Rapid Electron Dynamics at Fe Atoms in Nanocrystalline Li0 ... - Core

ARTICLE pubs.acs.org/JPCC

Rapid Electron Dynamics at Fe Atoms in Nanocrystalline Li0.5FePO4 € ssbauer Spectrometry Studied by Mo Hongjin Tan* and Brent Fultz Keck Laboratory, California Institute of Technology, Pasadena, California 91125, United States ABSTRACT: Two-phase mixtures of Li0.5FePO4 with crystal sizes as small as 25 nm were prepared by solid-state reaction, ball milling, and chemical delithiation. M€ossbauer spectra of nanocrystalline Li0.5FePO4 found evidence for a thin layer of Fe3þ at the crystal surfaces. Spectra acquired at temperatures from 25 to 225 °C showed thermally driven electronic relaxations, where the electric field gradients (EFG) of the main Fe3þ and Fe2þ spectral components decreased with temperature. The isomer shifts (IS) of Fe3þ and Fe2þ showed similar thermal trends, indicative of valence fluctuations caused by small polaron hopping. The activation energies obtained from the temperature dependence of the EFG were 410 meV for Fe3þ and 330 meV for Fe2þ, and an activation energy of 400 meV was obtained for the IS of both. The rapid valence electron hopping between Fe sites is intrinsic to electronic conductivity in LixFePO4, which is calculated to be higher than most reports for bulk material.

’ INTRODUCTION Electrode materials for lithium ion batteries require high ionic and electronic conductivities, high capacity, low cost, and environmental compatibility. The cathode material LixFePO41 meets many of these criteria, but it has the electronic structure of an insulator. The electrical conductivity of LixFePO4 has been enhanced by carbon coating,2
6 but there may be an additional improvement by preparing this material in nanocrystalline form. Several methods of nanocrystal synthesis have produced better electrochemical performance and faster charge conduction as compared to large crystals of LiFePO4.7
15 Recent experiments and simulations have addressed how nanocrystals of LixFePO4 have altered kinetics and thermodynamics,15
22 but there have been few basic studies on electron mobility. Small polaron hopping23 is the likely mechanism for charge conduction in olivine LixFePO4.24,25 A small polaron includes the displacements of the positions of neighboring atoms when there is a change of valence at a central atom. For example, the Fe
O bond distance shortens by about 5% if an Fe2þ ion loses an electron to become an Fe3þ. Moving this electronic hole to an adjacent Fe site requires moving the local distortion too, often immobilizing the charge at low temperatures. The charge plus distorted environment, called a small polaron, moves at higher temperatures when atomic vibrations bring the local atomic structure of the adjacent site to a configuration compatible with bond distances and angles for Fe3þ. The electron then moves more rapidly than the ions. The thermally activated polaron hopping frequency f(T), as explained by Mott,23 is f ðTÞ ¼ ν

e2 1 cð1
cÞe
2Rr e
Q =kB T r kB T

ð1Þ

which includes the frequencies, ν, of phonons that move adjacent r 2011 American Chemical Society

Fe and O atoms, the concentrations of the Fe2þ and Fe3þ, c and 1
c, an overlap of the adjacent Fe electron wave functions across the distance r, and an activation energy for achieving the conditions for polaron hopping, Q. For bulk LiFePO4, an assessment of Q gave a value of approximately 650 meV.26 Density functional theory calculations on free polaron motion gave a much lower value of 200 meV. However, because the polaron environment is likely affected by the presence of Liþ ions, a higher activation energy is expected.25 M€ossbauer spectrometry gives a view of the electron density and electron dynamics from the perspective of nuclei of iron atoms. The static electron density was used to characterize the fractions of heterosite (Li-poor) and triphylite (Li-rich) phases in LixFePO4 by M€ossbauer spectrometry measurements on samples in an electrochemical cell.27 Previous studies on Fe2þ/Fe3þ mixed-valence systems showed how the dynamics of thermally activated charge transfers cause distortions of M€ossbauer spectra.28
30 More recently, small polaron hopping in LixFePO4 was studied by measurements at elevated temperatures of Fe isomer shifts (ISs; characteristic of the charge density at 57Fe nuclei) and electric quadrupole splittings (EQSs; characteristic of the electric field gradient, EFG, at 57Fe nuclei).31
33 Especially at temperatures approaching 200 °C, rapid valence fluctuations were seen clearly in the solid solution phase of LixFePO4, although not in two-phase mixtures of the equilibrium heterosite and triphylite phases.32,33 These charge dynamics showed only a weak dependence on the concentration of Li, x, but the difference between activation energies for Fe2þ (approximately 510 meV)

