Three-dimensional structures and lithium-ion conduction pathways of (Li2S)x(GeS2)100 − x superionic glasses

Solid State Ionics 280 (2015) 44–50

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Three-dimensional structures and lithium-ion conduction pathways of (Li2S)x(GeS2)100 − x superionic glasses Kazuhiro Mori a,⁎, Kozo Furuta a, Yohei Onodera a, Kenji Iwase b, Toshiharu Fukunaga a a b

Research Reactor Institute, Kyoto University, 2-1010 Asashiro-Nishi, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan Department of Materials Science and Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan

a r t i c l e

i n f o

Article history: Received 8 April 2015 Received in revised form 10 August 2015 Accepted 14 August 2015 Available online 2 September 2015 JEL classification: A6100 structure of liquids and solids A6610E ionic conduction Keywords: Lithium-ion conducting glass Local structure Neutron diffraction X-ray diffraction Reverse Monte Carlo modeling Bond valence sum

a b s t r a c t The conduction pathways of Li ions in (7Li2S)x(GeS2)100 − x glasses (x = 40, 50, and 60) were predicted and visualized by combining reverse Monte Carlo (RMC) modeling and the bond valence sum (BVS) approach, using synchrotron X-ray and time-of-flight neutron diffraction data. The conduction pathways of the Li ions could be classified into four grades, according to the magnitude of |ΔV(Li)|: (I) |ΔV(Li)| b 0.04 (i.e., relatively stable regions for the Li ions), (II) 0.04 ≤ |ΔV(Li)| b 0.07, (III) 0.07 ≤ |ΔV(Li)| b 0.10, and (IV) 0.10 ≤ |ΔV(Li)| b 0.13; here, |ΔV(Li)| is the mismatch of the BVS for Li ions, V(Li). These were used to obtain a clear understanding of the movement of the Li ions in the (7Li2S)x(GeS2)100 − x glasses. It was also found that there is a definite relationship between the topology of the conduction pathways of the Li ions and the activation energy, Ea, of the electrical conduction. © 2015 Elsevier B.V. All rights reserved.

1. Introduction All-solid-state lithium-ion batteries (LIBs) are needed for large-scale applications, such as next-generation electric vehicles and energy storage systems, because they show higher power capacities, energy densities, lifespan, and reliabilities than organic liquid electrolytes [1,2]. Sulfide-based lithium glasses have attracted much attention as solid electrolytes in such all-solid-state LIBs because of their high ionic conductivities [3–9]. Although the sulfide-based lithium glasses are normally extremely hygroscopic, Li2S–GeS2 glasses are not as highly hygroscopic [10]. Therefore, the use of Li2S–GeS2 glasses as solid electrolytes reduces the technological difficulties related to their handling and packing in all-solid-state LIBs. The electrochemical properties of (Li2S)x(GeS2)100− x glasses have been extensively studied over the past few decades [11–13]. These glasses can be synthesized by rapid quenching (RQ) from the melt; the electrical conductivity (corresponding to the ionic conductivity), σ, increases significantly with increasing Li content. For example, the σ value of the (Li2S)60(GeS2)40 glass is ≈10−4 S/cm at room temperature (RT). The (Li2S)x(GeS2)100− x glasses can also be prepared by mechanical alloying (MA) with a high-energy ball-mill. The σ values of ⁎ Corresponding author. Tel.: +81 72 451 2363; fax: +81 72 451 2635. E-mail address: [email protected] (K. Mori).

http://dx.doi.org/10.1016/j.ssi.2015.08.010 0167-2738/© 2015 Elsevier B.V. All rights reserved.

the (Li2S)x(GeS2)100 − x glasses obtained by MA were comparable to those produced using RQ. In order to understand the conduction mechanism of Li ions in the (Li2S)x(GeS2)100− x glasses, detailed information on their atomic configurations is required. Structural studies of (Li2S)x(GeS2)100 − x glasses have been carried out using synchrotron X-ray diffraction (SXRD) and time-of-flight neutron diffraction (TOF-ND), and, from this, the three-dimensional structure of the (Li2 S) 50 (GeS 2) 50 glass has been visualized using reverse Monte Carlo (RMC) modeling [14–16]. However, the conduction pathways of Li ions in these (Li2S)x(GeS2)100− x glasses are still unknown owing to their amorphous structures; in addition, the relationship between the electrochemical and the structural properties is still unclear. The maximum entropy method (MEM) provides a well known, and powerful, tool for the visualization of the conduction pathways of fast ions in crystalline solids [17,18]. In this visualization methodology, however, high temperatures are essential for transforming the atomic motion from vibrations to diffusion. This approach no longer applies to glassy fast-ion conductors. The bond valence sum (BVS) approach is becoming more viable as an alternative tool for predicting and visualizing the conduction pathways of fast ions in both crystalline and amorphous superionic conductors at RT [19–22]. For example, the visualization of conduction pathways of Li ions in (Li2S)x(P2S5)100− x superionic glasses has been reported using both RMC modeling and the BVS approach [23].

