NMR Study of Fluoride Ion Diffusion in Potassium-Doped β-PbF₂ Citation Cannon, David Maxwell (1978) NMR Study of Fluoride Ion Diffusion in Potassium-Doped β-PbF₂. Master's thesis, California Institute of Technology. doi:10.7907/8dgg-dx50. https://resolver.caltech.edu/CaltechTHESIS:03292010-111321744 Abstract Fluoride ion motion in a KF-doped β-PbF_2 crystal was studied by measuring the ^(19)F relaxation times T_1, T_2, and T_(1p). Measurements were made on a 56.4 MHz pulsed spectrometer over the temperature range -101°C to 22°C; the T_(1p) data were taken in a rotating magnetic field of 6.8 G. Two sets of T_2 data were taken, yielding activation energies of 0.17 ± 0.01 eV and 0.18 ± 0.01 eV. Activation energies obtained from T_1 and T_(1p) data were 0.17 ± 0.01 eV and 0.34 ± 0.02 eV, and a correlation time of 2.9 µsec was observed at -20°C, the temperature at which the T_(1p) minimum occurs. Comparison of these data with previously published results shows that potassium-doping is more effective than sodium-doping in activating fluorine motion. It is believed that T_1 relaxation is dominated by a mechanism other than anionic diffusion. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Vaughan, Robert W. Thesis Committee: Unknown, Unknown Defense Date: 10 March 1978 Record Number: CaltechTHESIS:03292010-111321744 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:03292010-111321744 DOI: 10.7907/8dgg-dx50 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5649 Collection: CaltechTHESIS Deposited By: Tony Diaz Deposited On: 15 Apr 2010 22:18 Last Modified: 13 Nov 2024 19:29 Thesis Files Preview PDF - Final Version See Usage Policy. 1MB Repository Staff Only: item control page

NMR STUDY OF FLUORIDE ION DIFFUSION IN POTASSIUM-DOPED B-PbF., Thesis by David M. Cannon In Partial Fulfillment of the Requirements for the Degree of Master of Science California Institute of Technology Pasadena, California 1978 (Submitted March 10, 1978) -ii- ACKNOWLEDGMENTS I wish to thank the California Institute of Technology and the A.R.C.S. Foundation for their financial support. I am very grateful to Professor Robert Vaughan for his patient assistance in scientific matters as well as for his friendship and concern toward me as an individual. It has been a real pleasure to associate with the other members of the Vaughan group, both in and out of the lab. Finally, greatest thanks are extended to my wife Ana Maria. I cannot adequately express my appreciation for her patience, selflessness, and encouragement. This thesis is dedicated to her. ~iii-~ ABSTRACT Fluoride ion motion in a K¥-doped B-PbF, erystal was studied by 19 measuring the ““F relaxation times Ty: Tos and T Measurements lp° were made on a 56.4 MHz pulsed spectrometer over the temperature range -1OL°C to 22°C; the T,_ data were taken in a rotating magnetic lo field of 6.8 G. Two sets of Ty data were taken, yielding activation energies of 0.17 + 0.01 eV and 0.18 + 0.01 eV. Activation energies obtained from Ty and Ti) data were 0.17 + 0.01 eV and 0.34 + 0.02 eV, and a correlation time of 2.9 sec was observed at -20°C, the temperature at which the Tip minimum occurs. Comparison of these data with previously published results shows that potassium-doping is more effective than sodium-doping in activating fluorine motion. It is believed that Ty relaxation is dominated by a mechanism other than anionic diffusion. -j{yv= TABLE OF CONTENTS I. NMR RELAXATION PROCESSES AND SOLID STATE DIFFUSION II. FLUORIDE ION DIFFUSION IN POTASSIUM-DOPED 8-PbF Introduction. . 2. 6 1 6 © oe ew he ww we Experimental Details. . . . 2.» «6 e« es ees Results . 2. 6 2 6 © © we ew ew ww we wee Discussion, « « « 6 + 6 © © © © © © ww Conclusion. . 2 6 + see s+ ee ee we we References, «2. 6+ ss se + se we we ww wewe APPENDIX: PULSED-NMR LOCK SYSTEM . . . 6 +» ee © « 2 e 22 24 32 34 35 37 -l- I. NMR RELAXATION PROCESSES AND SOLID STATE DIFFUSION The experimental work described in this thesis involves the use of NMR techniques to study anion diffusion in the fast ionic conductor B-PbF.. Specifically, the relaxation times Ty Tos and Tho were measured as a function of temperature. Accordingly, this section gives a brief discussion of these relaxation processes and their relationship to solid state diffusion. If a sample containing a non-zero nuclear magnetic moment is placed in a magnetic field, a small component of magnetization will form in the z direction (along the field). This magnetization can be rotated to the xy plane by a radio-frequency (rf) pulse with effective field perpendicular to the z direction. After the pulse, the component of ‘magnetization in the xy plane (My) will begin to shrink. For a liquid or motionally narrowed solid, Mey will be seen to decay exponentially with a time constant To> the spin-spin relaxation time. Simultaneously the z component of magnetization will return exponentially to its equilibrium value; the time constant for this process is called Ty): The width of an NMR line in frequency space contains contributions from several