Received: January 5, 2011 Revised: March 17, 2011 Published: March 30, 2011 7787

dx.doi.org/10.1021/jp200127b | J. Phys. Chem. C 2011, 115, 7787–7792

The Journal of Physical Chemistry C

ARTICLE

similar phases. In addition, we report evidence that the nanocrystalline materials have an enrichment of Fe3þ at crystal surfaces.

’ EXPERIMENTAL SECTION Nanocrystalline LiFePO4 was prepared by a solid-state reaction with precursors of Fe(C2O4) 3 2H2O, NH4H2PO4, and Li2CO3, followed by milling in a Fritsch planetary ball mill, as described previously.35 The LiFePO4 crystal size was controlled by varying the ball-to-powder weight ratio and milling time. The two-phase mixture of nano-Li0.5FePO4 was prepared by chemically oxidizing Fe2þ in an acetonitrile solution with NO2BF4. A PANalytical X'pert PRO X-ray diffractometer (XRD) with Cu KR radiation, a ZEISS 1550 VP field-emission scanning electron microscope (FE-SEM), and a Tecnai F30 transmission electron microscope (TEM) were used to determine crystal sizes, microstructure, and phase fractions. M€ossbauer spectrometry was performed in transmission geometry, with a 57Co in Rh source mounted on a Wissel MVT1000 Doppler drive unit. Data acquisition and synchronization were controlled by a LabVIEW system with a buffered counter. Velocity calibration of the spectrometer was referenced to room temperature R-Fe spectra. For in situ measurements, samples were heated in an electrical resistance furnace at fixed temperatures, monitored by a few thermocouples. Spectra were acquired for 12 h after 1 h of equilibration at each temperature. After they were cooled back to room temperature, the samples were checked again by XRD and M€ossbauer spectrometry to determine phase fractions. Distributions of EQS energies (EQ) were analyzed by the method of Le Ca€er and Dubois34 using a linear correlation between IS and quadrupole splitting for each valence.

Figure 1. (a) SEM image of 25 nm Li0.5FePO4 showing agglomeration into larger secondary particles. (b) TEM dark-field (DF) image of 25 nm Li0.5FePO4 showing internal crystal sizes in the range of 20
30 nm. (c) XRD of 25 nm Li0.5FePO4, obtained with Cu KR radiation.

and Fe3þ (approximately 570 meV) suggests an additional electronic effect on Fe2þ caused by Liþ ion motions.33 The EQS is sensitive to the structural and electronic environment of 57Fe atoms, and when there are multiple environments in a sample, it is typical to observe a distribution of EQSs. An EQS distribution can be obtained by fitting the measured spectra to sums of doublets with various centroid shifts (i.e., ISs). We used the software package of Le Ca€er and Dubois34 to analyze the spectra in this study. In the present study of nanocrystalline Li0.5FePO4 prepared as a mixture of heterosite and triphylite phases, the interpretation emphasized the effects of temperature on change dynamics, not local environments. Unlike LixFePO4 with large crystals studied previously as a two-phase mixture of heterosite and triphylite,32,33 thermal relaxations of the EQS and IS in nanocrystalline Li0.5FePO4 were observed at temperatures below 200 °C. This indicates a much faster rate of small polaron hopping and electron dynamics in nanocrystalline material with

