Structure-property relationships in lithium superionic conductors

energy materials

ISSN 2052-5206

Structure–property relationships in lithium superionic conductors having a Li10GeP2S12-type structure Satoshi Hori,a Sou Taminato,a Kota Suzuki,a Masaaki Hirayama,a Yuki Katoa,b,c and Ryoji Kannoa*

Received 20 July 2015 Accepted 20 November 2015

Edited by K. Chapman, Argonne National Laboratory, USA Keywords: superionic conductor; MEM analysis; lithium battery; solid state battery. CCDC references: 1438232; 1438233; 1438234; 1438235; 1438236; 1438237 Supporting information: this article has supporting information at journals.iucr.org/b

a

Department of Electronic Chemistry, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori, Yokohama 226-8502, Japan, bBattery Research Division, Higashifuji Technical Center, Toyota Motor Corporation, 1200 Mishuku, Susono, Shizuoka 410-1193, Japan, and cBattery AT, Advanced Technology 1, TOYOTA MOTOR EUROPE NV/SA, Hoge Wei 33A B-1930, Zaventem, Belgium. *Correspondence e-mail: [email protected]

The crystal structures of the superionic conductors Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12, both having a Li10GeP2S12 (LGPS)-type structure, were determined by neutron diffraction analysis over the temperature range 12– 800 K. The maximum entropy method was also employed to clarify the lithium distribution in these materials. The Sn system showed one-dimensional diffusion in the c direction over a wide temperature range, even though the Ge-based system typically exhibits three-dimensional conduction at higher temperatures. The ionic conduction mechanisms of analogous Si, Ge and Sn phases with LGPS-type structures are discussed on the basis of the observed structural parameter changes.

1. Introduction

# 2015 International Union of Crystallography

Acta Cryst. (2015). B71, 727–736

Electrochemical storage devices such as lithium batteries represent key technologies in our modern society because of the growing demands for purely electric vehicles, power backup devices and grid-level energy storage (Armand & Tarascon, 2008; Dunn et al., 2011). As various electrode materials with high energy and power densities have been developed, a concurrent requirement for high-performance electrolytes that can provide fast ionic conductivity and are electrochemically and thermally stable (Goodenough & Kim, 2010) has arisen. As a result of the discovery of Li10GeP2S12 (LGPS), a new class of lithium superionic conductor (Kamaya et al., 2011), solid electrolytes show promise as the best means of satisfying these rigorous demands, and thus all-solid-state configurations are emerging as an attractive option for nextgeneration energy storage systems. LGPS exhibits a roomtemperature conductivity of the order of 102 S cm1, equal to or even exceeding the values obtained from liquid electrolytes, in addition to a wide electrochemical window of up to 5 V. Previous studies motivated by these attractive properties have demonstrated the exceptional performance of all-solid-state batteries using LGPS (Kato et al., 2012), and there have been reports of the synthesis of modified LGPS compositions (Bron et al., 2013; Hori et al., 2014; Whiteley et al., 2014) as promising solid electrolytes for use in batteries. The LGPS conduction mechanism has also been studied in conjunction with examinations of the crystal structure, since information regarding the structure–conductivity relationship is helpful when designing and predicting the next-generation superionic conductors (Fujimura et al., 2013; Wang et al., http://dx.doi.org/10.1107/S2052520615022283

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energy materials 2015). LGPS shows a unique structure, in which lithium ions are distributed along the c-axis in a three-dimensional framework composed of tetrahedral PS4 and GeS4 units (Kamaya et al., 2011; Kuhn et al., 2013). To date, theoretical calculations (Mo et al., 2012; Adams & Prasada Rao, 2012; Du et al., 2014) have suggested that the primary one-dimensional conduction occurs along the c-axis, with secondary conduction pathways over the ab-plane. As noted, it is highly desirable to develop an understanding of the conduction mechanism by comparing mechanisms suggested by theoretical simulations with experimental data. Experimentally derived results for various conductivity and structural parameters over a wide range of temperatures are expected to be especially helpful in reinforcing or validating simulations, since it is difficult to consistently apply theoretical calculation techniques over the range of low to high temperatures. As an example, structural stability data have been estimated only at 0 K based on ab initio calculations, while conductivity values have been calculated using molecular dynamics simulations based on extrapolation from high temperatures to lower temperatures assuming a constant activation energy. In reality, however, superionic conductors have been found to exhibit changes in structural parameters and thus to have different activation energies over various temperature ranges (Kwon et al., 2015). Structural analysis using neutron diffraction can provide data over a wide temperature range, allowing a more precise understanding of the ionic conduction mechanism at high temperatures and providing information on the phase change to a high ionic conduction state (Yashima et al., 2005; Nishimura et al., 2008). In the present study, the structures for the tin- and silicon-based LGPS phases were examined based on neutron diffraction data obtained for powder samples at 12, 300 and 800 K and at 17, 300 and 800 K for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12, respectively. The maximum entropy method (MEM; Sakata et al., 1993) was applied in the case of the Sn-based material to visualize changes in the Li distribution from low to high temperatures. The structural changes

that occur with variations in temperature are discussed in relation to the lithium conduction pathways.