K. Mori et al. / Solid State Ionics 280 (2015) 44–50

In this study, (Li2S)x(GeS2)100 − x superionic glasses with different Li content were synthesized by MA, and electrical conductivity, SXRD, and TOF-ND measurements were carried out. We have succeeded in predicting and visualizing the conduction pathways of Li ions in these (Li2S)x(GeS2)100− x glasses by combining RMC modeling and the BVS approach, using SXRD and TOF-ND data. We discuss the relationship between the topology of the conduction pathways of Li ions and the activation energy for electrical conduction in the (Li2S)x(GeS2)100− x glasses.

and S N (Q). According to the Faber–Ziman definition, S X(Q) and S N(Q) can be described by the partial structure factors, S X i − j (Q) and SNi − j(Q), SX ðQ Þ ¼

wXi− j SXi− j ;

ð1aÞ

SN ðQ Þ ¼

X

N wN i− j Si− j ;

ð1bÞ

i; j

where wXi − j and wNi − j are the weighting factors, defined by wXi− j ¼

ci c j f i f j 2

hf i

;

ð2aÞ

(a) S N(Q)

4

TOF-ND

2 0 -2

S X(Q)

-4

SXRD

0 0

5

20

S N(Q)

4 TOF-ND

2 0 -2 -4

SXRD

0 0

5

2.2. SXRD and TOF-ND experiments

10 15 –1 Q/Å

20

S N(Q)

(c) TOF-ND

5 0 -5

S X(Q)

The SXRD experiments were performed using a horizontal two-axis diffractometer on the BL04B2 beam line of the SPring-8 synchrotron radiation facility [24]. The energy of the incident X-ray beam was 61.4 keV. The (7Li2S)x(GeS2)100− x glasses were encapsulated in a quartz capillary (2 mm in diameter) under a high-purity Ar gas atmosphere. The SXRD data were collected at RT in the Q range of 0.2–23 Å–1, where Q is the magnitude of the scattering vector (=4πsinθ/λ, where θ is half of the scattering angle, 2θ, and λ is the X-ray (or neutron) wavelength). The TOF-ND experiments were performed using the total scattering spectrometer NOVA at the BL21 beam line of the Materials and Life Science Experimental Facility (MLF), Japan Proton Accelerator Research Complex (J-PARC) [25]. The samples were placed in a cylindrical, 6-mm-diameter vanadium-nickel-alloy holder. The TOF-ND data were collected at RT in the Q range of 0.5–23 Å−1 using the 20°, 45°, and 90° detector banks. Appropriate corrections, related to polarization, multiple scattering, absorption, and incoherent scattering, were applied to the SXRD and TOF-ND data to obtain the X-ray and neutron structure factors, SX(Q)

10 15 –1 Q/Å

(b)

S X(Q)