sources. There is a contribution from 1/T, due to the finite lifetime of a nucleus in any eigenstate. Magnetic field inhomogeneities may also broaden a line. For solids, however, the largest contribution to the linewidth usually comes from dipole-dipole interactions between nuclei, Ty processes involve energy exchange between the nuclear spins and the lattice. Following any process which destroys the thermal -2- equilibrium between spins and lattice, qT) processes restore the two systems to equilibrium. Consequently, T, is known as the spin-lattice 1 relaxation time. A third relaxation process is called T° OF Ty) in the rotating frame. InaT 1p the magnetization until it lies along the y' axis (x' and y' are experiment, an rf pulse along the x' axis rotates axes in a reference frame which rotates about the z axis at the radio frequency). Immediately after the pulse, the phase of the rf signal is changed by 90° and a "locking" field along the y' axis is generated. The magnetization then relaxes along the y' axis in a process similar to Ty. The major difference is that the locking field in a Ty is several orders of magnitude smaller than the Zeeman field along ° experiment which Ty) relaxation takes place. This makes Tho more sensitive to low frequency motions than Ty: To» Th and T, relaxation processes are induced by microscopic 1p fluctuations in the magnetic field at individual nuclei. Such fluctuations can be caused by the bodily movement of nuclear dipoles through the lattice, a situation which occurs when diffusion takes place. The direction and frequency of these fluctuations are important. They must occur in a direction perpendicular to the direction of relaxation and are most effective if they have the same frequency as the rotating magnetization. From these considerations several qualitative predictions can be made. Ty relaxation should be most effectively induced by fluctuations in the xy plane at the Larmor frequency Wo*VH, (y is the gyromagnetic ratio of the nuclei and Hy is the strength of the static Zeeman field). Similarly Ty processes -~3— should be effected by xy fluctuations at Wy and also by static and very low frequency (w=0) movements in the z direction. We expect T,_ to lo be caused by frequencies at w, as well as by those near w =yH where 1 Hy is the strength of the locking field. These statements can be more quantitatively expressed by the use of a “correlation function" G(t) and its Fourier transform the “spectral density function" J(w). One may think of G(r) as the probability that a nucleus will experience the same magnetic environment at time t as it did at time t' = t-1. The correlation function is characterized by some critical time To called the “correlation time.” For diffusing nuclei, T, is the average time between hops. Taking the Fourier transform of G(t) gives Jw), a function which gives the motional frequencies of hopping nuclei. It contains frequencies up to approximately wel/t.. The relaxation rates W/T,, 1/T,, and 1/T,, are simply linear combinations of spectral density functions. An important property of the spectral density function is that the area under the curve, i.e., pRsw)au, does not vary with To If J(w) is plotted for several values of To it is seen in Fig. l that for a specific value of w=w', J(w') has a maximum value for Tt al/w'. Since for Ty» we are interested in Fourier components at waw, we expect that a plot of Ty) vs. T, will have a minimum when tT al/w- Similarly, Th) vs. T should have a minimum near tT =1/o,- Using the functions G(t) and J(w), various quantitative expressions have been derived for relaxation rates in terms of spectral density functions. For dipole-dipole interactions -4- between identical spins, the following have been obtained, 2” 1/T, = C {3(w,) + 43(20,)} (1) L/t, = c {$5(0) +23) + J(2u_)} (2) 2 2 ° ° = 2 1/7), = ¢ {$ J(2w,) + F Iw.) + J(2u,)} (3) Here C is a constant for a given material. In order to evaluate these expressions, the functions J(w) must be known. Normally an exponential correlation function is assumed: G(t) = h?exp{-|t|/t } (4) where h® ts a measure of the strength of interaction between nuclei. It then follows that the spectral density function is a Lorentzian: J(u) = 2n?z /{1 + (wt,)?}. (5) Combining (5) with (1), (2), and (3) gives expressions for T., Tos and T, in terms of Th Fig. 2 gives a typical plot of 1 lo in (T,, Tos and T,) vs. in TO. The curve for Ty has been drawn to reflect the fact that for very long TO Tt) assumes a rigid lattice value. As T, becomes shorter, T, begins to increase, resulting in 2 motional narrowing of the resonance line. qT has a minimum when t *1/2w whereas T reaches its minimum at 1 =l/2w,. Since w >>w,, c fe) c 1 ° 1 lo \ _L i) iw Fig. 1. J(w) plotted for three values of TO J(w') has its maximum value for TO l/w'. 