2. Experimental All samples were synthesized using solid-state reactions. In this process, mixtures of P2S5 (Aldrich, > 99.9%), Li2S (Idemitsu Kosan, > 99.9%), SiS2 (Mitsuwa Chemical, 99%) and SnS2 (Koujundo Chemical Laboratory, > 99%) were ground in a ball-milling apparatus (Fritsch P7) for 40 h. Pelletized samples were sealed in a silica tube at 10 Pa and heated at 823 K for 72 h, applying a 2.2 K min1 heating rate and a 0.60 K min1 cooling rate. Samples were characterized by X-ray diffraction (XRD) and AC impedance measurements. XRD patterns of the powdered samples were obtained using an X-ray diffractometer (Rigaku, SmartLab) with Cu K radiation. In preparation for AC impedance measurements, pelletized samples were heated at 823 K for 8 h and then coated with gold powder on both sides to produce electrodes. The AC impedance values of samples were measured using a frequency response analyzer (National Instruments nF and Solartron 1260 for measurements above and below 213 K, respectively) by applying 10–100 mV over the frequency range 100 Hz to 3 MHz. The neutron diffraction data were obtained using time-offlight (TOF) diffractometers: iMateria at the Material and Life Science Experimental Facility (MLF) of the Japan Proton Accelerator Research Complex (J-PARC). In these studies, samples were sealed in a 6 mm diameter vanadium cell under Ar using an indium ring. Diffraction data were collected for 8 h at several temperatures: 12, 300 and 800 K in the case of Li9.81Sn0.81P2.19S12 and 17, 300 and 800 K in the case of Li10.35Si1.35P1.65S12. Structural parameters were refined using the Z-Rietveld refinement programs (Oishi et al., 2009) and profile parameters were refined using a pseudo-Voigt profile function. Nuclear density distributions were calculated employing the maximum entropy method (MEM), using crystal structure factors and standard deviations obtained by Rietveld refinement. All MEM calculations were performed using the Z-MEM algorithm in the Z-Code software package (Ishikawa, Zhang et al., 2014), which employs the conventional Sakata–Sato algorithm with zeroth-order single-pixel approximation (Sakata & Sato, 1990; Sakata et al., 1993). In these calculations, the unit cell was divided into 66 66 96 pixels and the Z-three-dimensional algorithm was used to generate nuclear density maps of structures (Ishikawa, Yonemura et al., 2014).

3. Results and discussion Figure 1 Sample characterization: (a) X-ray diffraction patterns for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12, together with that of Li10GeP2S12, and (b) variations in conductivity with temperature for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12. A conductivity plot for Li10.05Ge1.05P1.95S12 is also provided for comparison purposes (Kwon et al., 2015).

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Lithium superionic conductors

3.1. Sample characterization

The samples were synthesized using conventional solidstate reactions based on the compositions Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12, which are reported to show the highest ionic conductivity as evaluated by AC impedance measureActa Cryst. (2015). B71, 727–736

energy materials ments of the solid-solution system Li10 + M1 + P2 S12 (M = Si, Sn). Fig. 1(a) shows the XRD patterns acquired for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12 at room temperature together with the pattern for the original LGPS phase. All of the diffraction patterns are similar to one another, indicating that isostructural phases were obtained. Although the XRD patterns obtained using Cu K radiation indicated pure phase characteristics, a Li3PO4 phase in Li10.35Si1.35P1.65S12 and unknown impurity phases in both Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12 were detected by neutron diffraction measurements, as described in a later section. Conductivity was measured at varying temperatures and Fig. 1(b) presents Arrhenius plots for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12. The conductivity values determined at 298 K were 5.5 103 and 6.5 103 S cm1 for the Sn- and Si-based materials, respectively, and these are in good agreement with previously reported data (Hori et al., 2014). These results indicate that the desired materials were successfully synthesized. The Arrhenius conductivity plots show a bend in the conductivity curves

for both samples, just as was formerly observed for the original LGPS phase at approximately 373 K. 3.2. Neutron diffraction measurements

Neutron diffraction patterns were obtained over a wide temperature range. Fig. 2 illustrates the profile fit and difference patterns for Li9.81Sn0.81P2.19S12 at 12, 300 and 800 K, and for Li10.35Si1.35P1.65S12 at 17, 300 and 800 K. The calculated intensities are indicated by solid lines and the differences between the observed and calculated intensities are provided below the fitting patterns. The neutron diffraction patterns at all temperatures were indexed to the tetragonal cell with space group P42/nmc and no changes were observed in the diffraction patterns, indicating that there were no phase changes accompanied by symmetry changes over the temperature range from 17 to 800 K. This observation is in agreement with the phase stabilities suggested by the phase diagram including Li10GeP2S12 (Hori et al., 2015). The lattice and structural parameters were refined by the Rietveld method using the same structural model reported previously: four lithium sites; Li1(16h), Li2(4d), Li3(8f) and Li4(4c); two sites for M (= Si, Sn) and P atoms; [M1/P1](4d) and P2(2b); three sites for sulfide atoms; S1(8g), S2(8g) and S3(8g). Intensity data for interplanar ˚ for spacings of 1.2 < d < 7.3 A Li9.81Sn0.81P2.19S12 and 1.4 < d < ˚ 7.3 A for Li10.35Si1.35P1.65S12 (corresponding to time-of-flight ranges of approximately 12–73 ms and 14–73 ms, respectively) were used for Rietveld analysis. In the case of the Sn-based material, the TOF regions 34.7–36.1 ms and 56.9–58.5 ms were excluded from the refinement owing to the appearance of very weak peaks due to an unknown impurity phase that was not detectable by XRD measurements with Cu K radiation. Similarly, the TOF regions 21.4–21.6 ms and 39.7–41.8 ms were excluded during the refinement of the Si-based material. In addition, a multi-phase model incorporating the LGPS-type and an impurity phase, Li3PO4, was employed for the Si-based material. Refinements proceeded until an agreement factor, Rwp, of less than 0.035 was Figure 2 obtained at all temperatures. The Observed, calculated and difference plots for the Rietveld analysis of (a) Li9.81Sn0.81P2.19S12 and (b) Li atom site-occupancy parameter, Li10.35Si1.35P1.65S12. Bragg positions are indicated by vertical marks. For the Si-based materials, the lower vertical marks represent Bragg positions for a secondary Li3PO4 phase. g, was refined in each case, applying Acta Cryst. (2015). B71, 727–736

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energy materials Table 1 Structural parameters for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12. ˚ 2), U11 (A ˚ 2), U22 (A ˚ 2), U33 (A ˚ 2), U12 (A ˚ 2), U13 (A ˚ 2) and U23 (A ˚ 2)] were refined individually for Li10.35Si1.35P1.65S12. Note: atomic displacement parameters [Uiso (A Site

