geodynamic model of a solid ULVZ (Bower et al., 2011), we can directly correlate inferred sound velocities to mineralogy and predicted ULVZ shapes. Our combined geodynamic and mineral physics model of a solid ULVZ can be used to explore the relationship between the observed sound velocities and mineralogy of ULVZs with added insight into ULVZ morphology. vii Contents Acknowledgements iv Abstract vi List of Tables xii 1 Introduction 2 1.1 Ultralow-Velocity Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Sound velocities of (Mg0.16 Fe0.84 )O measured by Nuclear Resonant Inelastic XRay Scattering 6 2.1 Nuclear Resonant Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Nuclear Resonant Inelastic X-Ray Scattering (NRIXS) . . . . . . . . . . . . . 7 2.1.2 Synchrotron Mössbauer Spectroscopy (SMS) . . . . . . . . . . . . . . . . . . 8 2.2 Experiments and Data Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Ultralow-Velocity Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Nuclear Resonant Spectroscopy of (Mg0.06 Fe0.94 )O at high pressure with in-situ X-ray Diffraction 21 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 viii 3.4 3.3.1 NRIXS with in-situ XRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.2 SMS with in-situ XRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.1 XRD: Isothermal Equation of State . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.2 SMS: Magnetic Ordering Transition . . . . . . . . . . . . . . . . . . . . . . . 29 3.4.3 NRIXS: Sound Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4 Thermal Equation of State of (Mg0.06 Fe0.94 )O 41 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4.1 Phase Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4.2 Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.5.1 Effect of Buffering on Equation of State . . . . . . . . . . . . . . . . . . . . . 51 4.5.2 Effect of Composition on the Thermal Equation of State of (Mg,Fe)O . . . . 54 Rhombohedral Distortion of (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . 56 4.5 4.6 5 Implications for Ultralow-velocity Zones 5.1 5.2 61 Physical Mixing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1.1 Extrapolation of Magnesiowüstite properties to the CMB . . . . . . . . . . . 61 5.1.2 Mixture of Magnesiowüstite and Ambient Mantle . . . . . . . . . . . . . . . . 63 5.1.3 Mixture of Magnesiowüstite and Silicate Perovskite . . . . . . . . . . . . . . . 64 5.1.4 Dynamics of a Solid-state ULVZ . . . . . . . . . . . . . . . . . . . . . . . . . 66 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Bibliography 70 ix A 82 A.1 Synthesis and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.1.1 (Mg0.16 Fe0.84 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.1.2 (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 A.1.3 Fe1−x O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 A.2 Additional Thermodynamic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.2.1 (Mg0.16 Fe0.84 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.2.2 (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A.3 Sound Velocities of FeO from Nuclear Resonant Inelastic X-ray Scattering . . . . . . 86 x List of Figures 1.1 Modal Mineralogy of the Earth’s Mantle . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Setup of Nuclear Resonant Scattering measurements at Sector 3-ID-B of the Advanced 3 Photon Source (APS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Sample NRIXS spectrum of (Mg.06 Fe.94 )O . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Sample Mössbauer spectra of (Mg.06 Fe.94 )O . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Energy scans (raw NRIXS spectra) of (Mg.16 Fe.84 )O at 300 K over 0 to 120 GPa . . . 11 2.5 Partial projected phonon density of states (PDOSs) of (Mg.16 Fe.84 )O. . . . . . . . . . 12 2.6 Time spectra of (Mg.16 Fe.84 )O from synchrotron Mössbauer spectroscopy. . . . . . . . 13 2.7 Determination of the Debye sound velocity of (Mg.15 Fe.85 )O at 0 and 121 GPa. . . . . 14 2.8 Debye sound velocities of (Mg.16 Fe.84 )O (this study) and of Fe.947 O (Struzhkin et al., 2001) at 300 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.9 VP and VS of (Mg.16 Fe.84 )O determined from VD compared to PREM and ULVZs . . 16 2.10 Voigt-Reuss-Hill (VRH) mixing of VP , VS , and density of (Mg.16 Fe.84 )O with PREM . 19 3.1 Cubic to rhombohedral transition pressures in the literature . . . . . . . . . . . . . . . 22 3.2 Illustration of Bragg’s law in X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . 24 3.3 (Mg0.06 Fe0.94 )O loaded for SMS study . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Pressure-volume data of (Mg0.06 Fe0.94 )O at 300 K, measured in the SMS study . . . . 28 3.5 Pressure-Volume equation of state of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . 30 3.6 Synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . 31 3.7 In-situ synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . 32 xi 3.8 Raw NRIXS spectra of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . . . . . . . . 33 3.9 PDOSs of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.10 Debye velocity determination using psvl . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.11 Debye velocity (VD ) of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . . . . . . . . 37 3.12 VD of (Mg0.06 Fe0.94 )O compared to FeO and (Mg0.65 Fe0.35 )O at 300 K, as a function of density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.13 Compressional (VP ) and shear (VS ) wave velocities of (Mg0.06 Fe0.94 )O at 300 K . . . . 39 4.1 Example XRD spectra at 85 GPa showing peak identifications for B2-NaCl, hcp-Fe, Ne, and (Mg0.06 Fe0.94 )O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Phase identification of (Mg0.06 Fe0.94 )O in P –T space. . . . . . . . . . . . . . . . . . . 48 4.3 P -V -T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the buffered experiment 50 4.4 P -V -T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the unbuffered experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.5 Overlay of data and equations of state of buffered and unbuffered (Mg0.06 Fe0.94 )O . . 53 4.6 Comparison of volume measurements and equations of state of (Mg0.06 Fe0.94 )O to B1FeO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 54 Thermal expansion of buffered (Mg0.06 Fe0.94 )O at 1900 K as a function of pressure, compared to FeO, (Mg0.64 Fe0.36 )O and MgO. . . . . . . . . . . . . . . . . . . . . . . . 55 4.8 Evolution of d-spacings of (Mg0.06 Fe0.94 )O as a function of pressure . . . . . . . . . . 57 4.9 Evolution of c/a ratios of rhombohedral (Mg0.06 Fe0.94 )O as a function of pressure at 300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.10 Pressure-volume data of quenched, rhombohedral (Mg0.06 Fe0.94 )O at 300 K . . . . . . 59 5.1 Debye velocity as a function of density of (Mg.16 Fe.84 )O, (Mg.06 Fe.94 )O, and FeO . . 62 5.2 Mixing models: VP , VS , and density of (Mg.16 Fe.84 )O+PREM . . . . . . . . . . . . . 64 5.3 Mixing models: VP , VS , and density of (Mg.16 Fe.84 )O+Pv . . . . . . . . . . . . . . . 66 5.4 Dynamic model interpretation of mixing models at 4000 K . . . . . . . . . . . . . . . 68 xii A.1 Secondary electron image of (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . . 83 A.2 NRIXS spectra of FeO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 A.3 PDOS of FeO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 xiii List of Tables 1.1 Summary of experiments presented in this thesis . . . . . . . . . . . . . . . . . . . . . 2.1 Summary of pressure, density, Debye sound velocity (VD ), and compressional (VP ) and 5 shear (VS ) wave speeds of (Mg.16 Fe.84 )O. . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1 Details of the (Mg0.06 Fe0.94 )O NRIXS experiment . . . . . . . . . . . . . . . . . . . . 26 3.2 XRD results of the (Mg0.06 Fe0.94 )O SMS experiment . . . . . . . . . . . . . . . . . . . 27 3.3 Equations of state fit to the (Mg0.06 Fe0.94 )O dataset. . . . . . . . . . . . . . . . . . . 29 3.4 Debye Velocity (VD ) of (Mg0.06 Fe0.94 )O as a function of in-situ density . . . . . . . . 36 3.5 Summary of sound velocities of (Mg0.06 Fe0.94 )O as a function of pressure . . . . . . . 40 4.1 Pressure-volume-temperature data for the buffered experiment . . . . . . . . . . . . . 45 4.2 Pressure-volume-temperature data for the unbuffered experiment . . . . . . . . . . . . 46 4.3 3rd-order Birch-Murnaghan equation of state parameters for the buffered dataset using hcp-Fe as a pressure marker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 3rd-order Birch-Murnahan equation of state parameters the both the buffered and unbuffered dataset using B2-NaCl as a pressure marker . . . . . . . . . . . . . . . . . 4.5 49 50 Equation of state parameters using B2-NaCl as a pressure marker, with K0T fixed to 180 GPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.6 Pressure-volume data for the buffered experiment at 300 K. . . . . . . . . . . . . . . . 60 5.1 Model parameters for mixing model “Mw+PREM” . . . . . . . . . . . . . . . . . . . 64 5.2 Model parameters for mixing model “Mw+Pv” . . . . . . . . . . . . . . . . . . . . . . 66 xiv 5.3 Model parameters for mixing model “Mw+PREM” and “Mw+Pv” at 4000 K . . . . . 68 A.1 Thermodynamic parameters calculated directly from the PDOS of (Mg0.16 Fe0.84 )O. . 84 A.2 Thermodynamic parameters calculated directly from the PDOS of (Mg0.06 Fe0.94 )O . . 85 A.3 Summary of FeO density and Debye Velocities . . . . . . . . . . . . . . . . . . . . . . 86 1 2 Chapter 1 Introduction Study of the interior of the earth is crucial to understanding both the processes by which a planet was formed and the future impact of deep interior dynamics. Much has been learned from seismic studies, probing the propagation of sound waves through the earth. Seismic reflectors deep in the earth such as those located at 410, 660 and 2900 km below the earth’s surface have been interpreted as chemical boundaries or phase changes, supported by experimental studies of model compositions of primitive mantle material. The major discontinuities in the mantle are believed to correspond to phase changes, where olivine transforms to the high pressure polymorph wadsleyite at the 410 km discontinuity, then breaks down to form ferropericlase and perovskite at the 660 discontinuity (e.g. Irifune, 1994, Figure 1.1). The mantle layer between the core-mantle boundary and the D” discontinuity spans a depth range in Earth’s lower mantle from up to 350 km above the liquid outer core to the outer core itself, corresponding to a proposed temperature range of 3300-4300 K and 115 to 135 GPa. Intermittent detection of this discontinuity suggests that the core-mantle boundary (CMB) layer is compositionally distinct and/or represents a different phase assemblage (e.g. Lay et al., 2008; Sidorin et al., 1999). 1.1 Ultralow-Velocity Zones At the base of the D” layer, 5-20 km thick patches have been observed in which the VP and VS sound velocities are reduced by 5-10% and 10-30% (Thorne and Garnero, 2004). Reduced seismic 3 Orthopyroxene Garnet Clinopyroxene Olivine (Mg,Fe,Ca)3Al2Si3O12 (Mg,Fe)2SiO4 Transition zone Wadsleyite (Mg,Fe)2SiO4 Ringwoodite (Mg,Fe)2SiO4 Majorite garnet (Mg,Fe,Ca)3(Mg,Si,Al)2Si3O12 Lower Mantle Ferropericlase (Mg,Fe)O Magnesium silicate Perovskite (Mg,Fe)(Si,Al)O3 Calcium silicate perovskite CaSiO3 Upper Mantle Figure 1.1: Modal mineralogy of the earth’s mantle, assuming a pyrolite mantle. The upper mantle (0-440 km below the earth’s surface) is mostly comprised of olivine garnet, and pyroxenes (Mg,Fe)2 Si2 O6 . The lower mantle (660 to 2900 km below the earth’s surface) is comprised of Caand (Mg,Fe)- silicate perovskite and (Mg,Fe)O. Highlighted in blue is ferropericlase, the Fe-poor member of the MgO-FeO solid solution. Iron-rich members are named magnesiowüstite. Figure is adapted from (Frost et al., 2004) velocities in this ultra-low velocity zone, or ULVZ, were first attributed to partial melting due to drastic velocity reductions, sharp upper boundaries, and a strong correlation with hot spots on the surface (e.g. Williams and Garnero, 1996; Williams et al., 1998; Lay et al., 2004). A sound velocity decrement ratio ∂VP /∂VS of 1:3 has been shown to be consistent with partial melt (Berryman, 2000). Numerous seismic studies of the core-mantle boundary indicate that ULVZ distribution is patchy and sometimes associated with edges or the interior of large low shear velocity provinces (McNamara et al., 2010). Fine-scale one-dimensional structure of some ULVZs have been probed, finding a steep positive velocity gradient with depth, implying complex interior morphology (Rost et al., 2006). Multiple concave-down ULVZs clustered together have been invoked to explain PKP precursors in 4 a two-dimensional study, giving the first seismic insight into ULVZ shape (Wen and Helmberger , 1998). Partial melting of ambient mantle would require the fortuitous intersection of the mantle solidus with the base of the core-mantle boundary. Recent work into the equations of state of fayalite Fe2 SiO4 liquid and subsequent analysis shows that partial melting of chondrite or peridotite liquid is unlikely to be gravitationally stable at the base of the mantle (Thomas et al., 2012). It has been proposed that enriched residues of a crystallizing mantle could be depleted in Si and enriched in FeO enough to form ULVZs (Labrosse et al., 2007; Nomura et al., 2011). Dynamic studies exploring the stability of partially-molten ULVZs show that the amounts of liquid required to reduce the velocities of an assemblage would percolate and pool at the base of the mantle rather than remain suspended in a ULVZ (Hernlund and Tackley, 2007). Partial melt can be maintained km’s above the CMB if the ULVZ is stirred (Hernlund and Jellinek , 2010). Further studies of melt geometry explore mechanisms to retain greater melt fraction (Wimert and Hier-Majumder , 2012; Hier-Majumder and Abbott, 2010, e.g.). In the end, a seemingly simple explanation is complicated by large unknowns in grain boundary properties, melt viscosity, and melt sound velocities. Solid ULVZs have also been considered in the literature, in the form of FeO/FeSi alloy (Manga and Jeanloz , 1996) or iron-enriched post-perovskite (Mao et al., 2006), but are no longer considered stable in the hot core-mantle boundary regions in which ULVZs are found. In this thesis, we introduce and explore another alternative: iron-rich (Mg,Fe)O. The partitioning behavior of iron between perovskite(Pv), post-perovskite(PPv), and (Mg,Fe)O varies widely based on experimental conditions. Recently, it has been suggested that iron preferentially partitions in (Mg,Fe)O in the presence of Pv and PPv based on analyses of quenched phase assemblages from pressures and temperatures of 100 GPa and ∼1800 K (Auzende et al., 2008; Sinmyo et al., 2008). An enhanced iron content and subsequent uptake by (Mg,Fe)O could result in a composition much more iron-rich than previously considered. Therefore, it is of interest to study the elasticity of iron-rich (Mg,Fe)O at core-mantle boundary conditions, as it may shed light on seismic 5 observations in this region. 1.2 Thesis Overview This thesis is divided into three studies of iron-rich oxide, the experiments for which are summarized in Table 1.1. All of these studies are united by the use of X-ray scattering techniques using synchrotron radiation to measure the elasticity of iron-rich (Mg,Fe)O. We synthesized our own samples for this study, and describe the samples in Section A.1. Using a diamond anvil cell to create pressures approaching those of the core-mantle boundary and occasionally in-situ laser heating to create temperatures approaching those of the earth’s interior, we measured material properties relevant to the study of the earth’s mantle, namely sound velocities and densities. Chapter 2 is a study of (Mg.16 Fe.84 )O using nuclear resonant inelastic X-Ray scattering (NRIXS) and synchrotron Mössbauer spectroscopy (SMS). Chapter 3 measured the sound velocities and magnetic state of (Mg.06 Fe.94 )O using the methods described in Chapter 2 with a few key differences, including the use of in-situ X-ray diffraction to measure lattice spacing of the sample and map it directly to a combined XRD/SMS study of the same material. Chapter 4 describes the P -V -T equation of state of (Mg.06 Fe.94 )O. Finally, we close in Chapter 5 with a mixing model that combines the results of our work with dynamic calculations of a solid ULVZ. Chapter 2 3 4 A.3 beamlines APS 3-ID-B ALS 12.2.2 APS 3-ID-B APS 3-ID-B APS 13-ID-D APS 13-ID-D APS 3-ID-B ALS 12.2.2 APS 13-ID-D beamtime dates 10/08, 7/09 4/09 8/11, 10/12 2/13 7/11 2/12 8/11, 3/12 5/11 2/12 information collected NRIXS, in-situ SMS XRD NRIXS, in-situ SMS SMS with in-situ XRD XRD XRD with Fe buffer NRIXS XRD XRD P -T conditions 300 K, 0-121 GPa 300 K, 0 GPa 300 K, 0-81 GPa 300 K, 8-52 GPa 300-1950 K, 32-120 GPa 300-1800 K, 30-70 GPa 300 K, 0-100 GPa 300 K, 0 GPa 300 K, 100 GPa Table 1.1: Summary of experiments presented in this thesis samples Mw84 Mw84 Mw94 Mw94 Mw94 Mw94 FeO FeO FeO  6 Chapter 2 Sound velocities of (Mg0.16Fe0.84)O measured by Nuclear Resonant Inelastic X-Ray Scattering∗ * This chapter has been previously published as: Wicks, J. K., J. M. Jackson, and W. Sturhahn (2010), Very low sound velocities in iron-rich (Mg,Fe)O: Implications for the core-mantle boundary region, Geophys. Res. Lett., 37, L15304. A re-evaluation of this data is briefly discussed in Chapter 5 2.1 Nuclear Resonant Scattering Nuclear resonant scattering (NRS) methods take advantage of the fact that nuclei, much like electrons, can be excited into higher energy states, which are organized into discrete energy levels. A resonance energy is the energy that corresponds to the excitation of a nucleus into one of these higher energy levels, at which energy the absorption cross-section of the nucleus is much higher. Whether a nucleus is accessible for nuclear resonant studies is a function of both nuclear excitation energy and lifetime of the excited state. We refer the reader to references such as Sturhahn (2004) that introduce the spectroscopy technique and Sturhahn (2000) that describes the software. In addition, Sturhahn and Jackson (2007) discusses NRS techniques in the context of geophysical application. 7 2.1.1 Nuclear Resonant Inelastic X-Ray Scattering (NRIXS) Nuclear resonant inelastic X-ray scattering (NRIXS) is a technique that probes the lattice vibrations in which the resonant atoms participate. It is complementary to techniques such as Raman spectroscopy and infrared spectroscopy in that it measures vibrations of a lattice, but differs in both information and execution. Most notably, there are no selection rules for NRIXS, so no vibrations are missed based on symmetry. However, because it is isotope-specific, the vibrations measured are a projection of lattice vibrations onto the resonant isotope. Figure 2.1: Setup of Nuclear Resonant Scattering measurements at Sector 3-ID-B of the Advanced Photon Source. Figure adapted from (Sturhahn and Jackson, 2007). Figure 2.1 shows a cartoon of the setup of nuclear resonant scattering measurements at Sector 3-ID-B of the Advanced Photon Source (APS). The synchrotron radiation (SR) of the APS is a third-generation light source capable of producing X-rays with high flux and brilliance. In Sector 3 of the APS a series of monochromators eliminate all energies except the resonance energy with a 1 meV bandwidth. In the case of 57 Fe, the resonance energy is 14.4125 keV, and the energies corresponding to inelastic scattering are obtained by tuning the energy around the resonance peak. Incoherent scattering is measured radially as close to the sample as possible using avalanche photodiodes detectors (APDs), and produce the NRIXS spectra. Coherent scattering is measured in the forward direction, further downstream, which gives us the shape of the elastic peak, which reflects the source, and the synchrotron Mössbauer spectrum if measured in the time domain. Figure 2.2 shows an example energy scan collected in an NRIXS experiment. The elastic peak 8 at the origin corresponds to recoilless absorption and emission. Peaks on either side of the elastic peak correspond to phonon annihilation (anti-Stokes) or creation (Stokes). The spectrum measured in the forward direction gives the shape of the elastic peak, and is scaled and subtracted from the NRIXS spectrum to isolate the vibrations. 10000 1 atm , 300 K counts per 7 seconds 1000 100 FWHM = 1.08 meV 10 1 -50 0 Energy (meV) 50 100 Figure 2.2: Sample energy scan (raw NRIXS spectrum) of (Mg.06 Fe.94 )O around the 57 Fe resonance energy of 14.4125 keV at ambient pressure and temperature. The spectrum independently measured in the forward direction gives the shape of the elastic peak (red). The spectrum measured radially captures the inelastic absorptions corresponding to lattice vibrations (black). 2.1.2 Synchrotron Mössbauer Spectroscopy (SMS) Mössbauer spectroscopy measures small changes to nuclear energy levels in response to its environment. From this technique, we gain information about the electronic and magnetic environment of a nucleus that has an accessible resonance (e.g. 57 Fe). Nuclear energy levels are sensitive to the electric field gradient, which couples with the quadrupole 9 8 GPa, 300 K 10000 counts with stainless steel 1000 100 without stainless steel 10 20 40 60 80 100 120 140 Time (ns) Figure 2.3: Left: Synchrotron Mössbauer spectra of (Mg.06 Fe.94 )O at 8 GPa, with and without stainless steel reference. Right: Conventional Mössbauer spectrum of (Mg.06 Fe.94 )O at 0 GPa, with a fit drawn in red corresponding to a quadrupole splitting of 1 mm/s and isomer shift of 0.8 mm/s, consistent with divalent iron. moment of the nucleus. An asymmetric electronic distribution around the nucleus, then, results in quadrupole splitting. Nuclear energy levels split even further in the presence of electric or magnetic fields. Synchrotron Mössbauer spectroscopy measures the Rayleigh scattering of excited resonant nuclei, where a superposition of different emitted energies reflecting nuclear level splitting can be measured using detectors as a function of time. Figure 2.3 shows an example of typical Mössbauer spectra of (Mg.06 Fe.94 )O at low pressures. Higher pressure data is discussed in Chapter 3. A quadrupole splitting of energy manifests as a split peak in conventional spectra (right), and as an oscillational frequency in synchrotron Mössbauer spectra (left). In conventional spectra, the isomer shift measured gives the energy shift of the ground energy level with respect to the gamma ray source, typically 57 Co embedded in stainless steel. In synchrotron Mössbauer spectroscopy, isomer shift is determined by measuring a sample twice, with and without a reference absorber in the beam. Advantages of synchrotron Mössbauer spectroscopy over conventional methods include no source broadening, no background, and high photon flux at the resonance energy of the 57 Fe atom, permitting high quality spectra with reasonable count times of samples even at high pressure. 10 2.2 Experiments and Data Evaluation The (Mg.16 57 Fe.84 )O sample was synthesized at room pressure in a gas-mixing furnace. Details of synthesis and purity can be found in section A.1. Three panoramic diamond anvil cells (DACs) were prepared for this experiment. The panoramic DACs were designed and machined at Caltech. Beveled anvils with 250 and 300 µm-flat culet diameters were used. A 140 µm sample chamber was drilled out of a pre-indented beryllium gasket for each DAC, and the sample was loaded in the center of a boron epoxy insert to increase sample thickness, aid in gasket stability, and reduce pressure gradients. In one of the three DAC setups, a NaCl pressure medium was included with the sample, and no boron epoxy was used. Small ruby spheres were loaded close to the sample in all DACs to determine pressure before and after data collection using the characteristic ruby fluorescence line shift according to the non-hydrostatic ruby pressure scale (Mao et al., 1978). High-pressure nuclear resonance scattering experiments were conducted at Sector 3-ID-B of the Advanced Photon Source at Argonne National Laboratory (Sturhahn and Jackson, 2007, Figure 2.1). The storage ring was operated in top-up mode with 24 bunches separated by 153 ns. The X-ray energy incident on the sample had a bandwidth of 1.2 meV and was tuned around the 14.4125 keV nuclear resonance of 57 Fe (Toellner et al., 2001). Time-delayed photons resulting from nuclear excitation of the 57 Fe isotope in (Mg.16 Fe.84 )O were collected using three avalanche photodiode detectors (APDs) positioned radially around the DAC. At each pressure, inelastically scattered photons were collected over select energy ranges spanning -80 meV to +100 meV. Nuclear resonance inelastic X-ray scattering (NRIXS) spectra were collected from ambient pressure to 121 GPa at 300 K. Raw spectra are shown in Figure 2.4. From the measured energy spectra, the partial projected phonon density of states (PDOS) pertaining to the Fe site was extracted using methods described in (Sturhahn, 2004). PDOSs are shows in Figure 2.5. A fourth APD was positioned in the forward direction with two goals: 1) to measure the resolution function independently for accurate sound velocity determination and 2) to measure the time spectra using synchrotron Mössbauer spectroscopy for local magnetic environment determination of the 57 Fe 11 46 GPa 121 GPa 41 GPa Counts Counts 110 GPa 28 GPa 21 GPa 102 GPa 97 GPa 15 GPa 1000 1000 11 GPa 88 GPa 100 100 80 GPa 4 GPa 65 GPa 10 10 55 GPa 1 ambient -100 1 -50 0 50 100 -100 Energy (meV) -50 0 50 100 Energy (meV) Figure 2.4: Raw NRIXS spectra of (Mg.16 Fe.84 )O at 300 K at different pressures over 0 to 120 GPa, measured at Sector 3-ID-B of the Advanced Photon Source. They are offset in the y-direction for clarity. (Figure 2.6). The Debye sound velocity, VD , is related to the low-energy region of the PDOS in the following manner:  V (E) = m E2 2π 2 h̄3 ρ D(E)  31 and VD = V (0) , (2.1) where m is the mass of the resonant nucleus, ρ is the mass density of the sample, and D(E) is the PDOS. Values of V (E) were calculated from the measured PDOS and matched to an empirical function f (E) ≈ VD {1 − (E/E0 )2 }, where E0 and VD are optimized in a standard least-square-fit procedure (Jackson et al., 2009). The energy region for the fit was chosen between 4 and 14 meV. The lower limit of the energy range is chosen to avoid errors resulting from the subtraction of the elastic contributions and is mainly determined by the energy bandwidth of the X-rays. The upper limit is chosen as the maximum possible energy that permits an acceptably small χ2 value in D(E,V) D(E,V) D(E,V) D(E,V) D(E,V) D(E,V) D(E,V) 12 ambient 55 GPa 4 GPa 65 GPa 11 GPa 80 GPa 15 GPa 88 GPa 21 GPa 97 GPa 28 GPa 102 GPa 41 GPa 110 GPa 46 GPa 121 GPa D(E,V) 200 100 0 0 20 40 60 Energy (meV) 80 100 0 20 40 60 Energy (meV) 80 100 Figure 2.5: Partial projected phonon density of states (PDOSs) of (Mg.16 Fe.84 )O, extracted from the NRIXS scans using the PHOENIX software. 13 ambient 65 GPa 2 10 2 10 0 0 10 10 4 GPa 80 GPa 2 10 2 10 0 0 10 10 11 GPa 88 GPa 2 2 10 10 0 0 10 15 GPa 2 10 0 counts counts 10 97 GPa 2 10 0 10 10 28 GPa 2 10 102 GPa 2 10 0 0 10 10 46 GPa 2 10 110 GPa 2 10 0 0 10 10 55 GPa 2 10 121 GPa 2 10 0 10 0 20 40 60 80 Time (ns) 100 120 10 20 40 60 80 Time (ns) 100 120 Figure 2.6: Time spectra of (Mg.16 Fe.84 )O from synchrotron Mössbauer spectroscopy. The ambient pressure spectrum is characterized by slow oscillations, consistent with no magnetic ordering. Fast oscillations appear in the spectrum at 28 GPa. A magnetically-ordered state is stable between 28 and 110 GPa. At 121 GPa, the fast oscillations have disappeared, which is indicative of a spin transition to a low-spin state of the Fe 3d-electron configuration. Error bars are shown for every fourth point, and each data point represents a binning of 4. 14 Figure 2.7: Determination of the Debye sound velocity of (Mg Fe )O at ambient pressure and .15 .85 Figure 5: (Supplemental) Determination of the(2.1). Debye velocity ofof(Mg .15 Fe.85 )O at am121 GPa. Symbols show values of Equation Solid sound lines show the best fit the empirical f (E)GPa. as explained in the text. bient pressurefunction and 121 Symbols show values of Equation (2). Solid lines show the best t of the empirical function f (E) as explained in the text. The lower limit of the energy range is the fit procedure. Figure 2.7 shows V (E), the fitted function f (E), and the optimum value of VD chosen to avoid errors resulting from the subtraction of the elastic contributions and is mainly ambient pressure and 121 GPa. lines illustrate extrapolations using is thechosen best fits to determined byforthe energy bandwidth ofDashed the x-rays (27).theThe upper limit as the max2 imum possible energy thatsound permits an acceptably small χ value in the t procedure. Dashed obtain the Debye velocities. lines illustrate the extrapolations using the best ts to obtain the Debye sound velocityies. In Figure 2.8, we plot VD ’s determined for the entire pressure range. For comparison, we also show VD ’s of Fe.947 O that we determined from the PDOSs reported in a published NRIXS study, which was conducted at 300 K up to 49 GPa (Struzhkin et al., 2001). For an isotropic solid, VD is related to the seismically relevant aggregate compressional (VP ) and shear (VS ) velocities by 3/VD3 = (1/VP3 ) + (2/VS3 ) and VP2 − (4/3)VS2 = K0S /ρ = Vφ2 16 (2.2) 15 Debye Velocity (km/s) 4.2 3.8 3.4 3.0 (Mg.16Fe.84)O FeO 2.6 0 20 40 60 80 100 120 140 Pressure (GPa) Figure 2.8: Debye sound velocities determined from the PDOS of (Mg.16 Fe.84 )O (this study) and of Fe.947 O (Struzhkin et al., 2001) at 300 K. where K0S is the adiabatic bulk modulus at ambient temperature, ρ is the density, and Vφ is the bulk sound velocity. K0S is related to the isothermal bulk modulus, K0T , by K0S = K0T (1 + αγT ). K0S can be approximated by K0T , because at room temperature αγT ≤ 0.01 for most materials (Angel and Jackson, 2002). The isothermal third order Birch-Murnaghan weighted equation of state (EOS) from a high-pressure powder x-ray diffraction study up to 93 GPa on (Mg.22 Fe.78 )O, a similar composition to that used in our NRIXS measurements, provided the values K0T =191.2±5.5 GPa 0 and K0T =2.5±0.1 (Zhuravlev et al., 2010). The pressure-dependent density of (Mg.16 Fe.84 )O was obtained by rescaling this EOS with our initial density of 5.69(7) g/cm3 . X-ray diffraction spectra of our sample were taken at select pressures, including ambient, at the Advanced Light Source at Lawrence Berkeley National Laboratory, confirming our choice of EOS and pressure scale. The seismically relevant VP and VS values determined at each pressure point are shown for the entire pressure range (Figure 2.9, Table 2.1). 