1n (T)> Tyo? T,) ln Te. Fig. 2. Typical relaxation curves in (T,> T) > T,) vs. in TO p -6- Tho is more sensitive to low frequency motions than is T To L° the left and right of the minima the plots of In Ty and in Tho are linear with slopes of -1 and +1. For short 1, (t,<<1/w)) the three relaxation rates become equal. How does the measurement of NMR relaxation rates contribute to an understanding of solid state diffusion? The answer to this lies in the fact that correlation times are an essential feature of both processes, relaxation and diffusion. For simple diffusion, the diffusion coefficient Def, where Pal/t, is the jump frequency. Further- more, for thermally activated motion with an activation energy E*, the jump frequency is given by T = [ exp(-E*/kT). (6) When this situation occurs Int, = -In T+ EA/kI (7) and a plot of In (T,; Ty» T1 vs. 1/T will have the form given in Fig. 2. The slope of the lines gives a value for E*, and the value of T, ¢an be determined for the temperatures at which Tt) and Tho minima occur. This approach to studying solid state diffusion nicely complements more traditional methods which directly measure bulk diffusion properties. The latter techniques can be used only indirectly to infer atomic mechanisms which cause diffusion. In contrast, the ~7~ NMR approach does not directly measure diffusion but is a more straight- forward means of determining atomic behavior. The combined use of these two approaches can be valuable in elucidating the atomic mechanisms which effect diffusion. References 1, Abragam, The Principles of Nuclear Magnetism (Oxford University Press, London, 1961), ch. 8. 25.8. Boyce, J.C. Mikkelsen, and M. O'Keeffe, Solid State Commun. 21, 955 (1977). ~g- may be attainable. Accordingly, some effort has been made to ascertain the mechanism of fonic motion in PbF,» but no unequivocal model has as yet emerged, This introduction gives a brief survey of the work which has been done to characterize ionic diffusion in this substance. Lead fluoride is known to occur in two crystal structures. The orthorhombic a form is generally considered the low-temperature form. Upon heating, this is changed to the cubic 8 form, which has the CaF, (fluorite) structure (see Fig. 3). Sauka” reported that this structure change occurs at 315°C, whereas Kennedy et al.> observed the transition in the range 334°-344°; others have reported temperatures of 200°-400°C.” After cooling, the 8 structure may be retained metastably; its melting point is recorded as g22°c.4 Of the two structures, the 8 modification is the better tonic conductor, and most research has involved that form. Hereafter, all references to POF, in this thesis will designate the 8 form unless explicitly stated otherwise. Most studies of ionic motion in B-PbF, have involved conductivity measurements. In 1921, Tubandt? measured the transport numbers of the lead and fluoride ions and reported that only fluoride ion motion contributed to the conductivity. More recently, Kennedy et al.? measured a negative ion transference number of 0.93 for pure B-PbF., and Liang and Joshi® observed a similar value of 0.94 for a-PbF, 3, 7-9 doped with YF Additional studies have been made to determine 3° the electronic contribution to the total conductivity; these have produced values in the range 1074-1.0% for the electronic contribution under various conditions. Taken together, these results demonstrate that the conducting properties of PbF, are a result of ionic motion -10- Fig. 3a (left). The positions of the atoms within the unit cell of fluorite, CaF,, projected on a cube face. Lettered circles refer to the corresponding spheres of Fig. 3b. Fig. 3b (right). A perspective packing drawing showing the distribution of the atoms of CaF, within the unit cube, -1l- within the fluoride sublattice. This conductivity is thermally activated, and a number of investigations??? )9 have been made concerning the temperature dependence of the conductivity, These have led to the recognition of three roughly defined sections in the o vs. T curve for nominally pure lead fluoride. These sections are distinguished by differing values of AH, the activation enthalpy, in the three temperature regions. The room-temperature conductivity of pure B-PbF,, is near 1078 (ohm-cm) 2, As the temperature is raised, the conductivity increases with an activation energy which has generally been reported in the range 0.50-0.70 eV. Several studiesr??t>»16,18 have indicated that at some elevated temperature, o begins to increase more rapidly (AH increases), indicating the possibility that a different diffusion mechanism prevails in this second temperature region. This change in behavior has been observed at temperatures in the range 180°-310°C. However, other investigators have gone to even higher temperatures without observing an increase in AH. This is indicative of the lack of agreement which exists in conductivity data for "pure" PbF,. A summary of such data is presented in Table 1. A third type of conductivity behavior is observed at very high temperature. Derrington and O'Keeffer? observed a sharp decrease in OH from 450°-575°C: o remained almost constant as the temperature was increased from 575°C through the melting point. Benz’ noted a similar decrease in AH near 400°C. Both