g

x

y

z

Uiso†

U11

U22

U33

U12

U13

U23

˚ , Rwp = 0.0318, Rp = 0.0287, S = Rwp/Re = 2.09, RB = 0.0270, RF = (a-1) T = 12 K, Li9.81Sn0.81P2.19S12, space group P42/nmc (137), a = 8.70054 (3), c = 12.68610 (8) A 0.0404 Li1 16h (x, y, z) 0.486 (6) 0.2551 (5) 0.2718 (4) 0.1817 (4) 0.083 (3) 0.102 (8) 0.035 (5) 0.111 (5) 0.012 (3) 0.007 (4) 0.051 (4) Li2 4d (0, 12, z) 0.781 (8) 0 0.5 0.0607 (6) 0.105 (3) 0.071 (6) 0.039 (5) 0.204 (8) 0 0 0 11 Li3 8f (x, x, 0) 0.717 (13) 0.2408 (4) 0.2408 (4) 0 0.180 (6) 0.074 (5) = U (Li3) 0.394 (13) 0.034 (4) 0.115 (4) = U13(Li3) Li4 4c (0, 0, z) 0.744 (9) 0 0 0.2458 (4) 0.052 (3) 0.034 (6) 0.080 (6) 0.043 (5) 0 0 0 Sn1 4d (0, 12, z) 0.405 0 0.5 0.68727 (10) 0.0243 (3) 0.0271 (11) 0.0268 (10) 0.0191 (10) 0 0 0 P1 4d (0, 12, z) = 1 g(Sn1) = x(Sn1) = y(Sn1) = z(Sn1) = Uiso(Sn1) = U11(Sn1) = U22(Sn1) = U33(Sn1) 0 0 0 11 1 P2 2b (0, 0, 2) 1 0 0 0.5 0.0241 (5) 0.0212 (8) = U (P2) 0.0300 (16) 0 0 0 S1 8g (0, y, z) 1 0 0.18890 (18) 0.40917 (16) 0.0265 (6) 0.0486 (14) 0.0186 (15) 0.0121 (13) 0 0 0.0030 (15) S2 8g (0, y, z) 1 0 0.29195 (19) 0.1023 (2) 0.0437 (6) 0.0531 (16) 0.0332 (14) 0.0448 (15) 0 0 0.0083 (13) S3 8g (0, y, z) 1 0 0.7005 (2) 0.78737 (16) 0.0298 (7) 0.0339 (16) 0.0290 (13) 0.0265 (15) 0 0 0.0033 (14) ˚ , Rwp = 0.0276, Rp = 0.0233, S = Rwp/Re = 2.00, RB = 0.0423, RF = (a-2) T = 300 K, Li9.81Sn0.81P2.19S12, space group P42/nmc (137), a = 8.73764 (3), c = 12.71660 (7) A 0.0485. Li1 16h (x, y, z) 0.473 (5) 0.2562 (4) 0.2740 (4) 0.1866 (4) 0.093 (3) 0.093 (6) 0.081 (5) 0.105 (5) 0.005 (3) 0.004 (4) 0.016 (4) Li2 4d (0, 12, z) 0.803 (7) 0 0.5 0.0511 (5) 0.100 (3) 0.109 (6) 0.041 (4) 0.149 (6) 0 0 0 11 Li3 8f (x, x, 0) 0.750 (10) 0.2431 (3) 0.2431 (3) 0 0.223 (6) 0.085 (4) = U (Li3) 0.499 (15) 0.055 (4) 0.121 (4) = U13(Li3) Li4 4c (0, 0, z) 0.709 (7) 0 0 0.2440 (4) 0.072 (3) 0.036 (6) 0.091 (6) 0.090 (5) 0 0 0 Sn1 4d (0, 12, z) 0.405 0 0.5 0.68834 (8) 0.0272 (3) 0.0296 (9) 0.0326 (9) 0.0193 (7) 0 0 0 P1 4d (0, 12, z) = 1g(Sn1) = x(Sn1) = y(Sn1) = z(Sn1) = Uiso(Sn1) = U11(Sn1) = U22(Sn1) = U33(Sn1) 0 0 0 11 1 P2 2b (0, 0, 2) 1 0 0 0.5 0.0295 (4) 0.0268 (7) = U (P2) 0.0349 (14) 0 0 0 S1 8g (0, y, z) 1 0 0.18790 (14) 0.40867 (11) 0.0277 (5) 0.0549 (12) 0.0131 (11) 0.0151 (10) 0 0 0.0020 (10) S2 8g (0, y, z) 1 0 0.29308 (17) 0.10320 (18) 0.0485 (6) 0.0545 (14) 0.0411 (11) 0.0500 (12) 0 0 0.0054 (10) S3 8g (0, y, z) 1 0 0.70019 (18) 0.78795 (12) 0.0320 (5) 0.0389 (13) 0.0319 (10) 0.0251 (12) 0 0 0.0047 (11) ˚ , Rwp = 0.0276, Rp = 0.0329, S = Rwp/Re = 1.96, RB = 0.0330, RF = (a-3) T = 800 K, Li9.81Sn0.81P2.19S12, space group P42/nmc (137), a = 8.81049 (3), c = 12.79398 (7) A 0.0445. Li1 16h (x, y, z) 0.451 (7) 0.2815 (10) 0.2780 (7) 0.1970 (8) 0.182 (7) 0.181 (11) 0.050 (6) 0.32 (2) 0.017 (6) 0.124 (8) 0.027 (7) Li2 4d (0, 12, z) 0.798 (7) 0 0.5 0.0509 (5) 0.120 (4) 0.192 (10) 0.072 (5) 0.097 (6) 0 0 0 11 Li3 8f (x, x, 0) 0.795 (14) 0.2452 (4) 0.2452 (4) 0 0.276 (11) 0.079 (4) = U (Li3) 0.67 (3) 0.000 (5) 0.106 (4) = U13(Li3) Li4 4c (0, 0, z) 0.710 (9) 0 0 0.2406 (4) 0.119 (5) 0.082 (9) 0.230 (13) 0.044 (6) 0 0 0 0 0.5 0.69148 (10) 0.0420 (4) 0.0549 (13) 0.0367 (12) 0.0343 (11) 0 0 0 Sn1 4d (0, 12, z) 0.405 11 22 33 1 P1 4d (0, 2, z) = 1g(Sn1) = x(Sn1) = y(Sn1) = z(Sn1) = Uiso(Sn1) = U (Sn1) = U (Sn1) = U (Sn1) 0 0 0 11 P2 2b (0, 0, 12) 1 0 0 0.5 0.0424 (5) 0.0398 (9) = U (P2) 0.0476 (19) 0 0 0 S1 8g (0, y, z) 1 0 0.18796 (16) 0.40966 (15) 0.0478 (7) 0.0912 (19) 0.0231 (15) 0.0291 (15) 0 0 0.0219 (14) S2 8g (0, y, z) 1 0 0.2925 (2) 0.1040 (2) 0.0757 (8) 0.0781 (19) 0.0530 (14) 0.0961 (17) 0 0 0.0015 (15) S3 8g (0, y, z) 1 0 0.6970 (2) 0.79120 (15) 0.0510 (7) 0.0529 (18) 0.0531 (15) 0.0468 (16) 0 0 0.0325 (16) ˚ , Rwp = 0.0319, Rp = 0.0303, S = Rwp/Re = 2.21, RB = 0.0467, RF = (b-1) T = 17 K, Li10.35Si1.35P1.65S12, space group P42/nmc (137), a = 8.64390 (3), c = 12.50773 (8) A 0.0383. Li1 16h (x, y, z) 0.437 (4) 0.2574 (3) 0.2666 (3) 0.1929 (2) 0.0652 0.0782 0.0318 0.0856 0.0049 0.0094 0.03 Li2 4d (0, 12, z) 0.931 (4) 0 0.5 0.9456 (2) 0.0291 0.0473 0.037 0.00315 0 0 0 Li3 8f (x, x, 0) 0.845 (8) 0.24753 (17) 0.24753 (17) 0 0.170 0.0715 = U11(Li3) 0.366 0.0522 0.0884 = U13(Li3) Li4 4c (0, 0, z) 0.808 (4) 0 0 0.2510 (3) 0.0985 0.0718 0.168 0.0555 0 0 0 Si1 4d (0, 12, z) 0.675 0 0.5 0.68952 (8) 0.0206 0.0401 0.0166 0.005 0 0 0 P1 4d (0, 12, z) = 1 g(Si1) = x(Si1) = y(Si1) = z(Si1) = Uiso(Si1) = U11(Si1) = U22(Si1) = U33(Si1) 0 0 0 P2 2b (0, 0, 12) 1 0 0 0.5 0.0262 0.0282 = U11(P2) 0.0222 0 0 0 S1 8g (0, y, z) 1 0 0.18931 (11) 0.40750 (8) 0.0198 0.0432 0.006 0.0103 0 0 0.0003 S2 8g (0, y, z) 1 0 0.29798 (11) 0.09791 (8) 0.0221 0.0352 0.0128 0.0183 0 0 0.0105 S3 8g (0, y, z) 1 0 0.69485 (13) 0.78945 (8) 0.0186 0.0319 0.0122 0.0117 0 0 0.00149 ˚ , Rwp = 0.0313, Rp = 0.0297, S = Rwp/Re = 2.20, RB = 0.0495, RF = (b-2) T = 300 K, Li10.35Si1.35P1.65S12, space group P42/nmc (137), a = 8.68385 (5), c = 12.55589 (10) A 0.0436. Li1 16h (x, y, z) 0.458 (4) 0.2550 (4) 0.2692 (4) 0.1944 (3) 0.115 0.0755 0.0325 0.236 0.0007 0.0099 0.0598 Li2 4d (0, 12, z) 0.916 (4) 0 0.5 0.9463 (3) 0.0473 0.072 0.0533 0.0166 0 0 0 Li3 8f (x, x, 0) 0.800 (8) 0.2440 (2) 0.2440 (2) 0 0.186 0.094 = U11(Li3) 0.37 0.077 0.0938 = U13(Li3) Li4 4c (0, 0, z) 0.829 (5) 0 0 0.2476 (3) 0.11 0.0625 0.185 0.0825 0 0 0 Si1 4d (0, 12, z) 0.675 0 0.5 0.69004 (9) 0.0262 0.0319 0.0362 0.0104 0 0 0 P1 4d (0, 12, z) = 1g(Si1) = x(Si1) = y(Si1) = z(Si1) = Uiso(Si1) = U11(Si1) = U22(Si1) = U33(Si1) 0 0 0 P2 2b (0, 0, 12) 1 0 0 0.5 0.0376 0.0326 = U11(P2) 0.0476 0 0 0 S1 8g (0, y, z) 1 0 0.18822 (13) 0.40740 (9) 0.0355 0.0708 0.0189 0.0167 0 0 0.0059 S2 8g (0, y, z) 1 0 0.29734 (13) 0.10026 (10) 0.034 0.0459 0.0212 0.0347 0 0 0.0163 S3 8g (0, y, z) 1 0 0.69407 (13) 0.78954 (9) 0.0219 0.0309 0.0065 0.0282 0 0 0.0004 ˚ , Rwp = 0.0253, Rp = 0.0229, S = Rwp/Re = 1.69, RB = 0.0295, RF = (b-3) T = 800 K, Li10.35Si1.35P1.65S12, space group P42/nmc (137), a = 8.76517 (5), c = 12.67003 (12) A 0.0259. Li1 16h (x, y, z) 0.434 (6) 0.2505 (8) 0.2752 (7) 0.1938 (6) 0.153 0.076 0.0653 0.316 0.0081 0.0048 0.122 Li2 4d (0, 12, z) 0.883 (8) 0 0.5 0.9499 (4) 0.0521 0.097 0.0543 0.0052 0 0 0