’ RESULTS The as-prepared LiFePO4 (bulk-LiFePO4) was confirmed by XRD to have the olivine structure with a large crystal size, consistent with the 300 nm estimated from SEM and TEM. Using the Hall
Williamson method to interpret the X-ray line broadening,36 the ball-milled nanocrystalline LiFePO4 had a characteristic crystal size of 25 nm. The SEM and TEM images showed an aggregation of the nanocrystals into secondary particles of 0.5
1 μm (Figure 1). Figure 2 shows M€ossbauer spectra measured at room temperature on 25 nm LixFePO4 two-phase mixtures, with x = 0.65, 0.5, and 0.35. The two different valences, Fe3þ and Fe2þ, characteristic of heterosite and triphylite, respectively, show distinct EQSs and ISs. Consistent with previous work33 on 300 nm bulk-LixFePO4, spectra of the two-phase mixtures are approximately linear combinations of the two doublets of Fe3þ and Fe2þ. For the 25 nm nanocrystalline LixFePO4 (x = 0.65, 0.5, and 0.35), two maxima from Fe3þ and Fe2þ are prominent in distributions of the EQS energies, P(EQ) (peaks 1 and 2 in Figure 3a). The areal fractions of Fe3þ and Fe2þ, integrated from P(EQ) in Figure 3a, are consistent with their molar concentrations from Rietveld refinement of XRD patterns. Although XRD shows only two phases of triphylite and heterosite in the three samples, there is an extra intensity observable around 0.8 mm/s, peak 0 in Figure 3a, indicating another local configuration of Fe. For the different crystal sizes of 300, 70, and 25 nm, the areal fraction of peak 0 is approximately linear with the inverse of crystal size (Figure 3b) but independent of composition. Such a scaling is consistent with the presence of Fe3þ at crystal surfaces, 7788

dx.doi.org/10.1021/jp200127b |J. Phys. Chem. C 2011, 115, 7787–7792

The Journal of Physical Chemistry C

ARTICLE

Figure 2. Room temperature M€ossbauer spectra of two-phase mixtures of heterosite and triphylite in materials with 25 nm crystallites. (a) Li0.65FePO4, (b) Li0.5FePO4, and (c) Li0.35FePO4.

which may be too thin or too disordered to give a signature pattern in XRD. Figure 4 shows M€ossbauer spectra of 25 nm Li0.5FePO4, measured at temperatures from 25 to 210 °C. Upon heating, a gradual decrease of the EQS is visible in the spectra, starting around 145 °C. For samples with larger crystals, this change of M€ossbauer lineshapes with temperature was not observed for two-phase LixFePO4 at any composition x, although the solid solution phase of LixFePO4 shows similar behavior at slightly higher temperatures.33 Figure 5 presents distributions of EQS energies, EQ, fitted from the data of Figure 4 with the method of Le Ca€er and Dubois. As in the study of bulk crystalline LixFePO4 by M€ossbauer spectrometry using Le Ca€er's method,33 peaks 1 and 2 correspond to Fe3þ and Fe2þ, respectively. Although these two peaks change shape at temperatures above 145 °C, the ratio of their areas is approximately one from 25 to 200 °C, as expected for a two-phase mixture with a composition of x = 0.5. The areal fraction and center of peak 0 (EQ = 0.7 mm/s) for surface Fe3þ stays almost constant with temperature from 25 to 200 °C. This lack of temperature sensitivity is consistent with the observation that the crystallite size determined by XRD did not change after heating the sample in this temperature range. Figure 5 shows that the two major peaks shift to smaller EQ with increased temperature, particularly peak 2 for Fe2þ. These two peaks were fit to two Gaussian functions to obtain averaged values of EQ for Fe2þ and Fe3þ at each temperature, and results are shown in Figure 6a. The difference between the EQ measured at elevated temperatures and at room temperature, ΔEQ, is graphed versus 1/T in Figure 7a. The Arrhenius behavior gives an activation energy for Fe3þ of 410 meV, which is larger than the 330 meV obtained for Fe2þ. The ISs were in the range of 1.0
1.4 mm/s for Fe2þ and in the range of 0.4
0.8 mm/s for Fe3þ (Figure 6b). These are typical of high-spin configurations for both valences of Fe (S = 2 for Fe2þ and S = 5/2 for Fe3þ). At higher temperatures, the IS of Fe2þ decreased, but it increased for Fe3þ, so the ISs became more