16 14.0 PREM VP ULVZ VP 12.0 -10% ULVZ VS - 5% -10% -20% Velocity (km/s) 10.0 8.0 (Mg.16Fe.84)O VP 6.0 PREM VS -20% -30% 4.0 (Mg.16Fe.84)O VS 2.0 0 20 40 60 80 100 120 140 Pressure (GPa) Figure 2.9: VP (blue) and VS (red), of (Mg.16 Fe.84 )O determined from VD along with PREM (Dziewonski and Anderson, 1981) and ULVZs (Thorne and Garnero, 2004). ×: predicted sound velocities for (Mg.16 Fe.84 )O from an ultrasonic study on (Mg,Fe)O (Jacobsen et al., 2002). 2.3 Results At ambient pressure, the velocities of (Mg.16 Fe.84 )O are in good agreement with the trend in sound velocities for iron-rich (Mg,Fe)O (Jacobsen et al., 2002; Struzhkin et al., 2001, Figures 2.8, 2.9). In-situ synchrotron Mössbauer spectroscopy shows an absence of magnetic ordering (Figure 2.6) at low pressures, and detailed analysis reveals a quadrupole splitting of about 0.8 mm/s. At pressures approaching 28 GPa, both VD and VS of (Mg.16 Fe.84 )O decrease with increasing pressure (Figures 2.8, 2.9). The softening occurs in the vicinity of the transition from the paramagnetic state to a magnetically ordered state around 28 GPa (Figure 2.6). The presence of magnetic hyperfine fields is clear evidence for a magnetically ordered state demonstrating a magnetic transition in (Mg.16 Fe.84 )O around 28 GPa at 300 K—a finding in agreement with a conventional Mössbauer 17 Pressure (GPa) 0 4.0(3) 11.4(3) 15(3)* 21.0(4) 28(2) 41(1) 46(4) 55(3) 65(5) 80(5) 88(4) 97(5) 102(5) 110(4) 121(7) Density (g/cm3 ) 5.69(7) 5.81(8) 6.02(8) 6.1(1) 6.27(8) 6.44(9) 6.8(1) 6.9(1) 7.1(1) 7.4(1) 7.7(1) 7.9(1) 8.1(1) 8.2(2) 8.5(2) 8.7(2) VD (km/s) 3.23(2) 3.10(2) 3.05(3) 3.03(3) 3.05(2) 2.96(2) 3.23(2) 3.28(3) 3.21(4) 3.48(3) 3.64(5) 3.67(3) 3.74(3) 3.84(5) 3.92(2) 4.04(5) VP (km/s) 6.70(9) 6.70(9) 6.8(1) 6.8(1) 6.9(1) 6.9(1) 7.2(1) 7.2(1) 7.2(2) 7.4(2) 7.5(2) 7.5(2) 7.4(2) 7.5(2) 7.5(3) 7.4(3) VS (km/s) 2.86(2) 2.74(2) 2.70(3) 2.67(3) 2.69(2) 2.61(2) 2.85(2) 2.90(3) 2.84(3) 3.08(4) 3.22(5) 3.25(3) 3.32(3) 3.41(5) 3.48(4) 3.60(5) Table 2.1: Summary of pressure, density, Debye sound velocity (VD ), and compressional (VP ) and shear (VS ) sound velocities of (Mg.16 Fe.84 )O. Numbers in parenthesis reflect the error on the last digit. Errors in pressure reflect the standard deviation of pressures measured from multiple rubies surrounding the sample, measured before and after the x-ray measurement. Errors in ambient pressure density reflect the uncorrelated errors of unit cell volume measurement, sample composition, and assumed vacancies. Errors in VD incorporate fitting errors in the low-energy region of the PDOS (Figure 2.7) as well as the propagation of the errors in density and pressure. This error is then propagated further to the VP and VS errors. * NaCl pressure medium. study on (Mg.20 Fe.80 )O (Speziale et al., 2005). A similar softening is observed for Fe.947 O (Struzhkin et al., 2001, Figure 2.9) and other iron-rich (Mg,Fe)O samples (Jacobsen et al., 2004). This particular behavior has been associated with phonon-magnon coupling (Struzhkin et al., 2001) and has been attributed to c44 mode softening preceding the B1 to rhombohedral structural distortion (Mao et al., 1996). At 121 GPa the fast oscillations, thus the magnetic hyperfine fields, disappear in the time spectrum (Figure 2.6), and is consistent with the onset of a spin transition into a low-spin state of the Fe 3d-electron configuration. We note that at pressures above 100 GPa, VP ceases to increase and gradually softens. Such a behavior is consistent with a transition to a low spin state, as similar observations have been reported for iron-poor (Mg,Fe)O in the vicinity of a spin transition (Crowhurst et al., 2008). Most important, the very low pressure derivatives of VP and VS for (Mg.16 Fe.84 )O above 28 GPa persist to the highest pressure measured and ensure that this material retains ultra-low sound velocities at core-mantle boundary pressures. 18 2.4 Ultralow-Velocity Zones The shear sound velocity of (Mg.16 Fe.84 )O at 121 GPa is about 55% and 50% reduced compared to MgO (Murakami et al., 2009) and the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson, 1981), respectively. The VP /VS ratio at the highest pressure measured is 2.1±0.1, which falls within the VP /VS range of ULVZs (2.2±0.3) (Thorne and Garnero, 2004). The Poisson ratios (ν) determined from seismic ULVZ observations range from 0.30 to 0.41 and compare favorably to our value of 0.34±0.02 for iron-rich (Mg,Fe)O at 121 GPa and 300 K. At thousands of K and regardless of its structure (Lin et al., 2003), (Mg.16 Fe.84 )O is unlikely to be stiffer than it is at room temperature, which could result in even lower sound velocities at the CMB. As an illustration of the expected VP , VS , and density of a mechanical mixture containing iron-rich (Mg,Fe)O and ambient mantle material, we estimate the effect of temperature on (Mg.16 Fe.84 )O’s properties using MgO behavior as a proxy (Sinogeikin et al., 2000). Due to the highly uncertain elastic properties of silicates under CMB conditions, we employ PREM as our bound for the remaining silicate fraction, while recognizing that PREM values may underestimate silicate behavior. We then calculate the Voigt-Reuss-Hill mechanical mixing envelopes for VP , VS , and density (Watt et al., 1976) for a given vol% of (Mg.16 Fe.84 )O and PREM (Figure 2.10). To first order, mixing of just 12 vol% of (Mg.16 Fe.84 )O with 88 vol% silicates (represented here by PREM) matches signature seismic observations for the ULVZ (Figure 2.10). While ULVZ provinces are often considered to be patches of dense partial melt, no measurements exist for the sound velocities of partially molten mantle material at CMB conditions. The connection between ULVZs and partial melting was popularized by the correlation between ULVZ and hot spot locations (Williams et al., 1998). However, not all ULVZs are related spatially to hot spots. An alternative explanation of several ULVZ observations is a dense, localized solid layer containing some amount of iron-rich (Mg,Fe)O. A solid dense layer would not require the intersection of the local geotherm and solidus of the mantle and can produce low sound speeds independent of partial melting (Figure 2.10). This scenario would require a mechanism in which the (Mg,Fe)O phase becomes enriched in iron 19 VP range of observed values of ULVZs VP VRH mixing bounds of iron-rich (Mg,Fe) with PREM density VRH bounds VS ULVZ VS VRH mixing Figure 2.10: Voigt-Reuss-Hill (VRH) mixing of VP , VS , and density (red area) of (Mg.16 Fe.84 )O with PREM (see text for details). In orange boxes, we plot VP and VS of the ULVZ’s centered at 12 vol% (Mg.16 Fe.84 )O, which produces a ν of about 0.34. This particular calculation assumes a pressure of 123 GPa and a temperature of 2700 K. The widths of the ULVZ symbols are arbitrary. in localized areas of the CMB. It has been suggested that extensive iron enrichment could localize in patches in the vicinity of the CMB due to viscosity variations, because liquid iron can be pulled up into the lower mantle on the km scale (Kanda and Stevenson, 2006). Iron-rich pockets could represent residue of a fractional crystallization of primordial magma ocean (Labrosse et al., 2007). In representative mantle assemblages with typical amounts of iron, (Mg,Fe)O has been identified as the preferred iron sink (Auzende et al., 2008; Sinmyo et al., 2008). Chemical reaction studies between liquid iron and lower mantle perovskite or oxide have produced 20 a wide range of results, leading to interpretations ranging from production of FeSi and FeO (Knittle and Jeanloz , 1991; Song and Ahrens, 1994) to dissolution of oxygen into liquid iron (Takafuji et al., 2005; Frost et al., 2010). Further investigations exploring the dependence of these reactions on CMB fugacity and chemistry may address these discrepancies, which could be complicated by the possibility of disequilibria. 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Min., 32, 241–247, doi: 10.1007/s00269-005-0447-x. 81 Zhuravlev, K. K., J. M. Jackson, A. S. Wolf, J. K. Wicks, J. Yan, and S. M. Clark (2010), Isothermal compression behavior of (Mg,Fe)O using neon as a pressure medium, Phys. Chem. Min., 37, 465– 474, doi: 10.1007/s00269-009-0347-6.  21 Chapter 3 Nuclear Resonant Spectroscopy of (Mg0.06Fe0.94)O at high pressure with in-situ X-ray Diffraction 3.1 Introduction In Chapter 3, we established that iron-rich magnesium oxide (XF e = 0.84) is characterized by very low sound velocities, and found that a magnetic transition occurred between 15 and 28 GPa. In this chapter, we present a similar study on a different composition, (Mg0.06 Fe0.94 )O, hereafter referred to occasionally as Mw94. In addition to providing insight into the compositional dependence of sound velocities, this chapter also reflects improvements in the methodology since the publication of the previous work. Most notably, availability of in-situ XRD allowed us to directly measure the sample’s volume, and thus provide in-situ density (ρ) of our sample for every nuclear resonant scattering (NRS) measurement. This allows us to report the direct result of our NRIXS studies: the Debye sound velocity (VD ) at in-situ ρ. Finally, volumes of this material at room temperature measured as part of a synchrotron Mössbauer study (this chapter) and a thermal equation of state study (Chapter 4) give us an equation of state that is used to convert Debye velocities into compressional and shear wave speeds reliably. Another direct result of this study is the transition pressure of the paramagnetic to antiferromagnetic transition, also known as the Néel transition (Fujii et al., 2011, e.g.). Mössbauer and magnetic investigations have shown a compositional dependence in Néel temperature in the (Mg,Fe)O solid 22 solution, where projected transition pressure at 300 K coincides with the cubic to rhombohedral distortion (Speziale et al., 2005; Fujii et al., 2011). Other experimental studies, however, find that structural and magnetic transition pressures or temperatures do not coincide (Kantor et al., 2004, 2005, 2006; Glazyrin et al., 2011). 140 Transition Pressure (GPa) 120 100 Lin2003 80 60 Lin2003 Richet1989 Zhuravlev2010 40 Fei1992 Kantor2006 20 0 0 20 40 60 80 100 mol% FeO Figure 3.1: Cubic to rhombohedral transition pressures in the literature, as a function of composition. In red we plot our brackets on the magnetic transition pressure from synchrotron Mössbauer spectroscopy of (Mg0.16 Fe0.84 )O (Chapter 2) and (Mg0.06 Fe0.94 )O (this Chapter). In blue we plot the constraint on the cubic to rhombohedral structural transition from X-ray diffraction (Chapter 4). The dashed line indicates the cubic-rhombohedral phase boundary according to Fei et al. (2007a), and the dotted line indicates the same according to (Lin et al., 2003). Gray-filled circles are reported transition pressures in the literature (Mao et al., 2002; Jacobsen et al., 2005; Fei and Mao, 1994; Yagi et al., 1985; Zhuravlev et al., 2010; Lin et al., 2003; Shu et al., 1998a; Fei et al., 2007a; Kondo et al., 2004; Richet et al., 1989; Fei et al., 2007a; Kantor et al., 2006; Mao et al., 1996), whereas white-filled circles indicate maximum pressures of studies that did not see a transition (Fei et al., 1992; Richet et al., 1989; Lin et al., 2003). Experimental investigations of the structural transition find that increasing FeO component corresponds to a decrease in transition pressure (Lin et al., 2003; Shu et al., 1998b). The transition pressure is found to be very sensitive to hydrostaticity Shu et al. (1998a), and some studies found no 23 compositional dependence of transition pressure (Kondo et al., 2004). Figure 3.1 shows a summary of cubic to rhombohedral structural transition pressures in the literature, which may reflect a compositional dependence. We include our magnetic transition bounds for (Mg0.16 Fe0.84 )O (Chapter 2) and (Mg0.06 Fe0.94 )O (this Chapter), in addition to structural transition constraints for (Mg0.06 Fe0.94 )O (Chapter 4). We will describe a synchrotron Mössbauer (SMS) study of (Mg0.06 Fe0.94 )O over the pressure range 8 to 52 GPa with in-situ X-ray diffraction. Next, we will describe nuclear resonant inelastic X-ray scattering (NRIXS) measurements over the pressure range 0 to 80 GPa, also taken with in-situ SMS and X-ray diffraction. These results will be compared to an iron-poor sample, (Mg0.65 Fe0.35 )O (Chen et al., 2012) and to FeO (this study). 3.2 X-ray Diffraction The (Mg,Fe)O solid solution, excluding the end member FeO, is found in one of two crystal structures in the pressure and temperature range of studies that we conducted. In this chapter, at room pressure and temperature, (Mg0.06 Fe0.94 )O is face-centered cubic, also referred to as B1 or rocksalt structure. Its space group is F m-3m, and the first five reflections, i.e. first 3 lattice planes probed with increasing 2θ, are (111), (200), and (220), where the numbers (hkl) refer to the Miller indices of the lattice planes. In a cubic system, the spacing between lattice planes, or d−spacing, geometrically gives the lattice constant a: dhkl = a (h2 + k 2 + l2 )1/2 (3.1) At high pressure, between 8 and 40 GPa and depending on composition and hydrostatisticy of the sample environment, the cubic structure undergoes a distortion to a rhombohedral structure (space group R-3m). Rhombohedral unit cells are often described using a hexagonal coordinate system, which encompasses the rhombohedron (the c axis of the hexagonal cell corresponds to the long body-diagonal of the rhombohedral unit cell). In this description, the (111) reflection splits 24 into two: (003) and (101), the (200) is renamed as the (012) reflection, and the cubic (220) splits into hexagonal (110) and (104). X-ray diffraction is a scattering technique that measures the elastic, coherent scattering of Xrays off electrons (e.g. Fultz and Howe, 2008, and references therein). Powder XRD is variation of this technique that assumes that sampled grains are randomly oriented, such that scattering in the forward direction samples all allowed reflections. We apply this method to understand the changes in unit cell variations with pressure (and temperature, see Chapter 4). X-ray diffraction can often be performed with in-house X-ray diffractometers with fixed-wavelength sources. The small sample size of diamond anvil cell experiments, however, require higher-intensity radiation to achieve reasonable experiment times. The high flux and versatile energy range of synchrotron experiments make them ideally suited for high pressure experiments. See Duffy and Wang (1998) for a discussion on performing high pressure and temperature XRD experiments at the synchrotron. Figure 3.2: Illustration of Bragg’s law in X-ray diffraction. Elastic scattering occurs in all directions, but constructive interference occurs in directions in which the Bragg condition is satisfied: nλ = 2dsinθ. The XRD measurements presented in this chapter were measured in conjunction with nuclear resonant scattering experiments at Sector 3-ID-B of the Advanced Photon Source, where a MAR345 image plate is inserted downstream from the sample. The angle-dispersive X-ray pattern is integrated radially using the Fit2D software (Hammersley et al., 1996). A CeO2 standard is used to calibrate both the X-ray beam center and the distance between the X-ray focus spot and the detector. 25 The wavelength is optimized, in these experiments, for the resonance energy of 57 Fe of 14.4125 meV. This energy, by design, is not optimized for XRD. The ∼ 1 meV bandwidth provides relatively small flux compared to beam lines tailored for XRD, and the scattering cross-section of electrons at this energy is small. As a result, typical XRD exposures of oxides in a diamond anvil cell require 10 minutes at low pressure and up to 30 minutes at high pressure, whereas at tailored beam lines for XRD at high pressure (e.g. 13-ID-D, APS) exposures are ∼ 1 minute to 2 minutes. Nevertheless, in-situ XRD is required for accurate sound velocity determinations from NRIXS measurements, as the pressure gradients (and therefore uncertainty in the absence of in-situ XRD) can reach upwards of 10 GPa across 100 µm. 3.3 Experimental Details 3.3.1 NRIXS with in-situ XRD This high-pressure nuclear resonance scattering experiment was conducted at Sector 3-ID-B of the Advanced Photon Source at Argonne National Laboratory in August 2011 and October 2012. Three samples were prepared for this experiment. For the high pressure points, beveled anvils with 300 µm-culets were used. The (Mg0.06 Fe0.94 )O sample was embedded in boron epoxy, with rubies on either side, one on each culet. The pressure of the sample’s environment was tracked with both ruby fluorescence (Mao et al., 1986, only visible in compression to initial pressure point) and “diamond edge” Raman spectroscopy of diamond anvil culet (Akahama and Kawamura, 2006), but ultimately the pressure of the sample was determined with in-situ X-ray diffraction. The ambient pressure data point was taken in air. A low pressure data point (11.6 GPa) was taken of a sample loaded in a DAC with beveled 400 µm-culets, with beryllium gasket, and KCl pressure medium. We summarize the compression points measured in Table 3.1. At each compression point, we collected a series of inelastic spectra, a synchrotron Mössbauer spectrum, and an X-ray diffraction spectrum (often both before and after the NRS spectra). Raw spectra are shown in Figure 3.8. Energy scans were collected over a minimum energy range 26 Environment 1 2 3 4 5 6 air KCl, Be gasket B epoxy B epoxy B epoxy B epoxy Pruby a (GPa) 41.2 Psample b (GPa) 11.6 43.5, 48.4e 59.1 72, 76e 85 Energy range (meV) −80 → +100 −60 → +70 −60 → +80 −60 → +80 −60 → +80 −60 → +80 −70 → +130 Scans, count times 1 at 3 sec/pt, 1 at 4 sec/pt 1 at 3 sec/pt, 5 at 5 sec/pt 1 at 3 sec/pt, 3 at 5 sec/pt 1 at 3 sec/pt, 4 at 5 sec/pt 5 scans at 5 sec/pt 7 scans at 5 sec/pt 1 at 3 sec/pt, 5 at 5 sec/pt PXRD c (GPa) 0 9.61(2)d 42.7(7) 55(1) 64(2) 81.6(7) 81.1(8)f Table 3.1: Details of the (Mg0.06 Fe0.94 )O NRIXS experiment. a Pressures were determined off-line using ruby fluorescence (Mao et al., 1986). b Pressures were determined offline using the diamond edge (Akahama and Kawamura, 2006). c Pressures from XRD were determined from the combined equation of state of (Mg0.06 Fe0.94 )O, given in Table 3.3 and Figure 3.5. d Number in parenthesis gives the error on the last digit. e Two numbers listed indicate before and after measurements f Without increasing pressure, the highest compression point was remeasured in October 2012. of −60 → +70 meV. At the highest compression point (#6, ∼82 GPa), the energy scan was measured again in October 2012 with an extended energy range. 3.3.2 SMS with in-situ XRD Figure 3.3: (Mg0.06 Fe0.94 )O at 50 GPa in the Synchrotron Mössbauer study. The sample chamber is 150 µm across. This study was conducted at 300 K. Ruby sphere is located to the left. An independent synchrotron Mössbauer spectroscopy (SMS) experiment was carried out at Sector 3-ID-B of the Advanced Photon Source in February 2012. (Mg0.06 Fe0.94 )O was loaded in a diamond anvil cell with KCl as a pressure-transmitting medium in a rhenium metal gasket. A small ruby was included near the edge of the sample chamber (Figure 3.3). XRD and SMS were collected at 8 compression points over the range 7.8 to 52.4 GPa, determined by the equation of state of 27 KCl (Dewaele et al., 2012). Ruby fluorescence was used to track the pressure offline. As Sector 3 is optimized for NRS (not XRD), with relatively low flux at a low energy with low scattering efficiency off electrons, we only observed one reflection of (Mg0.06 Fe0.94 )O (200) and KCl (110). One reflection is enough to determine the unit cell volume for cubic symmetry, which both KCl and (Mg0.06 Fe0.94 )O are at low pressure. At high pressure, we can estimate rhombohedral distortion, assuming that rhombohedral distortion is solely a function of pressure. In Chapter 4, Figure 4.8 shows the evolution of d-spacings as a function of pressure, and gives the interpolation d012R ≈ − 0.0019 × P + 2.1064, a linear relationship between d-spacing of the rhombohedral (012) reflection and pressure. See Section 4.6 for more details. The d-spacings and resulting pressure of KCl and (Mg0.06 Fe0.94 )O are summarized in Table 3.2. (Mg0.06 Fe0.94 )O d200 are interpreted as either cubic volumes or rhombohedral volumes. Pruby (GPa) 7.92 11.72, 12.17 15.71, 16.59 19.71, 20.1 23.84, 24.17 28.08, 28.62 34.97 PKCl (GPa)a 7.79 13.09 19.16 22.92 29.51 35.73 43.47 52.43 d110 KCl (Å) 2.114 2.100 2.081 2.069 2.049 2.036 2.018 2.000 d200 Mw94 (Å) 2.481 2.415 2.360 2.333 2.293 2.262 2.228 2.196 Vol/atom (Å3 )C 9.443 9.258 9.015 8.851 8.605 8.439 8.223 8.005 Vol/atom (Å3 )R 8.646 8.487 8.275 8.058 Table 3.2: XRD results of the (Mg0.06 Fe0.94 )O SMS experiment. When two numbers are listed, ruby pressures correspond to before and after the SMS and XRD measurement. a KCl pressure is determined from the d-spacing of KCl using the equation of state of KCl (Dewaele et al., 2012). C and R subscripts indicate volumes assuming that the Mw94 d-spacing corresponds to the cubic (200) or rhombohedral (012) reflection. 3.4 Results 3.4.1 XRD: Isothermal Equation of State A Birch-Murnaghan equation of state was fit to the pressure-volume data given in Table 3.2, given by the equations: ( P (V ) = 3K0 fE (1 + 2fE ) 5 2 3 1 + (K00 − 4)fE 4 ) (3.2) 28 1 fE = 2 " V0 V ! 23 # −1 (3.3) where K0 is the initial bulk modulus, K00 is the pressure derivative of the bulk modulus, and fE is Eulerian strain. K00 fixed to 4. Pressure was determined by the equation of state of KCl (Dewaele et al., 2012), and the results are summarized in Table 3.3. In the first fit, sample volumes were interpreted as being cubic given the measured d200 (Table 3.2). Cubic sample volumes are plotted as black circles in Figure 3.4. In the second fit, the rhombohedral estimates of volumes were included. These two fits are plotted in Figure 3.4. 10 3 Volume/atom (A ) 9.5 9 8.5 8 7.5 0 10 20 30 Pressure (GPa) 40 50 60 Figure 3.4: Volume of (Mg0.06 Fe0.94 )O at 300 K determined by its (200) reflection, with pressure determined by the volume of B2-KCl, determined by its (110) reflection, using the equation of state 0 given by Dewaele et al. (2012). Black line is a Birch-Murnaghan equation of state with K0T fixed 3 to 4, giving V0 = 9.91(2) Å /atom, K0T = 160(2) GPa. Red circles show volumes assuming a rhombohedral structure (See text and Table 3.2), and the red dashed curve shows the fit calculated with those points included (V0 = 9.90(3) Å3 /atom, K0T = 164(4) GPa). Equation of state results are summarized in Table 3.3. In the third fit, the room temperature rhombohedral quench data from our high pressure and 29 temperature XRD experiment (Chapter 4) are also included. We plot this combined equation of state in Figure 3.5. This equation of state is used to determine pressure in the NRIXS study. Assume cubic Include rhombo Combineda V0 (Å3 ) 9.91(2) 9.90(3) 9.90446(f ixed) K0T (GPa) 160(2) 164(4) 189(4) 0 K0T 4 (fixed) 4 (fixed) 2.9(1) Table 3.3: Equations of state fit to the (Mg0.06 Fe0.94 )O dataset. a In this fit, the ambient temperature dataset was combined with the 300 K quench data of (Mg0.06 Fe0.94 )O from our high pressure and temperature XRD study (discussed in Chapter 4). 3.4.2 SMS: Magnetic Ordering Transition Figure 3.6 shows the spectra from the synchrotron Mössbauer experiment. Pressure determined by the equation of state of KCl are shown on the right. At low pressure the spectra are characterized by slow oscillations, consistent with no magnetic ordering. With increasing pressure, it is expected that the quadrupole splitting of the nuclear excited state should increase as inter-atom bond shortening accentuates the intra-atom electric field gradient, i.e. the rate of change of electric field at the nucleus. This effect is reflected in the SMS spectrum in the shortening of period between 8 and 13 GPa. This trend does not persist at higher pressures. At 19 GPa the period in the SMS spectrum has increased and continues to do so with pressure up to 23 GPa. At higher pressure the spectra are characterized by fast, irregular oscillations, indicative of a magnetically-ordered state coupled with thickness effects. The changes in the SMS spectrum preceding the magnetically-ordered state at 30 GPa are either indicative of a growing magnetically-ordered component, indicating a gradual transition, or some other change preceding a sharp transition. Careful fitting of the spectra is required. In Figure 3.7, SMS spectra measured in-situ in the NRIXS experiment are shown. Pressures listed are determined from the combined equation of state of (Mg0.06 Fe0.94 )O (Table 3.3) using the 30 10 3.1 3.05 3 9.5 K’0T 2.95 2.9 2.85 9 2.8 3 Volume/atom (Å ) 2.75 2.7 182 8.5 184 186 188 190 192 194 196 K0T (GPa) 8 7.5 7 6.5 0 20 40 60 Pressure (GPa) 80 100 120 Figure 3.5: Volume of (Mg0.06 Fe0.94 )O measured in the SMS experiment (black and red circles, also shown in Figure 3.4) and the thermal equation of state study in Chapter 4. Green circles are volumes of rhombohedral “quench” points after each heating cycle of (Mg0.06 Fe0.94 )O in the buffered experiments, described in Section 4.6 and summarized in Table 4.6. The black line is a Birch-Murnaghan equation of state with V0 = 9.90446 Å3 /atom (fixed), K0T = 189(4) GPa and 0 0 . = 2.9(1). Inset: 1σ error ellipse of K0T and K0T K0T d-spacings from in-situ XRD at each NRIXS pressure point (Table 3.4). Spectra were collected only over the pressure range 43-82 GPa, and all display magnetic ordering and thickness effects. As expected, there is no evidence of a spin transition in the pressure range probed by this study. 3.4.3 NRIXS: Sound Velocities NRIXS spectra were collected over the pressure range 0 to 82 GPa. Raw spectra are shown in Figure 3.8. The phonon peak around 19 meV at ambient pressure moves out to about 24 meV at 55 GPa as vibrations move to higher energy with pressure. We see the emergence of the multi-phonon contribution to the vibrational spectrum at around 80 meV, most visible in the extended energy 31 52 GPa counts 43 GPa 36 GPa 30 GPa 10000 23 GPa 19 GPa 1000 13 GPa 100 8 GPa 10 20 40 60 80 100 120 140 Time (ns) Figure 3.6: Synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K, with data binned into groups of 4. A magnetic transition occurs between 23 and 30 GPa. Pressures listed are determined from the equation of state of KCl (Dewaele et al., 2012). range of the 82 GPa pressure point. Energy scans from our NRIXS study were processed using the PHOENIX software (Sturhahn, 2000) using methods described in Sturhahn (2004). Resulting PDOSs are shown in Figure 3.9. 32 1x106 100000 Counts 10000 82 GPa 1000 64 GPa 100 55 GPa 10 43 GPa 1 0 20 40 60 80 100 120 Time (ns) Figure 3.7: In-situ synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K, with data binned into groups of 4. A magnetic transition occurs between 23 and 30 GPa. Pressures listed are determined from the combined equation of state of (Mg0.06 Fe0.94 )O, summarized in Table 3.3. The d-spacings from in-situ XRD used to calculate the pressure are listed in Table 3.4. Figure 3.10 shows, in detail, two different phonon dispersion models applied to the low-energy region of the PDOS to derive the Debye velocity using the psvl subroutine in PHOENIX. In this procedure, the PDOS is scaled according to Equation 2.1. A strict “Debye-like” region varies quadratically with energy, which would be flat in this scaling (red line, Figure 3.10). More data can be included if we don’t impose such a strict scaling, fitting instead an empirical function f (E) ≈ VD {1 − (E/E0 )2 } that projects to zero energy (blue line, Figure 3.10). In either case, the zero-energy limit of the scaled PDOS is the Debye velocity (VD ). The lower energy limit of the fitting region to obtain this intercept is limited by the successful subtraction of the elastic peak. The upper limit of the fitting region is determined both by visual inspection, the χ2 of fitting, and reasonable energy ranges where the phonons behave like an acoustic medium. Results from fitting in the psvl routine are presented in Table 3.4 and Figure 3.11. Fitting with 33 1e+09 1e+08 1e+07 counts 1e+06 1e+05 81 GPa 82 GPa 64 GPa 10000 55 GPa 1000 43 GPa 10 GPa 100 10 1 ambient 0.1 -100 -50 0 50 Energy (meV) 100 Figure 3.8: Raw NRIXS spectra of (Mg0.06 Fe0.94 )O at 300 K. Spectra are offset in the y-direction for clarity. 34 400 81 GPa D(E) 82 GPa 64 GPa 200 55 GPa 43 GPa 10 GPa 0 0 50 Energy (meV) ambient 100 Figure 3.9: Partial projected phonon density of states of (Mg0.06 Fe0.94 )O at 300 K, extracted from raw spectra using PHOENIX (Sturhahn, 2000). Spectra are offset in the y-direction for clarity. 35 3.8 57 GPa, 300 K 3.6 empirical fit 3.4 V(E) (km/s) quadratic fit 3.2 1 0.8 3 0.6 0.4 chi 2 2.8 0.2 2.6 0 5 10 15 20 25 0 Energy (meV) Figure 3.10: Debye velocity determination using the psvl subroutine in PHOENIX at 57 GPa. The PDOS is scaled according to Equation 2.1. A quadratic fit to V (E) best describes data up to 12 meV (red line). More of the PDOS can be included if an empirical function is instead used (blue line). VD is the intercept at E = 0 (red and blue circles). Open circles are the χ2 values calculated in psvl, plotted at the Emax of each calculation. 36 the quadratic requirement uses a smaller range of energy. in-situ d200 (Å) 2.480a 2.114 2.023, 2.022b 1.998, 1.995b 1.980, 1.975b 1.948, 1.946b 1.948 ρ (g/cc) 5.93(2) 6.23(3) 7.08(4) 7.36(4) 7.58(4) 7.95(3) 7.94(6) VD(normal) (km/s) 3.08(1) 2.97(2) 3.27(2) 3.40(2) 3.62(2) 3.78(2) 3.73(2) Emin − Emax(normal) (meV) 5.0 − 14.1 5.7 − 19.9 5.7 − 18.6 5.2 − 19.1 3.7 − 20.8 5.9 − 21.0 5.2 − 17.9 VD(quad) (km/s) Emax(quad) (meV) 2.94(2) 3.25(2) 3.3(2) 3.59(2) 3.69(2) 3.64(1) 10.7 10.6 12.1 10.7 10.9 9.0 Table 3.4: Debye Velocity (VD ) of (Mg0.06 Fe0.94 )O as a function of in-situ density, calculated with both the quadratic fit and normal fit. This data is shown in Figure 3.10. a This particular dspacing corresponds to the (111) reflection. b Two d-spacings correspond to before and after XRD measurements. Debye velocities of (Mg0.06 Fe0.94 )O are compared to those of (Mg0.65 Fe0.35 )O (Chen et al., 2012) and FeO (this study, Appendix A.3) in Figure 3.12. In this plot, the (Mg0.06 Fe0.94 )O and (Mg0.65 Fe0.35 )O densities were determined with in-situ XRD. The densities for FeO at low pressure was determined by volume measured with XRD at Sector 12.2.2 of the Advanced Light Source, and at high pressure by volume measured with XRD at Sector 13-ID-D, GSECARS in February 2012. Using the combined equation of state determined in Section 3.4.1, shown in Figure 3.5, we calculated pressure from our in-situ densities and the seismically relevant VP and VS from our VD . The results are summarized in Table 3.5. In Figure 3.13, we plot VP and VS as a function of pressure. For comparison, we plot the sound velocities of (Mg0.65 Fe0.35 )O, measured using NRIXS with in-situ XRD by Chen et al. (2012). At 70 GPa, (Mg0.65 Fe0.35 )O is just coming out of a spin transition, which is reflected in the low P-wave velocities. Between 100 and 140 GPa, the sound velocities of (Mg0.65 Fe0.35 )O are linear with pressure. (Mg0.65 Fe0.35 )O is more iron-rich than expected for typical lower mantle ferropericlase (Murakami et al., 2005), and could be present in in iron-enriched regions of the lower mantle. The sound velocities of (Mg0.06 Fe0.94 )O are much lower than those of (Mg0.65 Fe0.35 )O, and better able to explain ULVZs. 