Li Self-Diffusivities in Lithium Niobate Single Crystals as a Function of

Article pubs.acs.org/JPCC

Li Self-Diffusivities in Lithium Niobate Single Crystals as a Function of Li2O Content J. Rahn,† P. Heitjans,‡,§ and H. Schmidt*,†,§ †

Institut für Metallurgie, Thermochemie und Mikrokinetik, Technische Universität Clausthal, Robert-Koch-Str. 42, D-38678 Clausthal-Zellerfeld, Germany ‡ Institut für Physikalische Chemie und Elektrochemie, Leibniz Universität Hannover, Callinstrasse 3A, D-30167 Hannover, Germany § ZFM − Zentrum für Festkörperchemie und Neue Materialien, Leibniz Universität Hannover, Callinstrasse 3a, D-30167 Hannover, Germany ABSTRACT: Li self-diffusion is investigated in LiNbO3 single crystals at temperatures below 773 K by tracer diffusion experiments. Compared are single crystals with 49.9 mol % Li2O (near stoichiometric), 49.4 mol % Li2O, and 48.6 mol % Li2O (congruent). For the experiments, a thin ion-beam sputtered isotopeenriched 6LiNbO3 layer is used as a tracer source, and isotope depth profiling is done by secondary ion mass spectrometry. The temperature dependence of the diffusivities of all three types of samples can be described by Arrhenius laws with the same activation enthalpy of 1.33 eV; however, the diffusivities increase with decreasing amount of Li2O in the sample over the whole temperature range investigated, which is traced back to an increase in Li vacancy concentration. This is in agreement with a model of defect disorder consisting of a niobium antisite atom that is compensated by four lithium vacancies, (Nb···· Li + 4 V′Li). vacancies, (Nb···· ′ ).14 This model is supported by Li + 4 VLi 14,16 and density calculations.17 atomistic simulations For various applications of lithium niobate, self-diffusion of the constituents is of outermost importance. Many of the previously mentioned physical properties can be used in commercial devices only after a low-temperature heat treatment below 500 K in air or inert gas. The annealing induces a redistribution and diffusion of Li+ (and/or H+ impurity ions), which improves the technologically useful properties of LiNbO3. Characteristic processes are thermal fixing for optical data storage,18−20 purification from unwanted photoactive electrons (optical damage inhibition),7,8,21 waveguide fabrication by proton-exchange,22−24 and the improvement of ferroelectric domain switching.10,25 In addition, the formation, stability, and dissociation of defect clusters are closely related to diffusion properties.14 In contrast with impurity diffusion studies, reliable data on Li self-diffusion in LiNbO3 single crystals are very rare. (See refs 14 and 26.) Diffusion experiments are mainly restricted to nuclear magnetic resonance (NMR) studies and also to impedance spectroscopy or to the four-probe dc method (e.g., refs 26−33), while most of the data are limited to the high-temperature range above 773 K. A diffusion study based on mass tracers and stable isotopes was done at high temperatures above 1000 K.34

1. INTRODUCTION Lithium niobate (LiNbO3) is one of the technologically most important materials for optical, optoelectronic, and piezoelectric applications due to its ferroelectric, piezoelectric, acoustic, optical as well as ion conducting properties.1−5 These properties are combined with a high available quality, easy fabrication, and low cost of single crystals.6 Because of its versatile applications in the field of advanced photonics and optoelectronics, LiNbO3 is often termed as the “silicon of photonics”.7,8 The trigonal LiNbO3 phase (space group R3c) exhibits a wide solid solution region ranging from 44.0 mol % to ∼50.5 mol % Li2O.9 Single crystals produced by the Czochralski method commonly show the congruent composition of about 48.5 to 48.6 mol % Li2O; however, using the vapor transport equilibration (VTE) method (or other methods like the double-crucible method or the top seed solution method) the synthesis of near stoichiometric single crystals also becomes possible.9 Composition changes of Li2O within the solid solution range from the lithium-poor to the stoichiometric composition result in significant changes in the physical properties of the system. Typical examples are the Curie temperature, the ferroelectric coercive field, and photorefractive properties.1,10 Complex point defect formation is responsible for the nonstoichiometry and also strongly influences the observed changes in physical properties. Several defect models are proposed to realize off-stoichiometry in the Li-poor region,2,9,11−15 while for the congruent composition a niobium antisite atom is suggested that is compensated by four lithium © XXXX American Chemical Society