Figure 3. (a) EQS distribution P(EQ) of LixFePO4 with different crystal sizes, from the spectra of Figure 2. (b) Areal fraction of peak 0 with different crystal sizes, obtained by integrating the intensity below 1 mm/s in panel a.

similar. The formation of the solid solution phase stopped us from acquiring data above 230 °C, limiting the upper range of Figure 6b. The ISs for bulk Li0.6FePO4, on the other hand, are independent of temperature. The Arrhenius behavior of the ISs (Figure 7b) gave activation energies of 400 and 420 meV, essentially the same, for Fe2þ and Fe3þ. By fitting directly the plot of ΔEIS versus 1/T in Figure 6b, the activation energies for the IS dynamics of both Fe2þ and Fe3þ were about 400 meV with a prefactor of 1.0  1011 Hz.

’ DISCUSSION M€ossbauer spectrometry has a characteristic measurement time of τ = h/ε, where ε is the energy width of the nuclear resonance line, or the hyperfine interaction energy that gives rise to the EQS or IS (for 57Fe, ε = (v/c)14.41 keV, where v is the Doppler velocity and c is the speed of light). Values of τ from several nanoseconds to 100 ns give measurable effects in M€ossbauer spectra, and we use this feature to study thermal fluctuations of charge dynamics in LixFePO4. If electrons are thermally excited to a higher energy level on a 57 Fe atom, a widely used theory of Ingalls37 predicts a change in EFG from the anisotropy of the 3d orbital charge distribution of Fe2þ. A high-spin configuration of Fe2þ may have each of its first five 3d electrons occupying one d orbital, giving a spherical shell and no variation of EFG, but the sixth 3d electron has probabilities of occupying different orbitals, causing an EFG. With thermal energy, this sixth valence electron changes between these 7789

dx.doi.org/10.1021/jp200127b |J. Phys. Chem. C 2011, 115, 7787–7792

The Journal of Physical Chemistry C

ARTICLE

Figure 4. M€ossbauer spectra of 25 nm Li0.5FePO4 at elevated temperatures. Solid lines show fits from the hyperfine field distribution obtained by the method of Le C€aer and Dubois.34

Figure 6. (a) Values of EQS energy EQ (mm/s) obtained from Figure 5, corresponding to Fe2þ and Fe3þ. (b) Values of IS energy EIS (mm/s) of Fe2þ and Fe3þ vs temperature, from fitting M€ossbauer spectra of Figure 4, plotted together with EIS of Fe3þ and Fe2þ in the bulk Li0.6FePO4.32 The effect from the second-order Doppler shift was subtracted. Solid lines show fitting of the Arrhenius relation between IS and temperature, with an activation energy of about 400 meV and a prefactor of 1.0  1011 Hz. Figure 5. EQS distribution P(EQ) of 25 nm Li0.5FePO4 vs temperature, obtained from the spectra of Figure 4.

levels, and the charge distribution of Fe2þ appears more isotropic on the time scale of the M€ossbauer effect, reducing the EFG. Ingalls theory predicts no such effect on the EFG for Fe3þ, which has one electron in each 3d orbital. Nevertheless, we do observe a thermal reduction in EFG for Fe3þ. Furthermore, we also see a change in the IS, indicating fluctuations of charge at 57Fe atoms.32,33 For these two reasons, we discount the Ingalls theory for the main effects observed for LixFePO4. Thermal fluctuations of both the EQS and the IS with increased temperatures are consistent with electrons hopping between FeO6 octahedra, switching them between Fe2þ and Fe3þ configurations. Several previous studies reported this behavior in mixed-valence materials.28
30,38 At low temperatures, Fe valence electrons move infrequently between two corner-shared FeO6 octahedra, and the M€ossbauer spectra sample a static charge configuration when the electron dwell time is longer than the 100 ns lifetime of the