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energy materials Table 1 (continued)

Li3 Li4 Si1 P1 P2 S1 S2 S3

Site

g

x

y

z

Uiso†

U11

U22

U33

U12

U13

U23

8f (x, x, 0) 4c (0, 0, z) 4d (0, 12, z) 4d (0, 12, z) 2b (0, 0, 12) 8g (0, y, z) 8g (0, y, z) 8g (0, y, z)

0.904 (13) 0.747 (8) 0.675 = 1 g(Si1) 1 1 1 1

0.2408 (3) 0 0 = x(Si1) 0 0 0 0

0.2408 (3) 0 0.5 = y(Si1) 0 0.1873 (2) 0.29969 (18) 0.6901 (2)

0 0.2408 (6) 0.69087 (15) = z(Si1) 0.5 0.41033 (16) 0.10290 (15) 0.78983 (14)

0.257 0.126 0.0276 = Uiso(Si1) 0.0443 0.0504 0.0332 0.0301

0.152 0.0979 0.0387 = U11(Si1) 0.0382 0.0842 0.048 0.0391

= U11(Li3) 0.193 0.0234 = U22(Si1) = U11(P2) 0.0313 0.0172 0.0075

0.467 0.087 0.0206 = U33(Si1) 0.0566 0.0358 0.0344 0.0436

0.115 0 0 0 0 0 0 0

0.0849 0 0 0 0 0 0 0

= U13(Li3) 0 0 0 0 0.0016 0.0171 0.0032

† The form of the anisotropic atomic displacement parameters is exp½22 ðh2 a2 U 11 þ k2 b2 U 22 þ l2 c2 U 33 þ 2hka b U 12 þ 2hla c U 13 þ 2klb c U 23 Þ.

the constraint that the total number of Li atoms was fixed at the nominal compositions used for the synthesis of the material. During the initial stage of the refinement, the occupancy parameter of the Li2 site, which is assumed to be part of the LGPS-type structural framework, was fixed at 1.0 in order to stabilize the refinements. No corrections were made for preferred orientation. Because of the strong correlation between atomic displacement parameters and other parameters, atomic displacement parameters were constrained to the isotropic values at the initial stage of the refinement. After the refinement using isotropic atomic displacement parameters was stabilized, anisotropic atomic displacement parameters were refined individually for each atom until structural reliability (R) factors were not significantly improved. In the final refinement, simultaneous refinements were applied to all structural parameters of the Sn systems, and to the atomic positions and Li occupancies of the Si system. Associated standard uncertainties were obtained from the final refinement. As shown in Fig. 2, the calculated and observed patterns exhibit very good agreement. Table 1 lists the final R factors, lattice and structural parameters and the associated standard uncertainties. The agreement factors, Rwp, are less than 0.035

Figure 3 Variations in the lattice parameters of Li10.35Si1.35P1.65S12, Li9.81Sn0.81P2.19S12 and Li10.05Ge1.05P1.95S12 with temperature (Kwon et al., 2015). Acta Cryst. (2015). B71, 727–736

in all the refinements. The other R factors, including S, RF and RB, are also reasonable, indicating that the refinements were satisfactory with the structural models employed in this study. Lattice parameters at 300 K were determined to be a = ˚ for Li9.81Sn0.81P2.19S12 and a 8.73764 (3) and c = 12.71660 (7) A ˚ for Li10.35Si1.35P1.65S12. = 8.68385 (5) and c = 12.55589 (10) A These values are in good agreement with the reported values ˚ for the Sn system, calculated on of a = 8.7399 and c = 12.715 A the basis of synchrotron XRD data, and a = 8.6695 and c = ˚ for the Si system, obtained by neutron diffraction 12.536 A analysis (Hori et al., 2014). Fig. 3 summarizes the temperature dependence of the lattice parameters. Each phase showed a similar temperature variation, which is consistent with the evidence from diffraction patterns showing a lack of any symmetry changes. Table 2 summarizes the interatomic distances and bond angles. The average P2—S distances in the P2S4 tetrahedra ˚ for both Li9.81Sn0.81P2.19S12 and range from 2.00 to 2.02 A Li10.35Si1.35P1.65S12 at all temperatures, and are close to the sum ˚ ) and S (1.84 A ˚ ) (Shannon & of the ionic radii of P (0.17 A Prewitt, 1969). The average [M1/P1]—S distances at 300 K ˚ for were larger than the P2—S distances: 2.134 and 2.094 A the Sn- and Si-based materials, respectively. The difference in the bond distances corresponds to the difference in the ionic ˚ ) and Si (0.26 A ˚ ), such that the element with radii of Sn (0.59 A the larger ionic radius generates a larger bond distance. With increasing temperature, the average P2—S and [M1/P1]—S distances showed minimal variation within approximately ˚ . Conversely, the average Li—S distances exhibited a 0.02 A ˚ , indicating varialarger change ranging from 0.02 to 0.05 A tions in the lithium positions with increasing temperature. Schematic drawings of the structures of the LGPS-type Siand Sn-based materials are provided in Fig. 4. There are essentially four sets of crystallographically non-equivalent sites for Li atoms, two fourfold sets (Li2 and Li4), one eightfold set (Li3) and one 16-fold set (Li1), making a total of 32 sites for Li atoms per unit cell (Kwon et al., 2015). Among these sites, the Li1 and Li3 sites participate in one-dimensional ionic conduction, together with a two-dimensional pathway through the Li1 and Li4 sites in the ab-plane at high temperature for the Ge system. In contrast, the Li2 sites are considered to be less important in ionic conduction due to their crystallographic coordination environment. That is, the Li2 positions are blocked by (P/M)S4 tetrahedral units in the c Satoshi Hori et al.


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energy materials Table 2 ˚ ) and angles ( ) for Li9.81Sn0.81P2.19S12 and Li10.35Si1.35P1.65S12. Interatomic distances (A Li9.81Sn0.81P2.19S12

Li10.35Si1.35P1.65S12

Polyhedra

Bond

12 K

300 K

800 K

17 K

300 K

800 K

Li1S4 (Tetrahedra)

Li1i—S1vi Li1i—S2i Li1i—S3iv Li1i—S3viii Average Li2i—S1iii 2 Li2i—S2i 2 Li2i—S3i 2 Average Li3i—S1iii 2 Li3i—S2i 2 Average Li4i—S1vii 2 Li4i—S2i 2 Li4i—S3vii 2 Average [M1/P1]i—S2iv 2 [M1/P1]i—S3i 2 Average P2i—S1i 4 Average S1iii—Li2i—S1iv S1iv—Li2i–S2ii 4 S1iv—Li2i—S3ii 4 S2i—Li2i—S2ii S2ii—Li2i—S3i 2 S2i—Li2i—S3i 2 S3i—Li2i—S3ii Average S—Li2—S S1i—Li4i—S1ii S1i—Li4i—S2i 2 S1i—Li4i—S2ii 2 S1i—Li4i—S3vii 4 S2i—Li4i—S2ii S2i—Li4i—S3vii 4 S3vii—Li4i—S3viii Average S—Li4—S S2iii—[M1/P1]i—S2iv S3i—[M1/P1]i—S2iii 4 S3i—[M1/P1]i—S3ii Average S—P1—S S1i—P2i—S1vii 4 S1i—P2i—S1ii 2 Average S—P2—S