Received: May 7, 2015 Revised: June 15, 2015

A

DOI: 10.1021/acs.jpcc.5b04391 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C Compared with Nb and O, Li is already mobile in LiNbO3 at temperatures below 773 K.26 We recently presented actual studies on Li self-diffusion in congruent LiNbO3 single crystals at low temperatures between 379 and 773 K that were based on the use of stable 6Li tracers in combination with secondary ion mass spectrometry (SIMS)35 and neutron reflectometry.36,37 The results show that the diffusivities can be described in the given temperature range by a single Arrhenius straight line over 10 orders of magnitude with an activation enthalpy of 1.33 eV, which corresponds to the migration energy of a single Li vacancy. A dependence of Li diffusion on the crystallographic orientation was not found.38 In addition, impedance spectroscopy measurements were done on the same type of single crystal,39 proving that Li is the species that governs conductivity at least down to 473 K. The aim of the present work is to investigate the change of the Li self-diffusivity as a function of Li2O concentration within the stability range of LiNbO3 and to characterize near stoichiometric single crystals, which are of high importance for the improvement of technical applications.

Depth calibration was obtained by measuring the crater depth with a mechanical profilometer (Tencor, Alphastep).

3. RESULTS The 6Li atomic fraction as a function of sputter depth is given in Figure 1 for a characteristic sample in the as-deposited state

2. EXPERIMENTAL DETAILS The congruent LiNbO3 single crystals under investigation were supplied by Crystec, Germany (48.6 mol % Li2O). Further crystals were purchased from Del Mar Photonics, USA (49.4 mol % Li2O) and by Crystal Technology, USA (49.9 mol % Li2O). The noncongruent compositions were obtained using the VTE process at Leibniz-Institut für Kristallzüchtung, Berlin, Germany. The chemical composition was determined by UV absorption spectroscopy according to refs 40 and 41. 10 × 10 × 0.5 mm3 polished pieces were used for the experiments. Tracer deposition was carried out by depositing an about 40−60 nm thin layer of isotope-enriched 6LiNbO3 on the single crystal by ion beam sputtering using a commercial setup (IBS 681, Gatan) equipped with two Penning ion sources. Deposition was done at 5 keV and a current of ∼200 μA in argon at an operating pressure of 5 × 10−5 mbar and a base vacuum better than 5 × 10−7 mbar. During deposition, the specimen is rotated (30 rotations per minute) and rocked (rocking angle: 30°; rocking speed: 12° per second) to ensure a uniform coating of the sample. As sputter targets, sintered 6LiNbO3 was used. Details of sputter target preparation are given elsewhere.35 The diffusion anneals were carried out in ambient air in the temperature range below 773 K. A conventional resistance furnace or alternatively a rapid thermal annealing setup (AO 500, MBE, Germany) was used. Because of the fact that the tracer layer and the single crystal have the same chemical composition, pure isotope diffusion is measured during the experiments. The inward diffusion of 6Li ions from the sputter layer into the single crystal was determined by SIMS using a Cameca IMS 3f/4f machine equipped with a double-focused mass spectrometer. An O− primary ion beam (15 keV) was used to prevent electrical charging during the measurement. In the depth-profiling mode, the secondary ion intensities of 6Li+ and 7 + Li ions were recorded as a function of sputter time. Because the two Li isotopes are chemically identical, for diffusion analysis the intensity of the signals is converted into 6Li atomic fractions c(x, t) according to c(x , t ) =

I(6 Li) I(6 Li) + I(7Li)

Figure 1. 6Li atomic fraction as a function of depth for an as-deposited sample (49.4 mol % Li2O) (circles) and the sample annealed at 673 K for 100 min (squares). A least-squares fit of eq 2 to the experimental data is also indicated (line). The deviation of the fit from the experimental data for the as-deposited sample for c(x,t) < 0.25 is due to ion beam mixing, generally observed by SIMS experiments. In the present case it will not influence the correct determination of diffusivities.

and after annealing at 673 K. As is obvious, during annealing the 6Li tracer penetrates into the single crystal up to characteristic diffusion lengths of >200 nm. Experimentally determined depth profiles broadened after annealing can be described by the solution of Fick’s second law for self-diffusion across an interface42 c(x , t ) = c∞ +