studies published a conductivity of ~l (ohm-cm) > at the inflection point. This high temperature -12~- “(QT ‘Ja 208) zeded zejeT B UF paqoaziIoOd SEM 3nq Av GO*T SB pazizodea ATT eUTSTIO sem anTeA oul, ~—— 90°T O£9-OTE a £9° OTE-0€ aTsuzs ‘Atod gPremuoouas pue suuog S°L €9° OZE-SZ aTZuys wl? yoRaAys Tey 7 TT! SZY-OTE BZ 99° OTE-SZ eTsuys g TemIOCUS pue auuog 7 09° OST-SZ aTsuys “= 99° OTE-O8T S°9 0S°-6€" O8T-Sz &jod cpeeTH pue Apeuusy aL 89° OSE-SZ 4Tod pre upmuooy os €°9 8° ¢z-0S- a{suys ep Te 3 eXeys , TasueyyxAy --- S¥° 007-0€ --- zt te 2° neay T°L 29° OS€-SZ &jod g hiSor pue Suey7 O°S-T'L Ly° OST-Sz Ajod we? ozznpuey9 --- 276" 00-002 6°L a 007-SZ aTsuzs ort? 2? uewuocey ss L°L $9°-09° OS7-GSZ aTsuys ~~ TS*-L¥° OS7-SZ &tod Te 7 Kpouusy q- (mo-myo) (A?) HV (9,) a3uey -duay TeasAra s1zo0y ny 9.S% 1® 9 30T- Csqa-9 eand ATT euytuou jo sotTpnys A3FATIONpuos Pde) Azeuuns “LT 2FTqQPL -13- behavior was interpreted!® as being caused by a high degree of anion disorder, i.e., the anion sublattice had effectively melted even though the sample was still solid. This view was supported by the measurements of Derrington and O'Keeffe who observed virtually no change in the conductivity at the actual melting point of PbF.- Their estimate indicated that at 727°C, more than one tenth of the anions were in motion at a given instant. In order to better understand the mechanism of fluoride ion motion, several studies have been made using doped samples. The substitution of a monovalent metal ion in the PbF, lattice is expected to produce a fluoride ion vacancy. Similarly, the replacement of a PbF unit with a trivalent impurity should create an interstitial anion. By using such impurity-doped samples, the effect of known defects upon the conductivity can be examined. The results of conductivity experiments involving monovalent dopants are relatively unambiguous. Studies have been made on lead fluoride samples to which KF, NaF, and AgF dopants had been added, »19+18 See Table 2 for a summary of studies involving these doped samples. In each case, the effect of doping was to increase the conductivity and decrease the activation energy. Therefore, while there is some disagreement on details, it is well accepted that fluoride diffusion can be activated by anion vacancies. The results for trivalent doping are less clear-cut (see Table 2). In an experiment using a BiF.,~doped sample, Kennedy and Miles? detected a decrease in conductivity and an increase in AH as compared to a nominally pure sample. 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HV (9.) quedog Teysh19 S2OYy ANY DeSZ 38 9 BoT- asuey -duay Sofpnys sayto *saTdues pedop-quaTeati} 10j ejep seAyT3 uoyz30es ASMOT |yQ fsquedop JueTeAOUOM BuTATOAUT eaTqeq ay Jo jaed zoddn oy *’Add-g pedop jo satpnys AyfaTzAonpuood jo Aremns “¢ eT9FL -15- proceeds only by a vacancy mechanism at low temperature. Other conduc- tivity studies argue against this hypothesis. In an experiment involving trivalent rare-earth and Cr dopants, Arkhangel'skaya et_at.2? witnessed an increase in conductivity but observed no change in AH. Liang and Joshi® obtained a similar result for an YF.,-doped sample. They concluded that vacancies are responsible for diffusion in monovalent-doped samples, but that fluoride motion in pure and trivalent-doped samples is effected by an interstitial mechanism. They further suggested?” that the anomalous results of Kennedy and Miles! may have been due to a reaction between BiF, and the Pb electrodes. An alternate explanation, however, is that the "pure" sample used by Kennedy and Miles contained a significant number of extrinsic vacancies, and that trivalent doping merely annihilated these defects. More recently, Bonne and Schoonman’® found that o increased and AH decreased upon addition of LaF 4 to lead fluoride samples. They ascribed this phenomenon to extrinsic interstitials but proposed that fluoride motion in pure PbF, occurs via a vacancy mechanism. It thus appears that conductivity in B-PbF,, can be increased by trivalent or by monovalent dopants. The effects of these impurities differ in degree, however, as seen in Table 2. Whereas doping with KF may increase the room temperature value of o by three or four orders of magnitude, the substitution of trivalent dopants at comparable concentration levels produces a change of one or two orders of magnitude. It is also apparent that monovalent doping results in a significant decrease in activation energy, whereas the effect of trivalent impurities upon AH is much less obvious, While it is apparent that the high conductivity of POF, is due to -16- anion disorder, the exact nature of this disorder is not well understood. Most authors seem to agree that Frenkel disorder exists in the fluoride ion sublattice, and that diffusion may occur by either a vacancy or an interstitial mechanism. No consensus has been reached, however, concerning the relative contributions of these mechanisms to the total conductivity, nor whether diffusion in nominally pure 8-PbF,, is activated by extrinsic or intrinsic defects. Although electrochemists have attempted to deal with these issues, there are several reasons why conclusions drawn from conductivity experiments alone may be tenuous. 