2.447 (5) 2.443 (4) 2.442 (4) 2.428 (4) 2.440 2.734 (2) 2.748 (7) 2.600 (6) 2.694 2.606 (4) 2.504 (3) 2.555 2.645 (5) 3.125 (4) 2.640 (2) 2.800 2.107 (2) 2.157 (2) 2.132 2.0073 (17) 2.0073 163.9 (4) 96.05 (8) 84.04 (18) 82.4 (2) 96.66 (19) 179.0 (4) 84.3 (2) 90.0 76.84 (16) 87.21 (11) 164.0 (3) 97.18 (7) 108.74 (18) 84.67 (5) 161.7 (2) 90.62 118.46 (17) 107.52 (11) 107.89 (12) 109.40 109.24 (6) 109.93 (12) 109.47

2.474 (4) 2.482 (4) 2.408 (4) 2.446 (4) 2.453 2.7746 (17) 2.668 (5) 2.692 (5) 2.712 2.599 (3) 2.534 (2) 2.567 2.661 (5) 3.125 (4) 2.6510 (17) 2.812 2.1074 (18) 2.1597 (17) 2.134 2.0111 (12) 2.0111 158.8 (2) 97.79 (9) 81.9 (2) 85.31 (18) 96.82 (14) 177.9 (3) 81.04 (17) 89.9 76.21 (15) 86.86 (10) 163.1 (3) 96.93 (7) 110.06 (18) 84.95 (5) 162.3 (2) 90.63 118.17 (13) 107.54 (10) 108.18 (12) 109.42 109.48 (7) 109.45 (9) 109.47

2.379 (6) 2.754 (11) 2.415 (7) 2.461 (6) 2.502 2.7952 (18) 2.697 (5) 2.663 (5) 2.718 2.593 (4) 2.571 (3) 2.582 2.724 (5) 3.113 (4) 2.7002 (18) 2.846 2.143 (2) 2.1541 (19) 2.149 2.0195 (15) 2.0195 159.2 (2) 97.62 (9) 82.1 (2) 85.37 (19) 96.65 (15) 178.0 (3) 81.34 (18) 89.9 74.86 (17) 86.70 (12) 161.6 (3) 96.86 (7) 111.74 (19) 85.16 (6) 162.7 (2) 90.67 117.07 (17) 108.01 (6) 107.36 (11) 109.41 109.12 (5) 110.17 (11) 109.47

2.474 (3) 2.537 (3) 2.412 (3) 2.352 (3) 2.444 2.7275 (11) 2.584 (2) 2.579 (2) 2.630 2.5297 (17) 2.5035 (11) 2.517 2.551 (3) 3.210 (3) 2.6858 (12) 2.816 2.0886 (12) 2.0973 (12) 2.093 2.0040 (9) 2.0040 159.87 (12) 97.40 (4) 82.39 (10) 85.03 (9) 96.72 (7) 178.26 (14) 81.54 (9) 89.9 79.79 (12) 86.73 (8) 166.52 (18) 98.31 (6) 106.74 (12) 83.54 (13) 158.28 (16) 90.62 113.46 (12) 109.08 (9) 106.84 (11) 109.44 109.47 (6) 109.48 (7) 109.47

2.509 (4) 2.522 (4) 2.393 (3) 2.387 (3) 2.453 2.7512 (13) 2.614 (3) 2.591 (3) 2.652 2.577 (2) 2.508 (13) 2.543 2.588 (4) 3.176 (3) 2.6973 (12) 2.820 2.0900 (14) 2.0978 (13) 2.094 2.0052 (10) 2.0052 159.53 (14) 97.55 (5) 82.24 (13) 84.64 (11) 97.11 (9) 178.25 (17) 81.13 (10) 89.9 78.34 (13) 86.45 (8) 164.8 (2) 97.71 (6) 108.75 (14) 84.21 (16) 160.08 (18) 90.64 114.72 (12) 108.74 (9) 106.90 (11) 109.43 109.63 (7) 109.15 (8) 109.47

2.576 (7) 2.489 (8) 2.375 (6) 2.477 (7) 2.479 2.786 (2) 2.616 (4) 2.624 (5) 2.675 2.617 (4) 2.534 (2) 2.576 2.704 (7) 3.155 (5) 2.744 (2) 2.868 2.080 (2) 2.085 (2) 2.083 1.9965 (17) 1.9965 159.3 (2) 97.66 (8) 82.0 (2) 84.32 (17) 98.43 (14) 177.2 (3) 78.81 (16) 89.9 74.77 (2) 86.23 (14) 161.0 (4) 96.44 (10) 112.8 (3) 85.5 (3) 163.8 (3) 90.6 115.18 (15) 108.80 (12) 106.08 (14) 109.41 108.89 (9) 110.63 (9) 109.47

Li2S6 (Octahedra)

Li3S4 (Tetrahedra) Li4S6 (Octahedra)

[M1/P1]S4 (Tetrahedra) P2S4 (Tetrahedra) Li2S6 (Octahedra)

Li4S6 (Octahedra)

[M1/P1]S4 (Tetrahedra)

P2S4 (Tetrahedra)

Symmetry codes: (i) x; y; z; (ii) x; y; z; (iii) y þ 12 ; x þ 12 ; z þ 12; (iv) y þ 12 ; x þ 12 ; z þ 12; (v) x þ 12 ; y þ 12 ; z þ 12; (vi) x þ 12 ; y þ 12 ; z þ 12; (vii) y; x; z; (viii) y; x; z; (ix) x þ 12 ; y þ 12 ; z þ 12; (x) x þ 12 ; y þ 12 ; z þ 12; (xi) y; x; z; (xii) y; x; z; (xiii) x; y; z; (xiv) x; y; z; (xv) y þ 12 ; x þ 12 ; z þ 12; (xvi) y þ 12 ; x þ 12 ; z þ 12.

axis direction and by PS4 tetrahedral units in the a and b axis directions, suggesting a comparatively larger energy barrier must be overcome before migration is possible. Fig. 5(a) presents the temperature dependencies of the isotropic atomic displacement parameter, Uiso, for the Li1, Li2, Li3 and Li4 sites, together with those at the Li sites of the Ge system (Kwon et al., 2015). The atomic displacement parameters for these lithium sites undergo a considerable increase with increasing temperature compared with those observed for the Sn, Si, P and S sites (see Table 1). The large increase in parameters for the Li1 and Li3 sites indicates lithium migration along these sites at 800 K, which likely makes a significant contribution to the ionic conduction process. The transport of lithium ions via the Li1 and Li3 sites in a cooperative conduction mechanism has been proposed in a previous study