57

Fe nuclear excited state. The electron dynamics are faster at higher temperatures, and when valence electrons move between iron ions more frequently than 100 ns, the EFG is reduced because the ion appears more symmetrical on the time scale of the measurement. Likewise, the IS does not distinguish so clearly the Fe3þ and Fe2þ valences when charge is hopping rapidly. (In the high-temperature limit, not achieved in this investigation, Fe3þ and Fe2þ become indistinguishable by M€ossbauer spectrometry.) Our previous work on two-phase mixtures of LixFePO4 with larger crystals and compositions x = 0.8, 0.6, 0.45, and 0.3 showed little temperature dependence of the spectra in the temperature range from 25 to 210 °C.32,33 For the nanocrystalline materials of the present study, the temperature variation of the EFG was big enough to determine activation energies for Fe3þ of 410 meV and Fe2þ of 330 meV. These are smaller than for bulk materials prepared as solid solutions,33 where similar analysis gave activation energies for Fe3þ of 570 meV and Fe2þ of 510 meV. From previous measurements of electrical conductivity or AC 7790

dx.doi.org/10.1021/jp200127b |J. Phys. Chem. C 2011, 115, 7787–7792

The Journal of Physical Chemistry C

ARTICLE

Fe3þ, the other Fe site has the opposite trend, so M€ossbauer spectrometry cannot detect a difference in the fluctuation times of Fe2þ and Fe3þ. On the other hand, if the Liþ ions were performing diffusional jumps at rates comparable or faster than the polarons, it is possible that M€ossbauer spectrometry could detect a difference in the fluctuations of the EFG at Fe2þ and Fe3þ. The effects are expected to be larger at Fe2þ ions, which are more likely to have Liþ ions in their vicinity, possibly explaining the lower activation energy for the EQS at Fe2þ.33 With decreasing crystallite size, LixFePO4 will have more crystal surfaces and perhaps more grain boundaries and interfaces between heterosite and triphylite phases. Approximately, reducing the average crystal size from 300 to 25 nm could create 12 times more interface area. M€ossbauer spectrometry shows a spectral component of small EQS that likely originates with Fe3þ ions at crystal surfaces. The fraction of peak 0 in the spectrum (Figure 3a) increases from 6 to 14% when the crystal size decreases from 300 to 25 nm, approximately consistent with an increase of Fe 3þ on the surface layer over a characteristic thickness of one unit cell. There has been much interest in the thermodynamics of surfaces for nanoparticles of LixFePO4.9,17,20,44 A shell at the crystal surface enriched in Fe3þ and having an altered structure could play a role in the kinetics of lithiation. This shell may also affect the stability of the crystal against transformation to another phase. Surface effects were suggested as a possible reason for the kinetic stability of the solid solution phase of nanocrystalline LixFePO4 at low temperatures.22

Figure 7. Arrhenius plot of ln(ΔEQ) vs 1/T for Fe3þ and Fe2þ. Activation energies for EFG were obtained from the lines between 80 and 200 °C. (b) Arrhenius plot of ln(ΔEIS) vs 1/T for Fe3þ and Fe2þ. Activation energies for ISs were obtained from the lines between 80 and 200 °C.

impedance spectroscopy, the reported activation energies for electron mobility in LiFePO4 varied over a wide range from 150 to 750 meV.26,39
43 The dynamics of the thermally activated IS fluctuations originate with small polaron hopping and give detailed information about charge mobility. For a prefactor of 1.0  1011, obtained from constants in eq 1, and an activation of 400 meV, we obtain hopping frequencies at 25 °C of about 2.8  107 Hz. Using the Nernst
Einstein relation, the polaron hopping rate can be converted to electrical conductivity, giving 1.4  10
7 S/cm at 25 °C. We find a lower activation energy for the EQS broadening for Fe2þ than Fe3þ, 330 vs 410 meV. The activation energy for the EQS of Fe3þ is essentially the same as for the IS, consistent with a common origin in small polaron hopping. The Ingalls explanation would perhaps lower the activation energy for the EQS of Fe2þ, but we suggest this lower activation energy may originate with neighboring Liþ ions or vacancies. This coupling was suggested in previous work25,31 as an extra binding energy barrier added to free polarons, but this idea was discounted by others.26 If a Liþ ion were in a static position near one of the two Fe sites of the polaron hop, it should bias the nearby Fe toward Fe2þ, making a higher barrier for the electron to leave this site than to return. Although this site may spend more time as Fe2þ than