37 4.5 quadratic fit empirical fit VD (km/s) 4 3.5 3 2.5 5.5 6 6.5 7 7.5 8 8.5 density (g/cc) Figure 3.11: Debye velocity (VD ) of (Mg0.06 Fe0.94 )O at 300 K as a function of density. Fits in which a quadratic form of the low-energy region of the PDOS is assumed are shown in white, while a more flexible parameterization of the low-energy region results in Debye velocities shown in gray (empirical fit), as described in the text. Figure 3.10 illustrates the difference between the two fitting routines. 38 Fe1-xO (Mg0.06Fe0.94)O (Mg0.64Fe0.36)O Figure 3.12: (VD ) of (Mg0.06 Fe0.94 )O compared to FeO (Section A.3) and (Mg0.65 Fe0.35 )O (Chen et al., 2012) at 300 K, as a function of in-situ density. (Mg0.65 Fe0.35 )O and (Mg0.06 Fe0.94 )O volumes were measured in-situ at Sector 3-ID-B of the Advanced Photon Source (APS). The volumes of FeO were measured at Sector 12.2.2 of the Advanced Light Source (low density) and at Sector 13-ID-D of the APS (high density). (Mg0.16 Fe0.84 )O is not included in this figure as its volume was not measured in-situ at either Sector 3-ID-B or Sector 13-ID-D. 39 12 Mw94 Fp35 Velocity (km/s) 10 8 V P 6 4 VS 2 0 20 40 60 80 100 120 140 Pressure (GPa) Figure 3.13: Compressional (VP , red) and shear (VS , blue) wave velocities of (Mg0.06 Fe0.94 )O at 300 K, over the pressure range 0 to 82 GPa (circles). For comparison, the velocities of (Mg0.65 Fe0.35 )O are shown as light blue and red squares(Chen et al., 2012). 40 ρa,b (g/cc) 5.93(2) 6.23(3) 7.08(4) 7.36(4) 7.58(4) 7.95(3) 7.94(6) Pressurec (GPa) 0 9.61(2) 42.7(7) 55(1) 64(2) 81.6(7) 81.1(8) VD (km/s) 3.08(1) 2.97(2) 3.27(2) 3.40(2) 3.61(2) 3.78(2) 3.73(2) VP (km/s) 6.47(5) 6.63(6) 7.29(8) 7.48(8) 7.67(8) 7.89(9) 7.87(9) VS (km/s) 2.72(1) 2.62(2) 2.88(2) 3.01(2) 3.19(2) 3.34(2) 3.30(2) G (GPa) 43.9(4) 42.8(7) 58.9(8) 66.5(9) 77.0(9) 89(1) 86.5(8) K (GPa) 189(3) 216(4) 288(7) 324(8) 344(8) 377(9) 376(9) Table 3.5: Summary of sound velocities and bulk and shear moduli of (Mg0.06 Fe0.94 )O as a function of pressure. VP and VS are shown in Figure 3.13. a Number in parenthesis is the error on the last digit. b From Table 3.4. c Pressure is determined from the equation of state of (Mg0.06 Fe0.94 )O, summarized in Table 3.3.  41 Chapter 4 Thermal Equation of State of (Mg0.06Fe0.94)O 4.1 Introduction In the previous two chapters, we carried out nuclear resonant spectroscopy and X-ray diffraction on iron-rich (Mg,Fe)O at 300 K and reported properties as a function of pressure and composition. In this chapter, we explore this material in yet another dimension, temperature, measuring the equation of state of (Mg0.06 Fe0.94 )O at high pressures and temperatures. This study will allow us to explore the phase diagram and density of iron-rich (Mg,Fe)O at pressures and temperatures approaching those of Earth’s core-mantle boundary region. 4.2 Previous Studies Previous pressure-volume-temperature (P − V − T ) studies have shown that the MgO-FeO solid solution is complicated by the existence of phase transitions, a spin transition, and defect clustering as a function of FeO component. The MgO endmember is known to be cubic even beyond the pressure and temperature conditions of the earth’s mantle (Duffy and Ahrens, 1993). The FeO endmember is thought to be cubic at the pressures and temperatures of the interior of the earth, but at lower temperatures is found to transform to rhombohedral structure at moderate pressures (Shu et al., 1998a, e.g.) and then to the B8 NiAs structure at higher pressures (Fei and Mao, 1994; 42 Fischer et al., 2011b, e.g.). Iron-rich (Mg,Fe)O undergoes a cubic to rhombohedral phase transition at 8-40 GPa, with a phase transition pressure sensitive to both composition and hydrostaticity (Figure 3.1). Studies of the bulk modulus at 0 GPa as a function of composition show differing trends due to sample stoichiometry. Studies of non-stoichiometric, iron-rich (Mg,Fe)O show that both KS and KT decreases as a function of Fe concentration (Jacobsen et al., 2002; Richet et al., 1989), where KS is determined from direct measurements of volume, composition, and of VP and VS using ultrasonic interferometry, and KT is determined in a P − V compression study. The trend is opposite for stoichiometric samples, where ultrasonic interferometry studies for iron-poor samples display a positive trend of KS with increasing iron content (Jacobsen et al., 2002). In the iron endmember, KT does indeed depend on stoichiometry, with Fe0.99 O being much less compressible than Fe<0.98 O (Zhang, 2000). Thermal expansion, α = V1 ( δV δT )P has been shown to be insensitive to Fe content for Mgcontaining ferropericlase (Zhang and Kostak Jr , 2002). Yet, it appears to be sensitive to defect concentration. In the Fe end member, α is about 30% larger for Fe0.942 O than Fe0.987 O (Zhang and Zhao, 2005). In this study, we aim to measure the P − V − T equation of state (Mg0.06 Fe0.94 )O, first to constrain the thermoelasticity of iron-rich (Mg,Fe)O and second to see if these trends apply to the equation of state of iron-rich (Mg,Fe)O. 4.3 Experimental Details Two experiments were conducted in this study. For the unbuffered experiment, a symmetric diamond anvil cell with 300 µm-culet diamonds was prepared. (Mg0.06 Fe0.94 )O was lightly ground with NaCl powder (1:1 by volume) in an agate mortar under ethanol, allowed to dry, then pressed into a pellet. This mixture was loaded between two thin NaCl plates (<10 µm), and the remaining space in the rhenium gasket sample chamber was filled with neon using the COMPRES/GSECARS gas-loading system (Rivers et al., 2008). To keep the NaCl dehydrated, the pellet was consistently stored in a desiccator when not in use, and the loaded diamond anvil was placed under vacuum for about one hour and purged with argon before being put into the gas-loading system. In a second high 43 θ Figure 4.1: Example XRD spectra at 85 GPa showing peak identifications for B2-NaCl, hcp-Fe, and Ne. (Mg0.06 Fe0.94 )O is rhombohedral at room temperature (MwR , R-3m) and cubic at high temperature (MwC , Fm-3m). Pressures listed were determined by the equation of state of hcp-Fe (Dewaele et al., 2006; Murphy et al., 2011) pressure experiment, 250 µm-culet diamonds were used. Otherwise, the preparation differed in that the sample pellet also included a Fe metal (1:1 Mw94:Fe by weight) as an in-situ oxygen buffer and pressure marker. The high temperature powder diffraction experiments were conducted at the 13-ID-D beamline (GSECARS) at the Advanced Photon Source, Argonne National Laboratory. High temperatures were achieved in-situ by laser heating from both sides with a split infrared fiber laser (Prakapenka et al., 2008) with temperature determined spectroradiametrically on both up and downstream sides (e.g. Heinz and Jeanloz , 1987). Using an incident X-ray beam of λ = 0.3344 Å, angle-dispersive X-ray diffraction patterns were recorded onto a MAR165 CCD detector and subsequently integrated using Fit2D (Hammersley et al., 1996). Example spectra are shown in Figure 4.1. 44 The 2θ angles corresponding to lattice reflections of (Mg0.06 Fe0.94 )O, NaCl, Fe, and Ne were determined by fitting the spectra with Voigt peaks using Igor Pro (WaveMetrics, Lake Oswego, OR, USA). Unit cell volumes were determined using unweighted linear regression using the Unit Cell refinement software package (Holland and Redfern, 1997), which assumes a minimum uncertainty of 0.005 degrees on each lattice reflection, with errors on the unit cell weighted by goodness of fit. The B2-NaCl thermal equation of state of Fei et al. (2007b) was used to determine pressure in the unbuffered experiment, and to compare that dataset to the buffered experiment. Pressures in the second experiment were determined using the unit cell volume of hcp-iron. We used the Fe equation of state given by Dewaele et al. (2006) for the data collected at 300 K, and the quasiharmonic thermal pressure given by Murphy et al. (2011). The difference between the two pressure scales is small, with a resulting pressure increase of 0.01 to 0.4 GPa for the Murphy et al. (2011) values. To determine temperature and error of our measurements, we took the average and standard deviation of multiple temperature measurements, which are known to have a precision of 100 K (Shen et al., 2001). Errors in temperature and unit cell of NaCl and hcp-Fe were propagated into error in pressure assuming a Gaussian distribution of errors in a simple Monte Carlo error propagation. In the buffered experiment, the discrepancy between measured upstream and downstream temperatures, and the sharp diffraction peaks that show there is no temperature gradient, made it clear that we could not assume a Gaussian distribution. In order to not place undo constraints on the supposed temperature distribution, we used a flat distribution in the error propagation. Calculated volumes and pressures of the buffered dataset are presented in Table 4.1. Calculated volumes and pressures of the unbuffered dataset are presented in Table 4.2. 4.4 Results 4.4.1 Phase Identification In the P –T range of study, we identified cubic (Mg,Fe)O at high temperature and rhombohedral or a mixture of rhombohedral and cubic (Mg,Fe)O at room temperature. We interpret the mixture to be 45 Table 4.1: Pressure-volume-temperature data for the buffered experiment. a Pressure was determined by the equation of state of hcp-Fe from Dewaele et al. (2006) and Murphy et al. (2011). Pressurea (GPa) 116.5(7) 118(1) 118.0(9) 119(1) 120(2) 102.5(4) 103.0(4) 103.8(4) 104.8(6) 105.5(6) 106.4(9) 95.0(5) 95.3(7) 96(1) 97(1) 90.2(6) 90.5(6) 91.2(7) 93(1) 93(1) 93(1) 84.5(7) 84.4(8) 84.7(8) 85(1) 77.3(6) 77.5(8) 79(1) 79(1) 75.7(7) 76(1) 77(1) 77(1) 77(2) 72.4(8) 73(1) 73(1) 74(1) 75(2) 75(2) 60.1(8) 60.4(8) 61(1) 62(1) 63(1) 53.9(7) 54.2(9) 55(1) 56(1) 56(1) 57(1) 51(1) 50.0(8) 51(2) 38.4(4) 38.7(6) 39.0(7) 40(1) 40(1) 33.1(4) Temperature (K) 1056(13) 1218(85) 1295(124) 1436(191) 1649(278) 1124(29) 1212(15) 1370(36) 1563(108) 1646(109) 1852(166) 1184(61) 1296(139) 1426(193) 1620(228) 1201(111) 1303(107) 1459(130) 1707(204) 1807(246) 1917(216) 1105(119) 1162(144) 1270(152) 1379(193) 1051(64) 1135(130) 1332(193) 1460(260) 1089(145) 1169(211) 1285(247) 1356(298) 1490(346) 1119(155) 1179(211) 1268(275) 1454(277) 1626(359) 1604(350) 1131(128) 1205(156) 1364(189) 1520(265) 1671(308) 1136(100) 1205(141) 1356(247) 1466(255) 1558(291) 1631(308) 1311(245) 1177(164) 1435(328) 1324(51) 1370(76) 1416(122) 1581(246) 1643(294) 300 VolM w94 (Å3 ) 6.94(3) 6.94(2) 6.95(2) 6.95(2) 6.95(2) 7.17(1) 7.17(2) 7.19(2) 7.19(1) 7.19(2) 7.20(2) 7.26(3) 7.29(1) 7.30(2) 7.34(1) 7.40(2) 7.43(2) 7.43(3) 7.45(2) 7.45(2) 7.43(1) 7.52(3) 7.52(3) 7.52(2) 7.54(3) 7.65(2) 7.66(2) 7.66(2) 7.66(1) 7.70(1) 7.71(1) 7.72(1) 7.72(1) 7.74(1) 7.80(2) 7.81(2) 7.81(3) 7.81(2) 7.81(2) 7.81(1) 8.05(2) 8.05(2) 8.06(2) 8.06(2) 8.07(2) 8.21(1) 8.22(1) 8.22(1) 8.23(1) 8.23(1) 8.23(1) 8.33(1) 8.32(1) 8.34(1) 8.69(1) 8.69(1) 8.70(1) 8.72(1) 8.72(1) 8.58(3) VolN aCl (Å3 ) 20.10(2) 20.13(3) 20.11(2) 20.12(3) 20.11(2) 20.86(2) 20.87(2) 20.89(2) 20.89(2) 20.89(2) 20.90(2) 21.5(1) 21.45(9) 21.5(1) 21.5(1) 21.66(2) 21.68(2) 21.68(2) 21.69(2) 21.70(2) 21.71(2) 21.98(4) 22.00(3) 22.00(3) 21.98(2) 22.44(3) 22.45(3) 22.45(3) 22.47(3) 22.69(2) 22.65(2) 22.67(2) 22.66(3) 22.67(3) 23.00(3) 23.02(3) 23.05(4) 23.04(3) 23.06(2) 23.03(3) 24.02(7) 24.03(6) 24.01(4) 24.04(4) 24.06(4) 24.74(5) 24.74(6) 24.72(7) 24.76(6) 24.75(6) 24.77(7) 25.29(4) 25.27(4) 25.31(3) 27.07(7) 27.12(4) 27.11(6) 27.15(6) 27.13(7) 26.99(5) VolF e (Å3 ) 16.50(2) 16.50(2) 16.51(2) 16.53(2) 16.55(2) 16.90(1) 16.90(1) 16.92(1) 16.94(1) 16.94(1) 16.97(1) 17.13(1) 17.16(1) 17.18(1) 17.19(1) 17.29(1) 17.31(1) 17.33(1) 17.36(1) 17.37(1) 17.40(1) 17.45(1) 17.48(2) 17.50(1) 17.52(1) 17.70(2) 17.71(2) 17.73(2) 17.75(2) 17.77(1) 17.78(1) 17.79(1) 17.80(1) 17.83(1) 17.90(1) 17.91(1) 17.92(1) 17.94(1) 17.97(1) 17.97(1) 18.41(2) 18.42(2) 18.45(2) 18.47(1) 18.50(1) 18.70(3) 18.71(3) 18.72(3) 18.74(2) 18.75(2) 18.76(2) 18.94(2) 18.91(2) 18.95(2) 19.63(2) 19.63(3) 19.64(3) 19.65(3) 19.66(2) 19.50(2) 46 Table 4.2: Pressure-volume-temperature data for the unbuffered experiment. a Pressure was determined from the equation of state of B2-NaCl (Fei et al., 2007b). Pressurea (GPa) 71.5(4) 71.7(6) 72.0(5) 71.4(4) 71.7(5) 71.9(4) 70(1) 70.0(9) 70.5(7) 69.9(7) 70.1(7) 70.5(9) 67.4(9) 67.7(7) 68.0(6) 64.9(6) 67.4(6) 67.8(5) 67.9(6) 68.1(6) 63.3(3) 63.6(2) 64.1(4) 63.6(2) 63.8(3) 64.1(3) 60.5(5) 61.1(2) 61.4(3) 58.2(1) 60.9(9) 61(1) 62.1(8) 57.6(3) 58.0(5) 58.4(4) 58.3(4) 55.1(2) 57.9(4) 58.1(3) 58.4(2) 58.8(6) 55.2(2) 55.7(3) 56.2(5) 56.1(3) 56.1(4) 53.0(2) 55.9(6) 56.1(3) 56.4(3) 53.0(2) 54(2) Temperature (K) 1227(11) 1312(14) 1442(28) 1208(23) 1317(27) 1413(26) 1192(44) 1306(62) 1433(19) 1173(15) 1279(36) 1396(49) 1226(28) 1293(17) 1403(20) 300 1180(23) 1306(7) 1351(15) 1420(16) 1216(7) 1295(2) 1412(17) 1212(10) 1289(11) 1430(13) 1215(27) 1335(14) 1424(15) 300 1210(10) 1322(17) 1446(23) 1203(24) 1317(40) 1424(43) 1390(20) 300 1207(36) 1308(12) 1382(19) 1451(37) 300 1245(22) 1337(18) 1371(16) 1386(32) 300 1270(23) 1346(18) 1422(15) 300 1224(38) VolM w94 (Å3 ) 7.77(2) 7.78(2) 7.79(2) 7.77(2) 7.78(2) 7.78(2) 7.85(5) 7.84(3) 7.85(1) 7.82(3) 7.83(3) 7.85(3) 7.89(6) 7.89(5) 7.9(5) 7.77(1) 7.88(5) 7.89(5) 7.89(5) 7.9(4) 7.96(4) 7.97(4) 7.97(3) 7.95(3) 7.96(3) 7.97(3) 8.05(5) 8.05(4) 8.05(3) 7.91(3) 8.08(8) 8.04(5) 8.03(1) 8.13(4) 8.13(3) 8.13(3) 8.13(3) 7.93(6) 8.11(3) 8.12(3) 8.12(3) 8.13(3) 7.98(3) 8.18(3) 8.18(2) 8.18(2) 8.17(2) 8.02(1) 8.15(3) 8.16(3) 8.17(2) 8.03(2) 8.21(4) VolN aCl (Å3 ) 22.84(3) 22.85(5) 22.88(4) 22.85(3) 22.86(4) 22.88(4) 22.99(8) 23.00(5) 23.01(5) 22.96(6) 22.98(4) 22.99(6) 23.21(7) 23.21(6) 23.22(5) 23.06(5) 23.18(5) 23.20(5) 23.21(5) 23.22(5) 23.58(2) 23.59(2) 23.60(3) 23.55(1) 23.57(2) 23.60(3) 23.86(4) 23.86(1) 23.87(3) 23.70(1) 23.82(9) 23.84(9) 23.81(7) 24.16(3) 24.18(3) 24.19(2) 24.18(3) 24.02(2) 24.13(2) 24.16(2) 24.16(1) 24.16(5) 24.01(2) 24.39(2) 24.39(4) 24.41(3) 24.41(3) 24.24(2) 24.38(6) 24.40(2) 24.40(3) 24.24(2) 24.6(2) Pressurea (GPa) 55(1) 55(1) 56(1) 56(1) 51.9(5) 54.4(8) 54.7(6) 55.4(6) 55.3(8) 51.9(1) 47(1) 48(1) 48.2(9) 48.8(9) 44.6(7) 45(1) 46(1) 46(1) 47(1) 42.5(8) 41(1) 42.0(9) 43(1) 42.8(8) 38.9(6) 35(1) 39(1) 39(1) 39(1) 40(1) 40(1) 35.8(6) 38.4(9) 39(1) 39.7(9) 35.9(6) 31.4(6) 34.6(9) 35.0(9) 35.3(8) 35.5(7) 31.9(4) 29.8(7) 33(1) 33.6(9) 34(1) 30.1(4) 31.9(9) 32(1) 32.4(9) 32.4(7) 32.8(5) Temperature (K) 1396(42) 1579(16) 1670(24) 1731(9) 300 1140(21) 1239(6) 1437(16) 1483(53) 300 1195(20) 1398(34) 1591(24) 1760(26) 300 1248(24) 1429(15) 1613(15) 1705(35) 300 1186(32) 1387(6) 1561(33) 1584(12) 300 300 1265(35) 1398(37) 1395(23) 1562(38) 1613(28) 300 1165(51) 1436(45) 1594(17) 300 300 1207(77) 1295(68) 1384(50) 1475(25) 300 300 1224(31) 1454(41) 1630(31) 300 1235(36) 1384(65) 1526(21) 1391(60) 1510(31) VolM w94 (Å3 ) 8.22(3) 8.23(2) 8.23(1) 8.24(1) 8.09(5) 8.15(8) 8.16(6) 8.18(3) 8.22(1) 8.06(3) 8.39(4) 8.4(3) 8.41(2) 8.42(1) 8.24(3) 8.42(5) 8.42(4) 8.44(3) 8.45(2) 8.34(4) 8.55(2) 8.56(2) 8.57(2) 8.57(2) 8.4(3) 8.55(7) 8.62(4) 8.63(4) 8.63(4) 8.65(4) 8.65(4) 8.53(9) 8.6(3) 8.63(3) 8.65(4) 8.48(1) 8.63(4) 8.72(1) 8.73(1) 8.76(1) 8.77(1) 8.61(2) 8.62(11) 8.76(2) 8.79(1) 8.81(1) 8.66(4) 8.75(7) 8.78(5) 8.82(4) 8.79(4) 8.81(4) VolN aCl (Å3 ) 24.6(1) 24.6(1) 24.6(1) 24.6(1) 24.37(6) 24.49(8) 24.51(7) 24.52(6) 24.56(6) 24.37(1) 25.5(2) 25.5(1) 25.5(1) 25.51(1) 25.25(9) 25.7(2) 25.7(2) 25.8(2) 25.8(1) 25.54(1) 26.2(2) 26.3(1) 26.3(1) 26.3(1) 26.0(1) 26.7(2) 26.7(2) 26.7(2) 26.7(2) 26.8(1) 26.8(1) 26.5(1) 26.7(1) 26.7(2) 26.8(1) 26.5(1) 27.3(1) 27.4(1) 27.4(1) 27.4(1) 27.4(1) 27.19(8) 27.6(1) 27.6(2) 27.7(1) 27.8(2) 27.53(8) 27.9(2) 28.0(2) 28.0(2) 27.93(9) 27.95(8) 47 a result of incomplete back-transformation of cubic to rhombohedral phase on quench. We plot our results in Figure 4.2. Our before-heating points are shown in gray, bracketing the room temperature cubic-rhombohedral transition between 13 and 24 GPa. Representative error bars (bottom right) show the discrepancy in average standard deviation of temperature measurements between the two experiments. The phase identifications presented in Figure 4.2 are consistent with previous results in that there is no observable B8-structured (Mg0.06 Fe0.94 )O in the pressure and temperature range studied (Kondo et al., 2004). Our study, however, disagrees with the location of the rhombohedral-cubic phase boundary of iron-rich (Mg,Fe)O at high temperature. Where we find no evidence of rhombohedral (Mg0.06 Fe0.94 )O at the high temperatures explored in our study, Kondo et al. (2004) find a transition of cubic to rhombohedral (Mg0.1 Fe0.9 )O and (Mg0.05 Fe0.95 )O at 1100 to 1500 K, 70 to 100 GPa (Figure 4.2). 4.4.2 Equations of State The buffered and unbuffered datasets were fit to a 3rd-order Birch-Murnaghan equation of state using EOSFIT (Angel , 2000), with the following relations: ( P (V ) = 3K0 fE (1 + 2fE ) 1 fE = 2 " 5 2 V0 V 3 1 + (K00 − 4)fE 4 ! 23 ) (4.1) # −1 (4.2) V0 (T ) = V0 (T0 ) exp(α0 (T − T0 )) ∂K K(T ) = K0 + (T − T0 ) ∂T (4.3) ! (4.4) P where P is pressure in GPa, K0 is the bulk modulus in GPa at the reference pressure, in our case the isothermal bulk modulus at either 0 or 30 GPa, fE is Eulerian strain, V and V0 are volume and initial volume, respectively, in units of Å3 /atom. In the high temperature formulation (Equations 48 Figure 4.2: Phase identification of (Mg0.06 Fe0.94 )O in P –T space. (Mg0.06 Fe0.94 )O is cubic (unbuffered: white boxes, buffered: black boxes) at high temperature and rhombohedral (unbuffered: white diamonds, buffered: black diamonds) at room temperature, with exception of some quench measurements that contained a mixture of cubic and rhombohedral phases. Before-heating points are shown below 25 GPa in gray. Light gray lines: the latest phase diagram of wüstite (Fei and Mao, 1994; Fischer and Campbell , 2010; Fischer et al., 2011b,a; Kondo et al., 2004; Ozawa et al., 2010, 2011). Red line: rhombohedral-cubic phase boundary of (Mg0.1 Fe0.9 )O and (Mg0.05 Fe0.95 )O measured by Kondo et al. (2004). Representative error bars are also shown in the lower right corner. 49 Table 4.3: 3rd-order Birch-Murnaghan equation of state parameters for the buffered dataset using hcp-Fe as a pressure marker (Dewaele et al., 2006; Murphy et al., 2011). Reference pressure of either 0 or 30 GPa result in equivalent equations of state. P0 = 0 GPa P0 = 30 GPa 3 V0 (Å ) 9.88(9) 8.6(3) K0T (GPa) 193(14) 275(11) 0 K0T 3.0(2) 2.6(2) α0 (×10−5 K−1 ) 4.2(7) 3.2(4) ∂K/∂T (GPa/K) −0.017(6) −0.021(7) 4.3,4.4), T and T0 are temperature and reference temperature, respectively, in Kelvin, α0 is the thermal expansion coefficient, in units of K−1 , and ∂K/∂T is the isobaric temperature derivative of the bulk modulus, in units of (GPa/K). The equation of state of the buffered dataset (32 to 117 GPa) was fit using pressures given by the equation of state of hcp-Fe (Dewaele et al., 2006; Murphy et al., 2011, (Table 4.3)). The fitted V0 from our study is 9.89(7) Å3 /atom, when using hcp-Fe metal as a pressure indicator, which is consistent with our starting material volume of 9.90(1) Å3 /atom, measured on the sample outside of the diamond anvil cell, which in turn is consistent with our Mössbauer measurement + showing that Fe2 is below detection limit (< 2%). The range of fitted K0 includes that predicted for nearly stoichiometric (Mg,Fe)O (Jacobsen et al., 2002) . Figure 4.3 shows the results from this buffered experiment, showing volume as a function of pressure and temperature. Also shown are the volumes measured as we compressed the cell before the heating experiment began. We did not include these points in the fit. The steeper ∂V /∂P of these points, i.e. lower K0 , is more consistent with (Mg,Fe)O containing >2% vacancies (Zhang, 2000; Jacobsen et al., 2002). Table 4.4 shows the fitting results of both buffered and unbuffered datasets with reference pressures of either P0 = 0 GPa or P0 = 30 GPa, using pressure determined by the equation of state of B2-NaCl (Fei et al., 2007b). The limited pressure range (30 to 70 GPa) of the unbuffered dataset proved difficult to fit without external constraints, so we fixed ∂K/∂T to that of the buffered dataset. If, instead of fixing V0 of one dataset to the other, we fix K0 to 180 GPa, the predicted bulk modulus for a stoichiometric 50 10 1900 1800 9.5 1700 9 8.5 1500 1400 8 Temperature (K) Volume/atom (Å3) 1600 1300 7.5 1200 7 1100 0 20 40 60 80 Pressure (GPa) 100 120 Figure 4.3: P − V − T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the buffered experiment. Pressures were determined using the equation of state of Fe (Dewaele et al., 2006; Murphy et al., 2011). Open circles: pre-experiment volumes at pressures determined by the equation of state of B1-NaCl (JCPDS 5-0628). Table 4.4: 3rd-order Birch-Murnahan equation of state parameters the both the buffered and unbuffered dataset using B2-NaCl as a pressure marker (Fei et al., 2007b). In both cases, the ∂K/∂T of the unbuffered dataset is fixed to that of the buffered. P0 = 0 GPa P0 = 30 GPa buffered unbuffered buffered unbuffered V0 (Å3 ) 9.85(8) 9.8(1) 8.69(3) 8.64(1) K0T (GPa) 202(12) 201(24) 276(9) 283(11) 0 K0T 2.7(1) 3.0(4) 2.3(1) 2.6(5) α0 (×10−5 K−1 ) 3.3(6) 3.6(1) 2.5(4) 2.89(7) ∂K/∂T (GPa/K) −0.013(5) −0.013 (f ixed) −0.016(7) −0.016 (f ixed) 51 Table 4.5: Equation of state parameters using B2-NaCl as a pressure marker (Fei et al., 2007b), where we fix K0T to 180 GPa. buffered unbuffered 3 V0 (Å ) 10.0(3) 9.9(1) K0T (GPa) 180 (f ixed) 180 (f ixed) 0 K0T 2.95(7) 3.29(6) α0 (×10−5 K−1 ) 3.0(7) 3.41(7) ∂K/∂T (GPa/K) −0.010(5) −0.010 (f ixed) magnesiowüstite (Jacobsen et al., 2002), we again get equation of state parameters that yield values consistent with our previous fits (Table 4.5). Figure 4.4 shows the results from the unbuffered experiment, showing volume change of (Mg0.06 Fe0.94 )O as a function of pressure and temperature, using NaCl as a pressure marker (Fei et al., 2007b). 4.5 Discussion 4.5.1 Effect of Buffering on Equation of State In Figure 4.5, we compare the first dataset to the second, showing example volumes and isotherms at 1200, 1500, and 1800 K. At 50 GPa, the calculated thermal expansion coefficients are αbuf f ered = 2.1(6) × 10−5 K−1 and αunbuf f ered = 2.6(1) × 10−5 K−1 . We first note that the sole room temperature quench point of the buffered dataset is consistent with the unbuffered dataset (Figure 4.5, black filled circle and squares), and the room temperature equations of state are consistent (Table 4.4). The initial thermal expansion coefficient (α0 ) of the two datasets are also consistent within error. The discrepancy between un-annealed (before heating) low pressure and annealed (heated) high pressure measurements suggests a physical difference between cold-compressed and annealed ironrich (Mg,Fe)O even without an Fe metal buffer. It has been proposed that vacancy concentrations in non-stoichiometric FeO-bearing samples are reduced with the exsolution of (Fe,Mg)Fe2 O4 at high pressure and temperature according to (M gx F ey )O → a(M gx0 F e1−x0 )F e2 O4 + b(M gx00 F ey00 )O (4.5) 52 9 1700 8.8 1600 3 1500 8.4 1400 8.2 8 Temperature (K) Volume/atom (Å ) 8.6 1300 7.8 1200 7.6 20 30 40 50 Pressure (GPa) 60 70 80 Figure 4.4: P − V − T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the unbuffered experiment with ∂K/∂T fixed to that of the buffered experiment. Equation of state parameters corresponding to these curves are those in Table 4.4. 53 8.9 Mw94 (buffered) Mw94 (unbuffered) 1900 1800 8.8 1700 8.7 3 Volume/atom (Å ) 1600 8.6 1500 8.5 1400 1300 8.4 1200 8.3 1100 8.2 30 35 40 Pressure (GPa) 45 50 Figure 4.5: Overlay of data and equations of state of (Mg0.06 Fe0.94 )O in both experiments. The unbuffered (squares, solid lines) and buffered (circles, dashed lines) datasets are in good agreement where they overlap in pressure-temperature conditions. 54 Mw94 (this study) FeO (Fischer et al., 2011) 2100 2000 7.2 1900 7.15 7.1 1700 1600 7.05 1500 Temperature (K) Volume/atom (Å3) 1800 7 1400 6.95 1300 1200 6.9 1100 6.85 100 105 110 115 Pressure (GPa) 120 Figure 4.6: Comparison of volume measurements and equations of state of buffered (Mg0.06 Fe0.94 )O (circles, solid lines) to B1-FeO (squares, dashed lines) (Fischer et al., 2011b). where (x00 + y 00 ) > (x + y), ensuring the stoichiometry of the (Mg,Fe)O phase regardless of oxygen fugacity (Zhang and Zhao, 2005; McCammon et al., 1998). If this were true in our case, it would also explain the similarity between the buffered and unbuffered datasets at high pressure and temperature. 4.5.2 Effect of Composition on the Thermal Equation of State of (Mg,Fe)O In Figure 4.6, we compare (Mg0.06 Fe0.94 )O to the equation of state and volumes of FeO (Fischer et al., 2011b) to determine the effect of incorporation of Mg on the equation of state FeO. Both experiments were conducted with in-situ Fe metal buffer/pressure marker. At our highest pressure, 117 GPa, we were not able to discern a difference between the thermal expansion of Mw94 and FeO (α(M g0.06 F e0.94 )O = 1.5(7) × 10−5 K−1 and αF eO ≈ 1.4(1) × 10−5 K−1 ). 55 FeO (Fischer et al., 2011) (Mg0.06Fe0.94)O (this study) 6 (Mg Fe 0.64 )O (van Westrenen et al., 2005) 0.36 MgO (Dubrovinsky et al., 1997) _ (x10−5 K−1) 5 4 3 2 1 1900 K 0 20 40 60 80 100 120 Pressure (GPa) Figure 4.7: Thermal expansion at 1900 K as a function of pressure (Table 4.3), compared to FeO (Fischer et al., 2011b), (Mg0.64 Fe0.36 )O (Westrenen et al., 2005), and MgO (Dubrovinsky and Saxena, 1997). Dashed lines show areas of extrapolated curves, and error bars shown are the 1σ error in thermal expansion coefficient. In Figure 4.7, we plot the thermal expansion of different members of the (Mg,Fe)O solid solution as a function of pressure, at 1900 K. At ambient pressure, the thermal expansion of MgO, (Mg0.64 Fe0.36 )O, and FeO vary as a function of composition. Within our experimental uncertainties, we cannot resolve a compositional effect on the thermal expansion of (Mg,Fe)O at high pressures. Given the different experimental conditions of our buffered and unbuffered datasets, Fe/Mg compositional variation may also be a concern. It is imaginable that buffering with Fe metal could lead to a different Fe/Mg ratio in the (Mg,Fe)O than the mechanism in Equation 4.5 would. However, given that we cannot distinguish (Mg0.06 Fe0.94 )O from FeO, if our buffered (Mg0.06 Fe0.94 )O were slightly enriched in Fe compared to the unbuffered (Mg0.06 Fe0.94 )O, we would not know how to distinguish the two without sample recovery. 56 4.6 Rhombohedral Distortion of (Mg0.06 Fe0.94 )O Volumes and lattice parameters of rhombohedral-structured (Mg0.06 Fe0.94 )O were fit using methods described above. As depicted in Figure 4.2, rhombohedral (Mg0.06 Fe0.94 )O was stable at room temperature at pressures higher than 20 GPa. In the unbuffered experiment, room temperature patterns revealed a mixture of rhombohedral and cubic phases, while in the buffered experiment, only rhombohedrally-structured (Mg,Fe)O was present higher than 34 GPa. Figure 4.8 shows the evolution of the lattice reflections of (Mg0.06 Fe0.94 )O. Before-heating points, shown in gray, show the cubic (111), (200) and (220) reflections that split accordingly: (111)C → (003)R +(101)R and (220)C → (104)R +(110)R . These five reflections were used to refine the unit cell volume. Black circles show measurements of the buffered dataset, and are less scattered than the white circles. Pressure was determined using the (111) and (200) reflections of solid neon (Dewaele et al., 2008) or by the (100), (200), (101), (102), (110), (103), and (112) reflections of hcp-iron (Dewaele et al., 2006). Despite the obvious mismatch between the two datasets in the (003) reflection below 47 GPa, the two datasets appear to agree within scatter above 47 GPa. This observation is more apparent in Figure 4.9, which shows the c/a ratio of the hexagonal unit cell for each measurement. Above 55 GPa, the c/a ratios of the two datasets are indistinguishable. Another observation we note here is the leveling off of the distortion, apparently starting at 70 GPa. This dataset shown in Figure 4.10, combined with the low-pressure measurements taken at Sector 3-ID-B (Section 3.4.1), was used to constrain the equation of state of (Mg0.06 Fe0.94 )O at 300 K for use in determining the pressure and sound velocities from NRIXS data (see 3.4.1). 57 1#0#1#before#hea6ng# 2.6# 0#0#3#before#hea6ng# 1#0#1#unbuffered# 1#0#1#buffered# 2.5# "0#0#3#unbuffered# (1#1#1)C# 0#0#3#buffered# (0#0#3)R# d-spacing (Å)! 2.4# 2.3# 2.2# (1#0#1)R# 2.1# 2# 0# 20# 40# 60# 80# 100# 120# Pressure (GPa)! 2.2# "unbuffered#dac#9"# 2.15# "buffered1# (2#0#0)C# d-spacing (Å) ! 2.1# "before#hea<ng"# 2.05# 2# (0#1#2)R# 1.95# 1.9# 1.85# 0# 20# 40# 60# 80# 100# 120# Pressure (GPa)! 1.55# 1#0#4#unbuffered# 1#0#4#buffered# 1#1#0#unbuffered# 1#1#0#buffered# 1#1#0#before#hea:ng# 1#0#4#before#hea:ng# (2#2#0)C# 1.5# d-spacing (Å)! 1.45# (1#0#4)R# 1.4# 1.35# (1#1#0)R# 1.3# 1.25# 0# 20# 40# 60# 80# 100# 120# Pressure (GPa)! Figure 4.8: Evolution of d-spacings of (Mg0.06 Fe0.94 )O as a function of pressure. Gray circles: before heating experiment began. White circles: unbuffered dataset. Black circles: buffered dataset. Pressure was determined from the unit cell of neon (Dewaele et al., 2008). 58 2.69% Fe.93O (Jacobsen et al., 2005)! c/a ratio! 2.64% 2.59% Mw78 (Zhuravlev et al. 2010)! 2.54% 2.49% unbuffered! cubic% buffered! 2.44% 0% 20% 40% 60% 80% 100% 120% Pressure (GPa)! Figure 4.9: Evolution of c/a ratios of rhombohedral (Mg0.06 Fe0.94 )O as a function of pressure at 300 K. White circles: unbuffered dataset. Black circles: buffered dataset. Pressure was determined from the unit cell of neon (Dewaele et al., 2008). Error bars are determined from the unit cell refinement. 59 10 300 K, rhombohedral 9.5 Volume/atom (A3) 9 o 8.5 8 7.5 7 6.5 0 20 40 60 80 100 120 Pressure (GPa) Figure 4.10: Pressure-volume data of quenched, rhombohedral (Mg0.06 Fe0.94 )O at 300 K, with pressure determined either by hcp-Fe (Dewaele et al., 2006, gray squares) or Ne (Dewaele et al., 2012, blue circles). Quench points are those after each heating cycle. Black line is a 3rd-order Vinet equation of state fit to the data using pressure determined from the equation of state of neon, where 0 V0 = 9.65(7) Å3 /atom, K0T = 281(22) GPa, and K0T = 0.6(4). 