⎛ h − x ⎞⎤ (c0 − c∞) ⎡ ⎛ h + x ⎞ ⎟ + erf⎜ ⎟ ⎢erf⎜⎝ ⎝ R ⎠⎥⎦ ⎣ 2 R ⎠ (2) 6

where c∞ = 0.075 is the natural abundance of Li in the single crystal and c0 = 0.96 is that in the tracer layer. The original thickness of the as-deposited tracer layer is denoted as h, which was determined by SIMS to range between 40−60 nm, depending on the sample under investigation. The quantity R, describing the broadening of the tracer profile, is treated as a fit parameter. The self-diffusivity, D, at time t is determined from the difference in R of the diffusion profile and of the starting profile according to D = (R2(t) − R2(0))/4t. Typical examples for such fits can also be seen in Figure 1. A time dependence of diffusivities is not observed within error limits. In Figure 2 the determined tracer diffusivities are plotted as a function of reciprocal temperature for the three types of crystals investigated. The data for the congruent crystal were already published in ref 35. The diffusivities of each type of crystal obey the Arrhenius law D = D0 exp( −ΔH /kBT )

(3)

with an activation enthalpy of ΔH and a pre-exponential factor of D0. As is obvious from Figure 2, the diffusivities of the congruent crystal are highest and decrease with increasing Li2O content in the whole temperature range investigated. All three types of data sets can be well-described with an activation

(1) B


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The Journal of Physical Chemistry C

4 four lithium vacancies (Nb···· Li + 4V′Li). Accordingly, the defect structure of Li-deficient LiNbO3 can be written as15

x x x (Li Li )1 − 5x (Nb···· Li )x (v′Li)4x (Nb Nb)(OO)3

(5)

using Krö ger−Vinck notation, where the fraction of Li vacancies is given by f v = 4x and the number of Nb antisites is given by x. From the Li2O concentration, experimentally determined by UV absorption spectroscopy, the fraction of Li vacancies, f v, can be calculated according to formula 5. In addition, f v can also be calculated from eq 4. In Figure 3, f v as

Figure 2. Diffusivities of Li in LiNbO3 single crystals as a function of reciprocal temperature for a Li2O content of 49.9 mol % (near stoichiometric), 49.4 mol %, and 48.6 mol % (congruent), respectively. The diffusivities for the congruent crystal were already published in ref 35.

enthalpy of 1.33 eV (see Figure 2), as found for the congruent crystal.35 The corresponding pre-exponential factors are given in Table 1. They also decrease significantly with increasing Li2O Table 1. Pre-Exponential Factors, D0, According to Equation 4 of LiNbO3 Single Crystals with Different Li2O Fractions for an Activation Enthalpy of 1.33 eV Li2O fraction (mol %)

temperature range (K)

pre-exponential factor (m2/s)

48.6 49.4 49.9

423−773 473−773 473−773

1.7 × 10−7 4.5 × 10−8 1.5 × 10−8

Figure 3. Li vacancy concentration, f v, in LiNbO3 single crystals. Plotted is f v (from D0), as calculated from the pre-exponential factor according to eq 4 versus f v (from Li2O), as calculated from the experimentally determined Li2O content according to eq 5. The straight line with the slope one through the origin is a guide to the eye.

calculated from the pre-exponential factor according to eq 4 is plotted versus f v as calculated from the Li2O content according to eq 5. We observe an excellent agreement between both quantities, especially if it is kept in mind that the characteristic vibration frequency, ν0, and the entropy of ionic motion, ΔS, are not precisely known. This result clearly confirms the (Nb···· Li + 4 VLi ′ ) defect as the dominating defect structure in LiNbO3. This model is also supported by experimental X-ray and neutron diffraction studies43,44 and density functional theory calculations.45 Note that Schottky or Frenkel pair formation close to the stoichiometric composition is not considered here. In the literature, there is a further common model discussed for the intrinsic point defect structures in LiNbO3.14 There, niobium antisites are compensated by niobium vacancies according to a defect given by (5 Nb···· ′′′′′). The Li + 4 VNb validity of this model can be ruled out here because a variation of the Li2O content and the corresponding change of the number of Nb vacancies are not expected to modify Li diffusion taking place via Li vacancies.