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based on ab initio and molecular dynamics simulations (Xu et al., 2012). In contrast, the value of the parameter for the Li2 site exhibited less variation with increasing temperature and was smaller than those of the Li1 and Li3 sites at 800 K, indicating that the Li2 sites make a lesser contribution to ionic conduction, as was previously proposed based on a consideration of crystallographic coordination in the original study (Kamaya et al., 2011). This reduced contribution of the Li2 site to conduction is also suggested by molecular dynamics analysis of Li10GeP2S12, and it has been reported that Li ions at Li2 sites must overcome a greater energy barrier prior to migration compared with the Li ions at the other three sites (Du et al., 2014). In addition to one-dimensional conduction via Li1 and Li3 sites, two-dimensional conduction over the abplane is also suggested by theoretical calculations (Mo et al., Acta Cryst. (2015). B71, 727–736

energy materials

Figure 4 Schematic drawings of Si- and Sn-based materials with LGSP-type structures. Each structure is composed of Li2(4d)S6, (M/P)S4 tetrahedra and P2(2b)S4 tetrahedra (shown in the left panel) as well as Li1(16h)S4 tetrahedra, Li3(8f)S4 tetrahedra and Li4(4c)S6 octahedra (shown in the right panel). Dotted lines represent the unit cell. The left panel shows that Li2S6 octahedra and (M1/P1)S4 tetrahedra form a onedimensional framework with P2S4 tetrahedra situated between the Li2S6 octahedra by corner sharing to connect the one-dimensional chains, thus forming a three-dimensional framework structure. The right panel shows that Li1S4 and Li3S4 tetrahedra form one-dimensional chains by edge sharing along the caxis. These Li1—Li3 one-dimensional chains are connected by Li4S6 octahedra that share edges with Li1S4 tetrahedral sites. The left panel includes undulating arrows indicating the Li conduction pathways proposed in a previous study (Kwon et al., 2015); either –Li1–Li3–Li1–Li1– pathways along the c-axis or – Li1–Li4–Li1–Li1– pathways over the ab-plane.

Figure 5 Temperature dependence of structural data with regard to Li atoms: (a) isotropic atomic displacement parameters at Li1, Li2, Li3 and Li4 sites, (b) site occupancies at Li1, Li2, Li3 and Li4 sites, and (c) Li—Li interatomic distances. Symmetry codes are provided in Table 2. All the error bars, which indicate standard deviations, are smaller than the symbols used. The data for the Ge system are from a previous study (Kwon et al., 2015). Acta Cryst. (2015). B71, 727–736

Satoshi Hori et al.

2012; Adams & Prasada Rao, 2012). Experimental studies of the Ge system have suggested that Li4 sites, rather than Li2 sites, play a key role in ionic conduction over the ab-plane at high temperatures (Kwon et al., 2015), which is consistent with the lower migration energy determined for the Li4 site compared with the Li2 site (Du et al., 2014). The variation in the Li4 site parameter is found to be different in each system. The Si and Sn systems exhibit smaller values than the Ge system at 800 K, indicating that the ab-plane conduction is less important in the Si and Sn systems, even at high temperatures. Fig. 5(b) presents the temperature dependencies of the occupancy parameters at the Li1, Li2, Li3 and Li4 sites. The occupancy of the Li2 sites in the Li9.81Sn0.81P2.19S12 system is evidently lower than that in Li10.35Si1.35P1.65S12 and Li10.05Ge1.05P1.95S12, likely as a result of the lower quantity of Li ions in the unit cell. The variation of the Li2 occupancy value with temperature is seen to be similar in each system, a result that is consistent with our assumption that Li ions at the Li2 sites form the LGPS-type structural framework rather than playing a key role in ionic conduction. The variations at the other three Li sites are seen to differ between the Sn and Ge systems. As the temperature is increased from 12 to 800 K, the Li3 site occupancy parameter increases from 0.717 (13) to 0.795 (14) for the Sn system. In contrast, the Li4 and Li1 site parameters for the Sn system decrease from 0.744 (9) (12 K) to 0.710 (9) (800 K) and from 0.486 (6) (12 K) to 0.451 (7) (800 K), respectively. A similar trend is observed in the case of the Si system. We believe that the increased occupancy at the Li3 sites together with the decrease at the Li4 sites observed for the Sn system result from the migration of Li ions along a more significant conduction pathway via Li3 sites as opposed to the reduced conductivity pathway


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energy materials via Li4 sites. This conclusion is based on the results of theoretical computations that indicate a reduced activation energy for conduction along the c-axis compared with conduction over the ab-plane (Mo et al., 2012). In contrast, the increased occupancy at the Li3 sites together with the decrease at the Li1 sites observed in the case of the Sn system might result from a shift to a more uniform distribution of Li ions along the c-axis that in turn promotes ionic conduction. Based on these results, we propose that the conduction pathway in the Sn system lies along the c-axis through the Li1 and Li3 sites rather than over the ab-plane through the Li4 sites, while activated ionic conduction over the ab-plane is suggested for the Ge system (Kwon et al., 2015). However, more conclusive information regarding structural changes could be obtained by conducting precise thermal measurements and clarifying the vibrational modes of the various atoms. Fig. 5(c) presents the variations in the interatomic distances with temperature. Although no significant changes are observed for the Si-based material, the variations in the Li1— Li1 and Li1—Li3 distances show similar trends for each system. The changes in these distances with increasing temperature are larger than the variations of the Li2—Li3 distances, indicating that the Li1 and Li3 sites are more closely related to the high ionic conduction at high temperature. In the Ge system, the Li1—Li4 distances decrease continuously with increasing temperature, suggesting more highly activated ionic conduction via the Li1 and Li4 sites at high temperatures (Kwon et al., 2015). Changes in the Li1—Li4 distances for the

Sn and Si systems are different from those in the Ge system; no remarkable changes are observed for the Sn system, while the Si system shows a continuous increase in the Li1—Li4 distances. These variations in the interatomic distances as functions of temperatures are consistent with the temperature dependencies of the atomic displacement parameters and occupancies. Thus, the Li1 and Li3 sites contribute significantly to the conduction pathway while the Li4 sites do not play an important role in the ionic conduction in the Sn system compared with their role in the Ge system. 3.3. MEM analysis