60 Table 4.6: Pressure-volume data for the buffered experiment at 300 K. a Pressure was determined from the equation of state of hcp-Fe (Dewaele et al., 2006). b Pressure was determined from the equation of state of Ne (Dewaele et al., 2008). c Volumes of hcp-Fe were refined using 7 reflections: (100),(200), (101), (102), (110), (103), and (112). d Volumes of Ne were determined using 2 to 3 reflections of (111), (200), and (220). e Measurements after each heating cycle is referred to in the text as “quench” points. PF e a (GPa) 112.8(8) 112.9(6)e 98.3(5) 98.7(4)e 89.5(9) 90.4(4)e 85.1(3) 85.8(2)e 80.5(4) 80.8(3)e 74.0(4) 74.7(4)e 71.3(3) 71.6(4)e 67.9(7) 68.3(4)e 55.4(6) 55(1)e 48.6(6) 49.1(8)e 48.3(7) 45.6(4)e 38(1) 39(1)e 33(1) 33.1(4)e PN e b (GPa) 113(1) 113.3(9) 98(2) 98(3) 90(2) 92(1) 86(1) 86(2) 82(1) 81(1) 75(1) 75.8(6) 73(1) 73.3(6) 68(1) 68(1) 58(1) 57(1) 50.1(3) 51.5(2) 46.5(3) 46.8(3) 39(1) 40(1) 34(2) 33(2) V olF e c Å3 16.45(2) 16.45(1) 16.84(2) 16.83(1) 17.10(3) 17.08(1) 17.24(1) 17.218(8) 17.39(1) 17.38(1) 17.62(2) 17.59(1) 17.71(1) 17.70(1) 17.84(3) 17.83(2) 18.35(3) 18.38(5) 18.66(3) 18.64(4) 18.68(4) 18.81(2) 19.23(4) 19.15(2) 19.52(3) 19.50(2) V olN e d Å3 25.39(7) 25.36(5) 26.4(2) 26.4(2) 26.9(1) 26.8(1) 27.3(1) 27.2(1) 27.66(9) 27.7(1) 28.3(1) 28.21(6) 28.5(1) 28.45(6) 29.0(1) 29.0(1) 30.2(1) 30.3(1) 31.35(5) 31.12(3) 31.93(5) 31.89(5) 33.3(3) 33.2(2) 34.5(4) 34.7(5) V olM w Å3 /atom 6.84(1) 6.81(5) 7.10(5) 7.04(4) 7.20(7) 7.20(6) 7.31(5) 7.30(6) 7.41(5) 7.39(4) 7.56(3) 7.56(3) 7.63(3) 7.62(3) 7.78(4) 7.73(3) 8.08(3) 7.94(2) 8.18(6) 8.11(2) 8.22(3) 8.17(6) 8.47(4) 8.42(1) 8.55(4) 8.58(3) aM w Å 2.612(7) 2.60(1) 2.64(1) 2.65(1) 2.66(1) 2.66(1) 2.672(9) 2.67(2) 2.683(8) 2.683(8) 2.703(5) 2.704(6) 2.712(8) 2.71(1) 2.731(7) 2.727(5) 2.777(6) 2.751(3) 2.78(1) 2.781(4) 2.800(6) 2.79(1) 2.825(7) 2.819(2) 2.845(6) 2.846(5) cM w Å 6.90(3) 6.87(5) 6.99(5) 6.98(5) 7.05(5) 7.04(4) 7.09(4) 7.08(6) 7.13(3) 7.12(3) 7.17(2) 7.16(2) 7.18(1) 7.18(2) 7.22(2) 7.20(2) 7.26(2) 7.27(1) 7.32(3) 7.26(1) 7.27(2) 7.27(3) 7.35(3) 7.34(1) 7.32(2) 7.34(2) V olN aCl Å3 20.10(4) 20.05(4) 20.84(2) 20.78(2) 21.42(9) 21.24(2) 21.62(3) 21.53(2) 21.92(3) 21.88(3) 22.39(3) 22.31(2) 22.62(2) 22.57(2) 22.99(4) 22.87(2) 23.9(1) 23.88(4) 24.70(5) 24.58(3) 25.15(2) 25.12(2) 26.27(6) 26.13(2) 26.8(1) 26.99(5)  61 Chapter 5 Implications for Ultralow-velocity Zones 5.1 Physical Mixing Models To explore the expected sound velocities and density of an ultralow-velocity zone containing iron-rich (Mg,Fe)O, we can construct simple models that combine the properties of iron-rich (Mg,Fe)O and mantle silicates. We show that a small amount of iron-rich (Mg,Fe)O can greatly reduce the average sound velocity of an aggregate assemblage. When combined with a geodynamic model of a solid ULVZ (Bower et al., 2011), we can directly correlate inferred sound velocities to mineralogy and predicted ULVZ shapes. Our combined geodynamic and mineral physics model of a solid ULVZ can be used to explore the relationship between the observed sound velocities and mineralogy of ULVZs with added insight into ULVZ morphology. 5.1.1 Extrapolation of Magnesiowüstite properties to the CMB Re-evaluation of sound velocities of (Mg.16 Fe.84 )O occurred after publication, which was presented unaltered in Chapter 2. Updates include a re-analysis of the sample, finding the composition to be (Mg0.18 Fe0.78 Ti0.04 )O. In addition, we assume that equation of state of (Mg.16 Fe.84 )O can be approximated by that of (Mg.06 Fe.94 )O, rather than that of (Mg.12 Fe.78 )O. This equation of state choice should be more self-consistent, as both samples were made in the exact same way. Updated Debye velocities of (Mg.16 Fe.84 )O are shown in Figure 5.1, underlying those of (Mg.06 Fe.94 )O and 62 FeO presented in Chapter 3. Mw94 Mw84 FeO 4.5 VD (km/s) 4 3.5 3 5.5 6 6.5 7 7.5 8 8.5 9 density (g/cc) Figure 5.1: Debye velocity as a function of density of (Mg.16 Fe.84 )O, (Mg.06 Fe.94 )O, and FeO. (Mg0.06 Fe0.94 )O volumes were measured in-situ at Sector 3-ID-B of the Advanced Photon Source (APS). The volumes of FeO were measured at Sector 12.2.2 of the Advanced Light Source (low density) and at Sector 13-ID-D of the APS (high density). The volumes of (Mg0.16 Fe0.84 )O above ambient pressure were not measured, but estimated using ruby pressure, initial volume measured 0 = at the ALS, and the equation of state parameters (Mg.06 Fe.94 )O: of K0T = 189(4) GPa and K0T 2.9(1). Figure updated from Figure 3.12 to include recalculated (Mg.16 Fe.84 )O. The Debye velocities in Figure 5.1 exhibit a linear increase as a function of density above 6.5 g/cc, independent of composition. As the highest density of (Mg.16 Fe.84 )O at 8.7 g/cc corresponds to a pressure of 121 GPa, we extrapolate that this linear trend is valid up to the core-mantle boundary pressure of 135 GPa. In the latest formulation of the mixing model, presented below, the Debye sound velocities of (Mg.06 Fe.94 )O are linearly extrapolated to 135 GPa. This choice is made for self-consistency reasons, as it is the only dataset with in-situ volumes mapped directly onto its own equation of state. Here we assert that the Debye sound velocity as a function of density of (Mg.16 Fe.84 )O is the same as that of (Mg.06 Fe.94 )O, since we cannot discern a difference. This assumption, however, introduces a slight inconsistency in the parameterization of Debye velocity with other compositions, which will 63 have to be worked out before this model can be published. Namely, this simple extrapolation to the CMB gives a (Mg.16 Fe.84 )O density of 8.63 g/cc, which is lower than the highest density plotted in Figure 5.1. We estimate the sound velocities of (Mg.16 Fe.84 )O at high temperature by using the temperature derivatives ∂VP /∂T = −4.64×10−4 (km s−1 K−1 ) and ∂VS /∂T = −3.85×10−4 (km s−1 K−1 ), measured for MgO up to 20 GPa and 1650 K (Kono et al., 2010). Density is adjusted for high temperature using the equation of state we measured on buffered (Mg.06 Fe.94 )O (Chapter 4, Table 4.3). 5.1.2 Mixture of Magnesiowüstite and Ambient Mantle One such model represents a mixture of iron-rich (Mg,Fe)O and ambient mantle, and is hereafter referred to as “Mw+PREM”. Prior versions of this model were published in Wicks et al. (2010) (Chapter 2) and updated in Bower et al. (2011), and mixes iron-rich oxide with surrounding lower mantle represented by the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson, 1981). This binary mixture can be thought of as a disequilibrium assemblage of lower mantle material mixed with iron-rich oxide. Considering a physical mixing scenario in which an iron-rich oxide is combined with ambient mantle has two advantages. First, it is generally accepted that a large fraction of the lower mantle is made up of silicate perovskite, due to the fact that the expected sound velocities and density of perovskite largely agree with PREM. Using the seismic velocities and densities of PREM, therefore, should be a good approximation to using sound velocities and densities of perovskite, although it likely represents a mixture of phases. Second, without knowing the mechanism by which a ULVZ is formed, it is conceivable that a ULVZ can simply be a mixture of lower mantle and core material. There is increasing evidence for complexity on the core side of the core-mantle boundary which could be an expression of exsolved “sediments” on the top of the core (Buffett et al., 2000). Therefore, a ULVZ could simply be ambient mantle mixed with FeO, which is what this mixing model represents. We then calculate the Voigt and Reuss bounds for VP , VS , and density (Watt et al., 1976) for a 64 Table 5.1: Model parameters for mixing model “Mw+PREM” VP (km/s) VS (km/s) density (g/cc) PREM 13.714 7.2648 5.5613 Mw84 (2700 K) 7.3014 2.705 8.3001 Mw84 (4700 K) 6.3734 1.935 8.2288 given vol% of (Mg.16 Fe.84 )O and PREM at 135 GPa, choosing a low (2700 K) and high (4700 K) temperature estimates of the core-mantle boundary (Figure 5.2). Model parameters are listed in Table ??. Voigt (uniform stress) and Reuss (uniform strain) bounds bracket the upper and lower bounds of mixing of the bulk modulus K, shear modulus G and density ρ, from which we calculate VP and VS using Equation 2.2 and G = ρVS2 . ULVZ VP 12 8.5 27 8 -20% 00 K 47 10 00 K 7.5 VP 8 VP 4 700 270 0K K -10% 6 ULVZ VS Density (g/cc) Velocity (km/s) mw+PREM -5% mw+PREM 14 7 6.5 -30% +10% VS 2 4 6 700 +5% K VS 4700 K 5.5 2 0 0.2 0.4 0.6 volume fraction (Mg.16Fe.84)O 0.8 ULVZ - 1 0 0.2 0.4 0.6 0.8 1 volume fraction (Mg.16Fe.84)O Figure 5.2: Voigt (upper)-Reuss (lower) bounds of VP , VS (left), and density (right) of (Mg.16 Fe.84 )O with PREM at 135 GPa. Gray shading shows typical ULVZ velocities (-5-20% VP , -10-30 %VS , with respect to surrounding mantle) reported by seismology. Density is not very well constrained by seismology, but have been quoted at +8-10% (Rost et al., 2006; Idehara et al., 2007, e.g.). Dynamic models such as those by McNamara et al. (2010) predict ULVZs with densities of at least +5% with respect to surrounding mantle, yet models by Bower et al. (2011) create reasonable ULVZs corresponding to less than 5% density increase. To first order, mixing of just 20 vol% of (Mg.16 Fe.84 )O with 80 vol% silicates (represented here by PREM) matches signature seismic observations for the ULVZ (Figure 5.2). 5.1.3 Mixture of Magnesiowüstite and Silicate Perovskite A second mixing model, a prior version of which is published in Bower et al. (2011), again starts with the assumption that iron-rich oxide is present in a ULVZ and explores a possible equilibrium 65 assemblage of iron-rich (Mg,Fe)O and perovskite. Hereafter we refer to it as “Mw+Pv”. The partitioning behavior of Fe vs. Mg between the two phases has been probed at lower mantle pressures by numerous studies without much agreement, but recent studies show a preferential P v/M w partitioning of Fe into the oxide phase, which we adopt: KD ≈ 0.07 (Auzende et al., 2008; Sakai et al., 2009; Sinmyo et al., 2008), assuming an aluminum-free system. In addition to representing the P v/M w simple phase assemblage that we model in this mixture, a low KD is required by this exercise in order to achieve reasonable densities for appropriate velocity decrements. In other words, too much iron in perovskite would create ULVZs denser than those consistent with observed heights, with velocities that are not low enough. P v/M w Other studies find the partitioning behavior to be less extreme, determining KD P v/M w an assumed “pyrolite” mantle composition, or KD ≈ 0.42 for ≈ 1.11 in the presence of post-perovskite (Sinmyo et al., 2011). Partitioning behavior is known to be a function of composition, pressure, and the presence of post-perovskite, but with opposite conclusions between even the most recent studies, P v/M w KD is still an uncertainty (Sinmyo et al., 2011; Catalli et al., 2009). If we assert that (Mg.16 Fe.84 )O exists at the core-mantle boundary, a coexisting perovskite in P v/M w equilibrium would have the composition (Mg.72 Fe.28 )SiO3 , using KD ≈ 0.07 (Sakai et al., 2009; Auzende et al., 2008). This resulting assemblage is very Fe-rich, and would require a formation mechanism capable of making such an exotic composition. We model the densities and sound velocities of perovskite using a finite-strain model given by Li and Zhang (2005), making a compositional correction to the density. Bulk and shear moduli have also been predicted to be compositionallydependent (Kiefer et al., 2002), but we found the resulting differences to be negligible (Bower et al., 2011). We calculate the Voigt and Reuss bounds for VP , VS and density for a given vol% of (Mg.16 Fe.84 )O and (Mg.72 Fe.28 )SiO3 perovskite at 135 GPa and 2700 and 4700 K (Figure 5.3). The resulting mixing model is presented in Figure 5.3. Here, at X(M g,F e)O = 0, we see the temperature dependence of the modeled perovskite in both velocities and densities of the silicate fraction. The range of expected perovskite velocity at the two extreme temperature estimates is 66 Table 5.2: Model parameters for mixing model “Mw+Pv” VP (km/s) VS (km/s) density (g/cc) Pv (2700 K) 14.013 7.4287 5.7157 Pv (4700 K) 13.57 6.9129 5.4935 Mw84 (2700 K) 7.3014 2.705 8.3001 Mw84 (4700 K) 6.3734 1.935 8.2288 much larger than the difference between perovskite and PREM, which falls between the two. We conclude that the choice of silicate model (PREM vs (Mg,Fe)SiO3 ) then is not distinguishable given the uncertainty in temperature of the CMB region. 8.5 27 8 ULVZ VP 12 mw+Pv -5% mw+Pv 14 K 47 -20% 00 K 7.5 10 VP 8 VP 4 700 27 00 K K -10% 6 ULVZ VS Density (g/cc) Velocity (km/s) 00 7 6.5 -30% +10% 4 VS 2 VS 4700 2 0 0.2 0.4 0.6 0.8 6 700 ULVZ + +5% K K 5.5 1 volume fraction (Mg.16Fe.84)O 0 0.2 0.4 0.6 0.8 1 volume fraction (Mg.16Fe.84)O Figure 5.3: Voigt (upper)-Reuss (lower) bounds of VP , VS (left), and density (right) of (Mg.16 Fe.84 )O with (Mg,Fe)-perovskite. Gray shading same as in Figure 5.2 In both this model and in Mw+PREM, we find that only about 20% iron-rich magnesiowüstite is needed to drop the sound velocities of an assemblage. The density of perovskite is higher than PREM at 2700, but lower at 4700, so the density of Mw+Pv is greatly affected by temperature choice. As a result, the amount of Mw85 needed to match reported densities according to seismic studies jumps from 15% at 2700 K to 25% at 4700 K. 5.1.4 Dynamics of a Solid-state ULVZ The mixing models described above show that ULVZ velocities and densities can be adequately represented by a mixture of iron-rich (Mg,Fe)O and perovskite or silicate-rich surrounding mantle. We can take this model one step further by interpreting these models in the context of dynamic 67 models (Bower et al., 2011, specifically). We explored the morphologies of solid-state ULVZs in a two-dimensional dynamic model, solving the steady-state thickness and shape of ULVZs as a function of prescribed initial thickness and chemical vs. thermal buoyancy (Bower et al., 2011). By exploring a range of thicknesses and buoyancy numbers B, this study creates a range of candidate ULVZ sizes and shapes that can be mapped to mineral physics models via density and assumed temperature drop across the core-mantle ∆ρch Rb thermal boundary layer, according to the definition of buoyancy number: B = Ra = ρα∆T , where Rb Ra is the ratio of chemical to thermal Rayleigh numbers, ∆ρch is the chemical density anomaly of the ULVZ layer, ρ and α are density and thermal expansion of the mantle, and ∆T is the temperature drop across the CMB. More detailed descriptions of the dynamic models are found in Bower et al. (2011). Taking the density calculations of the two mixing models, and assuming a lower bound of ∆TCM B of 500 K and an upper bound of ∆TCM B =1500 K across the thermal boundary layer just above the core-mantle boundary, the range of dynamic models of Bower et al. (2011) map to volume fractions of ∼ 0.01 − 0.26 of (Mg.16 Fe.84 )O for the Mw+PREM model, and ∼ 0.03 − 0.29 for the Mw+Pv model. These models introduce a new kind of constraint: a much smaller density contrast, and therefore smaller amount of iron-rich (Mg,Fe)O, creates shapes with larger aspect ratios (height/width), whereas a larger density contrast and more iron-rich (Mg,Fe)O generally creates ULVZs that are flat yet wide. A seismic study that constrains the width and size of ULVZs now has a way to constrain density, assuming a solid mixed component. A recent review of the core mantle boundary suggests that a CMB temperature of ∼ 4000 K and a temperature drop across the CMB thermal boundary layer of ∼1200-1800K (Tackley, 2012) best satisfies combined seismological and mineral physics constraints.Our mixing models, then, can be recalculated at a CMB temperature of 4000 K and ∆TCM B of 1500 K to predict ULVZ morphologies. We plot the Voigt-Reuss-Hill curves in Figure 5.4. It’s important to note that the assumptions we made in these models can be revised as more is learned about the temperature and mineralogy of Earth’s core-mantle boundary. The high-iron 68 Table 5.3: Model parameters for mixing model “Mw+PREM” and “Mw+Pv” at 4000 K VP (km/s) VS (km/s) density (g/cc) PREM 13.714 7.2648 5.5613 Pv (4000 K) 13.712 7.0886 5.5795 Mw84 (4000 K) 6.6982 2.2045 8.23 Figure 5.4: Voigt-Reuss-Hill curves of VP and VS of the mixing of (Mg.16 Fe.84 )O with PREM (left) and (Mg,Fe)SiO3 -perovskite (right), at TCM B = 4000 K. Assuming an average temperature drop across the CMB thermal boundary layer of ∆TCM B = 1500K (Tackley, 2012), ULVZs with moderate velocity drops are consistent with 5% (Mg,Fe)O, and are consistent with smaller structures with high aspect ratio from Bower et al. (2011). ULVZs with larger velocity drops are consistent with ∼ 20% (Mg,Fe)O, and are consistent with wider, flatter structures. At a CMB temperature of 4000 K, the ULVZ shapes predicted by PREM vs perovskite are indistinguishable (left and right panels, respectively). content of a (Mg,Fe)O+Pv assemblage is too dense to explain ULVZs at cool temperatures, but adequately explains ULVZs at high temperatures (Bower et al., 2011). Knowing both the absolute temperature and the temperature drop across the thermal boundary layer would allow us to compare different scenarios as a function of density. Further studies on the mineral properties of mantle phases at high temperature are also required. One example is the extrapolation of sound velocities with temperature. Very few studies exist that measure the velocity derivatives of MgO at high temperature, and none exist in the ironbearing system. The velocity derivatives we used, measured up to 20 GPa and 1650 K, ∂VP /∂T = −4.64×10−4 (km s−1 K−1 ) and ∂VS /∂T = −3.85×10−4 (km s−1 K−1 ) (Kono et al., 2010), are slightly lower than those measured on MgO at room pressure, ∂VP /∂T = −6×10−4 (km s−1 K−1 ) and ∂VS /∂T = −5×10−4 (km s−1 K−1 ) (Sinogeikin et al., 2000). Applying these velocity derivatives at 69 121 GPa is likely overestimating the velocity drop with temperature. The effect of applying these velocity derivatives to iron-rich (Mg,Fe)O rather than MgO is unknown. 5.2 Conclusions In this work, we have experimentally determined the room temperature sound velocities of (Mg0.16 Fe0.84 )O and (Mg0.06 Fe0.94 )O as a function of pressure up to 121 GPa. We found that the trend in sound velocities was very strongly affected by magnetic transitions: by monitoring the magnetic state using synchrotron Mössbauer spectroscopy, we identified softening in the shear elastic properties of iron-rich (Mg,Fe)O preceding a magnetic transition. We have also presented the pressure-volume-temperature equation of state of (Mg0.06 Fe0.94 )O up to 115 GPa and 1900 K, measured both with and without an in-situ Fe buffer, and showed that we could not conclusively distinguish the two equations of state. This result is consistent with other studies of the (Mg,Fe)O solid solution that propose pressure-induced exsolution of Fe3+ , essentially “self-buffering” (Zhang and Zhao, 2005; McCammon et al., 1998). This result is important for practical reasons, as future high-temperature NRIXS studies will not need to have an in-situ buffer. The work we have completed forms the foundation for future experiments at high temperature. The room temperature sound velocities as a function of pressure form the reference curve for high temperature comparison, and the equation of state as a function of pressure and temperature is required to determined in-situ pressure of a high temperature velocity measurement. We combined the sound velocities and P -V -T equation of state to predict the properties of ironrich (Mg,Fe)O at high temperature, and made mixing models to predict the properties of example phase assemblages. Our overall conclusion, with different choices of mixing model, stayed the same: mixing small amounts of iron-rich (Mg,Fe)O with mantle silicate reproduces the characteristic sound velocities and shapes of ultralow-velocity zones.  82 Appendix A A.1 Synthesis and Characterization A.1.1 (Mg0.16 Fe0.84 )O MgO was dried at 1100◦ C overnight, then stoichiometrically combined with 95% enriched 57 Fe2 O3 (Advanced Materials Techonologies Ltd.) to produce an Fe/(Mg+Fe) ratio of 0.85. After being ground in an agate mortar, the oxide mixture was pressed into a pellet and reduced to form + (Mg,Fe2 )O in a gas-mixing 1 atm furnace. The pellet was equilibrated at 1400◦ C for two runs of 20 hours each just above the iron-wüstite fugacity buffer (an oxygen potential of 10−9.6 atm). Sample composition and homogeneity were measured using a JEOL JXA-8200 electron microprobe (Mg.158(2) Fe.842(2) )O, where the number in parentheses is the error on the last digit and the oxygen is assumed to be stoichiometric. Ambient pressure unit cell volume was measured with X-ray diffraction (9.79(4) Å/atom), resulting in a density determination of 5.69(7) g/cm3 . The magnetic signature of iron in our sample was determined by Mössbauer analysis at ambient pressure (Figure 2.6). The absence of a magnetically ordered component indicates that our sample is free of metallic iron and magnetite. Although the black color of the sample indicates that there may be trace amounts of trivalent iron, its concentration is below detection limits of Mössbauer (less than 3%). This will translate to vacancy concentrations of 0-3%, which we include in the density error bar. In June 2012, a re-measurement of the sample composition revealed the presence of Ti contamination in the sample, previously missed. A revised chemical formula is (Mg0.18 Fe0.78 Ti0.04 )O, which would correspond to a revised density of 5.7(1) g/cm3 . With likely errors on each subscript to be 83 0.01, a more thorough analysis is required to reduce the error bars. A.1.2 (Mg0.06 Fe0.94 )O (Mg0.06 Fe0.94 )O was synthesized by the same methods as above, using 57 Fe metal from Isoflex. Microprobe analysis of the synthesized material gives a sample composition of (Mg.0580(9) Fe.9420(9) Si.0021(9) )O, assuming that the oxygen is stoichiometric. A conventional Mössbauer spectrum (Figure 2.3) taken of the synthesized sample is consistent with divalent iron, and shows no indication of Fe3+ . A secondary electron image (Figure A.1) taken of the sample before microprobe analysis shows no indication of compositional heterogeneities. Figure A.1: Secondary electron image of (Mg0.06 Fe0.94 )O. A.1.3 Fe1−x O Fe1−x O was synthesized in March 2011 using the methods above, at 1300◦ C, a lower temperature to account for the melting point of FeO of 1395◦ C. The synthesis was carried out twice, using both the 57 Fe2 O3 source and the 57 Fe metal source, as it had been determined that the 57 Fe2 O3 source was contaminated with Ti. The aim of synthesizing with and without Ti was to determine whether or not the vibrational spectra and subsequent sound velocities were affected by the presence of minor Ti. Room pressure lattice parameter and density are listed in Table A.3. 84 A.2 Additional Thermodynamic Parameters Key thermodynamic information can be directly derived from the partial projected Phonon Density of States using the PHOENIX software (Sturhahn, 2000, www.nrixs.com). More detailed descriptions can be found in Sturhahn (2004). A.2.1 (Mg0.16 Fe0.84 )O P ressurea (GPa) 0 4.0(3) 11.4(3) 15(3) 21.0(4) 28(2) 41(1) 46(4) 55(3) 65(5) 80(5) 88(4) 97(5) 102(5) 110(4) 121(7) fLM 0.7129(8) 0.717(2) 0.713(2) 0.731(2) 0.727(2) 0.730(2) 0.751(2) 0.778(3) 0.760(3) 0.801(3) 0.814(3) 0.815(2) 0.826(2) 0.834(3) 0.840(2) 0.848(2) EK (meV/atom) 14.0(1) 14.0(2) 14.1(3) 14.2(3) 14.3(3) 14.2(3) 14.0(3) 14.2(3) 14.2(3) 14.5(3) 14.6(3) 14.9(2) 15.3(2) 15.2(4) 15.4(2) 15.6(3) Dav (N/m) 145(5) 145(11) 169(10) 167(14) 183(12) 171(12) 142(14) 177(15) 173(15) 222(12) 229(17) 281(8) 345(13) 326(19) 360(12) 388(16) fLM,Z 0.9069(3) 0.9071(7) 0.9090(8) 0.9112(8) 0.9138(7) 0.9136(8) 0.9153(8) 0.9208(8) 0.9189(9) 0.9263(7) 0.9281(7) 0.9306(5) 0.9336(5) 0.9340(8) 0.9359(4) 0.9377(6) EK,Z (meV/atom) 6.15(9) 6.1(2) 6.3(2) 6.4(3) 6.7(2) 6.6(2) 6.3(2) 6.9(2) 6.8(3) 7.5(2) 7.7(3) 8.3(2) 9.0(2) 8.8(3) 9.2(2) 9.5(2) Cvib (kB /atom) 2.75(1) 2.8(3) 2.74(4) 2.73(4) 2.71(3) 2.72(4) 2.76(4) 2.71(4) 2.72(5) 2.65(4) 2.64(4) 2.59(3) 2.52(3) 2.54(4) 2.50(2) 2.47(3) Svib (kB /atom) 3.57(1) 3.59(3) 2.45(2) 3.44(3) 3.33(3) 3.36(3) 3.36(3) 3.16(3) 3.22(3) 2.95(3) 2.90(3) 2.75(2) 2.61(2) 2.61(3) 2.53(2) 2.45(2) Table A.1: Thermodynamic parameters calculated directly from the partial-projected phonon density of states of (Mg0.16 Fe0.84 )O. a Pressures were determined from ruby fluorescence before and after the NRIXS measurement, from Table 2.1. fLM is the Lamb-Mössbauer factor. EK is the kinetic energy per resonant atom. Dav is the average force constant of the resonant atom. fLM,Z is the Lamb-Mössbauer factor at zero Kelvin. EK,Z is the kinetic energy per resonant atom at zero Kelvin. Cvib is the vibrational specific heat. Svib is the vibrational entropy per atom. 85 A.2.2 (Mg0.06 Fe0.94 )O P ressurea (GPa) 0 9.61(2) 42.7(7) 55(1) 64(2) 81.1(8) 81.6(7) fLM 0.700(1) 0.714(3) 0.773(2) 0.788(2) 0.813(2) 0.826(1) 0.828(2) EK (meV/atom) 14.2(1) [14.2(3)] [14.7(2)] [14.7(2)] [14.8(2)] [15.5(2)] 15.0(2) Dav (N/m) 162(5) [186(10)] [261(8)] [264(8)] [281(8)] [371(10)] 300(8) fLM,Z 0.9076(4) 0.9119(9) 0.9237(6) 0.9267(5) 0.9306(5) 0.9339(3) 0.9330(5) EK,Z (meV/atom) 6.18(8) [6.6(2)] [7.8(2)] [7.9(1)] [8.3(1)] [9.2(1)] 8.6(1) Cvib (kB /atom) 2.75(2) 2.72(4) 2.6(3) 2.61(3) 2.58(3) 2.50(1) 2.56(2) Svib (kB /atom) 3.57(2) 3.39(4) 2.95(2) 2.86(2) 2.73(2) 2.61(1) 2.66(2) Table A.2: Thermodynamic parameters calculated directly from the partial-projected phonon density of states of (Mg0.06 Fe0.94 )O. a Pressure determined from in-situ X-ray diffraction, from Table 3.1. fLM is the Lamb-Mössbauer factor. EK is the kinetic energy per resonant atom. Dav is the average force constant of the resonant atom. fLM,Z is the Lamb-Mössbauer factor at zero Kelvin. EK,Z is the kinetic energy per resonant atom at zero Kelvin. Cvib is the vibrational specific heat. Svib is the vibrational entropy per atom. EK and Dav reported in brackets denotes values possibly affected by higher energy vibrations not sampled by our limited energy range. 86 A.3 Sound Velocities of FeO from Nuclear Resonant Inelastic X-ray Scattering This section describes the determination of FeO Debye velocities presented in Figure 3.12. NRIXS spectra were taken at Sector 3 of the Advanced Photon Source in August 2011 and March 2012. The volume of FeO at ambient pressure was measured at Sector 12.2.2 of the Advanced Light Source. Using the (111), (200) and (220) reflections, the cubic volume was refined using the Unit Cell software. The resulting lattice parameter a = 4.306(1) corresponds to a composition of Fe0.941 O (McCammon and Liu, 1984). The volume of FeO at high pressure was measured at Sector 13-ID-D, GSECARS of the Advanced Photon Source in February 2012. Unit cell volumes at high pressure were determined using the rhombohedral reflections: (003), (101), (012), (104), and (110). Density was calculated assuming 0.5(5)% vacancies. Figure A.2 shows the raw NRIXS spectra of FeO. At ambient pressure, the energy scan range was -60 → +80 meV. At higher pressures, the scan range was increased to -65 → +80 meV and -70 → +100 meV. The partial projected phonon density of states was extracted for each pressure point using the PHOENIX software (Sturhahn, 2000) and are presented in Figure A.3. As described previously, Debye sound velocities were determined using psvl. Table A.3 summarizes the density and Debye sound velocities of FeO in addition to the refined unit cell parameters from X-ray diffraction. ρ (g/cc) 5.99(6)a 6.05(2) 8.3(1) 8.4(1) Emin − Emax meV 3.7 − 16.3a 3.2 − 17.1 4.5 − 14.8 4.2 − 19.8 VD (km/s) 2.87(1)a 2.88(1) 3.73(4) 3.88(3) Vol/atom Å3 10.06(2)a 9.98(4) 7.3(1) 7.2(1) a Å 4.318(8)a 4.306(2) 2.64(2) 2.63(2) c Å 7.26(9) 7.21(9) Table A.3: Summary of FeO density, energy range used to calculate Debye velocities, and Debye velocities. Volume and lattice parameters were refined using the program Unit Cell (Holland and Redfern, 1997). a Density calculated for Ti-containing oxide, estimated to have the chemical formula (Fe0.959 Ti0.041(1) )O (Chen et al., 2012). 87 FeO, 300 K 1e+06 1e+05 Counts 10000 8.4(1) g/cc 1000 100 8.3(1) g/cc 10 ambient 6.05(2) g/cc 1 -50 0 50 Energy (meV) Figure A.2: Raw NRIXS spectra of FeO at 300 K at three pressures. 100 88 200 FeO, 300 K ambient pressure, 6.05(2) g/cc D(E,V) 150 100 50 8.3(1) g/cc 8.4(1) g/cc 0 0 50 Energy (meV) 100 Figure A.3: Partial projected density of states (PDOS) of FeO, extracted from the energy scan using the PHOENIX software (Sturhahn, 2000). There is a marked difference in the distribution of vibrations between the ambient pressure spectrum and the high pressure spectra, which is also reflected in the calculated sound velocities. Debye sound velocities determined from the low-energy region of these PDOSs are plotted in Figure 3.12. 89  Sound Velocities and Equation of State of iron-rich (Mg,Fe)O Thesis by June K. Wicks In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2013 (Submitted ) ii © 2013 June K. Wicks All Rights Reserved iii iv Acknowledgements First and foremost, I want to thank my advisor Jennifer Jackson. You’ve believed in me through this whole process, and pushed me to become a better version of myself. Under your mentorship I’ve grown both personally and intellectually. I wouldn’t be here without you, and looking back I am amazed at how far we’ve come. I hope that someday I’ll become as innovative and well-respected a scientist as you are today. You’ve been the best role model. I am thankful to Paul Asimow and George Rossman for your friendship and mentorship, for helping me become a better teacher and a better scientist, and for always having your door open for me, even on weekends and holidays. Thank you George, for letting me hang out in the lab with you for hours at a time just for fun. Thank you Paul, for sharing your wife and kids with me, letting them be such an important part of my life. Thank you, Mike Gurnis, for taking the time to be on my committee and including me in the CSEDI discussions. Thanks to you and Dan Bower, I could learn about and appreciate first hand the insight from dynamic models of the deep earth. This collaboration has taught me so much and has given me a different perspective on future projects. I am grateful to Chi Ma, my mentor in the Analytical Facilities. Thanks for letting me putter around to learn the instruments, for letting me teach classes even though it was helping me more than it was helping the students, and for stepping back in and teaching me as well when I was in over my head. Thank you, John Beckett, for teaching me my way around the synthesis lab. Your thoughtful and thorough way of teaching gave me the good habits that I still have today. Thank you, Bin Chen, for the hours in the diamond anvil cell lab, teaching me the tricks you’ve learned along the way to make the successful cells. v I am so thankful to the great friendships that I have made, to those of you that supported me through this experience: Colette Caggiano, Lauren Edgar (roommate of 4+ years! longest relationship yet!), Melanie Channon, Andrew and Kelly Matzen, Danny and Dani Bower, Emily Hamecher, Aaron Wolf, Mike Baker, Dongzhou Zhang, Jeremy Boyce, and Jed Mosenfelder, and to the members of SSRG and secDEC, you know who you are. Thank you Kevin Lewis and John Bagert, for being my number one fans. These measurements were made with the help of graduate students Dongzhou Zhang, Aaron Wolf, and Caitlin Murphy, post-doctorate Bin Chen and post-doctorate Hasan Yavas. At the Advanced Photon Source, thank you to my co-authors from GSECARS: Vitali Prakapenka, Kirill Zhuravlev, and Sergey Tkachev. I am particularly grateful to the nuclear resonant and inelastic X-ray scattering group: Jiyong Zhao, Tom Toellner, Ercan Alp, and especially Wolfgang Sturhahn, who has played a large role in my mentorship as well. Support for this work was provided by the NSF-EAR 0711542 and CAREER EAR-0956166 (both awarded to JMJ) and CSEDI EAR-0855815 (awarded to MCG, DVH and JMJ). The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences(BES), of the U.S. Department of Energy(DOE) under Contract No. DE-AC02-05CH11231. High temperature X-ray diffraction and neon loading was performed at GeoSoilEnviroCARS (Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation Earth Sciences (EAR-1128799) and Department of Energy Geosciences (DE-FG02-94ER14466). Sector 3 operations, where the nuclear resonant experiments were conducted, are partially supported by COMPRES (NSF EAR 06-49658). Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract No. DE-AC02-06CH11357. Sample synthesis was carried out in the petrological facilities at Caltech. Microprobe analyses were carried out at the Caltech GPS Division Analytical Facility (funded in part by the MRSEC Program of the NSF under DMR-0080065). vi Abstract Ultralow-velocity zones (ULVZs) are small structures at the base of the mantle characterized by sound velocities up to 30% lower than those of surrounding mantle. In this thesis, we propose that iron-rich (Mg,Fe)O plays a key role in the observed sound velocities, and argue that chemically distinct, iron-enriched structures are consistent with both the low sound velocities and the measured shapes of ULVZs. We have determined the room temperature Debye sound velocity (VD ) of (Mg0.16 57 Fe0.84 )O up to 121 GPa using nuclear resonant inelastic X-ray scattering. Using an estimate of the equation of state, the seismically relevant compressional (VP ) and shear (VS ) wave velocities were calculated from the VD s. We have also determined the room temperature VD at multiple pressure points of (Mg0.06 57 Fe0.94 )O using nuclear resonant inelastic X-ray scattering and in-situ X-ray diffraction up to 80 GPa. The effect of the electronic environment of the iron sites on the velocities of both of these studies were tracked in-situ using synchrotron Mössbauer spectroscopy. We also present the pressure-volume-temperature equation of state of (Mg0.06 57 Fe0.94 )O determined up to pressures of 120 GPa and temperatures of 2000 K. We combine these studies with a simple Voigt-Reuss-Hill mixing model to predict the properties of a solid ULVZ and show that a small amount of iron-rich (Mg,Fe)O can greatly reduce the average sound velocity of an aggregate assemblage. When combined with a geodynamic model of a solid ULVZ (Bower et al., 2011), we can directly correlate inferred sound velocities to mineralogy and predicted ULVZ shapes. Our combined geodynamic and mineral physics model of a solid ULVZ can be used to explore the relationship between the observed sound velocities and mineralogy of ULVZs with added insight into ULVZ morphology. vii Contents Acknowledgements iv Abstract vi List of Tables xii 1 Introduction 2 1.1 Ultralow-Velocity Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Sound velocities of (Mg0.16 Fe0.84 )O measured by Nuclear Resonant Inelastic XRay Scattering 6 2.1 Nuclear Resonant Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Nuclear Resonant Inelastic X-Ray Scattering (NRIXS) . . . . . . . . . . . . . 7 2.1.2 Synchrotron Mössbauer Spectroscopy (SMS) . . . . . . . . . . . . . . . . . . 8 2.2 Experiments and Data Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Ultralow-Velocity Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Nuclear Resonant Spectroscopy of (Mg0.06 Fe0.94 )O at high pressure with in-situ X-ray Diffraction 21 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 viii 3.4 3.3.1 NRIXS with in-situ XRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.2 SMS with in-situ XRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.1 XRD: Isothermal Equation of State . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.2 SMS: Magnetic Ordering Transition . . . . . . . . . . . . . . . . . . . . . . . 29 3.4.3 NRIXS: Sound Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4 Thermal Equation of State of (Mg0.06 Fe0.94 )O 41 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4.1 Phase Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4.2 Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.5.1 Effect of Buffering on Equation of State . . . . . . . . . . . . . . . . . . . . . 51 4.5.2 Effect of Composition on the Thermal Equation of State of (Mg,Fe)O . . . . 54 Rhombohedral Distortion of (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . 56 4.5 4.6 5 Implications for Ultralow-velocity Zones 5.1 5.2 61 Physical Mixing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1.1 Extrapolation of Magnesiowüstite properties to the CMB . . . . . . . . . . . 61 5.1.2 Mixture of Magnesiowüstite and Ambient Mantle . . . . . . . . . . . . . . . . 63 5.1.3 Mixture of Magnesiowüstite and Silicate Perovskite . . . . . . . . . . . . . . . 64 5.1.4 Dynamics of a Solid-state ULVZ . . . . . . . . . . . . . . . . . . . . . . . . . 66 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Bibliography 70 ix A 82 A.1 Synthesis and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.1.1 (Mg0.16 Fe0.84 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.1.2 (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 A.1.3 Fe1−x O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 A.2 Additional Thermodynamic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.2.1 (Mg0.16 Fe0.84 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.2.2 (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A.3 Sound Velocities of FeO from Nuclear Resonant Inelastic X-ray Scattering . . . . . . 86 x List of Figures 1.1 Modal Mineralogy of the Earth’s Mantle . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Setup of Nuclear Resonant Scattering measurements at Sector 3-ID-B of the Advanced 3 Photon Source (APS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Sample NRIXS spectrum of (Mg.06 Fe.94 )O . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Sample Mössbauer spectra of (Mg.06 Fe.94 )O . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Energy scans (raw NRIXS spectra) of (Mg.16 Fe.84 )O at 300 K over 0 to 120 GPa . . . 11 2.5 Partial projected phonon density of states (PDOSs) of (Mg.16 Fe.84 )O. . . . . . . . . . 12 2.6 Time spectra of (Mg.16 Fe.84 )O from synchrotron Mössbauer spectroscopy. . . . . . . . 13 2.7 Determination of the Debye sound velocity of (Mg.15 Fe.85 )O at 0 and 121 GPa. . . . . 14 2.8 Debye sound velocities of (Mg.16 Fe.84 )O (this study) and of Fe.947 O (Struzhkin et al., 2001) at 300 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.9 VP and VS of (Mg.16 Fe.84 )O determined from VD compared to PREM and ULVZs . . 16 2.10 Voigt-Reuss-Hill (VRH) mixing of VP , VS , and density of (Mg.16 Fe.84 )O with PREM . 19 3.1 Cubic to rhombohedral transition pressures in the literature . . . . . . . . . . . . . . . 22 3.2 Illustration of Bragg’s law in X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . 24 3.3 (Mg0.06 Fe0.94 )O loaded for SMS study . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Pressure-volume data of (Mg0.06 Fe0.94 )O at 300 K, measured in the SMS study . . . . 28 3.5 Pressure-Volume equation of state of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . 30 3.6 Synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . 31 3.7 In-situ synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . 32 xi 3.8 Raw NRIXS spectra of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . . . . . . . . 33 3.9 PDOSs of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.10 Debye velocity determination using psvl . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.11 Debye velocity (VD ) of (Mg0.06 Fe0.94 )O at 300 K . . . . . . . . . . . . . . . . . . . . . 37 3.12 VD of (Mg0.06 Fe0.94 )O compared to FeO and (Mg0.65 Fe0.35 )O at 300 K, as a function of density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.13 Compressional (VP ) and shear (VS ) wave velocities of (Mg0.06 Fe0.94 )O at 300 K . . . . 39 4.1 Example XRD spectra at 85 GPa showing peak identifications for B2-NaCl, hcp-Fe, Ne, and (Mg0.06 Fe0.94 )O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Phase identification of (Mg0.06 Fe0.94 )O in P –T space. . . . . . . . . . . . . . . . . . . 48 4.3 P -V -T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the buffered experiment 50 4.4 P -V -T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the unbuffered experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.5 Overlay of data and equations of state of buffered and unbuffered (Mg0.06 Fe0.94 )O . . 53 4.6 Comparison of volume measurements and equations of state of (Mg0.06 Fe0.94 )O to B1FeO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 54 Thermal expansion of buffered (Mg0.06 Fe0.94 )O at 1900 K as a function of pressure, compared to FeO, (Mg0.64 Fe0.36 )O and MgO. . . . . . . . . . . . . . . . . . . . . . . . 55 4.8 Evolution of d-spacings of (Mg0.06 Fe0.94 )O as a function of pressure . . . . . . . . . . 57 4.9 Evolution of c/a ratios of rhombohedral (Mg0.06 Fe0.94 )O as a function of pressure at 300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.10 Pressure-volume data of quenched, rhombohedral (Mg0.06 Fe0.94 )O at 300 K . . . . . . 59 5.1 Debye velocity as a function of density of (Mg.16 Fe.84 )O, (Mg.06 Fe.94 )O, and FeO . . 62 5.2 Mixing models: VP , VS , and density of (Mg.16 Fe.84 )O+PREM . . . . . . . . . . . . . 64 5.3 Mixing models: VP , VS , and density of (Mg.16 Fe.84 )O+Pv . . . . . . . . . . . . . . . 66 5.4 Dynamic model interpretation of mixing models at 4000 K . . . . . . . . . . . . . . . 68 xii A.1 Secondary electron image of (Mg0.06 Fe0.94 )O . . . . . . . . . . . . . . . . . . . . . . . 83 A.2 NRIXS spectra of FeO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 A.3 PDOS of FeO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 xiii List of Tables 1.1 Summary of experiments presented in this thesis . . . . . . . . . . . . . . . . . . . . . 2.1 Summary of pressure, density, Debye sound velocity (VD ), and compressional (VP ) and 5 shear (VS ) wave speeds of (Mg.16 Fe.84 )O. . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1 Details of the (Mg0.06 Fe0.94 )O NRIXS experiment . . . . . . . . . . . . . . . . . . . . 26 3.2 XRD results of the (Mg0.06 Fe0.94 )O SMS experiment . . . . . . . . . . . . . . . . . . . 27 3.3 Equations of state fit to the (Mg0.06 Fe0.94 )O dataset. . . . . . . . . . . . . . . . . . . 29 3.4 Debye Velocity (VD ) of (Mg0.06 Fe0.94 )O as a function of in-situ density . . . . . . . . 36 3.5 Summary of sound velocities of (Mg0.06 Fe0.94 )O as a function of pressure . . . . . . . 40 4.1 Pressure-volume-temperature data for the buffered experiment . . . . . . . . . . . . . 45 4.2 Pressure-volume-temperature data for the unbuffered experiment . . . . . . . . . . . . 46 4.3 3rd-order Birch-Murnaghan equation of state parameters for the buffered dataset using hcp-Fe as a pressure marker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 3rd-order Birch-Murnahan equation of state parameters the both the buffered and unbuffered dataset using B2-NaCl as a pressure marker . . . . . . . . . . . . . . . . . 4.5 49 50 Equation of state parameters using B2-NaCl as a pressure marker, with K0T fixed to 180 GPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.6 Pressure-volume data for the buffered experiment at 300 K. . . . . . . . . . . . . . . . 60 5.1 Model parameters for mixing model “Mw+PREM” . . . . . . . . . . . . . . . . . . . 64 5.2 Model parameters for mixing model “Mw+Pv” . . . . . . . . . . . . . . . . . . . . . . 66 xiv 5.3 Model parameters for mixing model “Mw+PREM” and “Mw+Pv” at 4000 K . . . . . 68 A.1 Thermodynamic parameters calculated directly from the PDOS of (Mg0.16 Fe0.84 )O. . 84 A.2 Thermodynamic parameters calculated directly from the PDOS of (Mg0.06 Fe0.94 )O . . 85 A.3 Summary of FeO density and Debye Velocities . . . . . . . . . . . . . . . . . . . . . . 86 1 2 Chapter 1 Introduction Study of the interior of the earth is crucial to understanding both the processes by which a planet was formed and the future impact of deep interior dynamics. Much has been learned from seismic studies, probing the propagation of sound waves through the earth. Seismic reflectors deep in the earth such as those located at 410, 660 and 2900 km below the earth’s surface have been interpreted as chemical boundaries or phase changes, supported by experimental studies of model compositions of primitive mantle material. The major discontinuities in the mantle are believed to correspond to phase changes, where olivine transforms to the high pressure polymorph wadsleyite at the 410 km discontinuity, then breaks down to form ferropericlase and perovskite at the 660 discontinuity (e.g. Irifune, 1994, Figure 1.1). The mantle layer between the core-mantle boundary and the D” discontinuity spans a depth range in Earth’s lower mantle from up to 350 km above the liquid outer core to the outer core itself, corresponding to a proposed temperature range of 3300-4300 K and 115 to 135 GPa. Intermittent detection of this discontinuity suggests that the core-mantle boundary (CMB) layer is compositionally distinct and/or represents a different phase assemblage (e.g. Lay et al., 2008; Sidorin et al., 1999). 1.1 Ultralow-Velocity Zones At the base of the D” layer, 5-20 km thick patches have been observed in which the VP and VS sound velocities are reduced by 5-10% and 10-30% (Thorne and Garnero, 2004). Reduced seismic 3 Orthopyroxene Garnet Clinopyroxene Olivine (Mg,Fe,Ca)3Al2Si3O12 (Mg,Fe)2SiO4 Transition zone Wadsleyite (Mg,Fe)2SiO4 Ringwoodite (Mg,Fe)2SiO4 Majorite garnet (Mg,Fe,Ca)3(Mg,Si,Al)2Si3O12 Lower Mantle Ferropericlase (Mg,Fe)O Magnesium silicate Perovskite (Mg,Fe)(Si,Al)O3 Calcium silicate perovskite CaSiO3 Upper Mantle Figure 1.1: Modal mineralogy of the earth’s mantle, assuming a pyrolite mantle. The upper mantle (0-440 km below the earth’s surface) is mostly comprised of olivine garnet, and pyroxenes (Mg,Fe)2 Si2 O6 . The lower mantle (660 to 2900 km below the earth’s surface) is comprised of Caand (Mg,Fe)- silicate perovskite and (Mg,Fe)O. Highlighted in blue is ferropericlase, the Fe-poor member of the MgO-FeO solid solution. Iron-rich members are named magnesiowüstite. Figure is adapted from (Frost et al., 2004) velocities in this ultra-low velocity zone, or ULVZ, were first attributed to partial melting due to drastic velocity reductions, sharp upper boundaries, and a strong correlation with hot spots on the surface (e.g. Williams and Garnero, 1996; Williams et al., 1998; Lay et al., 2004). A sound velocity decrement ratio ∂VP /∂VS of 1:3 has been shown to be consistent with partial melt (Berryman, 2000). Numerous seismic studies of the core-mantle boundary indicate that ULVZ distribution is patchy and sometimes associated with edges or the interior of large low shear velocity provinces (McNamara et al., 2010). Fine-scale one-dimensional structure of some ULVZs have been probed, finding a steep positive velocity gradient with depth, implying complex interior morphology (Rost et al., 2006). Multiple concave-down ULVZs clustered together have been invoked to explain PKP precursors in 4 a two-dimensional study, giving the first seismic insight into ULVZ shape (Wen and Helmberger , 1998). Partial melting of ambient mantle would require the fortuitous intersection of the mantle solidus with the base of the core-mantle boundary. Recent work into the equations of state of fayalite Fe2 SiO4 liquid and subsequent analysis shows that partial melting of chondrite or peridotite liquid is unlikely to be gravitationally stable at the base of the mantle (Thomas et al., 2012). It has been proposed that enriched residues of a crystallizing mantle could be depleted in Si and enriched in FeO enough to form ULVZs (Labrosse et al., 2007; Nomura et al., 2011). Dynamic studies exploring the stability of partially-molten ULVZs show that the amounts of liquid required to reduce the velocities of an assemblage would percolate and pool at the base of the mantle rather than remain suspended in a ULVZ (Hernlund and Tackley, 2007). Partial melt can be maintained km’s above the CMB if the ULVZ is stirred (Hernlund and Jellinek , 2010). Further studies of melt geometry explore mechanisms to retain greater melt fraction (Wimert and Hier-Majumder , 2012; Hier-Majumder and Abbott, 2010, e.g.). In the end, a seemingly simple explanation is complicated by large unknowns in grain boundary properties, melt viscosity, and melt sound velocities. Solid ULVZs have also been considered in the literature, in the form of FeO/FeSi alloy (Manga and Jeanloz , 1996) or iron-enriched post-perovskite (Mao et al., 2006), but are no longer considered stable in the hot core-mantle boundary regions in which ULVZs are found. In this thesis, we introduce and explore another alternative: iron-rich (Mg,Fe)O. The partitioning behavior of iron between perovskite(Pv), post-perovskite(PPv), and (Mg,Fe)O varies widely based on experimental conditions. Recently, it has been suggested that iron preferentially partitions in (Mg,Fe)O in the presence of Pv and PPv based on analyses of quenched phase assemblages from pressures and temperatures of 100 GPa and ∼1800 K (Auzende et al., 2008; Sinmyo et al., 2008). An enhanced iron content and subsequent uptake by (Mg,Fe)O could result in a composition much more iron-rich than previously considered. Therefore, it is of interest to study the elasticity of iron-rich (Mg,Fe)O at core-mantle boundary conditions, as it may shed light on seismic 5 observations in this region. 1.2 Thesis Overview This thesis is divided into three studies of iron-rich oxide, the experiments for which are summarized in Table 1.1. All of these studies are united by the use of X-ray scattering techniques using synchrotron radiation to measure the elasticity of iron-rich (Mg,Fe)O. We synthesized our own samples for this study, and describe the samples in Section A.1. Using a diamond anvil cell to create pressures approaching those of the core-mantle boundary and occasionally in-situ laser heating to create temperatures approaching those of the earth’s interior, we measured material properties relevant to the study of the earth’s mantle, namely sound velocities and densities. Chapter 2 is a study of (Mg.16 Fe.84 )O using nuclear resonant inelastic X-Ray scattering (NRIXS) and synchrotron Mössbauer spectroscopy (SMS). Chapter 3 measured the sound velocities and magnetic state of (Mg.06 Fe.94 )O using the methods described in Chapter 2 with a few key differences, including the use of in-situ X-ray diffraction to measure lattice spacing of the sample and map it directly to a combined XRD/SMS study of the same material. Chapter 4 describes the P -V -T equation of state of (Mg.06 Fe.94 )O. Finally, we close in Chapter 5 with a mixing model that combines the results of our work with dynamic calculations of a solid ULVZ. Chapter 2 3 4 A.3 beamlines APS 3-ID-B ALS 12.2.2 APS 3-ID-B APS 3-ID-B APS 13-ID-D APS 13-ID-D APS 3-ID-B ALS 12.2.2 APS 13-ID-D beamtime dates 10/08, 7/09 4/09 8/11, 10/12 2/13 7/11 2/12 8/11, 3/12 5/11 2/12 information collected NRIXS, in-situ SMS XRD NRIXS, in-situ SMS SMS with in-situ XRD XRD XRD with Fe buffer NRIXS XRD XRD P -T conditions 300 K, 0-121 GPa 300 K, 0 GPa 300 K, 0-81 GPa 300 K, 8-52 GPa 300-1950 K, 32-120 GPa 300-1800 K, 30-70 GPa 300 K, 0-100 GPa 300 K, 0 GPa 300 K, 100 GPa Table 1.1: Summary of experiments presented in this thesis samples Mw84 Mw84 Mw94 Mw94 Mw94 Mw94 FeO FeO FeO 6 Chapter 2 Sound velocities of (Mg0.16Fe0.84)O measured by Nuclear Resonant Inelastic X-Ray Scattering∗ * This chapter has been previously published as: Wicks, J. K., J. M. Jackson, and W. Sturhahn (2010), Very low sound velocities in iron-rich (Mg,Fe)O: Implications for the core-mantle boundary region, Geophys. Res. Lett., 37, L15304. A re-evaluation of this data is briefly discussed in Chapter 5 2.1 Nuclear Resonant Scattering Nuclear resonant scattering (NRS) methods take advantage of the fact that nuclei, much like electrons, can be excited into higher energy states, which are organized into discrete energy levels. A resonance energy is the energy that corresponds to the excitation of a nucleus into one of these higher energy levels, at which energy the absorption cross-section of the nucleus is much higher. Whether a nucleus is accessible for nuclear resonant studies is a function of both nuclear excitation energy and lifetime of the excited state. We refer the reader to references such as Sturhahn (2004) that introduce the spectroscopy technique and Sturhahn (2000) that describes the software. In addition, Sturhahn and Jackson (2007) discusses NRS techniques in the context of geophysical application. 7 2.1.1 Nuclear Resonant Inelastic X-Ray Scattering (NRIXS) Nuclear resonant inelastic X-ray scattering (NRIXS) is a technique that probes the lattice vibrations in which the resonant atoms participate. It is complementary to techniques such as Raman spectroscopy and infrared spectroscopy in that it measures vibrations of a lattice, but differs in both information and execution. Most notably, there are no selection rules for NRIXS, so no vibrations are missed based on symmetry. However, because it is isotope-specific, the vibrations measured are a projection of lattice vibrations onto the resonant isotope. Figure 2.1: Setup of Nuclear Resonant Scattering measurements at Sector 3-ID-B of the Advanced Photon Source. Figure adapted from (Sturhahn and Jackson, 2007). Figure 2.1 shows a cartoon of the setup of nuclear resonant scattering measurements at Sector 3-ID-B of the Advanced Photon Source (APS). The synchrotron radiation (SR) of the APS is a third-generation light source capable of producing X-rays with high flux and brilliance. In Sector 3 of the APS a series of monochromators eliminate all energies except the resonance energy with a 1 meV bandwidth. In the case of 57 Fe, the resonance energy is 14.4125 keV, and the energies corresponding to inelastic scattering are obtained by tuning the energy around the resonance peak. Incoherent scattering is measured radially as close to the sample as possible using avalanche photodiodes detectors (APDs), and produce the NRIXS spectra. Coherent scattering is measured in the forward direction, further downstream, which gives us the shape of the elastic peak, which reflects the source, and the synchrotron Mössbauer spectrum if measured in the time domain. Figure 2.2 shows an example energy scan collected in an NRIXS experiment. The elastic peak 8 at the origin corresponds to recoilless absorption and emission. Peaks on either side of the elastic peak correspond to phonon annihilation (anti-Stokes) or creation (Stokes). The spectrum measured in the forward direction gives the shape of the elastic peak, and is scaled and subtracted from the NRIXS spectrum to isolate the vibrations. 10000 1 atm , 300 K counts per 7 seconds 1000 100 FWHM = 1.08 meV 10 1 -50 0 Energy (meV) 50 100 Figure 2.2: Sample energy scan (raw NRIXS spectrum) of (Mg.06 Fe.94 )O around the 57 Fe resonance energy of 14.4125 keV at ambient pressure and temperature. The spectrum independently measured in the forward direction gives the shape of the elastic peak (red). The spectrum measured radially captures the inelastic absorptions corresponding to lattice vibrations (black). 2.1.2 Synchrotron Mössbauer Spectroscopy (SMS) Mössbauer spectroscopy measures small changes to nuclear energy levels in response to its environment. From this technique, we gain information about the electronic and magnetic environment of a nucleus that has an accessible resonance (e.g. 57 Fe). Nuclear energy levels are sensitive to the electric field gradient, which couples with the quadrupole 9 8 GPa, 300 K 10000 counts with stainless steel 1000 100 without stainless steel 10 20 40 60 80 100 120 140 Time (ns) Figure 2.3: Left: Synchrotron Mössbauer spectra of (Mg.06 Fe.94 )O at 8 GPa, with and without stainless steel reference. Right: Conventional Mössbauer spectrum of (Mg.06 Fe.94 )O at 0 GPa, with a fit drawn in red corresponding to a quadrupole splitting of 1 mm/s and isomer shift of 0.8 mm/s, consistent with divalent iron. moment of the nucleus. An asymmetric electronic distribution around the nucleus, then, results in quadrupole splitting. Nuclear energy levels split even further in the presence of electric or magnetic fields. Synchrotron Mössbauer spectroscopy measures the Rayleigh scattering of excited resonant nuclei, where a superposition of different emitted energies reflecting nuclear level splitting can be measured using detectors as a function of time. Figure 2.3 shows an example of typical Mössbauer spectra of (Mg.06 Fe.94 )O at low pressures. Higher pressure data is discussed in Chapter 3. A quadrupole splitting of energy manifests as a split peak in conventional spectra (right), and as an oscillational frequency in synchrotron Mössbauer spectra (left). In conventional spectra, the isomer shift measured gives the energy shift of the ground energy level with respect to the gamma ray source, typically 57 Co embedded in stainless steel. In synchrotron Mössbauer spectroscopy, isomer shift is determined by measuring a sample twice, with and without a reference absorber in the beam. Advantages of synchrotron Mössbauer spectroscopy over conventional methods include no source broadening, no background, and high photon flux at the resonance energy of the 57 Fe atom, permitting high quality spectra with reasonable count times of samples even at high pressure. 10 2.2 Experiments and Data Evaluation The (Mg.16 57 Fe.84 )O sample was synthesized at room pressure in a gas-mixing furnace. Details of synthesis and purity can be found in section A.1. Three panoramic diamond anvil cells (DACs) were prepared for this experiment. The panoramic DACs were designed and machined at Caltech. Beveled anvils with 250 and 300 µm-flat culet diameters were used. A 140 µm sample chamber was drilled out of a pre-indented beryllium gasket for each DAC, and the sample was loaded in the center of a boron epoxy insert to increase sample thickness, aid in gasket stability, and reduce pressure gradients. In one of the three DAC setups, a NaCl pressure medium was included with the sample, and no boron epoxy was used. Small ruby spheres were loaded close to the sample in all DACs to determine pressure before and after data collection using the characteristic ruby fluorescence line shift according to the non-hydrostatic ruby pressure scale (Mao et al., 1978). High-pressure nuclear resonance scattering experiments were conducted at Sector 3-ID-B of the Advanced Photon Source at Argonne National Laboratory (Sturhahn and Jackson, 2007, Figure 2.1). The storage ring was operated in top-up mode with 24 bunches separated by 153 ns. The X-ray energy incident on the sample had a bandwidth of 1.2 meV and was tuned around the 14.4125 keV nuclear resonance of 57 Fe (Toellner et al., 2001). Time-delayed photons resulting from nuclear excitation of the 57 Fe isotope in (Mg.16 Fe.84 )O were collected using three avalanche photodiode detectors (APDs) positioned radially around the DAC. At each pressure, inelastically scattered photons were collected over select energy ranges spanning -80 meV to +100 meV. Nuclear resonance inelastic X-ray scattering (NRIXS) spectra were collected from ambient pressure to 121 GPa at 300 K. Raw spectra are shown in Figure 2.4. From the measured energy spectra, the partial projected phonon density of states (PDOS) pertaining to the Fe site was extracted using methods described in (Sturhahn, 2004). PDOSs are shows in Figure 2.5. A fourth APD was positioned in the forward direction with two goals: 1) to measure the resolution function independently for accurate sound velocity determination and 2) to measure the time spectra using synchrotron Mössbauer spectroscopy for local magnetic environment determination of the 57 Fe 11 46 GPa 121 GPa 41 GPa Counts Counts 110 GPa 28 GPa 21 GPa 102 GPa 97 GPa 15 GPa 1000 1000 11 GPa 88 GPa 100 100 80 GPa 4 GPa 65 GPa 10 10 55 GPa 1 ambient -100 1 -50 0 50 100 -100 Energy (meV) -50 0 50 100 Energy (meV) Figure 2.4: Raw NRIXS spectra of (Mg.16 Fe.84 )O at 300 K at different pressures over 0 to 120 GPa, measured at Sector 3-ID-B of the Advanced Photon Source. They are offset in the y-direction for clarity. (Figure 2.6). The Debye sound velocity, VD , is related to the low-energy region of the PDOS in the following manner:  V (E) = m E2 2π 2 h̄3 ρ D(E)  31 and VD = V (0) , (2.1) where m is the mass of the resonant nucleus, ρ is the mass density of the sample, and D(E) is the PDOS. Values of V (E) were calculated from the measured PDOS and matched to an empirical function f (E) ≈ VD {1 − (E/E0 )2 }, where E0 and VD are optimized in a standard least-square-fit procedure (Jackson et al., 2009). The energy region for the fit was chosen between 4 and 14 meV. The lower limit of the energy range is chosen to avoid errors resulting from the subtraction of the elastic contributions and is mainly determined by the energy bandwidth of the X-rays. The upper limit is chosen as the maximum possible energy that permits an acceptably small χ2 value in D(E,V) D(E,V) D(E,V) D(E,V) D(E,V) D(E,V) D(E,V) 12 ambient 55 GPa 4 GPa 65 GPa 11 GPa 80 GPa 15 GPa 88 GPa 21 GPa 97 GPa 28 GPa 102 GPa 41 GPa 110 GPa 46 GPa 121 GPa D(E,V) 200 100 0 0 20 40 60 Energy (meV) 80 100 0 20 40 60 Energy (meV) 80 100 Figure 2.5: Partial projected phonon density of states (PDOSs) of (Mg.16 Fe.84 )O, extracted from the NRIXS scans using the PHOENIX software. 13 ambient 65 GPa 2 10 2 10 0 0 10 10 4 GPa 80 GPa 2 10 2 10 0 0 10 10 11 GPa 88 GPa 2 2 10 10 0 0 10 15 GPa 2 10 0 counts counts 10 97 GPa 2 10 0 10 10 28 GPa 2 10 102 GPa 2 10 0 0 10 10 46 GPa 2 10 110 GPa 2 10 0 0 10 10 55 GPa 2 10 121 GPa 2 10 0 10 0 20 40 60 80 Time (ns) 100 120 10 20 40 60 80 Time (ns) 100 120 Figure 2.6: Time spectra of (Mg.16 Fe.84 )O from synchrotron Mössbauer spectroscopy. The ambient pressure spectrum is characterized by slow oscillations, consistent with no magnetic ordering. Fast oscillations appear in the spectrum at 28 GPa. A magnetically-ordered state is stable between 28 and 110 GPa. At 121 GPa, the fast oscillations have disappeared, which is indicative of a spin transition to a low-spin state of the Fe 3d-electron configuration. Error bars are shown for every fourth point, and each data point represents a binning of 4. 