content. This has the consequence that the diffusivities are shifted in parallel to lower values with increasing Li2O content in Figure 2, while the slope of the Arrhenius straight line remains constant. The lowest diffusivities are found for the near-stoichiometric crystal, about 1 order of magnitude lower than for the congruent one. As pointed out in ref 35, the activation enthalpy of ΔH = 1.33 eV can be identified as the activation enthalpy of Li ionic motion, which corresponds to the migration of a single charged Li vacancy in a frozen-in defect structure, even if the temperature is changed. According to Table 1, all three types of crystals under investigation show this diffusion mechanism, and the decrease in diffusivities with increasing Li2O content is due to the variation of the pre-exponential factor. In the present case of a frozen-in defect structure the preexponential factor in eq 3 is given by D0 = fv a 2ν0 exp(ΔS /kB)

(4)

4. CONCLUSIONS We carried out tracer diffusivity measurements using SIMS depth profiling to obtain precise data for lithium self-diffusion in LiNbO3 single crystals with different Li2O contents of 49.9 mol %, 49.4 mol %, and 48.5 mol % at temperatures below 773 K. For all three types of samples, the diffusion of lithium is governed by a lithium vacancy mechanism with an activation enthalpy of diffusion of 1.33 eV, identical to the migration enthalpy. The diffusivities increase with decreasing amount of Li2O in the sample, which is traced back to an increase in Li

where a = 3.771 Å is the Li−Li jump distance, f v = [VLi′]/ [LiLix] is the mole fraction of Li vacancies, and ν0 ≈ 2.5 × 1013 s−1 is a characteristic vibration frequency.14 The entropy of ionic motion is approximately assumed to be ΔS ≈ 0. Equation 4 states that the variation in diffusivities (parallel shift) is due to a change in Li vacancy concentration. As mentioned, the off-stoichiometry on the Li-deficient side of the stability range of LiNbO3 is expected to be realized by a defect model where a niobium antisite atom is compensated by 14