7 Li-enriched (7Li2S)x(GeS2)100− x glasses (x = 40, 50, and 60) were synthesized by MA of 7Li2S (99.9% purity, Kojundo Chemical Lab.) and GeS2 (99.99% purity, Kojundo Chemical Lab.) in the appropriate molar proportions. The use of the lithium isotope, 7Li, allowed the precise determination of the positions of Li ions in the neutron diffraction analysis, because the absorption cross section, σa, of the 7Li nuclei (0.045 b) is considerably smaller than that of the naturally occurring Li nuclei (70.5 b). The 7Li2S and GeS2 constituents were well mixed, and then put into a zirconia pot (80 cm3) with 500 zirconia balls (4 mm in diameter) under a high-purity Ar gas atmosphere. The mixtures were alloyed mechanically using a planetary ball-mill apparatus (P-5, Fritsch), with the conditions: 370 rpm for 60 h for the (7Li2S)40(GeS2)60 glass, 370 rpm for 100 h for the (7Li2S)50(GeS2)50 glass, and 370 rpm for 120 h for the (7Li2S)60(GeS2)40 glass. The (7Li2S)x(GeS2)100− x glasses were characterized using XRD with Cu Kα radiation (SmartLab, Rigaku): it was confirmed that amorphous halos are clearly observed for all the samples. Solid density measurements were performed using a dry pycnometer (AccuPyc1330, Shimadzu Co.) to obtain the number density of atoms, ρ0, for the (7Li2S)x(GeS2)100− x glasses. The estimated ρ0 values were: 0.047 atoms/Å3 for the (7Li2S)40(GeS2)60 glass, 0.050 atoms/Å3 for the (7Li2S)50(GeS2)50 glass, and 0.053 atoms/Å3 for the (7Li2S)60(GeS2)40 glass, respectively. Four-probe ac impedance measurements were performed using frequency response analyzers (6440B, Wayne Kerr Electronics Ltd., and AutoLab, Eco Chemie). Ag paste was smeared to form electrodes on the disk-shaped sintered samples (≈ 13 mm in diameter and ≈ 1.5 mm in thickness), and the samples were loaded into a cell for measurement of electrochemical properties under controlled atmospheres at high temperatures. The σ values of the (7Li2S)x(GeS2)100 − x glasses were measured at temperatures between 300 K and 375 K in the frequency range of 2 mHz to 3 MHz.

X i; j

2. Materials and methods 2.1. Synthesis and characterization of samples

45

SXRD 0 0

5

10 15 –1 Q/Å

20

Fig. 1. Experimental X-ray and neutron structure factors, SX(Q) and SN(Q), of (a) (7Li2S)40(GeS 2)60 glass, (b) (7Li2S)50(GeS2)50 glass, and (c) (7Li2S)60(GeS2)40 glass represented by plus marks (red). The solid lines (blue) indicate the calculated SX(Q) and SN(Q) obtained from RMC modeling

46

K. Mori et al. / Solid State Ionics 280 (2015) 44–50

10

-4

(7Li2S)x(GeS2)100 − x glass. The b values for 7Li, Ge, and S nuclei are − 2.22, 8.185, and 2.847 fm, respectively. Note that the wNi − j values for the 7Li–Ge and 7Li–S correlations are negative contributions to SN(Q) because of the negative b value for the 7Li nucleus.

/ S/cm

6 4 2

300K

10

2.3. RMC modeling and the BVS approach

-5

RMC modeling was performed using the computer program RMC++ [26,27]. We used cubic RMC cells with the following properties: the RMC cell had a 46.77-Å-long edge and 4800 atoms (7Li: 1280, Ge: 960, NBS: 1280, BS: 1280) for the (7Li2S)40(GeS2)60 glass; the RMC cell had a 45.82-Å-long edge and 4800 atoms (7Li: 1600, Ge: 800, NBS: 1600, BS: 800) for the (7Li2S)50(GeS2)50 glass; and the RMC cell had a 45.05-Å-long edge and 4800 atoms (7Li: 1920, Ge: 640, NBS: 1920, BS: 320) for the (7Li2S)60(GeS2)40 glass. It is worth noting that the S atoms can be classified into two types: bridging sulfurs (BS) and non-bridging sulfurs (NBS), respectively. The atomic compositions (7Li:Ge:S) for the RMC cells were consistent with the molar ratios of the respective glasses, and the ρ0 values were the same as those obtained from solid density measurements. All atoms were randomly located on the RMC cell as initial atomic configurations. In the RMC modeling, three constraint conditions were employed: (i) the coordination number of S atoms around a Ge atom, NGe–S, was four (i.e., GeS4 tetrahedral units were assumed to be formed), (ii) the coordination number of Ge atoms around an NBS atom, NNBS–Ge, was one, and (iii) the coordination number of Ge atoms around a BS atom, NBS–Ge, was two. The threedimensional structures of the (7Li2S)x(GeS2)100− x glasses were visualized using the computer program VESTA [28]. The BVS approach, using the “softness-sensitive” BV (softBV) parameters, was employed to predict the conduction pathways of the Li ions in the RMC cells. The valence of a bond between a cation M and its coordinating anion N is given by

6 4 2

10

-6

40

50 x / mol%

60

Fig. 2. Electrical conductivities of (7Li2S)40(GeS2)60 glass, (7Li2S)50(GeS2)50 glass, and (7Li2S)60(GeS2)40 glass at 300 K. The dashed line is drawn for visual comparison.