1. In most cases, the purity of the samples in these studies was not known, If the conductivity is very sensitive to small impurity levels, deviations in reported data for “nominally pure" lead fluoride could be due to differences in sample composition. 2. The direct measurement of ionic conductivity requires the use of some form of electrode. This creates the possibility of interfacial effects which introduce uncertainty into any conclusions regarding bulk conductivity. 3. Even if interfacial effects could be entirely eliminated, a conductivity study would only demonstrate a macroscopic property of the material. Interpretation in terms of a microscopic model would be hazardous because there would be no way of separating effects due to such factors as grain boundary diffusion or sample inhomogeneity. The use of NMR techniques to study anion motion in PbF, avoids -17- some of these problems. Obviously, the need for electrodes is eliminated. Since NMR looks at all the 19, nuclei in a sample, it is possible to determine whether conductivity is due to motion of all the nuclei or to an effect such as grain boundary diffusion. The 19, nucleus is easily detected and the movement of that ion through the lattice should be evidenced in the relaxation data as discussed in Chapter I of this thesis, If relaxation is dominated by a simple hopping motion of fluorine nuclei, curves similar to those depicted in Fig. 2 are expected. Deviations from that form would indicate a significant contribution from other relaxation mechanisms. Thus, by applying NMR techniques to the study of samples of well known composition, valuable information can be obtained regarding the nature of anion motion. Although the application of NMR techniques to the lead fluoride 14, 21-26 have been problem has not been extensive, several studies made. These are summarized in Table 3. The first NMR analysis was made by Mahajan and Rao“ who measured the linewidth of a-PbF, over the temperature range -50°-190°C. They | reported the onset of motional narrowing at -10°C and an activation energy of 0.35 eV. Comparison of these values with results obtained in later studies suggests that the sample used by Mahajan and Rao probably contained impurities which increased fluorine mobility. Hwang, Engelsberg, and Lowe?? did pulsed NMR measurements on PbF. in the cubic and orthorhombic forms and showed that ionic motion in the 8 structure was significantly greater than in the a. In the same paper, results were reported for a sample of B-PbF, which had been sodium-doped. It was found that this doping caused motional narrowing -18- ol --- -—n— L ‘paestnd $/° ~~ os Ty ‘ pes tnd yl OOT ~-— g Atod ey ‘ pas tnd "TR Ja woKog 62° --~ OT] *pastnd ¢ 60z* a Ty ‘ pestnd 12° ~~ den O/m zZT°O aTsuts ey *pastnd yz te? sueay €9°-6¢° oe e sup o/W 60°-€0° g Ajtod YIPFAsuTT ‘Mo pt TP qa uewuooYyos ze" ooT- “den o/u Zz g Atod €L° 08 --- eTsuTs --~ O£T i aTsuts ey * pestnd ez qa Buenyg ze" --- a= TL ‘pastnd -—~ on --— g Atod ey ‘ pastnd a ~~ --- n ATod a 0S -~+- aTsuys UIPFAeuyT ‘Mo zz Te 3? oorpusyey GE’ oTt- --- vn Ajtod yspTaeuzT ‘mo 2078 pue uefeyey (A?) aV (9,) °T®N quedog yeqysé19 poy zy sioy{ny "OW, JO Josug Add JO Setpnjas yWN Jo Azewung ‘¢ eTqey ~19- to occur at a much lower temperature (-100°C) than in the pure sample, and that the value of AE was significantly reduced. These findings agree qualitatively with results from conductivity experiments. In order to more quantitatively compare results obtained by NMR and conductivity methods, Schoonman et _al./4 studied a poly- crystalline sample of B-PbF, using each of the two approaches. They reported AH = ,59-.63 eV from NMR linewidth measurements and AH = .68 eV from conductivity. Furthermore, they calculated the diffusion coef- ficient at 27°C from the two sets of data and obtained results which agreed to within a factor of 3.5. Their conclusion was that NMR line- narrowing and tonic conductivity were both caused by motion of all fluoride ions within the sample. In a pulsed-NMR study of B-PbF,, Hwang et al.“ measured relaxation rates as a function of temperature for two Na-doped samples of well known chemical composition. It was found that Ty « 1/N and Ty «= N where N is the ratio of doping levels in the two samples. Activation energies of 0.205, 0.27, and 0.29 eV were obtained for Ty» To» and T, relaxation. Although T, showed a strong pressure 1p dependence (as expected for a diffusional relaxation mechanism) T was found to have little dependence upon pressure. Furthermore, the value for Ty was found to be essentially independent of Hy even though data were taken in the long correlation-time region Cr, >> L/w) where Ty would be expected to be proportional to H? if Ty were controlled by fluorine motion. These observations led Hwang et al. to conclude that fluoride ton diffusion was the controlling mechanism in T, and T, relaxation, whereas T, was dominated by a different relaxation lp 1 mechanism. ~20~ In addition to the NMR studies previously described, two experiments have been performed in which magnetic resonance was used to study PbF, at high temperature. Boyce, Mikkelsen, and O'Keeffe?