’ CONCLUSION Nanocrystalline Li0.5FePO4 powders were synthesized by solid-state reaction followed by ball milling. X-ray diffractometry showed them to be two-phase mixtures of Li-rich triphylite and Li-poor heterosite with characteristic crystal sizes as small as 25 nm. M€ossbauer spectrometry showed a spectral component from Fe3þ that increased with the inverse of crystallite size, correlating to the amount of crystal surface. M€ossbauer spectrometry also showed a decrease with temperature of the electric field gradients (EFG) at 57Fe3þ and 57Fe2þ nuclei in nanocrystalline Li0.5FePO4, a behavior not seen in two-phase materials with larger crystal sizes. The ISs of Fe3þ and Fe2þ showed a similarly anomalous temperature dependence, merging together with temperature as is characteristic of valence fluctuations because of small polaron hopping between FeO6 octahedra. Both IS and electric quadrupole effects indicate a fluctuation time of order 10 ns at a temperature of order 200 °C. The activation energies for the IS fluctuations were approximately 400 meV, and the activation energies for the EFG fluctuations were 410 meV for Fe3þ and 330 meV for Fe2þ. The activation energies are lower in these 25 nm nanocrystalline materials than reported for comparable two-phase bulk materials, indicating a higher intrinsic electrical conductivity. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We acknowledge help from Dr. Chi Ma with SEM work and C. M. Garland with TEM work (facility supported by the MRSEC 7791

dx.doi.org/10.1021/jp200127b |J. Phys. Chem. C 2011, 115, 7787–7792

The Journal of Physical Chemistry C Program of NSF under Award Number DMR-0520565). We thank K. Amine, I. Belharouak, and Argonne National Laboratory for providing LiFePO4 material. This work was supported by General Motors.