14 Figure 2.7: Determination of the Debye sound velocity of (Mg Fe )O at ambient pressure and .15 .85 Figure 5: (Supplemental) Determination of the(2.1). Debye velocity ofof(Mg .15 Fe.85 )O at am121 GPa. Symbols show values of Equation Solid sound lines show the best fit the empirical f (E)GPa. as explained in the text. bient pressurefunction and 121 Symbols show values of Equation (2). Solid lines show the best t of the empirical function f (E) as explained in the text. The lower limit of the energy range is the fit procedure. Figure 2.7 shows V (E), the fitted function f (E), and the optimum value of VD chosen to avoid errors resulting from the subtraction of the elastic contributions and is mainly ambient pressure and 121 GPa. lines illustrate extrapolations using is thechosen best fits to determined byforthe energy bandwidth ofDashed the x-rays (27).theThe upper limit as the max2 imum possible energy thatsound permits an acceptably small χ value in the t procedure. Dashed obtain the Debye velocities. lines illustrate the extrapolations using the best ts to obtain the Debye sound velocityies. In Figure 2.8, we plot VD ’s determined for the entire pressure range. For comparison, we also show VD ’s of Fe.947 O that we determined from the PDOSs reported in a published NRIXS study, which was conducted at 300 K up to 49 GPa (Struzhkin et al., 2001). For an isotropic solid, VD is related to the seismically relevant aggregate compressional (VP ) and shear (VS ) velocities by 3/VD3 = (1/VP3 ) + (2/VS3 ) and VP2 − (4/3)VS2 = K0S /ρ = Vφ2 16 (2.2) 15 Debye Velocity (km/s) 4.2 3.8 3.4 3.0 (Mg.16Fe.84)O FeO 2.6 0 20 40 60 80 100 120 140 Pressure (GPa) Figure 2.8: Debye sound velocities determined from the PDOS of (Mg.16 Fe.84 )O (this study) and of Fe.947 O (Struzhkin et al., 2001) at 300 K. where K0S is the adiabatic bulk modulus at ambient temperature, ρ is the density, and Vφ is the bulk sound velocity. K0S is related to the isothermal bulk modulus, K0T , by K0S = K0T (1 + αγT ). K0S can be approximated by K0T , because at room temperature αγT ≤ 0.01 for most materials (Angel and Jackson, 2002). The isothermal third order Birch-Murnaghan weighted equation of state (EOS) from a high-pressure powder x-ray diffraction study up to 93 GPa on (Mg.22 Fe.78 )O, a similar composition to that used in our NRIXS measurements, provided the values K0T =191.2±5.5 GPa 0 and K0T =2.5±0.1 (Zhuravlev et al., 2010). The pressure-dependent density of (Mg.16 Fe.84 )O was obtained by rescaling this EOS with our initial density of 5.69(7) g/cm3 . X-ray diffraction spectra of our sample were taken at select pressures, including ambient, at the Advanced Light Source at Lawrence Berkeley National Laboratory, confirming our choice of EOS and pressure scale. The seismically relevant VP and VS values determined at each pressure point are shown for the entire pressure range (Figure 2.9, Table 2.1). 16 14.0 PREM VP ULVZ VP 12.0 -10% ULVZ VS - 5% -10% -20% Velocity (km/s) 10.0 8.0 (Mg.16Fe.84)O VP 6.0 PREM VS -20% -30% 4.0 (Mg.16Fe.84)O VS 2.0 0 20 40 60 80 100 120 140 Pressure (GPa) Figure 2.9: VP (blue) and VS (red), of (Mg.16 Fe.84 )O determined from VD along with PREM (Dziewonski and Anderson, 1981) and ULVZs (Thorne and Garnero, 2004). ×: predicted sound velocities for (Mg.16 Fe.84 )O from an ultrasonic study on (Mg,Fe)O (Jacobsen et al., 2002). 2.3 Results At ambient pressure, the velocities of (Mg.16 Fe.84 )O are in good agreement with the trend in sound velocities for iron-rich (Mg,Fe)O (Jacobsen et al., 2002; Struzhkin et al., 2001, Figures 2.8, 2.9). In-situ synchrotron Mössbauer spectroscopy shows an absence of magnetic ordering (Figure 2.6) at low pressures, and detailed analysis reveals a quadrupole splitting of about 0.8 mm/s. At pressures approaching 28 GPa, both VD and VS of (Mg.16 Fe.84 )O decrease with increasing pressure (Figures 2.8, 2.9). The softening occurs in the vicinity of the transition from the paramagnetic state to a magnetically ordered state around 28 GPa (Figure 2.6). The presence of magnetic hyperfine fields is clear evidence for a magnetically ordered state demonstrating a magnetic transition in (Mg.16 Fe.84 )O around 28 GPa at 300 K—a finding in agreement with a conventional Mössbauer 17 Pressure (GPa) 0 4.0(3) 11.4(3) 15(3)* 21.0(4) 28(2) 41(1) 46(4) 55(3) 65(5) 80(5) 88(4) 97(5) 102(5) 110(4) 121(7) Density (g/cm3 ) 5.69(7) 5.81(8) 6.02(8) 6.1(1) 6.27(8) 6.44(9) 6.8(1) 6.9(1) 7.1(1) 7.4(1) 7.7(1) 7.9(1) 8.1(1) 8.2(2) 8.5(2) 8.7(2) VD (km/s) 3.23(2) 3.10(2) 3.05(3) 3.03(3) 3.05(2) 2.96(2) 3.23(2) 3.28(3) 3.21(4) 3.48(3) 3.64(5) 3.67(3) 3.74(3) 3.84(5) 3.92(2) 4.04(5) VP (km/s) 6.70(9) 6.70(9) 6.8(1) 6.8(1) 6.9(1) 6.9(1) 7.2(1) 7.2(1) 7.2(2) 7.4(2) 7.5(2) 7.5(2) 7.4(2) 7.5(2) 7.5(3) 7.4(3) VS (km/s) 2.86(2) 2.74(2) 2.70(3) 2.67(3) 2.69(2) 2.61(2) 2.85(2) 2.90(3) 2.84(3) 3.08(4) 3.22(5) 3.25(3) 3.32(3) 3.41(5) 3.48(4) 3.60(5) Table 2.1: Summary of pressure, density, Debye sound velocity (VD ), and compressional (VP ) and shear (VS ) sound velocities of (Mg.16 Fe.84 )O. Numbers in parenthesis reflect the error on the last digit. Errors in pressure reflect the standard deviation of pressures measured from multiple rubies surrounding the sample, measured before and after the x-ray measurement. Errors in ambient pressure density reflect the uncorrelated errors of unit cell volume measurement, sample composition, and assumed vacancies. Errors in VD incorporate fitting errors in the low-energy region of the PDOS (Figure 2.7) as well as the propagation of the errors in density and pressure. This error is then propagated further to the VP and VS errors. * NaCl pressure medium. study on (Mg.20 Fe.80 )O (Speziale et al., 2005). A similar softening is observed for Fe.947 O (Struzhkin et al., 2001, Figure 2.9) and other iron-rich (Mg,Fe)O samples (Jacobsen et al., 2004). This particular behavior has been associated with phonon-magnon coupling (Struzhkin et al., 2001) and has been attributed to c44 mode softening preceding the B1 to rhombohedral structural distortion (Mao et al., 1996). At 121 GPa the fast oscillations, thus the magnetic hyperfine fields, disappear in the time spectrum (Figure 2.6), and is consistent with the onset of a spin transition into a low-spin state of the Fe 3d-electron configuration. We note that at pressures above 100 GPa, VP ceases to increase and gradually softens. Such a behavior is consistent with a transition to a low spin state, as similar observations have been reported for iron-poor (Mg,Fe)O in the vicinity of a spin transition (Crowhurst et al., 2008). Most important, the very low pressure derivatives of VP and VS for (Mg.16 Fe.84 )O above 28 GPa persist to the highest pressure measured and ensure that this material retains ultra-low sound velocities at core-mantle boundary pressures. 18 2.4 Ultralow-Velocity Zones The shear sound velocity of (Mg.16 Fe.84 )O at 121 GPa is about 55% and 50% reduced compared to MgO (Murakami et al., 2009) and the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson, 1981), respectively. The VP /VS ratio at the highest pressure measured is 2.1±0.1, which falls within the VP /VS range of ULVZs (2.2±0.3) (Thorne and Garnero, 2004). The Poisson ratios (ν) determined from seismic ULVZ observations range from 0.30 to 0.41 and compare favorably to our value of 0.34±0.02 for iron-rich (Mg,Fe)O at 121 GPa and 300 K. At thousands of K and regardless of its structure (Lin et al., 2003), (Mg.16 Fe.84 )O is unlikely to be stiffer than it is at room temperature, which could result in even lower sound velocities at the CMB. As an illustration of the expected VP , VS , and density of a mechanical mixture containing iron-rich (Mg,Fe)O and ambient mantle material, we estimate the effect of temperature on (Mg.16 Fe.84 )O’s properties using MgO behavior as a proxy (Sinogeikin et al., 2000). Due to the highly uncertain elastic properties of silicates under CMB conditions, we employ PREM as our bound for the remaining silicate fraction, while recognizing that PREM values may underestimate silicate behavior. We then calculate the Voigt-Reuss-Hill mechanical mixing envelopes for VP , VS , and density (Watt et al., 1976) for a given vol% of (Mg.16 Fe.84 )O and PREM (Figure 2.10). To first order, mixing of just 12 vol% of (Mg.16 Fe.84 )O with 88 vol% silicates (represented here by PREM) matches signature seismic observations for the ULVZ (Figure 2.10). While ULVZ provinces are often considered to be patches of dense partial melt, no measurements exist for the sound velocities of partially molten mantle material at CMB conditions. The connection between ULVZs and partial melting was popularized by the correlation between ULVZ and hot spot locations (Williams et al., 1998). However, not all ULVZs are related spatially to hot spots. An alternative explanation of several ULVZ observations is a dense, localized solid layer containing some amount of iron-rich (Mg,Fe)O. A solid dense layer would not require the intersection of the local geotherm and solidus of the mantle and can produce low sound speeds independent of partial melting (Figure 2.10). This scenario would require a mechanism in which the (Mg,Fe)O phase becomes enriched in iron 19 VP range of observed values of ULVZs VP VRH mixing bounds of iron-rich (Mg,Fe) with PREM density VRH bounds VS ULVZ VS VRH mixing Figure 2.10: Voigt-Reuss-Hill (VRH) mixing of VP , VS , and density (red area) of (Mg.16 Fe.84 )O with PREM (see text for details). In orange boxes, we plot VP and VS of the ULVZ’s centered at 12 vol% (Mg.16 Fe.84 )O, which produces a ν of about 0.34. This particular calculation assumes a pressure of 123 GPa and a temperature of 2700 K. The widths of the ULVZ symbols are arbitrary. in localized areas of the CMB. It has been suggested that extensive iron enrichment could localize in patches in the vicinity of the CMB due to viscosity variations, because liquid iron can be pulled up into the lower mantle on the km scale (Kanda and Stevenson, 2006). Iron-rich pockets could represent residue of a fractional crystallization of primordial magma ocean (Labrosse et al., 2007). In representative mantle assemblages with typical amounts of iron, (Mg,Fe)O has been identified as the preferred iron sink (Auzende et al., 2008; Sinmyo et al., 2008). Chemical reaction studies between liquid iron and lower mantle perovskite or oxide have produced 20 a wide range of results, leading to interpretations ranging from production of FeSi and FeO (Knittle and Jeanloz , 1991; Song and Ahrens, 1994) to dissolution of oxygen into liquid iron (Takafuji et al., 2005; Frost et al., 2010). Further investigations exploring the dependence of these reactions on CMB fugacity and chemistry may address these discrepancies, which could be complicated by the possibility of disequilibria. Nevertheless, the low sound velocities of iron-rich (Mg,Fe)O provide compelling motivation to explore the distribution of iron-rich (Mg,Fe)O in the core-mantle boundary region. 21 Chapter 3 Nuclear Resonant Spectroscopy of (Mg0.06Fe0.94)O at high pressure with in-situ X-ray Diffraction 3.1 Introduction In Chapter 3, we established that iron-rich magnesium oxide (XF e = 0.84) is characterized by very low sound velocities, and found that a magnetic transition occurred between 15 and 28 GPa. In this chapter, we present a similar study on a different composition, (Mg0.06 Fe0.94 )O, hereafter referred to occasionally as Mw94. In addition to providing insight into the compositional dependence of sound velocities, this chapter also reflects improvements in the methodology since the publication of the previous work. Most notably, availability of in-situ XRD allowed us to directly measure the sample’s volume, and thus provide in-situ density (ρ) of our sample for every nuclear resonant scattering (NRS) measurement. This allows us to report the direct result of our NRIXS studies: the Debye sound velocity (VD ) at in-situ ρ. Finally, volumes of this material at room temperature measured as part of a synchrotron Mössbauer study (this chapter) and a thermal equation of state study (Chapter 4) give us an equation of state that is used to convert Debye velocities into compressional and shear wave speeds reliably. Another direct result of this study is the transition pressure of the paramagnetic to antiferromagnetic transition, also known as the Néel transition (Fujii et al., 2011, e.g.). Mössbauer and magnetic investigations have shown a compositional dependence in Néel temperature in the (Mg,Fe)O solid 22 solution, where projected transition pressure at 300 K coincides with the cubic to rhombohedral distortion (Speziale et al., 2005; Fujii et al., 2011). Other experimental studies, however, find that structural and magnetic transition pressures or temperatures do not coincide (Kantor et al., 2004, 2005, 2006; Glazyrin et al., 2011). 140 Transition Pressure (GPa) 120 100 Lin2003 80 60 Lin2003 Richet1989 Zhuravlev2010 40 Fei1992 Kantor2006 20 0 0 20 40 60 80 100 mol% FeO Figure 3.1: Cubic to rhombohedral transition pressures in the literature, as a function of composition. In red we plot our brackets on the magnetic transition pressure from synchrotron Mössbauer spectroscopy of (Mg0.16 Fe0.84 )O (Chapter 2) and (Mg0.06 Fe0.94 )O (this Chapter). In blue we plot the constraint on the cubic to rhombohedral structural transition from X-ray diffraction (Chapter 4). The dashed line indicates the cubic-rhombohedral phase boundary according to Fei et al. (2007a), and the dotted line indicates the same according to (Lin et al., 2003). Gray-filled circles are reported transition pressures in the literature (Mao et al., 2002; Jacobsen et al., 2005; Fei and Mao, 1994; Yagi et al., 1985; Zhuravlev et al., 2010; Lin et al., 2003; Shu et al., 1998a; Fei et al., 2007a; Kondo et al., 2004; Richet et al., 1989; Fei et al., 2007a; Kantor et al., 2006; Mao et al., 1996), whereas white-filled circles indicate maximum pressures of studies that did not see a transition (Fei et al., 1992; Richet et al., 1989; Lin et al., 2003). Experimental investigations of the structural transition find that increasing FeO component corresponds to a decrease in transition pressure (Lin et al., 2003; Shu et al., 1998b). The transition pressure is found to be very sensitive to hydrostaticity Shu et al. (1998a), and some studies found no 23 compositional dependence of transition pressure (Kondo et al., 2004). Figure 3.1 shows a summary of cubic to rhombohedral structural transition pressures in the literature, which may reflect a compositional dependence. We include our magnetic transition bounds for (Mg0.16 Fe0.84 )O (Chapter 2) and (Mg0.06 Fe0.94 )O (this Chapter), in addition to structural transition constraints for (Mg0.06 Fe0.94 )O (Chapter 4). We will describe a synchrotron Mössbauer (SMS) study of (Mg0.06 Fe0.94 )O over the pressure range 8 to 52 GPa with in-situ X-ray diffraction. Next, we will describe nuclear resonant inelastic X-ray scattering (NRIXS) measurements over the pressure range 0 to 80 GPa, also taken with in-situ SMS and X-ray diffraction. These results will be compared to an iron-poor sample, (Mg0.65 Fe0.35 )O (Chen et al., 2012) and to FeO (this study). 3.2 X-ray Diffraction The (Mg,Fe)O solid solution, excluding the end member FeO, is found in one of two crystal structures in the pressure and temperature range of studies that we conducted. In this chapter, at room pressure and temperature, (Mg0.06 Fe0.94 )O is face-centered cubic, also referred to as B1 or rocksalt structure. Its space group is F m-3m, and the first five reflections, i.e. first 3 lattice planes probed with increasing 2θ, are (111), (200), and (220), where the numbers (hkl) refer to the Miller indices of the lattice planes. In a cubic system, the spacing between lattice planes, or d−spacing, geometrically gives the lattice constant a: dhkl = a (h2 + k 2 + l2 )1/2 (3.1) At high pressure, between 8 and 40 GPa and depending on composition and hydrostatisticy of the sample environment, the cubic structure undergoes a distortion to a rhombohedral structure (space group R-3m). Rhombohedral unit cells are often described using a hexagonal coordinate system, which encompasses the rhombohedron (the c axis of the hexagonal cell corresponds to the long body-diagonal of the rhombohedral unit cell). In this description, the (111) reflection splits 24 into two: (003) and (101), the (200) is renamed as the (012) reflection, and the cubic (220) splits into hexagonal (110) and (104). X-ray diffraction is a scattering technique that measures the elastic, coherent scattering of Xrays off electrons (e.g. Fultz and Howe, 2008, and references therein). Powder XRD is variation of this technique that assumes that sampled grains are randomly oriented, such that scattering in the forward direction samples all allowed reflections. We apply this method to understand the changes in unit cell variations with pressure (and temperature, see Chapter 4). X-ray diffraction can often be performed with in-house X-ray diffractometers with fixed-wavelength sources. The small sample size of diamond anvil cell experiments, however, require higher-intensity radiation to achieve reasonable experiment times. The high flux and versatile energy range of synchrotron experiments make them ideally suited for high pressure experiments. See Duffy and Wang (1998) for a discussion on performing high pressure and temperature XRD experiments at the synchrotron. Figure 3.2: Illustration of Bragg’s law in X-ray diffraction. Elastic scattering occurs in all directions, but constructive interference occurs in directions in which the Bragg condition is satisfied: nλ = 2dsinθ. The XRD measurements presented in this chapter were measured in conjunction with nuclear resonant scattering experiments at Sector 3-ID-B of the Advanced Photon Source, where a MAR345 image plate is inserted downstream from the sample. The angle-dispersive X-ray pattern is integrated radially using the Fit2D software (Hammersley et al., 1996). A CeO2 standard is used to calibrate both the X-ray beam center and the distance between the X-ray focus spot and the detector. 25 The wavelength is optimized, in these experiments, for the resonance energy of 57 Fe of 14.4125 meV. This energy, by design, is not optimized for XRD. The ∼ 1 meV bandwidth provides relatively small flux compared to beam lines tailored for XRD, and the scattering cross-section of electrons at this energy is small. As a result, typical XRD exposures of oxides in a diamond anvil cell require 10 minutes at low pressure and up to 30 minutes at high pressure, whereas at tailored beam lines for XRD at high pressure (e.g. 13-ID-D, APS) exposures are ∼ 1 minute to 2 minutes. Nevertheless, in-situ XRD is required for accurate sound velocity determinations from NRIXS measurements, as the pressure gradients (and therefore uncertainty in the absence of in-situ XRD) can reach upwards of 10 GPa across 100 µm. 3.3 Experimental Details 3.3.1 NRIXS with in-situ XRD This high-pressure nuclear resonance scattering experiment was conducted at Sector 3-ID-B of the Advanced Photon Source at Argonne National Laboratory in August 2011 and October 2012. Three samples were prepared for this experiment. For the high pressure points, beveled anvils with 300 µm-culets were used. The (Mg0.06 Fe0.94 )O sample was embedded in boron epoxy, with rubies on either side, one on each culet. The pressure of the sample’s environment was tracked with both ruby fluorescence (Mao et al., 1986, only visible in compression to initial pressure point) and “diamond edge” Raman spectroscopy of diamond anvil culet (Akahama and Kawamura, 2006), but ultimately the pressure of the sample was determined with in-situ X-ray diffraction. The ambient pressure data point was taken in air. A low pressure data point (11.6 GPa) was taken of a sample loaded in a DAC with beveled 400 µm-culets, with beryllium gasket, and KCl pressure medium. We summarize the compression points measured in Table 3.1. At each compression point, we collected a series of inelastic spectra, a synchrotron Mössbauer spectrum, and an X-ray diffraction spectrum (often both before and after the NRS spectra). Raw spectra are shown in Figure 3.8. Energy scans were collected over a minimum energy range 26 Environment 1 2 3 4 5 6 air KCl, Be gasket B epoxy B epoxy B epoxy B epoxy Pruby a (GPa) 41.2 Psample b (GPa) 11.6 43.5, 48.4e 59.1 72, 76e 85 Energy range (meV) −80 → +100 −60 → +70 −60 → +80 −60 → +80 −60 → +80 −60 → +80 −70 → +130 Scans, count times 1 at 3 sec/pt, 1 at 4 sec/pt 1 at 3 sec/pt, 5 at 5 sec/pt 1 at 3 sec/pt, 3 at 5 sec/pt 1 at 3 sec/pt, 4 at 5 sec/pt 5 scans at 5 sec/pt 7 scans at 5 sec/pt 1 at 3 sec/pt, 5 at 5 sec/pt PXRD c (GPa) 0 9.61(2)d 42.7(7) 55(1) 64(2) 81.6(7) 81.1(8)f Table 3.1: Details of the (Mg0.06 Fe0.94 )O NRIXS experiment. a Pressures were determined off-line using ruby fluorescence (Mao et al., 1986). b Pressures were determined offline using the diamond edge (Akahama and Kawamura, 2006). c Pressures from XRD were determined from the combined equation of state of (Mg0.06 Fe0.94 )O, given in Table 3.3 and Figure 3.5. d Number in parenthesis gives the error on the last digit. e Two numbers listed indicate before and after measurements f Without increasing pressure, the highest compression point was remeasured in October 2012. of −60 → +70 meV. At the highest compression point (#6, ∼82 GPa), the energy scan was measured again in October 2012 with an extended energy range. 3.3.2 SMS with in-situ XRD Figure 3.3: (Mg0.06 Fe0.94 )O at 50 GPa in the Synchrotron Mössbauer study. The sample chamber is 150 µm across. This study was conducted at 300 K. Ruby sphere is located to the left. An independent synchrotron Mössbauer spectroscopy (SMS) experiment was carried out at Sector 3-ID-B of the Advanced Photon Source in February 2012. (Mg0.06 Fe0.94 )O was loaded in a diamond anvil cell with KCl as a pressure-transmitting medium in a rhenium metal gasket. A small ruby was included near the edge of the sample chamber (Figure 3.3). XRD and SMS were collected at 8 compression points over the range 7.8 to 52.4 GPa, determined by the equation of state of 27 KCl (Dewaele et al., 2012). Ruby fluorescence was used to track the pressure offline. As Sector 3 is optimized for NRS (not XRD), with relatively low flux at a low energy with low scattering efficiency off electrons, we only observed one reflection of (Mg0.06 Fe0.94 )O (200) and KCl (110). One reflection is enough to determine the unit cell volume for cubic symmetry, which both KCl and (Mg0.06 Fe0.94 )O are at low pressure. At high pressure, we can estimate rhombohedral distortion, assuming that rhombohedral distortion is solely a function of pressure. In Chapter 4, Figure 4.8 shows the evolution of d-spacings as a function of pressure, and gives the interpolation d012R ≈ − 0.0019 × P + 2.1064, a linear relationship between d-spacing of the rhombohedral (012) reflection and pressure. See Section 4.6 for more details. The d-spacings and resulting pressure of KCl and (Mg0.06 Fe0.94 )O are summarized in Table 3.2. (Mg0.06 Fe0.94 )O d200 are interpreted as either cubic volumes or rhombohedral volumes. Pruby (GPa) 7.92 11.72, 12.17 15.71, 16.59 19.71, 20.1 23.84, 24.17 28.08, 28.62 34.97 PKCl (GPa)a 7.79 13.09 19.16 22.92 29.51 35.73 43.47 52.43 d110 KCl (Å) 2.114 2.100 2.081 2.069 2.049 2.036 2.018 2.000 d200 Mw94 (Å) 2.481 2.415 2.360 2.333 2.293 2.262 2.228 2.196 Vol/atom (Å3 )C 9.443 9.258 9.015 8.851 8.605 8.439 8.223 8.005 Vol/atom (Å3 )R 8.646 8.487 8.275 8.058 Table 3.2: XRD results of the (Mg0.06 Fe0.94 )O SMS experiment. When two numbers are listed, ruby pressures correspond to before and after the SMS and XRD measurement. a KCl pressure is determined from the d-spacing of KCl using the equation of state of KCl (Dewaele et al., 2012). C and R subscripts indicate volumes assuming that the Mw94 d-spacing corresponds to the cubic (200) or rhombohedral (012) reflection. 3.4 Results 3.4.1 XRD: Isothermal Equation of State A Birch-Murnaghan equation of state was fit to the pressure-volume data given in Table 3.2, given by the equations: ( P (V ) = 3K0 fE (1 + 2fE ) 5 2 3 1 + (K00 − 4)fE 4 ) (3.2) 28 1 fE = 2 " V0 V ! 23 # −1 (3.3) where K0 is the initial bulk modulus, K00 is the pressure derivative of the bulk modulus, and fE is Eulerian strain. K00 fixed to 4. Pressure was determined by the equation of state of KCl (Dewaele et al., 2012), and the results are summarized in Table 3.3. In the first fit, sample volumes were interpreted as being cubic given the measured d200 (Table 3.2). Cubic sample volumes are plotted as black circles in Figure 3.4. In the second fit, the rhombohedral estimates of volumes were included. These two fits are plotted in Figure 3.4. 10 3 Volume/atom (A ) 9.5 9 8.5 8 7.5 0 10 20 30 Pressure (GPa) 40 50 60 Figure 3.4: Volume of (Mg0.06 Fe0.94 )O at 300 K determined by its (200) reflection, with pressure determined by the volume of B2-KCl, determined by its (110) reflection, using the equation of state 0 given by Dewaele et al. (2012). Black line is a Birch-Murnaghan equation of state with K0T fixed 3 to 4, giving V0 = 9.91(2) Å /atom, K0T = 160(2) GPa. Red circles show volumes assuming a rhombohedral structure (See text and Table 3.2), and the red dashed curve shows the fit calculated with those points included (V0 = 9.90(3) Å3 /atom, K0T = 164(4) GPa). Equation of state results are summarized in Table 3.3. In the third fit, the room temperature rhombohedral quench data from our high pressure and 29 temperature XRD experiment (Chapter 4) are also included. We plot this combined equation of state in Figure 3.5. This equation of state is used to determine pressure in the NRIXS study. Assume cubic Include rhombo Combineda V0 (Å3 ) 9.91(2) 9.90(3) 9.90446(f ixed) K0T (GPa) 160(2) 164(4) 189(4) 0 K0T 4 (fixed) 4 (fixed) 2.9(1) Table 3.3: Equations of state fit to the (Mg0.06 Fe0.94 )O dataset. a In this fit, the ambient temperature dataset was combined with the 300 K quench data of (Mg0.06 Fe0.94 )O from our high pressure and temperature XRD study (discussed in Chapter 4). 3.4.2 SMS: Magnetic Ordering Transition Figure 3.6 shows the spectra from the synchrotron Mössbauer experiment. Pressure determined by the equation of state of KCl are shown on the right. At low pressure the spectra are characterized by slow oscillations, consistent with no magnetic ordering. With increasing pressure, it is expected that the quadrupole splitting of the nuclear excited state should increase as inter-atom bond shortening accentuates the intra-atom electric field gradient, i.e. the rate of change of electric field at the nucleus. This effect is reflected in the SMS spectrum in the shortening of period between 8 and 13 GPa. This trend does not persist at higher pressures. At 19 GPa the period in the SMS spectrum has increased and continues to do so with pressure up to 23 GPa. At higher pressure the spectra are characterized by fast, irregular oscillations, indicative of a magnetically-ordered state coupled with thickness effects. The changes in the SMS spectrum preceding the magnetically-ordered state at 30 GPa are either indicative of a growing magnetically-ordered component, indicating a gradual transition, or some other change preceding a sharp transition. Careful fitting of the spectra is required. In Figure 3.7, SMS spectra measured in-situ in the NRIXS experiment are shown. Pressures listed are determined from the combined equation of state of (Mg0.06 Fe0.94 )O (Table 3.3) using the 30 10 3.1 3.05 3 9.5 K’0T 2.95 2.9 2.85 9 2.8 3 Volume/atom (Å ) 2.75 2.7 182 8.5 184 186 188 190 192 194 196 K0T (GPa) 8 7.5 7 6.5 0 20 40 60 Pressure (GPa) 80 100 120 Figure 3.5: Volume of (Mg0.06 Fe0.94 )O measured in the SMS experiment (black and red circles, also shown in Figure 3.4) and the thermal equation of state study in Chapter 4. Green circles are volumes of rhombohedral “quench” points after each heating cycle of (Mg0.06 Fe0.94 )O in the buffered experiments, described in Section 4.6 and summarized in Table 4.6. The black line is a Birch-Murnaghan equation of state with V0 = 9.90446 Å3 /atom (fixed), K0T = 189(4) GPa and 0 0 . = 2.9(1). Inset: 1σ error ellipse of K0T and K0T K0T d-spacings from in-situ XRD at each NRIXS pressure point (Table 3.4). Spectra were collected only over the pressure range 43-82 GPa, and all display magnetic ordering and thickness effects. As expected, there is no evidence of a spin transition in the pressure range probed by this study. 3.4.3 NRIXS: Sound Velocities NRIXS spectra were collected over the pressure range 0 to 82 GPa. Raw spectra are shown in Figure 3.8. The phonon peak around 19 meV at ambient pressure moves out to about 24 meV at 55 GPa as vibrations move to higher energy with pressure. We see the emergence of the multi-phonon contribution to the vibrational spectrum at around 80 meV, most visible in the extended energy 31 52 GPa counts 43 GPa 36 GPa 30 GPa 10000 23 GPa 19 GPa 1000 13 GPa 100 8 GPa 10 20 40 60 80 100 120 140 Time (ns) Figure 3.6: Synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K, with data binned into groups of 4. A magnetic transition occurs between 23 and 30 GPa. Pressures listed are determined from the equation of state of KCl (Dewaele et al., 2012). range of the 82 GPa pressure point. Energy scans from our NRIXS study were processed using the PHOENIX software (Sturhahn, 2000) using methods described in Sturhahn (2004). Resulting PDOSs are shown in Figure 3.9. 32 1x106 100000 Counts 10000 82 GPa 1000 64 GPa 100 55 GPa 10 43 GPa 1 0 20 40 60 80 100 120 Time (ns) Figure 3.7: In-situ synchrotron Mössbauer spectra of (Mg0.06 Fe0.94 )O at 300 K, with data binned into groups of 4. A magnetic transition occurs between 23 and 30 GPa. Pressures listed are determined from the combined equation of state of (Mg0.06 Fe0.94 )O, summarized in Table 3.3. The d-spacings from in-situ XRD used to calculate the pressure are listed in Table 3.4. Figure 3.10 shows, in detail, two different phonon dispersion models applied to the low-energy region of the PDOS to derive the Debye velocity using the psvl subroutine in PHOENIX. In this procedure, the PDOS is scaled according to Equation 2.1. A strict “Debye-like” region varies quadratically with energy, which would be flat in this scaling (red line, Figure 3.10). More data can be included if we don’t impose such a strict scaling, fitting instead an empirical function f (E) ≈ VD {1 − (E/E0 )2 } that projects to zero energy (blue line, Figure 3.10). In either case, the zero-energy limit of the scaled PDOS is the Debye velocity (VD ). The lower energy limit of the fitting region to obtain this intercept is limited by the successful subtraction of the elastic peak. The upper limit of the fitting region is determined both by visual inspection, the χ2 of fitting, and reasonable energy ranges where the phonons behave like an acoustic medium. Results from fitting in the psvl routine are presented in Table 3.4 and Figure 3.11. Fitting with 33 1e+09 1e+08 1e+07 counts 1e+06 1e+05 81 GPa 82 GPa 64 GPa 10000 55 GPa 1000 43 GPa 10 GPa 100 10 1 ambient 0.1 -100 -50 0 50 Energy (meV) 100 Figure 3.8: Raw NRIXS spectra of (Mg0.06 Fe0.94 )O at 300 K. Spectra are offset in the y-direction for clarity. 