> measured Ty» To» and Ty, to 700°C and observed anomalous changes in each of these parameters at 250°C and 450°C. Subsequently, Hogg, Vernon, and Jaccarino”® measured the linewidth of a Mn-doped sample and found the same type of behavior at high temperatures. They speculated that these anomalies could be explained by the effects of paramagnetic impurity fons. These studies, however, are not directly relevant to the present work. To summarize, it has been shown via conductivity and magnetic resonance experiments that substantial fluoride ion motion takes place in B-PbF,,. The degree to which this occurs is highly dependent upon impurities within the sample; the especially high sensitivity to monovalent dopants suggests that differences among various "pure" samples may be at least partially due to trace quantities of monovalent impurities. The alkaline earth fluorides, which have the same crystal structure as B-PbF,, do not show this high degree of anion mobility, nor do they experience the same lowering of activation energy upon addition of monovalent dopants. The reasons for these differences are not known. Thus, a fundamental understanding of the diffusion mechanism in B-PbF,, is still lacking. The objective of the present experiment was to determine the effect of cation size upon fluorine mobility in monovalent-—doped B-PbF,. This was to be done by measuring Ty» To» and Tho as a function of temperature for a potassium-doped single crystal, and by comparing -21- these values with the data published by Hwang et al.24 for a sodium- doped sample. Several interesting yet perplexing results have emerged from this work. -22- Experimental Details A single crystal of potassium-doped (10.01 wt %) was ordered from Optovac, Inc. Spectrographic and wet chemical analyses were made to determine chemical composition. These revealed the presence of 0.008 wt % potassium. The wet chemical analysis also detected sodium, but it is presently not known whether that is a real crystal impurity or a result of the analysis technique. At the time of this writing, an attempt is being made to obtain a mass spectrographic analysis of the sample, An attempt was made to orient the crystal using the back-reflection Laue method. This was abandoned, however, when it was discovered that the crystal was severely twinned. All NMR data were taken on a 56.4 MHz pulsed spectrometer. Temperature was varied between -101°C and 22°C, and temperature readings were generally accurate to +2°C. qT, was obtained by recording the on-resonance free induction decay at each temperature. These fid's were interpreted as consisting of two components at temperatures above -60°C (see Results section). The Ty values reported in this paper were obtained from the narrow-line component. This was done by plotting ln My vs. t and taking the slope of this curve for long t, after the signal from the broad-line component had become negligible. Ty was measured using a 90° -~t-90° pulse sequence (see Farrar and Becker,“ pg. 22). This sequence was performed for at least five values of + and a plot was made of In [A(™) - A(r)] vs. + where A() is the fid amplitude for t 2 5T, and A(r) is the fid amplitude for 1 % Th. 1 ~23- These plots were nonlinear (see Results section), indicating the presence of more than one component. Ty was taken as the slope of the line for short t; this value for T, was believed to represent the spin-lattice 1 relaxation time of the narrow-line component. T1o was measured by producing a 90° pulse along the x' axis followed immediately by a holding pulse of length t and amplitude 6.8 G along the y' axis. The amplitude, A(t) of the fid obtained after termination of the holding pulse was recorded for at least five values of t and a plot was made of in A(t) vs. Tt. T1 was taken as the slope of a line for short T, corresponding to Tio of the narrow-line component. -24- Results The crystal used in this study was of reasonably good quality as demonstrated by the clarity of its Laue photographs. Such a photograph is reproduced in Fig. 4. The crystal was not single, however, since different portions of the sample were found to have different orientations. It appeared that the crystal may have been composed of thin lammelae of alternating orientation. Free induction decays were found to be Gaussian in the rigid- lattice temperature region. This is evidenced by the linearity of a plot of log M,, vs. t? for fid's in this regime (see Fig. 5). As the temperature was raised, a motionally narrowed component began to appear at about -60°C. This component made an increasing contribution to the total signal as the temperature was further increased. At room temperature, V96% of the signal came from the motionally narrowed component. Figs. 6 and 7 show