wN i− j ¼

ci c j bi b j 2

hbi

;

ð2bÞ

and hf i ¼

X

ci f i ;

ð3aÞ

ci bi ;

ð3bÞ

i

hbi ¼

X i

where ci (cj) is the concentration of species i (j). In Eqs. (2a) and (3a), fi (fj) indicates the atomic scattering factor at Q = 0 for i (j), and b fN indicates the average f of the (7Li2S)x(GeS2)100 − x glass. The f values for 7Li, Ge, and S atoms are 3, 32, and 16 electrons, respectively. In Eqs. (2b) and (3b), bi (bj) indicates the coherent scattering length for i (j), and bbN indicates the average scattering length of the

sM−N ¼ expfðR0 −RM−N Þ=Bg;

where RM–N is the bond length between M and N, and R0 = 1.46652 Å and B = 0.653 Å are empirical parameters, describing the bonds

100

(a)

20

ð4Þ

(b)

50 x = 60

x = 60 0

0 RDF N(r)

RDF X(r)

20

x = 50 0

50 x = 50 0

20 50 x = 40

x = 40

0

0 0

1

2

3 r/Å

4

5

6

0

1

2

3 r/Å

4

5

6

Fig. 3. Radial distribution functions, (a) RDFX(r) and (b) RDFN(r), of (7Li2S)40(GeS2)60 glass (x = 40), (7Li2S)50(GeS2)50 glass (x = 50), and (7Li2S)60(GeS2)40 glass (x = 60) obtained by the Fourier transformation of SX(Q) and SN(Q), respectively. The first positive peaks (*) in RDFX(r) and RDFN(r) correspond to the Ge–S correlation and the second negative peaks (#) in RDFN(r) correspond to the 7Li–S correlation.

K. Mori et al. / Solid State Ionics 280 (2015) 44–50

between Li+ and S2− [29–32]. The BVS value, V(M), for all bonds between M and N, within a cut-off radius, Rcut-off (≤6.0 Å), was estimated as V ðMÞ ¼

X

sM−N :

ð5Þ

N

3. Results and discussion Fig. 1 shows the structure factors, SX(Q) and SN(Q), of the ( Li2S)x(GeS2)100 − x glasses (x = 40, 50, and 60), obtained from the SXRD and TOF-ND experiments. The electrical conductivities at 300 K, σ300K, of the (7Li2S)x(GeS2)100 − x glasses were measured; σ300K increased dramatically with increasing x, with linear behavior as it approached the order of 10−4 S/cm (see Fig. 2). The radial distribution function (RDF) analysis was performed using the SX(Q) and SN(Q) data. The atomic pair distribution functions, gX(r) and gN(r), and RDFX(r) and RDFN(r) were obtained by the Fourier transformation of SX(Q) and SN(Q), that is, 7

g X ðr Þ ¼ 1 þ

g N ðr Þ ¼ 1 þ

1 2π 2 rρ0 1 2π 2 rρ0

Z

Q max Q min

Z

Q max Q min

n o Q SX ðQ Þ−1 sinðQ r ÞdQ ;

ð6aÞ

n o Q SN ðQ Þ−1 sinðQr ÞdQ ;

ð6bÞ

47

difficult to separate from each other and evaluate precisely the coordination numbers of S atoms around a 7Li ion, NLi–S. The average NLi–S values, bNLi–SN, were obtained from the 7LiSn polyhedral analysis in RMC modeling, as mentioned below. RMC modeling was performed using both the S X(Q) and the SN(Q) data. As shown in Fig. 1, excellent fits were obtained between the observed and the calculated SX(Q) and SN(Q) values for all the samples. The three-dimensional structures of the (7Li2S)40(GeS2)60, (7 Li2 S) 50(GeS2 ) 50, and ( 7Li 2S)60 (GeS2 )40 glasses are illustrated in Fig. 4(a), (b), and (c); they all exhibit three-dimensional networks of corner-sharing GeS4 tetrahedral units (henceforth termed “GeS4 tetrahedral network”), together with 7 Li ions. Fig. 4(d), (e), and (f) show the distributions of 7 LiS n units within r = 3.2 Å. There were obvious indications of several types of 7LiSn units in the (7 Li2 S) x (GeS2 )100 − x glasses. The NLi–S value was assessed within r = 3.2 Å for each sample. Fig. 5 shows the distribution of NLi–S varying between 1 and 6, and the b NLi–SN values are listed in Table 1. For the ( 7Li 2S)40 (GeS2 )60 glass, the 7LiS4 units (N Li–S = 4) had the

and RDF X ðr Þ ¼ 4πr 2 ρ0 g X ðr Þ;