34 400 81 GPa D(E) 82 GPa 64 GPa 200 55 GPa 43 GPa 10 GPa 0 0 50 Energy (meV) ambient 100 Figure 3.9: Partial projected phonon density of states of (Mg0.06 Fe0.94 )O at 300 K, extracted from raw spectra using PHOENIX (Sturhahn, 2000). Spectra are offset in the y-direction for clarity. 35 3.8 57 GPa, 300 K 3.6 empirical fit 3.4 V(E) (km/s) quadratic fit 3.2 1 0.8 3 0.6 0.4 chi 2 2.8 0.2 2.6 0 5 10 15 20 25 0 Energy (meV) Figure 3.10: Debye velocity determination using the psvl subroutine in PHOENIX at 57 GPa. The PDOS is scaled according to Equation 2.1. A quadratic fit to V (E) best describes data up to 12 meV (red line). More of the PDOS can be included if an empirical function is instead used (blue line). VD is the intercept at E = 0 (red and blue circles). Open circles are the χ2 values calculated in psvl, plotted at the Emax of each calculation. 36 the quadratic requirement uses a smaller range of energy. in-situ d200 (Å) 2.480a 2.114 2.023, 2.022b 1.998, 1.995b 1.980, 1.975b 1.948, 1.946b 1.948 ρ (g/cc) 5.93(2) 6.23(3) 7.08(4) 7.36(4) 7.58(4) 7.95(3) 7.94(6) VD(normal) (km/s) 3.08(1) 2.97(2) 3.27(2) 3.40(2) 3.62(2) 3.78(2) 3.73(2) Emin − Emax(normal) (meV) 5.0 − 14.1 5.7 − 19.9 5.7 − 18.6 5.2 − 19.1 3.7 − 20.8 5.9 − 21.0 5.2 − 17.9 VD(quad) (km/s) Emax(quad) (meV) 2.94(2) 3.25(2) 3.3(2) 3.59(2) 3.69(2) 3.64(1) 10.7 10.6 12.1 10.7 10.9 9.0 Table 3.4: Debye Velocity (VD ) of (Mg0.06 Fe0.94 )O as a function of in-situ density, calculated with both the quadratic fit and normal fit. This data is shown in Figure 3.10. a This particular dspacing corresponds to the (111) reflection. b Two d-spacings correspond to before and after XRD measurements. Debye velocities of (Mg0.06 Fe0.94 )O are compared to those of (Mg0.65 Fe0.35 )O (Chen et al., 2012) and FeO (this study, Appendix A.3) in Figure 3.12. In this plot, the (Mg0.06 Fe0.94 )O and (Mg0.65 Fe0.35 )O densities were determined with in-situ XRD. The densities for FeO at low pressure was determined by volume measured with XRD at Sector 12.2.2 of the Advanced Light Source, and at high pressure by volume measured with XRD at Sector 13-ID-D, GSECARS in February 2012. Using the combined equation of state determined in Section 3.4.1, shown in Figure 3.5, we calculated pressure from our in-situ densities and the seismically relevant VP and VS from our VD . The results are summarized in Table 3.5. In Figure 3.13, we plot VP and VS as a function of pressure. For comparison, we plot the sound velocities of (Mg0.65 Fe0.35 )O, measured using NRIXS with in-situ XRD by Chen et al. (2012). At 70 GPa, (Mg0.65 Fe0.35 )O is just coming out of a spin transition, which is reflected in the low P-wave velocities. Between 100 and 140 GPa, the sound velocities of (Mg0.65 Fe0.35 )O are linear with pressure. (Mg0.65 Fe0.35 )O is more iron-rich than expected for typical lower mantle ferropericlase (Murakami et al., 2005), and could be present in in iron-enriched regions of the lower mantle. The sound velocities of (Mg0.06 Fe0.94 )O are much lower than those of (Mg0.65 Fe0.35 )O, and better able to explain ULVZs. 37 4.5 quadratic fit empirical fit VD (km/s) 4 3.5 3 2.5 5.5 6 6.5 7 7.5 8 8.5 density (g/cc) Figure 3.11: Debye velocity (VD ) of (Mg0.06 Fe0.94 )O at 300 K as a function of density. Fits in which a quadratic form of the low-energy region of the PDOS is assumed are shown in white, while a more flexible parameterization of the low-energy region results in Debye velocities shown in gray (empirical fit), as described in the text. Figure 3.10 illustrates the difference between the two fitting routines. 38 Fe1-xO (Mg0.06Fe0.94)O (Mg0.64Fe0.36)O Figure 3.12: (VD ) of (Mg0.06 Fe0.94 )O compared to FeO (Section A.3) and (Mg0.65 Fe0.35 )O (Chen et al., 2012) at 300 K, as a function of in-situ density. (Mg0.65 Fe0.35 )O and (Mg0.06 Fe0.94 )O volumes were measured in-situ at Sector 3-ID-B of the Advanced Photon Source (APS). The volumes of FeO were measured at Sector 12.2.2 of the Advanced Light Source (low density) and at Sector 13-ID-D of the APS (high density). (Mg0.16 Fe0.84 )O is not included in this figure as its volume was not measured in-situ at either Sector 3-ID-B or Sector 13-ID-D. 39 12 Mw94 Fp35 Velocity (km/s) 10 8 V P 6 4 VS 2 0 20 40 60 80 100 120 140 Pressure (GPa) Figure 3.13: Compressional (VP , red) and shear (VS , blue) wave velocities of (Mg0.06 Fe0.94 )O at 300 K, over the pressure range 0 to 82 GPa (circles). For comparison, the velocities of (Mg0.65 Fe0.35 )O are shown as light blue and red squares(Chen et al., 2012). 40 ρa,b (g/cc) 5.93(2) 6.23(3) 7.08(4) 7.36(4) 7.58(4) 7.95(3) 7.94(6) Pressurec (GPa) 0 9.61(2) 42.7(7) 55(1) 64(2) 81.6(7) 81.1(8) VD (km/s) 3.08(1) 2.97(2) 3.27(2) 3.40(2) 3.61(2) 3.78(2) 3.73(2) VP (km/s) 6.47(5) 6.63(6) 7.29(8) 7.48(8) 7.67(8) 7.89(9) 7.87(9) VS (km/s) 2.72(1) 2.62(2) 2.88(2) 3.01(2) 3.19(2) 3.34(2) 3.30(2) G (GPa) 43.9(4) 42.8(7) 58.9(8) 66.5(9) 77.0(9) 89(1) 86.5(8) K (GPa) 189(3) 216(4) 288(7) 324(8) 344(8) 377(9) 376(9) Table 3.5: Summary of sound velocities and bulk and shear moduli of (Mg0.06 Fe0.94 )O as a function of pressure. VP and VS are shown in Figure 3.13. a Number in parenthesis is the error on the last digit. b From Table 3.4. c Pressure is determined from the equation of state of (Mg0.06 Fe0.94 )O, summarized in Table 3.3. 41 Chapter 4 Thermal Equation of State of (Mg0.06Fe0.94)O 4.1 Introduction In the previous two chapters, we carried out nuclear resonant spectroscopy and X-ray diffraction on iron-rich (Mg,Fe)O at 300 K and reported properties as a function of pressure and composition. In this chapter, we explore this material in yet another dimension, temperature, measuring the equation of state of (Mg0.06 Fe0.94 )O at high pressures and temperatures. This study will allow us to explore the phase diagram and density of iron-rich (Mg,Fe)O at pressures and temperatures approaching those of Earth’s core-mantle boundary region. 4.2 Previous Studies Previous pressure-volume-temperature (P − V − T ) studies have shown that the MgO-FeO solid solution is complicated by the existence of phase transitions, a spin transition, and defect clustering as a function of FeO component. The MgO endmember is known to be cubic even beyond the pressure and temperature conditions of the earth’s mantle (Duffy and Ahrens, 1993). The FeO endmember is thought to be cubic at the pressures and temperatures of the interior of the earth, but at lower temperatures is found to transform to rhombohedral structure at moderate pressures (Shu et al., 1998a, e.g.) and then to the B8 NiAs structure at higher pressures (Fei and Mao, 1994; 42 Fischer et al., 2011b, e.g.). Iron-rich (Mg,Fe)O undergoes a cubic to rhombohedral phase transition at 8-40 GPa, with a phase transition pressure sensitive to both composition and hydrostaticity (Figure 3.1). Studies of the bulk modulus at 0 GPa as a function of composition show differing trends due to sample stoichiometry. Studies of non-stoichiometric, iron-rich (Mg,Fe)O show that both KS and KT decreases as a function of Fe concentration (Jacobsen et al., 2002; Richet et al., 1989), where KS is determined from direct measurements of volume, composition, and of VP and VS using ultrasonic interferometry, and KT is determined in a P − V compression study. The trend is opposite for stoichiometric samples, where ultrasonic interferometry studies for iron-poor samples display a positive trend of KS with increasing iron content (Jacobsen et al., 2002). In the iron endmember, KT does indeed depend on stoichiometry, with Fe0.99 O being much less compressible than Fe<0.98 O (Zhang, 2000). Thermal expansion, α = V1 ( δV δT )P has been shown to be insensitive to Fe content for Mgcontaining ferropericlase (Zhang and Kostak Jr , 2002). Yet, it appears to be sensitive to defect concentration. In the Fe end member, α is about 30% larger for Fe0.942 O than Fe0.987 O (Zhang and Zhao, 2005). In this study, we aim to measure the P − V − T equation of state (Mg0.06 Fe0.94 )O, first to constrain the thermoelasticity of iron-rich (Mg,Fe)O and second to see if these trends apply to the equation of state of iron-rich (Mg,Fe)O. 4.3 Experimental Details Two experiments were conducted in this study. For the unbuffered experiment, a symmetric diamond anvil cell with 300 µm-culet diamonds was prepared. (Mg0.06 Fe0.94 )O was lightly ground with NaCl powder (1:1 by volume) in an agate mortar under ethanol, allowed to dry, then pressed into a pellet. This mixture was loaded between two thin NaCl plates (<10 µm), and the remaining space in the rhenium gasket sample chamber was filled with neon using the COMPRES/GSECARS gas-loading system (Rivers et al., 2008). To keep the NaCl dehydrated, the pellet was consistently stored in a desiccator when not in use, and the loaded diamond anvil was placed under vacuum for about one hour and purged with argon before being put into the gas-loading system. In a second high 43 θ Figure 4.1: Example XRD spectra at 85 GPa showing peak identifications for B2-NaCl, hcp-Fe, and Ne. (Mg0.06 Fe0.94 )O is rhombohedral at room temperature (MwR , R-3m) and cubic at high temperature (MwC , Fm-3m). Pressures listed were determined by the equation of state of hcp-Fe (Dewaele et al., 2006; Murphy et al., 2011) pressure experiment, 250 µm-culet diamonds were used. Otherwise, the preparation differed in that the sample pellet also included a Fe metal (1:1 Mw94:Fe by weight) as an in-situ oxygen buffer and pressure marker. The high temperature powder diffraction experiments were conducted at the 13-ID-D beamline (GSECARS) at the Advanced Photon Source, Argonne National Laboratory. High temperatures were achieved in-situ by laser heating from both sides with a split infrared fiber laser (Prakapenka et al., 2008) with temperature determined spectroradiametrically on both up and downstream sides (e.g. Heinz and Jeanloz , 1987). Using an incident X-ray beam of λ = 0.3344 Å, angle-dispersive X-ray diffraction patterns were recorded onto a MAR165 CCD detector and subsequently integrated using Fit2D (Hammersley et al., 1996). Example spectra are shown in Figure 4.1. 44 The 2θ angles corresponding to lattice reflections of (Mg0.06 Fe0.94 )O, NaCl, Fe, and Ne were determined by fitting the spectra with Voigt peaks using Igor Pro (WaveMetrics, Lake Oswego, OR, USA). Unit cell volumes were determined using unweighted linear regression using the Unit Cell refinement software package (Holland and Redfern, 1997), which assumes a minimum uncertainty of 0.005 degrees on each lattice reflection, with errors on the unit cell weighted by goodness of fit. The B2-NaCl thermal equation of state of Fei et al. (2007b) was used to determine pressure in the unbuffered experiment, and to compare that dataset to the buffered experiment. Pressures in the second experiment were determined using the unit cell volume of hcp-iron. We used the Fe equation of state given by Dewaele et al. (2006) for the data collected at 300 K, and the quasiharmonic thermal pressure given by Murphy et al. (2011). The difference between the two pressure scales is small, with a resulting pressure increase of 0.01 to 0.4 GPa for the Murphy et al. (2011) values. To determine temperature and error of our measurements, we took the average and standard deviation of multiple temperature measurements, which are known to have a precision of 100 K (Shen et al., 2001). Errors in temperature and unit cell of NaCl and hcp-Fe were propagated into error in pressure assuming a Gaussian distribution of errors in a simple Monte Carlo error propagation. In the buffered experiment, the discrepancy between measured upstream and downstream temperatures, and the sharp diffraction peaks that show there is no temperature gradient, made it clear that we could not assume a Gaussian distribution. In order to not place undo constraints on the supposed temperature distribution, we used a flat distribution in the error propagation. Calculated volumes and pressures of the buffered dataset are presented in Table 4.1. Calculated volumes and pressures of the unbuffered dataset are presented in Table 4.2. 4.4 Results 4.4.1 Phase Identification In the P –T range of study, we identified cubic (Mg,Fe)O at high temperature and rhombohedral or a mixture of rhombohedral and cubic (Mg,Fe)O at room temperature. We interpret the mixture to be 45 Table 4.1: Pressure-volume-temperature data for the buffered experiment. a Pressure was determined by the equation of state of hcp-Fe from Dewaele et al. (2006) and Murphy et al. (2011). Pressurea (GPa) 116.5(7) 118(1) 118.0(9) 119(1) 120(2) 102.5(4) 103.0(4) 103.8(4) 104.8(6) 105.5(6) 106.4(9) 95.0(5) 95.3(7) 96(1) 97(1) 90.2(6) 90.5(6) 91.2(7) 93(1) 93(1) 93(1) 84.5(7) 84.4(8) 84.7(8) 85(1) 77.3(6) 77.5(8) 79(1) 79(1) 75.7(7) 76(1) 77(1) 77(1) 77(2) 72.4(8) 73(1) 73(1) 74(1) 75(2) 75(2) 60.1(8) 60.4(8) 61(1) 62(1) 63(1) 53.9(7) 54.2(9) 55(1) 56(1) 56(1) 57(1) 51(1) 50.0(8) 51(2) 38.4(4) 38.7(6) 39.0(7) 40(1) 40(1) 33.1(4) Temperature (K) 1056(13) 1218(85) 1295(124) 1436(191) 1649(278) 1124(29) 1212(15) 1370(36) 1563(108) 1646(109) 1852(166) 1184(61) 1296(139) 1426(193) 1620(228) 1201(111) 1303(107) 1459(130) 1707(204) 1807(246) 1917(216) 1105(119) 1162(144) 1270(152) 1379(193) 1051(64) 1135(130) 1332(193) 1460(260) 1089(145) 1169(211) 1285(247) 1356(298) 1490(346) 1119(155) 1179(211) 1268(275) 1454(277) 1626(359) 1604(350) 1131(128) 1205(156) 1364(189) 1520(265) 1671(308) 1136(100) 1205(141) 1356(247) 1466(255) 1558(291) 1631(308) 1311(245) 1177(164) 1435(328) 1324(51) 1370(76) 1416(122) 1581(246) 1643(294) 300 VolM w94 (Å3 ) 6.94(3) 6.94(2) 6.95(2) 6.95(2) 6.95(2) 7.17(1) 7.17(2) 7.19(2) 7.19(1) 7.19(2) 7.20(2) 7.26(3) 7.29(1) 7.30(2) 7.34(1) 7.40(2) 7.43(2) 7.43(3) 7.45(2) 7.45(2) 7.43(1) 7.52(3) 7.52(3) 7.52(2) 7.54(3) 7.65(2) 7.66(2) 7.66(2) 7.66(1) 7.70(1) 7.71(1) 7.72(1) 7.72(1) 7.74(1) 7.80(2) 7.81(2) 7.81(3) 7.81(2) 7.81(2) 7.81(1) 8.05(2) 8.05(2) 8.06(2) 8.06(2) 8.07(2) 8.21(1) 8.22(1) 8.22(1) 8.23(1) 8.23(1) 8.23(1) 8.33(1) 8.32(1) 8.34(1) 8.69(1) 8.69(1) 8.70(1) 8.72(1) 8.72(1) 8.58(3) VolN aCl (Å3 ) 20.10(2) 20.13(3) 20.11(2) 20.12(3) 20.11(2) 20.86(2) 20.87(2) 20.89(2) 20.89(2) 20.89(2) 20.90(2) 21.5(1) 21.45(9) 21.5(1) 21.5(1) 21.66(2) 21.68(2) 21.68(2) 21.69(2) 21.70(2) 21.71(2) 21.98(4) 22.00(3) 22.00(3) 21.98(2) 22.44(3) 22.45(3) 22.45(3) 22.47(3) 22.69(2) 22.65(2) 22.67(2) 22.66(3) 22.67(3) 23.00(3) 23.02(3) 23.05(4) 23.04(3) 23.06(2) 23.03(3) 24.02(7) 24.03(6) 24.01(4) 24.04(4) 24.06(4) 24.74(5) 24.74(6) 24.72(7) 24.76(6) 24.75(6) 24.77(7) 25.29(4) 25.27(4) 25.31(3) 27.07(7) 27.12(4) 27.11(6) 27.15(6) 27.13(7) 26.99(5) VolF e (Å3 ) 16.50(2) 16.50(2) 16.51(2) 16.53(2) 16.55(2) 16.90(1) 16.90(1) 16.92(1) 16.94(1) 16.94(1) 16.97(1) 17.13(1) 17.16(1) 17.18(1) 17.19(1) 17.29(1) 17.31(1) 17.33(1) 17.36(1) 17.37(1) 17.40(1) 17.45(1) 17.48(2) 17.50(1) 17.52(1) 17.70(2) 17.71(2) 17.73(2) 17.75(2) 17.77(1) 17.78(1) 17.79(1) 17.80(1) 17.83(1) 17.90(1) 17.91(1) 17.92(1) 17.94(1) 17.97(1) 17.97(1) 18.41(2) 18.42(2) 18.45(2) 18.47(1) 18.50(1) 18.70(3) 18.71(3) 18.72(3) 18.74(2) 18.75(2) 18.76(2) 18.94(2) 18.91(2) 18.95(2) 19.63(2) 19.63(3) 19.64(3) 19.65(3) 19.66(2) 19.50(2) 46 Table 4.2: Pressure-volume-temperature data for the unbuffered experiment. a Pressure was determined from the equation of state of B2-NaCl (Fei et al., 2007b). Pressurea (GPa) 71.5(4) 71.7(6) 72.0(5) 71.4(4) 71.7(5) 71.9(4) 70(1) 70.0(9) 70.5(7) 69.9(7) 70.1(7) 70.5(9) 67.4(9) 67.7(7) 68.0(6) 64.9(6) 67.4(6) 67.8(5) 67.9(6) 68.1(6) 63.3(3) 63.6(2) 64.1(4) 63.6(2) 63.8(3) 64.1(3) 60.5(5) 61.1(2) 61.4(3) 58.2(1) 60.9(9) 61(1) 62.1(8) 57.6(3) 58.0(5) 58.4(4) 58.3(4) 55.1(2) 57.9(4) 58.1(3) 58.4(2) 58.8(6) 55.2(2) 55.7(3) 56.2(5) 56.1(3) 56.1(4) 53.0(2) 55.9(6) 56.1(3) 56.4(3) 53.0(2) 54(2) Temperature (K) 1227(11) 1312(14) 1442(28) 1208(23) 1317(27) 1413(26) 1192(44) 1306(62) 1433(19) 1173(15) 1279(36) 1396(49) 1226(28) 1293(17) 1403(20) 300 1180(23) 1306(7) 1351(15) 1420(16) 1216(7) 1295(2) 1412(17) 1212(10) 1289(11) 1430(13) 1215(27) 1335(14) 1424(15) 300 1210(10) 1322(17) 1446(23) 1203(24) 1317(40) 1424(43) 1390(20) 300 1207(36) 1308(12) 1382(19) 1451(37) 300 1245(22) 1337(18) 1371(16) 1386(32) 300 1270(23) 1346(18) 1422(15) 300 1224(38) VolM w94 (Å3 ) 7.77(2) 7.78(2) 7.79(2) 7.77(2) 7.78(2) 7.78(2) 7.85(5) 7.84(3) 7.85(1) 7.82(3) 7.83(3) 7.85(3) 7.89(6) 7.89(5) 7.9(5) 7.77(1) 7.88(5) 7.89(5) 7.89(5) 7.9(4) 7.96(4) 7.97(4) 7.97(3) 7.95(3) 7.96(3) 7.97(3) 8.05(5) 8.05(4) 8.05(3) 7.91(3) 8.08(8) 8.04(5) 8.03(1) 8.13(4) 8.13(3) 8.13(3) 8.13(3) 7.93(6) 8.11(3) 8.12(3) 8.12(3) 8.13(3) 7.98(3) 8.18(3) 8.18(2) 8.18(2) 8.17(2) 8.02(1) 8.15(3) 8.16(3) 8.17(2) 8.03(2) 8.21(4) VolN aCl (Å3 ) 22.84(3) 22.85(5) 22.88(4) 22.85(3) 22.86(4) 22.88(4) 22.99(8) 23.00(5) 23.01(5) 22.96(6) 22.98(4) 22.99(6) 23.21(7) 23.21(6) 23.22(5) 23.06(5) 23.18(5) 23.20(5) 23.21(5) 23.22(5) 23.58(2) 23.59(2) 23.60(3) 23.55(1) 23.57(2) 23.60(3) 23.86(4) 23.86(1) 23.87(3) 23.70(1) 23.82(9) 23.84(9) 23.81(7) 24.16(3) 24.18(3) 24.19(2) 24.18(3) 24.02(2) 24.13(2) 24.16(2) 24.16(1) 24.16(5) 24.01(2) 24.39(2) 24.39(4) 24.41(3) 24.41(3) 24.24(2) 24.38(6) 24.40(2) 24.40(3) 24.24(2) 24.6(2) Pressurea (GPa) 55(1) 55(1) 56(1) 56(1) 51.9(5) 54.4(8) 54.7(6) 55.4(6) 55.3(8) 51.9(1) 47(1) 48(1) 48.2(9) 48.8(9) 44.6(7) 45(1) 46(1) 46(1) 47(1) 42.5(8) 41(1) 42.0(9) 43(1) 42.8(8) 38.9(6) 35(1) 39(1) 39(1) 39(1) 40(1) 40(1) 35.8(6) 38.4(9) 39(1) 39.7(9) 35.9(6) 31.4(6) 34.6(9) 35.0(9) 35.3(8) 35.5(7) 31.9(4) 29.8(7) 33(1) 33.6(9) 34(1) 30.1(4) 31.9(9) 32(1) 32.4(9) 32.4(7) 32.8(5) Temperature (K) 1396(42) 1579(16) 1670(24) 1731(9) 300 1140(21) 1239(6) 1437(16) 1483(53) 300 1195(20) 1398(34) 1591(24) 1760(26) 300 1248(24) 1429(15) 1613(15) 1705(35) 300 1186(32) 1387(6) 1561(33) 1584(12) 300 300 1265(35) 1398(37) 1395(23) 1562(38) 1613(28) 300 1165(51) 1436(45) 1594(17) 300 300 1207(77) 1295(68) 1384(50) 1475(25) 300 300 1224(31) 1454(41) 1630(31) 300 1235(36) 1384(65) 1526(21) 1391(60) 1510(31) VolM w94 (Å3 ) 8.22(3) 8.23(2) 8.23(1) 8.24(1) 8.09(5) 8.15(8) 8.16(6) 8.18(3) 8.22(1) 8.06(3) 8.39(4) 8.4(3) 8.41(2) 8.42(1) 8.24(3) 8.42(5) 8.42(4) 8.44(3) 8.45(2) 8.34(4) 8.55(2) 8.56(2) 8.57(2) 8.57(2) 8.4(3) 8.55(7) 8.62(4) 8.63(4) 8.63(4) 8.65(4) 8.65(4) 8.53(9) 8.6(3) 8.63(3) 8.65(4) 8.48(1) 8.63(4) 8.72(1) 8.73(1) 8.76(1) 8.77(1) 8.61(2) 8.62(11) 8.76(2) 8.79(1) 8.81(1) 8.66(4) 8.75(7) 8.78(5) 8.82(4) 8.79(4) 8.81(4) VolN aCl (Å3 ) 24.6(1) 24.6(1) 24.6(1) 24.6(1) 24.37(6) 24.49(8) 24.51(7) 24.52(6) 24.56(6) 24.37(1) 25.5(2) 25.5(1) 25.5(1) 25.51(1) 25.25(9) 25.7(2) 25.7(2) 25.8(2) 25.8(1) 25.54(1) 26.2(2) 26.3(1) 26.3(1) 26.3(1) 26.0(1) 26.7(2) 26.7(2) 26.7(2) 26.7(2) 26.8(1) 26.8(1) 26.5(1) 26.7(1) 26.7(2) 26.8(1) 26.5(1) 27.3(1) 27.4(1) 27.4(1) 27.4(1) 27.4(1) 27.19(8) 27.6(1) 27.6(2) 27.7(1) 27.8(2) 27.53(8) 27.9(2) 28.0(2) 28.0(2) 27.93(9) 27.95(8) 47 a result of incomplete back-transformation of cubic to rhombohedral phase on quench. We plot our results in Figure 4.2. Our before-heating points are shown in gray, bracketing the room temperature cubic-rhombohedral transition between 13 and 24 GPa. Representative error bars (bottom right) show the discrepancy in average standard deviation of temperature measurements between the two experiments. The phase identifications presented in Figure 4.2 are consistent with previous results in that there is no observable B8-structured (Mg0.06 Fe0.94 )O in the pressure and temperature range studied (Kondo et al., 2004). Our study, however, disagrees with the location of the rhombohedral-cubic phase boundary of iron-rich (Mg,Fe)O at high temperature. Where we find no evidence of rhombohedral (Mg0.06 Fe0.94 )O at the high temperatures explored in our study, Kondo et al. (2004) find a transition of cubic to rhombohedral (Mg0.1 Fe0.9 )O and (Mg0.05 Fe0.95 )O at 1100 to 1500 K, 70 to 100 GPa (Figure 4.2). 4.4.2 Equations of State The buffered and unbuffered datasets were fit to a 3rd-order Birch-Murnaghan equation of state using EOSFIT (Angel , 2000), with the following relations: ( P (V ) = 3K0 fE (1 + 2fE ) 1 fE = 2 " 5 2 V0 V 3 1 + (K00 − 4)fE 4 ! 23 ) (4.1) # −1 (4.2) V0 (T ) = V0 (T0 ) exp(α0 (T − T0 )) ∂K K(T ) = K0 + (T − T0 ) ∂T (4.3) ! (4.4) P where P is pressure in GPa, K0 is the bulk modulus in GPa at the reference pressure, in our case the isothermal bulk modulus at either 0 or 30 GPa, fE is Eulerian strain, V and V0 are volume and initial volume, respectively, in units of Å3 /atom. In the high temperature formulation (Equations 48 Figure 4.2: Phase identification of (Mg0.06 Fe0.94 )O in P –T space. (Mg0.06 Fe0.94 )O is cubic (unbuffered: white boxes, buffered: black boxes) at high temperature and rhombohedral (unbuffered: white diamonds, buffered: black diamonds) at room temperature, with exception of some quench measurements that contained a mixture of cubic and rhombohedral phases. Before-heating points are shown below 25 GPa in gray. Light gray lines: the latest phase diagram of wüstite (Fei and Mao, 1994; Fischer and Campbell , 2010; Fischer et al., 2011b,a; Kondo et al., 2004; Ozawa et al., 2010, 2011). Red line: rhombohedral-cubic phase boundary of (Mg0.1 Fe0.9 )O and (Mg0.05 Fe0.95 )O measured by Kondo et al. (2004). Representative error bars are also shown in the lower right corner. 49 Table 4.3: 3rd-order Birch-Murnaghan equation of state parameters for the buffered dataset using hcp-Fe as a pressure marker (Dewaele et al., 2006; Murphy et al., 2011). Reference pressure of either 0 or 30 GPa result in equivalent equations of state. P0 = 0 GPa P0 = 30 GPa 3 V0 (Å ) 9.88(9) 8.6(3) K0T (GPa) 193(14) 275(11) 0 K0T 3.0(2) 2.6(2) α0 (×10−5 K−1 ) 4.2(7) 3.2(4) ∂K/∂T (GPa/K) −0.017(6) −0.021(7) 4.3,4.4), T and T0 are temperature and reference temperature, respectively, in Kelvin, α0 is the thermal expansion coefficient, in units of K−1 , and ∂K/∂T is the isobaric temperature derivative of the bulk modulus, in units of (GPa/K). The equation of state of the buffered dataset (32 to 117 GPa) was fit using pressures given by the equation of state of hcp-Fe (Dewaele et al., 2006; Murphy et al., 2011, (Table 4.3)). The fitted V0 from our study is 9.89(7) Å3 /atom, when using hcp-Fe metal as a pressure indicator, which is consistent with our starting material volume of 9.90(1) Å3 /atom, measured on the sample outside of the diamond anvil cell, which in turn is consistent with our Mössbauer measurement + showing that Fe2 is below detection limit (< 2%). The range of fitted K0 includes that predicted for nearly stoichiometric (Mg,Fe)O (Jacobsen et al., 2002) . Figure 4.3 shows the results from this buffered experiment, showing volume as a function of pressure and temperature. Also shown are the volumes measured as we compressed the cell before the heating experiment began. We did not include these points in the fit. The steeper ∂V /∂P of these points, i.e. lower K0 , is more consistent with (Mg,Fe)O containing >2% vacancies (Zhang, 2000; Jacobsen et al., 2002). Table 4.4 shows the fitting results of both buffered and unbuffered datasets with reference pressures of either P0 = 0 GPa or P0 = 30 GPa, using pressure determined by the equation of state of B2-NaCl (Fei et al., 2007b). The limited pressure range (30 to 70 GPa) of the unbuffered dataset proved difficult to fit without external constraints, so we fixed ∂K/∂T to that of the buffered dataset. If, instead of fixing V0 of one dataset to the other, we fix K0 to 180 GPa, the predicted bulk modulus for a stoichiometric 50 10 1900 1800 9.5 1700 9 8.5 1500 1400 8 Temperature (K) Volume/atom (Å3) 1600 1300 7.5 1200 7 1100 0 20 40 60 80 Pressure (GPa) 100 120 Figure 4.3: P − V − T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the buffered experiment. Pressures were determined using the equation of state of Fe (Dewaele et al., 2006; Murphy et al., 2011). Open circles: pre-experiment volumes at pressures determined by the equation of state of B1-NaCl (JCPDS 5-0628). Table 4.4: 3rd-order Birch-Murnahan equation of state parameters the both the buffered and unbuffered dataset using B2-NaCl as a pressure marker (Fei et al., 2007b). In both cases, the ∂K/∂T of the unbuffered dataset is fixed to that of the buffered. P0 = 0 GPa P0 = 30 GPa buffered unbuffered buffered unbuffered V0 (Å3 ) 9.85(8) 9.8(1) 8.69(3) 8.64(1) K0T (GPa) 202(12) 201(24) 276(9) 283(11) 0 K0T 2.7(1) 3.0(4) 2.3(1) 2.6(5) α0 (×10−5 K−1 ) 3.3(6) 3.6(1) 2.5(4) 2.89(7) ∂K/∂T (GPa/K) −0.013(5) −0.013 (f ixed) −0.016(7) −0.016 (f ixed) 51 Table 4.5: Equation of state parameters using B2-NaCl as a pressure marker (Fei et al., 2007b), where we fix K0T to 180 GPa. buffered unbuffered 3 V0 (Å ) 10.0(3) 9.9(1) K0T (GPa) 180 (f ixed) 180 (f ixed) 0 K0T 2.95(7) 3.29(6) α0 (×10−5 K−1 ) 3.0(7) 3.41(7) ∂K/∂T (GPa/K) −0.010(5) −0.010 (f ixed) magnesiowüstite (Jacobsen et al., 2002), we again get equation of state parameters that yield values consistent with our previous fits (Table 4.5). Figure 4.4 shows the results from the unbuffered experiment, showing volume change of (Mg0.06 Fe0.94 )O as a function of pressure and temperature, using NaCl as a pressure marker (Fei et al., 2007b). 4.5 Discussion 4.5.1 Effect of Buffering on Equation of State In Figure 4.5, we compare the first dataset to the second, showing example volumes and isotherms at 1200, 1500, and 1800 K. At 50 GPa, the calculated thermal expansion coefficients are αbuf f ered = 2.1(6) × 10−5 K−1 and αunbuf f ered = 2.6(1) × 10−5 K−1 . We first note that the sole room temperature quench point of the buffered dataset is consistent with the unbuffered dataset (Figure 4.5, black filled circle and squares), and the room temperature equations of state are consistent (Table 4.4). The initial thermal expansion coefficient (α0 ) of the two datasets are also consistent within error. The discrepancy between un-annealed (before heating) low pressure and annealed (heated) high pressure measurements suggests a physical difference between cold-compressed and annealed ironrich (Mg,Fe)O even without an Fe metal buffer. It has been proposed that vacancy concentrations in non-stoichiometric FeO-bearing samples are reduced with the exsolution of (Fe,Mg)Fe2 O4 at high pressure and temperature according to (M gx F ey )O → a(M gx0 F e1−x0 )F e2 O4 + b(M gx00 F ey00 )O (4.5) 52 9 1700 8.8 1600 3 1500 8.4 1400 8.2 8 Temperature (K) Volume/atom (Å ) 8.6 1300 7.8 1200 7.6 20 30 40 50 Pressure (GPa) 60 70 80 Figure 4.4: P − V − T data and isotherms of B1-structured (Mg0.06 Fe0.94 )O in the unbuffered experiment with ∂K/∂T fixed to that of the buffered experiment. Equation of state parameters corresponding to these curves are those in Table 4.4. 53 8.9 Mw94 (buffered) Mw94 (unbuffered) 1900 1800 8.8 1700 8.7 3 Volume/atom (Å ) 1600 8.6 1500 8.5 1400 1300 8.4 1200 8.3 1100 8.2 30 35 40 Pressure (GPa) 45 50 Figure 4.5: Overlay of data and equations of state of (Mg0.06 Fe0.94 )O in both experiments. The unbuffered (squares, solid lines) and buffered (circles, dashed lines) datasets are in good agreement where they overlap in pressure-temperature conditions. 54 Mw94 (this study) FeO (Fischer et al., 2011) 2100 2000 7.2 1900 7.15 7.1 1700 1600 7.05 1500 Temperature (K) Volume/atom (Å3) 1800 7 1400 6.95 1300 1200 6.9 1100 6.85 100 105 110 115 Pressure (GPa) 120 Figure 4.6: Comparison of volume measurements and equations of state of buffered (Mg0.06 Fe0.94 )O (circles, solid lines) to B1-FeO (squares, dashed lines) (Fischer et al., 2011b). where (x00 + y 00 ) > (x + y), ensuring the stoichiometry of the (Mg,Fe)O phase regardless of oxygen fugacity (Zhang and Zhao, 2005; McCammon et al., 1998). If this were true in our case, it would also explain the similarity between the buffered and unbuffered datasets at high pressure and temperature. 4.5.2 Effect of Composition on the Thermal Equation of State of (Mg,Fe)O In Figure 4.6, we compare (Mg0.06 Fe0.94 )O to the equation of state and volumes of FeO (Fischer et al., 2011b) to determine the effect of incorporation of Mg on the equation of state FeO. Both experiments were conducted with in-situ Fe metal buffer/pressure marker. At our highest pressure, 117 GPa, we were not able to discern a difference between the thermal expansion of Mw94 and FeO (α(M g0.06 F e0.94 )O = 1.5(7) × 10−5 K−1 and αF eO ≈ 1.4(1) × 10−5 K−1 ). 55 FeO (Fischer et al., 2011) (Mg0.06Fe0.94)O (this study) 6 (Mg Fe 0.64 )O (van Westrenen et al., 2005) 0.36 MgO (Dubrovinsky et al., 1997) _ (x10−5 K−1) 5 4 3 2 1 1900 K 0 20 40 60 80 100 120 Pressure (GPa) Figure 4.7: Thermal expansion at 1900 K as a function of pressure (Table 4.3), compared to FeO (Fischer et al., 2011b), (Mg0.64 Fe0.36 )O (Westrenen et al., 2005), and MgO (Dubrovinsky and Saxena, 1997). Dashed lines show areas of extrapolated curves, and error bars shown are the 1σ error in thermal expansion coefficient. In Figure 4.7, we plot the thermal expansion of different members of the (Mg,Fe)O solid solution as a function of pressure, at 1900 K. At ambient pressure, the thermal expansion of MgO, (Mg0.64 Fe0.36 )O, and FeO vary as a function of composition. Within our experimental uncertainties, we cannot resolve a compositional effect on the thermal expansion of (Mg,Fe)O at high pressures. Given the different experimental conditions of our buffered and unbuffered datasets, Fe/Mg compositional variation may also be a concern. It is imaginable that buffering with Fe metal could lead to a different Fe/Mg ratio in the (Mg,Fe)O than the mechanism in Equation 4.5 would. However, given that we cannot distinguish (Mg0.06 Fe0.94 )O from FeO, if our buffered (Mg0.06 Fe0.94 )O were slightly enriched in Fe compared to the unbuffered (Mg0.06 Fe0.94 )O, we would not know how to distinguish the two without sample recovery. 56 4.6 Rhombohedral Distortion of (Mg0.06 Fe0.94 )O Volumes and lattice parameters of rhombohedral-structured (Mg0.06 Fe0.94 )O were fit using methods described above. As depicted in Figure 4.2, rhombohedral (Mg0.06 Fe0.94 )O was stable at room temperature at pressures higher than 20 GPa. In the unbuffered experiment, room temperature patterns revealed a mixture of rhombohedral and cubic phases, while in the buffered experiment, only rhombohedrally-structured (Mg,Fe)O was present higher than 34 GPa. Figure 4.8 shows the evolution of the lattice reflections of (Mg0.06 Fe0.94 )O. Before-heating points, shown in gray, show the cubic (111), (200) and (220) reflections that split accordingly: (111)C → (003)R +(101)R and (220)C → (104)R +(110)R . These five reflections were used to refine the unit cell volume. Black circles show measurements of the buffered dataset, and are less scattered than the white circles. Pressure was determined using the (111) and (200) reflections of solid neon (Dewaele et al., 2008) or by the (100), (200), (101), (102), (110), (103), and (112) reflections of hcp-iron (Dewaele et al., 2006). Despite the obvious mismatch between the two datasets in the (003) reflection below 47 GPa, the two datasets appear to agree within scatter above 47 GPa. This observation is more apparent in Figure 4.9, which shows the c/a ratio of the hexagonal unit cell for each measurement. Above 55 GPa, the c/a ratios of the two datasets are indistinguishable. Another observation we note here is the leveling off of the distortion, apparently starting at 70 GPa. This dataset shown in Figure 4.10, combined with the low-pressure measurements taken at Sector 3-ID-B (Section 3.4.1), was used to constrain the equation of state of (Mg0.06 Fe0.94 )O at 300 K for use in determining the pressure and sound velocities from NRIXS data (see 3.4.1). 