fid's taken at two temperatures in this motionally narrowed regime. Decay of the narrow component is seen to be exponential. T, and Th, decays were also seen to consist of more than one l component as illustrated in Figs. 8 and 9. The values of T, and T 1 lo for the narrow-line component were extracted by considering only the most rapidly decaying part of the curves. Two different sets of T. data were obtained over the entire temperature range of interest. The first set of measurements, with values designated as TAA), was made at the same time as the Ty data were taken. Following these measurements was an interval of several weeks before the next data were taken. During that time it was decided ~25~ Fig. 4. Back-reflection Laue photograph of doped B~PbF., crystal. The portion of the crystal being examined is in the [110] orientation. -26~ to repeat the T, experiment taking more signal averages. This was done concurrently with the Th) measurements, and values of T, obtained 2 in this second set of measurements are denoted T, (B). The values of T, obtained in these two data sets differ by a factor of ‘1.4. The reason for this discrepancy is not known at this time; the most likely explanation, however, is that the crystal orientation was different when the two sets of data were taken. Fig.10 is a plot of log (Tos T,> and Ty) vs. 1/T for potassium- doped B-PbF.. Both sets of Ty data are given. The two data sets yield the same slope, within experimental error. These slopes give activation energies of 0.18 + 0.01 eV for T, (A) and 0.17 + 0.01 eV for T, (B). The T,. curve has a minimum at T = ~20°C. The activation 1p energy for Tho at temperatures below the minimum is 0.34 + 0.02 eV. No Ty minimum was observed in the temperature range of this experiment. An activation energy for T, is not well defined because of the gentle 1 curve in the TF data. However, the three points taken at highest temperature appear to be collinear, and a line through these points gives an activation energy of 0.17 + 0.01 eV. -27~ a a | 0 100 200 300 400 500 600 700 t2 (usec?) Fig. 5. Log of M_ vs. t? taken from fid data points at T = ~69°C. The linearity of the plot demonstrates the Gaussian lineshape in this, the rigid lattice, temperature region. ~23- ‘9UTT ay3 JO sdoTs ay] se uayeR seM é L ‘Teusts Te8ION JO Zou SOANIFASuOD quauodUOD MOTAEN "0.6 = I 7e vsayxe. pry JQuauodwuos-oA], "4 °8Td (aes) 3 008 009 00% 002 0 *auTT e493 jo adoTs ay. se useyeR sem er *yTeusts T#I09 FO YCOSu SaqnyyAsuos quseuodmos mol1eN *0,07- = L 28 uayxe. pry Juauoduod-oml, ‘9 “*3Tq (sesh) 4 OST O0OT 0s 0 1 i a A(~) = A(t) /=29- 4 YJ t u 3 4 5 T 0 ol e ho t (sec) Fig. 8. T, decay taken at T = 6°C,. Ty) was taken as the slope of the liné shown above. A(t) -30~ t T T T T T T 0 ol 2 3 4 05 .6 7 t (msec) Fig. 9. T,. decay taken at T = -27°C. T,, was taken as the slope of the liné°shown above. ° -31- T (°C) -106 10° T a oa Ty (AE = 0,17 + 0.01 eV) 107) Th) (AE = 0.34 + 0.02 eV) 107? et ted Relaxation Time (sec) 1073 at tt T, (A) (AE = 0.18 + 0.01 eV) 1074 rerry tat Ty (B) (AE = 0.17 + 0,01 eV) it i i i L 3.0 5.5 4.0 4.5 5.0 5.5 6.0 1/T x 103 (°K) Fig. 10. Log of relaxation times vs. 1/T. Vertical error bars represent an estimate of precision for each Ty Ty » Or To value. Horizontal bars are uncertainty in measuring T. -32- Discussion From the relationship 2uy tT, = 1 at the The minimum, a value of tj 2.9 usec at T = -20°C is obtained. This compares with T° 16 usec at -20°C which is estimated from the data of Hwang et_al.24 for a sodium-doped crystal with a higher dopant concentration. This comparison suggests that potassium-doping is more effective than sodium- doping in activating fluorine motion. An estimate of the fluorine diffusion coefficient can be made from the relation D = d7/6r, where d is the jump distance of a fluorine atom. Letting d = 2.96 R (the fluorine-fluorine nearest neighbor il em2/sec at -20°C, distance) and 1, = 2.9 usec gives D = 5.0 x 10" This is consistent with the value obtained by extrapolating the conduc- tivity data of Liang and Joshi? to the same temperature. A quantitative comparison is not meaningful since the samples used in the two experiments contained different concentrations of KF dopant. An estimate was made of the expected contribution of fluoride ion motion to the relaxation rates 1/T,, 1/T,, and 1/T,,- The calculated 2 values of qT, and Th at -20°C are in good agreement with observed values at that temperature. However, the experimentally determined Ty is about two orders of magnitude smaller than the calculated value. This same phenomenon was reported by Hwang et_al.7* who inferred that Ty must be controlled by a mechanism other than fluorine motion. They suggested that electronic carriers might be responsible for Ty in sodium- doped PbF,- That mechanism may dominate Ty in the present case as well, although there is no direct evidence that that is the case. If T, and T, are both controlled by simple fluorine motion, 2 lo -33— the activation energies of these two processes should be equal. The