ð7aÞ

RDF N ðr Þ ¼ 4πr2 ρ0 g N ðr Þ;

ð7bÞ

where r is the interatomic distance. Fig. 3 shows the RDFX(r)s and RDFN(r)s of the (7Li2S)x(GeS2)100 − x glasses. The first positive peak at approximately 2.2 Å, marked with an asterisk (*), corresponds to the Ge–S correlation. The NGe–S was calculated using the following equation: 2

NGe−S ¼

1 W Ge−S h f i ; 2 cGe f Ge f S

ð8Þ

where cGe is the concentration of Ge, and WGe–S is the area of the first peak for the Ge–S correlation. From this, the NGe–S was estimated to be 4 (i.e., forming GeS 4 tetrahedral units), independent of x. The distances for the Ge–S correlation, l Ge–S , and the NGe–S values are listed in Table 1. This justifies using the constraint condition of (i) in the RMC modeling. In Fig. 3(b), the second negative peak at around 2.5 Å was assigned to the 7Li–S correlation; which results from the negative b of 7Li (–2.22 fm). The average distances for the 7 Li–S correlation, lLi–S, which were obtained from a least-squares fit using a Gaussian curve, are listed in Table 1. The negative peaks of the 7Li–S correlation were somewhat broad, so that they were very

Table 1 Distances and coordination numbers for the Ge–S first neighbor correlation (lGe–S and NGe–S) and the 7Li–S correlation (lLi–S and b NLi–SN) for (7Li2S)x(GeS2)100− x glasses (x = 40, 50, and 60). The lGe–S, NGe–S, and lLi–S values were obtained from the RDF analysis. The average NLi–S values, bNLi–SN, within r = 3.2 Å were obtained from the 7LiSn polyhedral analysis in RMC modeling.

x = 40 x = 50 x = 60

lGe–S (Å)

NGe–S

lLi–S (Å)

bNLi–SN

2.21 2.20 2.20

4.0 4.0 4.0

2.56 2.53 2.52

3.8 3.9 4.1

Fig. 4. Three-dimensional structures of (a) (7Li2S)40(GeS2)60 glass, (b) (7Li2S)50(GeS2)50 glass, and (c) (7Li2S)60(GeS2)40 glass obtained from the RMC modeling, which are illustrated using GeS4 tetrahedral units and 7Li ions. In (d), (e) and (f), the three-dimensional structures of (7Li2S)40(GeS2)60 glass, (7Li2S)50(GeS2)50 glass, and (7Li2S)60(GeS2)40 glass are illustrated using 7LiSn units (assessed within r = 3.2 Å).

48

K. Mori et al. / Solid State Ionics 280 (2015) 44–50

highest coordination among the 7LiSn units (41%), followed by the 7 LiS3 (NLi–S = 3) and 7LiS5 ones (NLi–S = 5). The 7LiS4 units occupied 43% of all 7 LiSn for the (7 Li2S) 50 (GeS2 ) 50 glass and 48% for the (7Li2S)60(GeS2)40 glass, respectively. This indicates that the Li ions prefer to form an atomic configuration surrounded by four S atoms. In addition, we note that while a 7LiSn unit is composed of both the NBS and BS atoms at lower x, the proportion of the NBS atoms in the 7LiSn unit gradually increases with increasing x. It has been reported that α-GeS2 crystals have a GeS4 tetrahedral network based on a monoclinic system (space group: Pc) [33]. Therefore, based on the existence of NBS atoms, the GeS4 tetrahedral network was partially broken by mixing with 7 Li2S during MA. The Li ions may, thus, probably be located in the space bound by the NBS atoms.