As noted, the observed changes in structural parameters are consistent with one another and with conductivity changes seen while increasing the temperature, although there are also correlations between the occupancy and atomic displacement parameters. The MEM analysis, which is a model-free method, also provides consistent results for structural parameter changes with temperature variations. In addition, MEM analysis in conjunction with the neutron diffraction data for Li9.81Sn0.81P2.19S12 allows visualization of the nuclear scattering density distribution. Fig. 6(a) shows the positive portion ˚ 3) of the scattering amplitude of the equicontour (2 fm A together with the (M1/P1)S4 and P2S4 tetrahedral units resulting from structural refinements. The scattering amplitude distributions correspond solely to the vertices and centers of the tetrahedra, which are occupied by S and P and/or Sn atoms, respectively. The scattering amplitude distributions at the S1 sites take the shape of an anisotropic ellipse rather than an isotropic sphere, a result that is consistent with the anisotropic atomic displacement parameters for the S1 site determined from Rietveld structural analysis. In contrast, the shapes of the equicontour surfaces generated for the S2, P2 and P1/Sn1 sites are rather complicated in comparison with simple spheroids. Fig. 6(b) depicts the three-dimensional equicontour surface of the lithium nuclear distribution (the negative portion of the scattering amplitude) obtained for Li9.81Sn0.81P2.19S12 at 800 K. At the iso-surface level of ˚ 3, the Li ions at the Li1, 0.6 fm A Li2, Li3 and Li4 sites may be identified based on the scattering Figure 6 amplitude distribution map. The Nuclear distributions of Li atoms in the Li9.81Sn0.81P2.19S12 unit cell at 800 K: (a) yellow contours showing ˚ 3) of the scattering amplitude and gray tetrahedra longitudinal shape of the nuclear the positive portion of the equicontour (2 fm A representing (P1/Sn1)S4 and P2S4 units, (b) three-dimensional equicontour surfaces of the lithium distribution at the Li3 sites is 3 3 ˚ ; middle: 0.3 fm A ˚ ; right: nuclear density distribution shown in green (left: 0.6 fm A consistent with the highly aniso3 ˚ 0.15 fm A ), and (c) contour maps for slices along the (110) plane showing the nuclear distributions tropic atomic displacement paraof lithium in Li9.81Sn0.81P2.19S12 at 12 K (left) and 800 K (middle) and Li10.05Ge1.95P1.05S12 at 750 K (Kwon et al., 2015) (right). meters observed for the Li3 sites.

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energy materials ˚ 3, Li1 and Li3 As the surface level increases to 0.3 fm A connect with one another and these connections become more ˚ 3, while the Li ions evident at the surface level of 0.15 fm A at the Li2 and Li4 sites remain isolated. This connected Li distribution via the Li1 and Li3 sites in conjunction with isolated Li2 and Li4 sites is also predicted by theoretical computations (Wang et al., 2015). The connected distribution of Li ions at the Li1 and Li3 sites indicates a comparatively uniform distribution of Li ions along the channel parallel to the c-axis, which is also in agreement with previous studies suggesting that one-dimensional chains of Li ions along the caxis form the backbone of the lithium conduction pathway. Fig. 6(c) displays slices of the equicontour map on the (110) plane for Li9.81Sn0.81P2.19S12 at 12 and 800 K along with data previously reported for Li10.05Ge1.05P1.95S12 at 750 K (Kwon et al., 2015). In the case of the Sn-based material, the nuclear density distribution spreads out over the Li1 and Li3 sites along the c-axis and this effect becomes more evident and more uniform with increasing temperature. Conversely, the Li2 and Li4 sites are isolated from one another, suggesting that the Li1 and Li3 sites are more relevant to the increase in ionic conductivity seen at higher temperatures compared with the Li2 and Li4 sites. In the case of the Ge system, continuous lithium distribution between the Li1 and Li4 sites is also observed at 750 K, in addition to the one-dimensional connection between Li1, Li1 and Li3 sites. This behavior is not observed for the Sn system at 800 K, which is consistent with the conduction mechanism suggested by the lithium distribution and the variations in the Uiso values at these sites. The difference in the dimensionality of the conduction mechanism between the Ge and Sn systems may account for the variation in conductivity between these two phases, as has been confirmed by both theoretical calculations and experimental work (Ong et al., 2013; Hori et al., 2014). Although diffraction studies in conjunction with a MEM analysis yield information regarding time and spatially averaged disorder and conduction pathways of the Li ions, it is still necessary to examine the dynamics of ionic motions to further clarify the quantitative details of the ionic conduction process. Nevertheless, MEM analysis in conjunction with neutron diffraction data still provides useful qualitative insights and suggests that the most significant conduction pathway in LGPS-type materials is along tetrahedrally coordinated Li1 and Li3 sites, an effect that has been previously proposed as the origin of superionic conductivity based on theoretical computations (Wang et al., 2015).

4. Conclusions The results of structural refinements of the Si and Sn systems with LGPS-type structures over the temperature range 12– 800 K may be summarized as follows. First, no phase changes accompanied by symmetry changes were observed over the entire temperature range examined. With increasing temperature, the occupancy at the Li3 site increases while that at the Li1 site decreases. In addition, the value of the isotropic atomic displacement parameter, Uiso, at the Li1 and Li3 sites Acta Cryst. (2015). B71, 727–736

shows a continuous increase as the temperature is raised from 12 to 800 K, and this increase is greater than those observed at the Li4 and Li2 sites. Finally, the Li1—Li1 and Li1—Li3 interatomic distances change to a greater degree than the Li2—Li3 and Li1—Li4 distances. The observed variations in occupancy and isotopic displacement parameters indicate that one-dimensional conduction is more important than twodimensional conduction through the Li4 sites. This conduction mechanism is also supported by MEM analysis of the Sn system.

Acknowledgements This study was supported by the Post-LiEAD project of the New Energy and Industry Technology Development Organization (NEDO), Japan. The computer program used for MEM analysis was developed through the NEDO RISING project. The neutron radiation experiments were carried out as projects approved by the Japan Proton Research Complex (JParc) (proposal Nos. 2014AM1004 and 2014PM0001).

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