energies of activation for the two sets of T, data agree with the 2 value of AH = 0.18 eV reported by Liang and Joshi® for their potassium-doped samples. However, the activation energy obtained for To is twice that for To: We are presently unable to account for this difference. The two-component relaxation curves which are observed in this experiment have not been reported in previous NMR studies of lead fluoride. The presence of more than one component reduces the accuracy of the relaxation data and complicates their interpretation. It is not known whether this behavior is caused by sample inhomogeneity or by some fundamental aspect of the diffusion process. =~34u Conclusion The results which have been obtained in this experiment are both interesting and perplexing. The NMR data for this potassium-doped B-PbF, crystal demonstrate anion mobility comparable to or greater than that reported for other B-PbF, samples. However, the quality of the crystal was less than expected, and this resulted in unforeseen complications. Further work in this area would be warranted if a crystal of better quality can be obtained. -35- References 12 wW.G. Wyckoff, Crystal Structures, 2nd edition, vol. 1 (Wiley- Interscience, New York, 1963) p. 240. va. Sauka, J. General Chem. USSR 19, 1453 (1949); from Chem. Absts. 44, 8964 (1950). 33H, Kennedy, R. Miles, and J. Hunter, J. Electrochem. Soc. 120, 1441 (1973). 4A. Jones, Proc. Phys. Soc. London, Sect. A 68, 165 (1955). °c, Tubandt, Z. Anorg. Chem. 115, 105 (1921). 6.0. Liang and A.V. Joshi, J. Electrochem. Soc. 122, 466 (1975). 2, Benz, Z. Phys. Chem. Neue Folge 95, 25 (1975). 85, Schoonman, G.A. Korteweg, and R.W. Bonne, Solid State Commun. 16, 9 (1975). Sav. Joshi and C.C. Liang, J. Electrochem. Soc. 124, 1253 (1977). 105. Schoonman, G.J. Dirksen, and G. Blasse, J. Solid State Chem. J, 245 (1973). at oe Gianduzzo, J. Pistre, and J. Salardenne, Electrocomponent Sci. Technol. 2, 55 (1975). 125M, Reau, J. Claverie, G. Campet, C. Deportes, D. Ravaine, J.L. Souquet, and A. Hammou, C.R. Acad. Sci., Ser. C 280, 325 (1975); from Chem. Absts. 83, 19959e (1975). 13y 4, Arkhangel'skaya, V.C. Erofeichev, and M.N. Kiseleva, Sov. Phys.- Solid State 14, 2953 (1973). 14, Schoonman, L.B. Ebert, C-H. Hsieh, and R.A. Huggins, J. Appl. Phys. 46, 2873 (1975). 1554, Kennedy and R.C. Miles, J. Electrochem. Soc. 123, 47 (1976). 16p wy, Bonne and J. Schoonman, Solid State Commun. 18, 1005 (1976). 17 I.D. Raistrick, C. Ho, Y.W. Hu, and R.A. Huggins, J. Electroanal. Chem. 77, 319 (1977). 18) Ww. Bonne and J. Schoonman, J. Electrochem. Soc. 124, 28 (1977). 190k. Derrington and M. O'Keeffe, Nature (London), Phys. Sci. 246, 44 (1973). ~36= 20. ¢. Liang and A.V. Joshi, J. Electrochem. Soc. 122, 1642 (1975). aly. Mahajan and B.D. Rao, Chem. Phys. Lett. 10, 29 (1971). 225 P, Mahendroo, N.S.K. Menon, and J.L. Marchant, Magn. Reson. Relat. Phenom., Proc. Congr. AMPERE, 18th 1, 237 (1974). 230 y, Hwang, M. Engelsberg, and I.J. Lowe, Chem. Phys. Lett. 30, 303 (1975). 24m vy, Hwang, I.J. Lowe, K.F. Lau, and R.W. Vaughan, J. Chem. Phys. 65, 912 (1976). 255 .B. Boyce, J.C. Mikkelsen, M. O'Keeffe, Solid State Commun. 21, 955 (1977). 262 p, Hogg, S.P. Vernon, and V. Jaccarino, Phys. Rev. Lett. 39, 481 (1977). 279 0c, Farrar and E.D. Becker, Pulse and Fourier Transform NMR (Academic Press, New York, 1971). -37- APPENDIX: PULSED-NMR LOCK SYSTEM Before this thesis project was undertaken, a new pulsed-NMR lock system was constructed to replace the cw system which was previously in use on our 56.4 MHz spectrometer, The new system contains a crystal oscillator which produces an rf signal at a desired frequency. This signal is gated to produce rf pulses which are amplified and sent through a quadrature hybrid to the sample probe. The probe transmits the rf pulses to the sample and receives the NMR signal in return. This signal is sent back through the quadrature hybrid to a "receiver" where it is amplified. Since the probe receives and transmits signals, the quadrature hybrid is used to isolate the receiver from the rf pulses. The signal from the receiver is phase detected to produce a slightly off-resonant free induction decay (fid) signal. A sample~and-hold device samples a small part of the fid at a zero-crossing and an integrator accumulates these samplings over time. The integrator thus produces a de signal whose level will be zero if the system is properly locked. If the integrated signal is non-zero a flux stabilizer adjusts the magnet current until proper locking is achieved. This system is schematized in Fig.11, I was responsible for building the rf part of the system, the part lying above the dashed line in Fig.11. The digital part of the system was constructed by the Chemical Engineering Electronics Shop. -38- suaqashs YOOT YNN—-pesytnd jo oT yewayas aap yy T due 4 ak mall zoqersaquy Pf 7 OF FT FIPS Fe qouseu xNnTJ A prToy pue aTdues ) aqoid aTdues t 1039930p ““ | ~~ asvyd Aaafove1 praqé aanjeipen < | N AO Je1IUET astnd y 33e3 | 103BTT FOS TeqsArz9 [eusTs soUatejaz h “Tl °3ta