57 1#0#1#before#hea6ng# 2.6# 0#0#3#before#hea6ng# 1#0#1#unbuffered# 1#0#1#buffered# 2.5# "0#0#3#unbuffered# (1#1#1)C# 0#0#3#buffered# (0#0#3)R# d-spacing (Å)! 2.4# 2.3# 2.2# (1#0#1)R# 2.1# 2# 0# 20# 40# 60# 80# 100# 120# Pressure (GPa)! 2.2# "unbuffered#dac#9"# 2.15# "buffered1# (2#0#0)C# d-spacing (Å) ! 2.1# "before#hea<ng"# 2.05# 2# (0#1#2)R# 1.95# 1.9# 1.85# 0# 20# 40# 60# 80# 100# 120# Pressure (GPa)! 1.55# 1#0#4#unbuffered# 1#0#4#buffered# 1#1#0#unbuffered# 1#1#0#buffered# 1#1#0#before#hea:ng# 1#0#4#before#hea:ng# (2#2#0)C# 1.5# d-spacing (Å)! 1.45# (1#0#4)R# 1.4# 1.35# (1#1#0)R# 1.3# 1.25# 0# 20# 40# 60# 80# 100# 120# Pressure (GPa)! Figure 4.8: Evolution of d-spacings of (Mg0.06 Fe0.94 )O as a function of pressure. Gray circles: before heating experiment began. White circles: unbuffered dataset. Black circles: buffered dataset. Pressure was determined from the unit cell of neon (Dewaele et al., 2008). 58 2.69% Fe.93O (Jacobsen et al., 2005)! c/a ratio! 2.64% 2.59% Mw78 (Zhuravlev et al. 2010)! 2.54% 2.49% unbuffered! cubic% buffered! 2.44% 0% 20% 40% 60% 80% 100% 120% Pressure (GPa)! Figure 4.9: Evolution of c/a ratios of rhombohedral (Mg0.06 Fe0.94 )O as a function of pressure at 300 K. White circles: unbuffered dataset. Black circles: buffered dataset. Pressure was determined from the unit cell of neon (Dewaele et al., 2008). Error bars are determined from the unit cell refinement. 59 10 300 K, rhombohedral 9.5 Volume/atom (A3) 9 o 8.5 8 7.5 7 6.5 0 20 40 60 80 100 120 Pressure (GPa) Figure 4.10: Pressure-volume data of quenched, rhombohedral (Mg0.06 Fe0.94 )O at 300 K, with pressure determined either by hcp-Fe (Dewaele et al., 2006, gray squares) or Ne (Dewaele et al., 2012, blue circles). Quench points are those after each heating cycle. Black line is a 3rd-order Vinet equation of state fit to the data using pressure determined from the equation of state of neon, where 0 V0 = 9.65(7) Å3 /atom, K0T = 281(22) GPa, and K0T = 0.6(4). 60 Table 4.6: Pressure-volume data for the buffered experiment at 300 K. a Pressure was determined from the equation of state of hcp-Fe (Dewaele et al., 2006). b Pressure was determined from the equation of state of Ne (Dewaele et al., 2008). c Volumes of hcp-Fe were refined using 7 reflections: (100),(200), (101), (102), (110), (103), and (112). d Volumes of Ne were determined using 2 to 3 reflections of (111), (200), and (220). e Measurements after each heating cycle is referred to in the text as “quench” points. PF e a (GPa) 112.8(8) 112.9(6)e 98.3(5) 98.7(4)e 89.5(9) 90.4(4)e 85.1(3) 85.8(2)e 80.5(4) 80.8(3)e 74.0(4) 74.7(4)e 71.3(3) 71.6(4)e 67.9(7) 68.3(4)e 55.4(6) 55(1)e 48.6(6) 49.1(8)e 48.3(7) 45.6(4)e 38(1) 39(1)e 33(1) 33.1(4)e PN e b (GPa) 113(1) 113.3(9) 98(2) 98(3) 90(2) 92(1) 86(1) 86(2) 82(1) 81(1) 75(1) 75.8(6) 73(1) 73.3(6) 68(1) 68(1) 58(1) 57(1) 50.1(3) 51.5(2) 46.5(3) 46.8(3) 39(1) 40(1) 34(2) 33(2) V olF e c Å3 16.45(2) 16.45(1) 16.84(2) 16.83(1) 17.10(3) 17.08(1) 17.24(1) 17.218(8) 17.39(1) 17.38(1) 17.62(2) 17.59(1) 17.71(1) 17.70(1) 17.84(3) 17.83(2) 18.35(3) 18.38(5) 18.66(3) 18.64(4) 18.68(4) 18.81(2) 19.23(4) 19.15(2) 19.52(3) 19.50(2) V olN e d Å3 25.39(7) 25.36(5) 26.4(2) 26.4(2) 26.9(1) 26.8(1) 27.3(1) 27.2(1) 27.66(9) 27.7(1) 28.3(1) 28.21(6) 28.5(1) 28.45(6) 29.0(1) 29.0(1) 30.2(1) 30.3(1) 31.35(5) 31.12(3) 31.93(5) 31.89(5) 33.3(3) 33.2(2) 34.5(4) 34.7(5) V olM w Å3 /atom 6.84(1) 6.81(5) 7.10(5) 7.04(4) 7.20(7) 7.20(6) 7.31(5) 7.30(6) 7.41(5) 7.39(4) 7.56(3) 7.56(3) 7.63(3) 7.62(3) 7.78(4) 7.73(3) 8.08(3) 7.94(2) 8.18(6) 8.11(2) 8.22(3) 8.17(6) 8.47(4) 8.42(1) 8.55(4) 8.58(3) aM w Å 2.612(7) 2.60(1) 2.64(1) 2.65(1) 2.66(1) 2.66(1) 2.672(9) 2.67(2) 2.683(8) 2.683(8) 2.703(5) 2.704(6) 2.712(8) 2.71(1) 2.731(7) 2.727(5) 2.777(6) 2.751(3) 2.78(1) 2.781(4) 2.800(6) 2.79(1) 2.825(7) 2.819(2) 2.845(6) 2.846(5) cM w Å 6.90(3) 6.87(5) 6.99(5) 6.98(5) 7.05(5) 7.04(4) 7.09(4) 7.08(6) 7.13(3) 7.12(3) 7.17(2) 7.16(2) 7.18(1) 7.18(2) 7.22(2) 7.20(2) 7.26(2) 7.27(1) 7.32(3) 7.26(1) 7.27(2) 7.27(3) 7.35(3) 7.34(1) 7.32(2) 7.34(2) V olN aCl Å3 20.10(4) 20.05(4) 20.84(2) 20.78(2) 21.42(9) 21.24(2) 21.62(3) 21.53(2) 21.92(3) 21.88(3) 22.39(3) 22.31(2) 22.62(2) 22.57(2) 22.99(4) 22.87(2) 23.9(1) 23.88(4) 24.70(5) 24.58(3) 25.15(2) 25.12(2) 26.27(6) 26.13(2) 26.8(1) 26.99(5) 61 Chapter 5 Implications for Ultralow-velocity Zones 5.1 Physical Mixing Models To explore the expected sound velocities and density of an ultralow-velocity zone containing iron-rich (Mg,Fe)O, we can construct simple models that combine the properties of iron-rich (Mg,Fe)O and mantle silicates. We show that a small amount of iron-rich (Mg,Fe)O can greatly reduce the average sound velocity of an aggregate assemblage. When combined with a geodynamic model of a solid ULVZ (Bower et al., 2011), we can directly correlate inferred sound velocities to mineralogy and predicted ULVZ shapes. Our combined geodynamic and mineral physics model of a solid ULVZ can be used to explore the relationship between the observed sound velocities and mineralogy of ULVZs with added insight into ULVZ morphology. 5.1.1 Extrapolation of Magnesiowüstite properties to the CMB Re-evaluation of sound velocities of (Mg.16 Fe.84 )O occurred after publication, which was presented unaltered in Chapter 2. Updates include a re-analysis of the sample, finding the composition to be (Mg0.18 Fe0.78 Ti0.04 )O. In addition, we assume that equation of state of (Mg.16 Fe.84 )O can be approximated by that of (Mg.06 Fe.94 )O, rather than that of (Mg.12 Fe.78 )O. This equation of state choice should be more self-consistent, as both samples were made in the exact same way. Updated Debye velocities of (Mg.16 Fe.84 )O are shown in Figure 5.1, underlying those of (Mg.06 Fe.94 )O and 62 FeO presented in Chapter 3. Mw94 Mw84 FeO 4.5 VD (km/s) 4 3.5 3 5.5 6 6.5 7 7.5 8 8.5 9 density (g/cc) Figure 5.1: Debye velocity as a function of density of (Mg.16 Fe.84 )O, (Mg.06 Fe.94 )O, and FeO. (Mg0.06 Fe0.94 )O volumes were measured in-situ at Sector 3-ID-B of the Advanced Photon Source (APS). The volumes of FeO were measured at Sector 12.2.2 of the Advanced Light Source (low density) and at Sector 13-ID-D of the APS (high density). The volumes of (Mg0.16 Fe0.84 )O above ambient pressure were not measured, but estimated using ruby pressure, initial volume measured 0 = at the ALS, and the equation of state parameters (Mg.06 Fe.94 )O: of K0T = 189(4) GPa and K0T 2.9(1). Figure updated from Figure 3.12 to include recalculated (Mg.16 Fe.84 )O. The Debye velocities in Figure 5.1 exhibit a linear increase as a function of density above 6.5 g/cc, independent of composition. As the highest density of (Mg.16 Fe.84 )O at 8.7 g/cc corresponds to a pressure of 121 GPa, we extrapolate that this linear trend is valid up to the core-mantle boundary pressure of 135 GPa. In the latest formulation of the mixing model, presented below, the Debye sound velocities of (Mg.06 Fe.94 )O are linearly extrapolated to 135 GPa. This choice is made for self-consistency reasons, as it is the only dataset with in-situ volumes mapped directly onto its own equation of state. Here we assert that the Debye sound velocity as a function of density of (Mg.16 Fe.84 )O is the same as that of (Mg.06 Fe.94 )O, since we cannot discern a difference. This assumption, however, introduces a slight inconsistency in the parameterization of Debye velocity with other compositions, which will 63 have to be worked out before this model can be published. Namely, this simple extrapolation to the CMB gives a (Mg.16 Fe.84 )O density of 8.63 g/cc, which is lower than the highest density plotted in Figure 5.1. We estimate the sound velocities of (Mg.16 Fe.84 )O at high temperature by using the temperature derivatives ∂VP /∂T = −4.64×10−4 (km s−1 K−1 ) and ∂VS /∂T = −3.85×10−4 (km s−1 K−1 ), measured for MgO up to 20 GPa and 1650 K (Kono et al., 2010). Density is adjusted for high temperature using the equation of state we measured on buffered (Mg.06 Fe.94 )O (Chapter 4, Table 4.3). 5.1.2 Mixture of Magnesiowüstite and Ambient Mantle One such model represents a mixture of iron-rich (Mg,Fe)O and ambient mantle, and is hereafter referred to as “Mw+PREM”. Prior versions of this model were published in Wicks et al. (2010) (Chapter 2) and updated in Bower et al. (2011), and mixes iron-rich oxide with surrounding lower mantle represented by the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson, 1981). This binary mixture can be thought of as a disequilibrium assemblage of lower mantle material mixed with iron-rich oxide. Considering a physical mixing scenario in which an iron-rich oxide is combined with ambient mantle has two advantages. First, it is generally accepted that a large fraction of the lower mantle is made up of silicate perovskite, due to the fact that the expected sound velocities and density of perovskite largely agree with PREM. Using the seismic velocities and densities of PREM, therefore, should be a good approximation to using sound velocities and densities of perovskite, although it likely represents a mixture of phases. Second, without knowing the mechanism by which a ULVZ is formed, it is conceivable that a ULVZ can simply be a mixture of lower mantle and core material. There is increasing evidence for complexity on the core side of the core-mantle boundary which could be an expression of exsolved “sediments” on the top of the core (Buffett et al., 2000). Therefore, a ULVZ could simply be ambient mantle mixed with FeO, which is what this mixing model represents. We then calculate the Voigt and Reuss bounds for VP , VS , and density (Watt et al., 1976) for a 64 Table 5.1: Model parameters for mixing model “Mw+PREM” VP (km/s) VS (km/s) density (g/cc) PREM 13.714 7.2648 5.5613 Mw84 (2700 K) 7.3014 2.705 8.3001 Mw84 (4700 K) 6.3734 1.935 8.2288 given vol% of (Mg.16 Fe.84 )O and PREM at 135 GPa, choosing a low (2700 K) and high (4700 K) temperature estimates of the core-mantle boundary (Figure 5.2). Model parameters are listed in Table ??. Voigt (uniform stress) and Reuss (uniform strain) bounds bracket the upper and lower bounds of mixing of the bulk modulus K, shear modulus G and density ρ, from which we calculate VP and VS using Equation 2.2 and G = ρVS2 . ULVZ VP 12 8.5 27 8 -20% 00 K 47 10 00 K 7.5 VP 8 VP 4 700 270 0K K -10% 6 ULVZ VS Density (g/cc) Velocity (km/s) mw+PREM -5% mw+PREM 14 7 6.5 -30% +10% VS 2 4 6 700 +5% K VS 4700 K 5.5 2 0 0.2 0.4 0.6 volume fraction (Mg.16Fe.84)O 0.8 ULVZ - 1 0 0.2 0.4 0.6 0.8 1 volume fraction (Mg.16Fe.84)O Figure 5.2: Voigt (upper)-Reuss (lower) bounds of VP , VS (left), and density (right) of (Mg.16 Fe.84 )O with PREM at 135 GPa. Gray shading shows typical ULVZ velocities (-5-20% VP , -10-30 %VS , with respect to surrounding mantle) reported by seismology. Density is not very well constrained by seismology, but have been quoted at +8-10% (Rost et al., 2006; Idehara et al., 2007, e.g.). Dynamic models such as those by McNamara et al. (2010) predict ULVZs with densities of at least +5% with respect to surrounding mantle, yet models by Bower et al. (2011) create reasonable ULVZs corresponding to less than 5% density increase. To first order, mixing of just 20 vol% of (Mg.16 Fe.84 )O with 80 vol% silicates (represented here by PREM) matches signature seismic observations for the ULVZ (Figure 5.2). 5.1.3 Mixture of Magnesiowüstite and Silicate Perovskite A second mixing model, a prior version of which is published in Bower et al. (2011), again starts with the assumption that iron-rich oxide is present in a ULVZ and explores a possible equilibrium 65 assemblage of iron-rich (Mg,Fe)O and perovskite. Hereafter we refer to it as “Mw+Pv”. The partitioning behavior of Fe vs. Mg between the two phases has been probed at lower mantle pressures by numerous studies without much agreement, but recent studies show a preferential P v/M w partitioning of Fe into the oxide phase, which we adopt: KD ≈ 0.07 (Auzende et al., 2008; Sakai et al., 2009; Sinmyo et al., 2008), assuming an aluminum-free system. In addition to representing the P v/M w simple phase assemblage that we model in this mixture, a low KD is required by this exercise in order to achieve reasonable densities for appropriate velocity decrements. In other words, too much iron in perovskite would create ULVZs denser than those consistent with observed heights, with velocities that are not low enough. P v/M w Other studies find the partitioning behavior to be less extreme, determining KD P v/M w an assumed “pyrolite” mantle composition, or KD ≈ 0.42 for ≈ 1.11 in the presence of post-perovskite (Sinmyo et al., 2011). Partitioning behavior is known to be a function of composition, pressure, and the presence of post-perovskite, but with opposite conclusions between even the most recent studies, P v/M w KD is still an uncertainty (Sinmyo et al., 2011; Catalli et al., 2009). If we assert that (Mg.16 Fe.84 )O exists at the core-mantle boundary, a coexisting perovskite in P v/M w equilibrium would have the composition (Mg.72 Fe.28 )SiO3 , using KD ≈ 0.07 (Sakai et al., 2009; Auzende et al., 2008). This resulting assemblage is very Fe-rich, and would require a formation mechanism capable of making such an exotic composition. We model the densities and sound velocities of perovskite using a finite-strain model given by Li and Zhang (2005), making a compositional correction to the density. Bulk and shear moduli have also been predicted to be compositionallydependent (Kiefer et al., 2002), but we found the resulting differences to be negligible (Bower et al., 2011). We calculate the Voigt and Reuss bounds for VP , VS and density for a given vol% of (Mg.16 Fe.84 )O and (Mg.72 Fe.28 )SiO3 perovskite at 135 GPa and 2700 and 4700 K (Figure 5.3). The resulting mixing model is presented in Figure 5.3. Here, at X(M g,F e)O = 0, we see the temperature dependence of the modeled perovskite in both velocities and densities of the silicate fraction. The range of expected perovskite velocity at the two extreme temperature estimates is 66 Table 5.2: Model parameters for mixing model “Mw+Pv” VP (km/s) VS (km/s) density (g/cc) Pv (2700 K) 14.013 7.4287 5.7157 Pv (4700 K) 13.57 6.9129 5.4935 Mw84 (2700 K) 7.3014 2.705 8.3001 Mw84 (4700 K) 6.3734 1.935 8.2288 much larger than the difference between perovskite and PREM, which falls between the two. We conclude that the choice of silicate model (PREM vs (Mg,Fe)SiO3 ) then is not distinguishable given the uncertainty in temperature of the CMB region. 8.5 27 8 ULVZ VP 12 mw+Pv -5% mw+Pv 14 K 47 -20% 00 K 7.5 10 VP 8 VP 4 700 27 00 K K -10% 6 ULVZ VS Density (g/cc) Velocity (km/s) 00 7 6.5 -30% +10% 4 VS 2 VS 4700 2 0 0.2 0.4 0.6 0.8 6 700 ULVZ + +5% K K 5.5 1 volume fraction (Mg.16Fe.84)O 0 0.2 0.4 0.6 0.8 1 volume fraction (Mg.16Fe.84)O Figure 5.3: Voigt (upper)-Reuss (lower) bounds of VP , VS (left), and density (right) of (Mg.16 Fe.84 )O with (Mg,Fe)-perovskite. Gray shading same as in Figure 5.2 In both this model and in Mw+PREM, we find that only about 20% iron-rich magnesiowüstite is needed to drop the sound velocities of an assemblage. The density of perovskite is higher than PREM at 2700, but lower at 4700, so the density of Mw+Pv is greatly affected by temperature choice. As a result, the amount of Mw85 needed to match reported densities according to seismic studies jumps from 15% at 2700 K to 25% at 4700 K. 5.1.4 Dynamics of a Solid-state ULVZ The mixing models described above show that ULVZ velocities and densities can be adequately represented by a mixture of iron-rich (Mg,Fe)O and perovskite or silicate-rich surrounding mantle. We can take this model one step further by interpreting these models in the context of dynamic 67 models (Bower et al., 2011, specifically). We explored the morphologies of solid-state ULVZs in a two-dimensional dynamic model, solving the steady-state thickness and shape of ULVZs as a function of prescribed initial thickness and chemical vs. thermal buoyancy (Bower et al., 2011). By exploring a range of thicknesses and buoyancy numbers B, this study creates a range of candidate ULVZ sizes and shapes that can be mapped to mineral physics models via density and assumed temperature drop across the core-mantle ∆ρch Rb thermal boundary layer, according to the definition of buoyancy number: B = Ra = ρα∆T , where Rb Ra is the ratio of chemical to thermal Rayleigh numbers, ∆ρch is the chemical density anomaly of the ULVZ layer, ρ and α are density and thermal expansion of the mantle, and ∆T is the temperature drop across the CMB. More detailed descriptions of the dynamic models are found in Bower et al. (2011). Taking the density calculations of the two mixing models, and assuming a lower bound of ∆TCM B of 500 K and an upper bound of ∆TCM B =1500 K across the thermal boundary layer just above the core-mantle boundary, the range of dynamic models of Bower et al. (2011) map to volume fractions of ∼ 0.01 − 0.26 of (Mg.16 Fe.84 )O for the Mw+PREM model, and ∼ 0.03 − 0.29 for the Mw+Pv model. These models introduce a new kind of constraint: a much smaller density contrast, and therefore smaller amount of iron-rich (Mg,Fe)O, creates shapes with larger aspect ratios (height/width), whereas a larger density contrast and more iron-rich (Mg,Fe)O generally creates ULVZs that are flat yet wide. A seismic study that constrains the width and size of ULVZs now has a way to constrain density, assuming a solid mixed component. A recent review of the core mantle boundary suggests that a CMB temperature of ∼ 4000 K and a temperature drop across the CMB thermal boundary layer of ∼1200-1800K (Tackley, 2012) best satisfies combined seismological and mineral physics constraints.Our mixing models, then, can be recalculated at a CMB temperature of 4000 K and ∆TCM B of 1500 K to predict ULVZ morphologies. We plot the Voigt-Reuss-Hill curves in Figure 5.4. It’s important to note that the assumptions we made in these models can be revised as more is learned about the temperature and mineralogy of Earth’s core-mantle boundary. The high-iron 68 Table 5.3: Model parameters for mixing model “Mw+PREM” and “Mw+Pv” at 4000 K VP (km/s) VS (km/s) density (g/cc) PREM 13.714 7.2648 5.5613 Pv (4000 K) 13.712 7.0886 5.5795 Mw84 (4000 K) 6.6982 2.2045 8.23 Figure 5.4: Voigt-Reuss-Hill curves of VP and VS of the mixing of (Mg.16 Fe.84 )O with PREM (left) and (Mg,Fe)SiO3 -perovskite (right), at TCM B = 4000 K. Assuming an average temperature drop across the CMB thermal boundary layer of ∆TCM B = 1500K (Tackley, 2012), ULVZs with moderate velocity drops are consistent with 5% (Mg,Fe)O, and are consistent with smaller structures with high aspect ratio from Bower et al. (2011). ULVZs with larger velocity drops are consistent with ∼ 20% (Mg,Fe)O, and are consistent with wider, flatter structures. At a CMB temperature of 4000 K, the ULVZ shapes predicted by PREM vs perovskite are indistinguishable (left and right panels, respectively). content of a (Mg,Fe)O+Pv assemblage is too dense to explain ULVZs at cool temperatures, but adequately explains ULVZs at high temperatures (Bower et al., 2011). Knowing both the absolute temperature and the temperature drop across the thermal boundary layer would allow us to compare different scenarios as a function of density. Further studies on the mineral properties of mantle phases at high temperature are also required. One example is the extrapolation of sound velocities with temperature. Very few studies exist that measure the velocity derivatives of MgO at high temperature, and none exist in the ironbearing system. The velocity derivatives we used, measured up to 20 GPa and 1650 K, ∂VP /∂T = −4.64×10−4 (km s−1 K−1 ) and ∂VS /∂T = −3.85×10−4 (km s−1 K−1 ) (Kono et al., 2010), are slightly lower than those measured on MgO at room pressure, ∂VP /∂T = −6×10−4 (km s−1 K−1 ) and ∂VS /∂T = −5×10−4 (km s−1 K−1 ) (Sinogeikin et al., 2000). Applying these velocity derivatives at 69 121 GPa is likely overestimating the velocity drop with temperature. The effect of applying these velocity derivatives to iron-rich (Mg,Fe)O rather than MgO is unknown. 5.2 Conclusions In this work, we have experimentally determined the room temperature sound velocities of (Mg0.16 Fe0.84 )O and (Mg0.06 Fe0.94 )O as a function of pressure up to 121 GPa. We found that the trend in sound velocities was very strongly affected by magnetic transitions: by monitoring the magnetic state using synchrotron Mössbauer spectroscopy, we identified softening in the shear elastic properties of iron-rich (Mg,Fe)O preceding a magnetic transition. We have also presented the pressure-volume-temperature equation of state of (Mg0.06 Fe0.94 )O up to 115 GPa and 1900 K, measured both with and without an in-situ Fe buffer, and showed that we could not conclusively distinguish the two equations of state. This result is consistent with other studies of the (Mg,Fe)O solid solution that propose pressure-induced exsolution of Fe3+ , essentially “self-buffering” (Zhang and Zhao, 2005; McCammon et al., 1998). This result is important for practical reasons, as future high-temperature NRIXS studies will not need to have an in-situ buffer. The work we have completed forms the foundation for future experiments at high temperature. 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Min., 37, 465– 474, doi: 10.1007/s00269-009-0347-6. 82 Appendix A A.1 Synthesis and Characterization A.1.1 (Mg0.16 Fe0.84 )O MgO was dried at 1100◦ C overnight, then stoichiometrically combined with 95% enriched 57 Fe2 O3 (Advanced Materials Techonologies Ltd.) to produce an Fe/(Mg+Fe) ratio of 0.85. After being ground in an agate mortar, the oxide mixture was pressed into a pellet and reduced to form + (Mg,Fe2 )O in a gas-mixing 1 atm furnace. The pellet was equilibrated at 1400◦ C for two runs of 20 hours each just above the iron-wüstite fugacity buffer (an oxygen potential of 10−9.6 atm). Sample composition and homogeneity were measured using a JEOL JXA-8200 electron microprobe (Mg.158(2) Fe.842(2) )O, where the number in parentheses is the error on the last digit and the oxygen is assumed to be stoichiometric. Ambient pressure unit cell volume was measured with X-ray diffraction (9.79(4) Å/atom), resulting in a density determination of 5.69(7) g/cm3 . The magnetic signature of iron in our sample was determined by Mössbauer analysis at ambient pressure (Figure 2.6). The absence of a magnetically ordered component indicates that our sample is free of metallic iron and magnetite. Although the black color of the sample indicates that there may be trace amounts of trivalent iron, its concentration is below detection limits of Mössbauer (less than 3%). This will translate to vacancy concentrations of 0-3%, which we include in the density error bar. In June 2012, a re-measurement of the sample composition revealed the presence of Ti contamination in the sample, previously missed. A revised chemical formula is (Mg0.18 Fe0.78 Ti0.04 )O, which would correspond to a revised density of 5.7(1) g/cm3 . With likely errors on each subscript to be 83 0.01, a more thorough analysis is required to reduce the error bars. A.1.2 (Mg0.06 Fe0.94 )O (Mg0.06 Fe0.94 )O was synthesized by the same methods as above, using 57 Fe metal from Isoflex. Microprobe analysis of the synthesized material gives a sample composition of (Mg.0580(9) Fe.9420(9) Si.0021(9) )O, assuming that the oxygen is stoichiometric. A conventional Mössbauer spectrum (Figure 2.3) taken of the synthesized sample is consistent with divalent iron, and shows no indication of Fe3+ . A secondary electron image (Figure A.1) taken of the sample before microprobe analysis shows no indication of compositional heterogeneities. Figure A.1: Secondary electron image of (Mg0.06 Fe0.94 )O. A.1.3 Fe1−x O Fe1−x O was synthesized in March 2011 using the methods above, at 1300◦ C, a lower temperature to account for the melting point of FeO of 1395◦ C. The synthesis was carried out twice, using both the 57 Fe2 O3 source and the 57 Fe metal source, as it had been determined that the 57 Fe2 O3 source was contaminated with Ti. The aim of synthesizing with and without Ti was to determine whether or not the vibrational spectra and subsequent sound velocities were affected by the presence of minor Ti. Room pressure lattice parameter and density are listed in Table A.3. 84 A.2 Additional Thermodynamic Parameters Key thermodynamic information can be directly derived from the partial projected Phonon Density of States using the PHOENIX software (Sturhahn, 2000, www.nrixs.com). More detailed descriptions can be found in Sturhahn (2004). A.2.1 (Mg0.16 Fe0.84 )O P ressurea (GPa) 0 4.0(3) 11.4(3) 15(3) 21.0(4) 28(2) 41(1) 46(4) 55(3) 65(5) 80(5) 88(4) 97(5) 102(5) 110(4) 121(7) fLM 0.7129(8) 0.717(2) 0.713(2) 0.731(2) 0.727(2) 0.730(2) 0.751(2) 0.778(3) 0.760(3) 0.801(3) 0.814(3) 0.815(2) 0.826(2) 0.834(3) 0.840(2) 0.848(2) EK (meV/atom) 14.0(1) 14.0(2) 14.1(3) 14.2(3) 14.3(3) 14.2(3) 14.0(3) 14.2(3) 14.2(3) 14.5(3) 14.6(3) 14.9(2) 15.3(2) 15.2(4) 15.4(2) 15.6(3) Dav (N/m) 145(5) 145(11) 169(10) 167(14) 183(12) 171(12) 142(14) 177(15) 173(15) 222(12) 229(17) 281(8) 345(13) 326(19) 360(12) 388(16) fLM,Z 0.9069(3) 0.9071(7) 0.9090(8) 0.9112(8) 0.9138(7) 0.9136(8) 0.9153(8) 0.9208(8) 0.9189(9) 0.9263(7) 0.9281(7) 0.9306(5) 0.9336(5) 0.9340(8) 0.9359(4) 0.9377(6) EK,Z (meV/atom) 6.15(9) 6.1(2) 6.3(2) 6.4(3) 6.7(2) 6.6(2) 6.3(2) 6.9(2) 6.8(3) 7.5(2) 7.7(3) 8.3(2) 9.0(2) 8.8(3) 9.2(2) 9.5(2) Cvib (kB /atom) 2.75(1) 2.8(3) 2.74(4) 2.73(4) 2.71(3) 2.72(4) 2.76(4) 2.71(4) 2.72(5) 2.65(4) 2.64(4) 2.59(3) 2.52(3) 2.54(4) 2.50(2) 2.47(3) Svib (kB /atom) 3.57(1) 3.59(3) 2.45(2) 3.44(3) 3.33(3) 3.36(3) 3.36(3) 3.16(3) 3.22(3) 2.95(3) 2.90(3) 2.75(2) 2.61(2) 2.61(3) 2.53(2) 2.45(2) Table A.1: Thermodynamic parameters calculated directly from the partial-projected phonon density of states of (Mg0.16 Fe0.84 )O. a Pressures were determined from ruby fluorescence before and after the NRIXS measurement, from Table 2.1. fLM is the Lamb-Mössbauer factor. EK is the kinetic energy per resonant atom. Dav is the average force constant of the resonant atom. fLM,Z is the Lamb-Mössbauer factor at zero Kelvin. EK,Z is the kinetic energy per resonant atom at zero Kelvin. Cvib is the vibrational specific heat. Svib is the vibrational entropy per atom. 85 A.2.2 (Mg0.06 Fe0.94 )O P ressurea (GPa) 0 9.61(2) 42.7(7) 55(1) 64(2) 81.1(8) 81.6(7) fLM 0.700(1) 0.714(3) 0.773(2) 0.788(2) 0.813(2) 0.826(1) 0.828(2) EK (meV/atom) 14.2(1) [14.2(3)] [14.7(2)] [14.7(2)] [14.8(2)] [15.5(2)] 15.0(2) Dav (N/m) 162(5) [186(10)] [261(8)] [264(8)] [281(8)] [371(10)] 300(8) fLM,Z 0.9076(4) 0.9119(9) 0.9237(6) 0.9267(5) 0.9306(5) 0.9339(3) 0.9330(5) EK,Z (meV/atom) 6.18(8) [6.6(2)] [7.8(2)] [7.9(1)] [8.3(1)] [9.2(1)] 8.6(1) Cvib (kB /atom) 2.75(2) 2.72(4) 2.6(3) 2.61(3) 2.58(3) 2.50(1) 2.56(2) Svib (kB /atom) 3.57(2) 3.39(4) 2.95(2) 2.86(2) 2.73(2) 2.61(1) 2.66(2) Table A.2: Thermodynamic parameters calculated directly from the partial-projected phonon density of states of (Mg0.06 Fe0.94 )O. a Pressure determined from in-situ X-ray diffraction, from Table 3.1. fLM is the Lamb-Mössbauer factor. EK is the kinetic energy per resonant atom. Dav is the average force constant of the resonant atom. fLM,Z is the Lamb-Mössbauer factor at zero Kelvin. EK,Z is the kinetic energy per resonant atom at zero Kelvin. Cvib is the vibrational specific heat. Svib is the vibrational entropy per atom. EK and Dav reported in brackets denotes values possibly affected by higher energy vibrations not sampled by our limited energy range. 86 A.3 Sound Velocities of FeO from Nuclear Resonant Inelastic X-ray Scattering This section describes the determination of FeO Debye velocities presented in Figure 3.12. NRIXS spectra were taken at Sector 3 of the Advanced Photon Source in August 2011 and March 2012. The volume of FeO at ambient pressure was measured at Sector 12.2.2 of the Advanced Light Source. Using the (111), (200) and (220) reflections, the cubic volume was refined using the Unit Cell software. The resulting lattice parameter a = 4.306(1) corresponds to a composition of Fe0.941 O (McCammon and Liu, 1984). The volume of FeO at high pressure was measured at Sector 13-ID-D, GSECARS of the Advanced Photon Source in February 2012. Unit cell volumes at high pressure were determined using the rhombohedral reflections: (003), (101), (012), (104), and (110). Density was calculated assuming 0.5(5)% vacancies. Figure A.2 shows the raw NRIXS spectra of FeO. At ambient pressure, the energy scan range was -60 → +80 meV. At higher pressures, the scan range was increased to -65 → +80 meV and -70 → +100 meV. The partial projected phonon density of states was extracted for each pressure point using the PHOENIX software (Sturhahn, 2000) and are presented in Figure A.3. As described previously, Debye sound velocities were determined using psvl. Table A.3 summarizes the density and Debye sound velocities of FeO in addition to the refined unit cell parameters from X-ray diffraction. ρ (g/cc) 5.99(6)a 6.05(2) 8.3(1) 8.4(1) Emin − Emax meV 3.7 − 16.3a 3.2 − 17.1 4.5 − 14.8 4.2 − 19.8 VD (km/s) 2.87(1)a 2.88(1) 3.73(4) 3.88(3) Vol/atom Å3 10.06(2)a 9.98(4) 7.3(1) 7.2(1) a Å 4.318(8)a 4.306(2) 2.64(2) 2.63(2) c Å 7.26(9) 7.21(9) Table A.3: Summary of FeO density, energy range used to calculate Debye velocities, and Debye velocities. Volume and lattice parameters were refined using the program Unit Cell (Holland and Redfern, 1997). a Density calculated for Ti-containing oxide, estimated to have the chemical formula (Fe0.959 Ti0.041(1) )O (Chen et al., 2012). 87 FeO, 300 K 1e+06 1e+05 Counts 10000 8.4(1) g/cc 1000 100 8.3(1) g/cc 10 ambient 6.05(2) g/cc 1 -50 0 50 Energy (meV) Figure A.2: Raw NRIXS spectra of FeO at 300 K at three pressures. 100 88 200 FeO, 300 K ambient pressure, 6.05(2) g/cc D(E,V) 150 100 50 8.3(1) g/cc 8.4(1) g/cc 0 0 50 Energy (meV) 100 Figure A.3: Partial projected density of states (PDOS) of FeO, extracted from the energy scan using the PHOENIX software (Sturhahn, 2000). There is a marked difference in the distribution of vibrations between the ambient pressure spectrum and the high pressure spectra, which is also reflected in the calculated sound velocities. Debye sound velocities determined from the low-energy region of these PDOSs are plotted in Figure 3.12. 89