’ REFERENCES (1) Padhi, A. K.; Nanjundaswamy, K. S.; Goodenough, J. B. J. Electrochem. Soc. 1997, 144, 1188. (2) Dominko, R.; Gaberscek, M.; Drofenik, J.; Bele, M.; Pejovnik, S.; Jamnik, J. J. Power Sources 2003, 119, 770. (3) Doeff, M. M.; Hu, Y.; Mclarnon, F.; Kostecki, R. Electrochem. Solid-State Lett. 2003, 6, A207. (4) Hsu, K. F.; Tsay, S. Y.; Hwang, B. J. J. Mater. Chem. 2004, 14, 2690. (5) Dominko, R.; Bele, M.; Gaberscek, M.; Remskar, M.; Hanzel, D.; Pejovnik, S.; Jamnik, J. J. Electrochem. Soc. 2005, 152, A607. (6) Gabrisch, H.; Wilcox, J. D.; Doeff, M. M. Electrochem. Solid-State Lett. 2006, 9, A360. (7) Delacourt, C.; Poizot, P.; Levasseur, S.; Masquelier, C. Electrochem. Solid-State Lett. 2006, 9, A352. (8) Gibot, P.; Casas-Cabanas, M.; Laffont, L.; Levasseur, S.; Carlach, P.; Hamelet, S.; Tarascon, J.-M.; Masquelier, C. Nat. Mater. 2008, 7, 741. (9) Meethong, N.; Kao, Y.-H.; Tang, M.; Huang, H.-Y.; Carter, W. C.; Chiang, Y.-M. Chem. Mater. 2008, 20, 6189. (10) Zaghib, K.; Mauger, A.; Kopec, M.; Gendron, F.; Julien, C. M. ECS Trans. 2009, 16, 31. (11) Kobayashi, G.; Nishimura, S.; Park, M.; Kanno, R.; Yashima, M.; Ida, T.; Yamada, A. Adv. Funct. Mater. 2009, 19, 395. (12) Jones, J. L.; Hung, J.-T.; Meng, Y. S. J. Power Sources 2009, 189, 702. (13) Kang, B.; Ceder, G. Nature 2009, 458, 190. (14) Konarova, M.; Taniguchi, I. J. Power Sources 2010, 195, 3661. (15) Malik, R.; Burch, D.; Bazant, M.; Ceder, G. Nano Lett. 2010, 10, 4123. (16) Wang, L.; Zhou, F.; Meng, Y.; Ceder, G. Phys. Rev. B 2007, 76, 165435. (17) Fisher, C. A. J.; Islam, M. S. J. Mater. Chem. 2008, 18, 1209. (18) Ellis, B.; Herle, P. S.; Rho, Y. H.; Nazar, L. F.; Dunlap, R.; Perry, L. K.; Ryan, D. H. Faraday Discuss. 2007, 134, 119. (19) Rho, Y. H.; Nazar, L. F.; Perry, L.; Ryan, D. J. Electrochem. Soc. 2007, 154, A283. (20) Tang, M.; Huang, H. Y.; Meethong, N.; Kao, Y. H.; Carter, W. C.; Chiang, Y. M. Chem. Mater. 2009, 21, 1557. (21) Burch, D.; Bazant, M. Z. Nano Lett. 2009, 9, 3795. (22) Tan, H. J.; Dodd, J. L.; Fultz, B. J. Phys. Chem. C 2009, 113, 20527. (23) Mott, N. F. J. Non-Cryst. Solids 1968, 1, 1. (24) Xu, Y.; Shankland, T.; Duba, A. Phys. Earth Planet. Inter. 2000, 118, 149. (25) Maxisch, T.; Zhou, F.; Ceder, G. Phys. Rev. B 2006, 73, 104301. (26) Zaghib, K.; Mauger, A.; Goodenough, J. B.; Gendron, F.; Julien, C. M. Chem. Mater. 2007, 19, 3740. (27) Andersson, A. S.; Kalska, B.; Haggstrom, L.; Thomas, J. O. Solid State Ionics 2000, 130, 41. (28) Amthauer, G.; Rossman, G. R. Phys. Chem. Miner. 1984, 11, 37. (29) Achim, C.; Bominaar, E. L.; Meyer, J.; Peterson, J.; Munck, E. J. Am. Chem. Soc. 1999, 121, 3704. (30) Achim, C.; Bominaar, E. L.; Staples, R. J.; Munck, E.; Holm, R. H. Inorg. Chem. 2001, 40, 4389. (31) Ellis, B.; Perry, L. K.; Ryan, D. H.; Nazar, L. F. J. Am. Chem. Soc. 2006, 128, 11416. (32) Dodd, J. L.; Halevy, I.; Fultz, B. J. Phys. Chem. C 2007, 111, 1563. (33) Tan, H. J.; Dodd, J. L.; Fultz, B. J. Phys. Chem. C 2009, 113, 2526. (34) Le Ca€er, G.; Dubois, J. M. J. Phys. E Sci. Instrum. 1979, 12, 1083.

ARTICLE

(35) Amine, K.; Liu, J.; Belharouak, I. Electrochem. Commun. 2005, 7, 669. (36) Klug, H. P.; Alexander, L. E. X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials; Wiley: New York, 1974. (37) Ingalls, R. Phys. Rev. 1964, 133, A787. (38) Danot, M.; Afanasov, M. I.; Fabritchnyi, P. B.; Golub, A. S.; Lenenko, N. D.; Novikov, Y. N.; Pokholok, K. V.; Presniakov, I. A. Solid State Ionics 2000, 128, 211. (39) Delacourt, C.; Laffont, L.; Bouchet, L.; Wurm, C.; Leriche, J. B.; Tarascon, J. M.; Masquelier, C. J. Electrochem. Soc. 2005, 152, A913. (40) Takahashi, M.; Tobishima, S.; Takei, K.; Sakurai, Y. Solid State Ionics 2002, 148, 283. (41) Chung, S. Y.; Bloking, J. T.; Chiang, Y. M. Nat. Mater. 2002, 1, 123. (42) Xu, Y. N.; Chung, S. Y.; Bloking, J. T.; Chiang, Y. M.; Ching, W. Y. Electrochem. Solid-State Lett. 2004, 7, A131. (43) Amin, R.; Maier, J. Solid State Ionics 2008, 178, 1831. (44) Wagemaker, M.; Mulder, F. M.; der Ven, A. V. Adv. Mater. 2009, 21, 2703.

7792

dx.doi.org/10.1021/jp200127b |J. Phys. Chem. C 2011, 115, 7787–7792