(a) 50

Ratio / %

40 30 20 10 0 1

2

3 4 NLi-S

5

6

1

2

3 4 NLi-S

5

6

1

2

3 4 NLi-S

5

6

(b) 50

The conduction pathways of Li ions in the (7Li2S)x(GeS2)100 − x glasses were visualized using the BVS approach. It is well known that there is a significant relationship between the conduction pathways of the Li ions and the areas of low BV mismatch, |ΔV(M)|, which is given by ΔV ðMÞ ¼ jBVSðM Þ−V id ðM Þj þ pðM Þ;

ð9Þ

where Vid(M) is the ideal ionic state of ion M (e.g., Vid(Li) = 1) and p(M) is the penalty function to avoid unphysical configurations. In general, sites with |ΔV(M)| b 0.04 are regarded as relatively “stable” sites for the M ions. To explore the Li stable sites in the (7Li2S)x(GeS2)100 − x glasses, the RMC cells were divided into 250 × 250 × 250 pixels (henceforth “volume elements”), with 0.18-Å-long edges, and then |ΔV(Li)| was calculated for each volume element, using Eq. (9). As a matter of course, the volume elements around Ge and S atoms were excluded from the |ΔV(Li)| calculations, as p(Li) = 0. From this, we obtained three-dimensional maps of the Li stable sites in the (7Li2S)x(GeS2)100 − x glasses. The volume occupied by these Li stable sites gradually increased with increasing x. However, the conduction pathways of the Li ions were still unclear, because the Li stable sites did not percolate between the two edges of an individual RMC cell. When the |ΔV(Li)| was increased, the Li stable sites spread further and connected with each other. Consequently, we succeeded in visualizing the connected pathways of the volume elements at the maximum value of |ΔV(Li)| (henceforth “|ΔV(Li)|max”), as illustrated in Fig. 6. The connected pathways of the volume elements were percolated to a sufficient degree between the two sides of the RMC cell, so that they could be regarded as the predicted conduction pathways of the Li ions in the (7Li2S)x(GeS2)100 − x glasses at RT. Furthermore, in order to understand definitely how the movement of the Li ions depends on the Li concentration in the conduction pathways, these pathways of the Li ions could be classified into four grades, according to the magnitude of |ΔV(Li)|: (I) |ΔV(Li)| b 0.04 (i.e., corresponding to the Li stable sites), (II) 0.04 ≤ |ΔV(Li)| b 0.07, (III) 0.07 ≤ |ΔV(Li)| b 0.10, and (IV) 0.10 ≤ |ΔV(Li)| b 0.13 (see

Ratio / %

40 30 20 10 0

(c) 50

Ratio / %

40 30 20 10 0

Fig. 5. Distributions of the coordination number of S atoms around a 7Li ion, NLi–S, for (a) (7Li2S)40(GeS2)60 glass, (b) (7Li2S)50(GeS2)50 glass, and (c) (7Li2S)60(GeS2)40 glass. They are assessed within r = 3.2 Å. The bars represent the ratio of non-bridging sulfurs, NBS (red), to the bridging sulfurs, BS (black), in 7LiSn units (n = 1, 2, 3, 4, 5, and 6)

Fig. 6. Conduction pathways of the Li ions in (a) (7Li2S)40(GeS2)60 glass, (b) (7Li2S)50(GeS2)50 glass, and (c) (7Li2S)60(GeS2)40 glass visualized using the BVS approach. The connected pathways (orange) obtained from the BV mismatch calculations using Eq. (9) correspond to the predicted conduction pathways of the Li ions in the solids at RT

K. Mori et al. / Solid State Ionics 280 (2015) 44–50

  Ea 1 ; kB T

ð10Þ

where σ0 is the pre-exponential factor, Ea is the activation energy, kB is the Boltzmann constant, and T is the temperature. The Ea values were estimated from the Arrhenius plot of σ obtained at various T for the (7Li2S)x(GeS2)100 − x glasses. As shown in Fig. 8(a), the Ea value decreased monotonically from 48 kJ/mol to 38 kJ/mol with increasing x. Since Ea corresponds to the potential barrier for the movement of the Li ions along the conduction pathways, this should be strongly associated with |ΔV(Li)|max. In fact, |ΔV(Li)|max decreased with increasing x (see Fig. 8(b)). Such a strong similarity between the behavior of |ΔV(Li)|max and Ea has also been found in (Li2S)x(P2S5)100 − x glasses [23]. Schematic diagrams representing the relationship between the |ΔV(Li)|max and the Ea for the movement of the Li ions along the conduction pathways are given in Fig. 9. At low x, the conduction pathways of the Li ions are mainly given by the regions with higher |ΔV(Li)| or Ea. At higher x, however, |ΔV(Li)|max or Ea decreases, and a number of Li stable regions, with |ΔV(Li)| b 0.04, appear in the conduction pathways of the Li ions. Thus, the high σ300K and low Ea for the (Li2S)60(GeSs)40 glass can be understood by considering the low |ΔV(Li)|max for the conduction pathways of the Li ions. Further investigations are now in progress to determine quantitatively the relationship between the |ΔV(Li)|max and Ea values.