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(16) Araujo, R. M.; Lengyel, K.; Jackson, R. A.; Kovacs, L.; Valerio, M. E. G. A Computational Study of Intrinsic and Extrinsic Defects in LiNbO3. J. Phys.: Condens. Matter 2007, 19, 046211-1−046211-10. (17) Kovacs, L.; Polgar, K. Density Measurements on LiNbO3 Crystals Confirming Nb Substitution for Li. Cryst. Res. Technol. 1986, 21, K101−K104. (18) Staebler, D. L.; Amodei, J. J. Thermally Fixed Holograms in LiNbO3. Ferroelectrics 1972, 3, 107−113. (19) Yariv, A.; Orlov, S. S.; Rakuljic, G. A. Holographic Storage Dynamics in Lithium Niobate: Theory and Experiment. J. Opt. Soc. Am. B 1996, 13, 2513−2523. (20) Buse, K.; Breer, S.; Peithmann, K.; Kapphan, S.; Gao, M.; Krätzig, E. Origin of Thermal Fixing in Photorefractive Lithium Niobate Crystals. Phys. Rev. B 1997, 56, 1225−1235. (21) Falk, M.; Woike, Th.; Buse, K. Charge Compensation Mechanism for Thermo-Electric Oxidization of Lithium Niobate Crystals. J. Appl. Phys. 2007, 102, 063529-1−063529-4. (22) Jackel, J.; Glass, A. M.; Peterson, G. E.; Rice, C. E.; Olson, D. H.; Veselka, J. J. Damage-resistant LiNbO3 Waveguides. J. Appl. Phys. 1984, 55, 269−270. (23) Birnie, D. P., III. Proton Exchange in Lithium Niobate as an Ambipolar Diffusion Process. Ferroelectrics 1996, 185, 29−32. (24) Alcázar, A.; Rams, J.; Cabrera, J. M.; Agulló-López, F. Proton Exchange of Quasistoichiometric LiNbO3. J. Appl. Phys. 1997, 82, 4752−4757. (25) Steigerwald, H.; Lilienblum, M.; von Cube, F.; Ying, Y. J.; Eason, R. W.; Mailis, S.; Sturman, B.; Soergel, E.; Buse, K. Origin of UVInduced Poling Inhibition in Lithium Niobate Crystals. Phys. Rev. B 2010, 82, 214105-1−214105-6. (26) Birnie, D., III. Review − Analysis of Diffusion in Lithium Niobate. J. Mater. Sci. 1993, 28, 302−315. (27) Heitjans, P.; Masoud, M.; Feldhoff, A.; Wilkening, M. NMR and Impedance Studies of Nanocrystalline and Amorphous Ion Conductors: Lithium Niobate as a Model System. Faraday Discuss. 2007, 134, 67−82. (28) Wilkening, M.; Bork, D.; Indris, S.; Heitjans, P. Diffusion in Amorphous LiNbO3 Studied by 7Li NMR − Comparison with the Nano- and Microcrystalline Material. Phys. Chem. Chem. Phys. 2002, 4, 3246−3251. (29) Halstead, T. K. Temperature Dependence of the Li NMR Spectrum and Atomic Motion in LiNbO3. J. Chem. Phys. 1970, 53, 3427−3435. (30) Mehta, A.; Chang, E. K.; Smyth, D. M. Ionic Transport in LiNbO3. J. Mater. Res. 1991, 6, 851−854. (31) Bork, D.; Heitjans, P. NMR Investigations on Ion Dynamics and Structure in Nanocrystalline and Polycrystalline LiNbO3. J. Phys. Chem. B 2001, 105, 9162−9170. (32) Brands, K.; Falk, M.; Haertle, D.; Woike, T.; Buse, K. Impedance Spectroscopy of Iron-doped Lithium Niobate Crystals. Appl. Phys. B: Lasers Opt. 2008, 91, 279−281. (33) Weidenfelder, A.; Shi, J.; Fielitz, P.; Borchardt, G.; Becker, K. D.; Fritze, H. Electrical and Electromechanical Properties of Stoichiometric Lithium Niobate at High-temperatures. Solid State Ionics 2012, 225, 26−29. (34) Ptashnik, V. B.; Dunaeva, T. Y.; Myasnikov, I. V. Self-diffusion of Lithium Ions in a Lithium-niobate Single-crystal. Inorg. Mater. 1985, 21, 1814−1817. (35) Rahn, J.; Hüger, E.; Dörrer, L.; Ruprecht, B.; Heitjans, P.; Schmidt, H. Li Self-diffusion in Lithium Niobate Single Crystals at Low Temperatures. Phys. Chem. Chem. Phys. 2012, 14, 2427−2433. (36) Hüger, E.; Rahn, J.; Stahn, J.; Geue, T.; Schmidt, H. Diffusivity Determination in Bulk Materials on Nanometric Length Scales Using Neutron Reflectometry. Phys. Rev. B 2012, 85, 214102-1−214102-8. (37) Hüger, E.; Rahn, J.; Geue, T.; Stahn, J.; Heitjans, P.; Schmidt, H. Lithium Diffusion in Congruent LiNbO3 Singel Crystals at Low Temperatures Probed by Neutron Reflectometry. Phys. Chem. Chem. Phys. 2014, 16, 8670−8674.

vacancy concentration due to off-stoichiometry. A maximum difference between near-stoichiometric and congruent single crystals of about 1 order of magnitude is observed. From the results, a model of defect disorder where a niobium antisite atom is compensated by four lithium vacancies (Nb···· Li + 4V′Li) is confirmed.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49-5323-722094. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Deutsche Forschungsgemeinschaft (DFG) in the framework of the research unit 1277 “molife” (Schm 1569/18-2 and He 1574/13-2) is gratefully acknowledged. We thank J. Shi for the determination of the Li2O content of the single crystals, S. Ganschow, A. Weidenfelder, and H. Fritze for supplying VTE-treated single crystals, and B. Ruprecht for the preparation of the sputter targets.