Fig. 7. Conduction pathways of the Li ions (enlarged for clarity). (a) (7Li2S)40(GeS2)60 glass, (b) (7Li2S)50(GeS2)50 glass, and (c) (7Li2S)60(GeS2)40 glass. The conduction pathways of the Li ions are classified into four grades, according to the magnitude of the BV mismatch for Li ions, |ΔV(Li)|: (I) |ΔV(Li)| b 0.04 (blue), (II) 0.04 ≤ |ΔV(Li)| b 0.07 (green), (III) 0.07 ≤ |ΔV(Li)| b 0.10 (orange), and (IV) 0.10 ≤ |ΔV(Li)| b 0.13 (red)

50

Ea / kJ/mol

lnðσT Þ ¼ lnσ 0 −

(a)

45

40

35 40

50 x / mol%

40

50 x / mol%

60

(b) 0.14 0.13

| ΔV (Li)|max

Fig. 7). Obviously, the |ΔV(Li)| for the conduction pathways of the Li ions decreased relatively with increasing x, which corresponds to a lowering of the potential barrier for the movement of the Li ions. The steady increase in σ with increasing T could be described by the Boltzmann distribution, that is,

49

0.12 0.11 0.10 0.09 60

Fig. 8. Comparison of the activation energy, Ea, and the maximum values of the BV mismatch for Li ions, |ΔV(Li)|max: (a) Ea as a function of the Li2S content x for (7Li2S)x(GeS2)100 − x glasses (open circles); (b) |ΔV(Li)|max as a function of x for (7Li2S)x(GeS2)100 − x glasses (open squares). Dashed lines are visual guides. The behavior of the Ea is quite similar to that of the |ΔV(Li)|max.

Fig. 9. Schematic illustrations of the relationship between the topology of the conduction pathways of Li ions and the potential energy profile: (a) ( 7Li2 S)x (GeS2 )100 − x glass with lower x and (b) that with higher x, respectively. The blue areas correspond to the Li+ “stable” regions. For each figure, the pink arrow denotes the migration directions of Li+ in the energy potential profile

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4. Conclusions We have performed SXRD and TOF-ND analyses using 7Li-enriched (7Li2S)x(GeS2)100 − x glasses (x = 40, 50, and 60), synthesized by MA, and succeeded in clearly visualizing the predicted conduction pathways of the Li ions at RT by combining RMC modeling and the BVS approach. The conduction pathways of Li ions could be classified into four grades, according to the magnitude of |ΔV(Li)|: (I) |ΔV(Li)| b 0.04 (i.e., corresponding to the Li stable sites), (II) 0.04 ≤ |ΔV(Li)| b 0.07, (III) 0.07 ≤ |ΔV(Li)| b 0.10, and (IV) 0.10 ≤ |ΔV(Li)| b 0.13. The |ΔV(Li)|max value gradually decreased with increasing x; simultaneously, Ea monotonically decreased from 48 kJ/mol to 38 kJ/mol. Thus, a great similarity was found between the behavior of |ΔV(Li)|max and Ea in the (7Li2S)x(GeS2)100 − x glasses. Acknowledgments We wish to acknowledge Prof. Toshiya Otomo of KEK for his help with the TOF-ND experiments, which were approved by the Neutron Scattering Program Advisory Committee of IMSS, KEK (Proposal No. 2014A0212). We thank Dr. Shinji Kohara of JASRI for his help with the SXRD experiments, which were performed at BL04B2 in SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2013B1411). This work was predominantly supported by a Grantin-Aid for Science Research (C), No. 15K06483, from Japan Society for the Promotion of Science (JSPS). This work was partially supported by the “Research and Development Initiative for Scientific Innovation of New General Battery (RISING project),” No. P09012, from the New Energy and Industrial Technology Development Organization (NEDO), Japan. References [1] J.-M. Tarascon, M. Armand, Nature 414 (2001) 359–367. [2] M. Armand, J.-M. Tarascon, Nature 451 (2008) 652–657. [3] R. Mercier, J.-P. Malugani, B. Fahys, G. Robert, Solid State Ionics 5 (1981) 663–666.

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