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REFERENCES

(1) Peng, Q.; Cohen, R. E. Origin of Pyroelectricity in LiNbO3. Phys. Rev. B 2011, 83, 220103-1−220103-4. (2) Properties of Lithium Niobate, Wong, K. K., Ed.; INSPEC Institution of Electrical Engineers: London, 2002. (3) The Handbook of Photonics; Gupta, M. C., Ballato, J., Eds.; CRC Press Taylor & Francis Group: Boca Raton, FL, 2007. (4) Gopalan, V.; Dierolf, V.; Scrymgeour, D. A. Defect-Domain Wall Interactions in Trigonal Ferroelectrics. Annu. Rev. Mater. Res. 2007, 37, 449−489. (5) Volk, T.; Wöhlecke, M. Lithium Niobate; Springer: Berlin, 2010. (6) Lüdtke, F.; Buse, K.; Sturman, B. Hidden Reservoir of Photoactive Electrons in LiNbO3 Crystals. Phys. Rev. Lett. 2012, 109, 026603-1−026603-5. (7) Sturman, B.; Kösters, M.; Haertle, D.; Becher, C.; Buse, K. Optical Cleaning Owing to the Bulk Photovoltaic Effect. Phys. Rev. B 2009, 80, 245319-1−245319-10. (8) Kösters, M.; Sturman, B.; Werheit, P.; Haertle, D.; Buse, K. Optical Cleaning of Congruent Lithium Niobate Crystals. Nat. Photonics 2009, 3, 510−513. (9) Bordui, P. F.; Norwood, R. G.; Jundt, D. H.; Fejer, M. M. Preparation and Characterization of Offcongruent Lithium Niobate Crystals. J. Appl. Phys. 1992, 71, 875−879. (10) Gopalan, V.; Mitchell, T. E.; Furukawa, Y.; Kitamura, K. The Role of Nonstoichiometry in 180° Domain Swiching of LiNbO3 Crystals. Appl. Phys. Lett. 1998, 72, 1981−1983. (11) Schirmer, O. F.; Thiemann, O.; Wöhlecke, M. Defects in LiNbO3 − I. Experimental Aspects. J. Phys. Chem. Solids 1991, 52, 185−200. (12) Prokhorov, A.; Kuzminov, Y. Physics and Chemistry of Crystalline Lithium Niobate; Hilger: Bristol, U.K., 1990. (13) Abrahams, S. C.; Marsh, P. Defect Structure on Composition in Lithium Niobate. Acta Crystallogr., B 1986, 42, 61−68. (14) Xu, H.; Lee, D.; Sinnott, S. B.; Dierolf, V.; Gopalan, V.; Phillpot, S. R. Structure and Diffusion of Intrinsic Defect Complexes in LiNbO3 from Density Functional Theory Calculations. J. Phys.: Condens. Matter 2010, 22, 135002-1−135002-7. (15) Shi, J.; Fritze, H.; Borchardt, G.; Becker, K.-D. Defect Chemistry, Redox Kinetics, and Chemical Diffusion of Lithium Deficient Lithium Niobate. Phys. Chem. Chem. Phys. 2011, 13, 6925−6930. D


Article

The Journal of Physical Chemistry C (38) Rahn, J.; Dörrer, L.; Ruprecht, B.; Heitjans, P.; Schmidt, H. Li Diffusion in (110) Oriented LiNbO3 Single Crystals. Defect Diffus. Forum 2013, 333, 33−38. (39) Ruprecht, B.; Rahn, J.; Schmidt, H.; Heitjans, P.; LowTemperature, D. C. Conductivity of LiNbO3 Single Crystals. Z. Phys. Chem. 2012, 226, 431−437. (40) Földvari, I.; Polgar, K.; Voszka, R.; Balasanyan, R. N. A Simple Method to Determine the Real Composition of LiNbO3 Crystals. Cryst. Res. Technol. 1984, 19, 1659−1661. (41) Kong, Y.; Zhang, W.; Chen, X.; Xu, J.; Zhang, G. OH− Absorption Spectra of Pure Lithium Niobate Crystals. J. Phys.: Condens. Matter 1999, 11, 2139−2143. (42) Crank, J. The Mathematics of Diffusion; Oxford University Press: Oxford, U.K., 1975. (43) Zotov, N.; Boysen, H.; Frey, F.; Metzger, T.; Born, E. Cation Substitution Models of Congruent LiNbO3 Investigated by X-ray and Neutron Powder Diffraction. J. Phys. Chem. Solids 1994, 55, 145−152. (44) Zhdanov, G. S.; Ivanov, S. A.; Kolontsova, W. V.; Korneev, A. E. X-Ray Diffuse Scattering From Single Crystal LiNbO3 and LiTa O3 as a Function of Temperature Between 20 − 750 °C. Ferroelectrics 1978, 21, 463−465. (45) Xu, H.; Lee, D.; He, J.; Sinnott, S. B.; Gopalan, V.; Dierolf, V.; Phillpot, S. R. Stability of Intrinsic Defects and Defect Clusters in LiNbO3 from Density Functional Theory Calculations. Phys. Rev. B 2008, 78, 174103-1−174103-12.

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Li Self-Diffusivities in Lithium Niobate Single Crystals as a Function of

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