Visualization of conduction pathways in lithium superionic conductors: Li2S-P2S5 glasses and Li7P3S11 glass–ceramic

Chemical Physics Letters 584 (2013) 113–118

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Visualization of conduction pathways in lithium superionic conductors: Li2S-P2S5 glasses and Li7P3S11 glass–ceramic Kazuhiro Mori a,⇑, Tomoharu Ichida a, Kenji Iwase b, Toshiya Otomo c, Shinji Kohara d Hajime Arai e, Yoshiharu Uchimoto f, Zempachi Ogumi e, Yohei Onodera a, Toshiharu Fukunaga a a

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 Institute of Materials Structure Science, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan d Synchrotron Radiation Research Institute/SPring-8, 1-1-1 Kouto, Sayo-gun, Hyogo 679-5198, Japan e Office of Society-Academia Collaboration for Innovation, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan f Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-Nihonmatsu-cho, Sakyo-ku, Kyoto 606-8501, Japan b c

a r t i c l e

i n f o

Article history: Received 7 July 2013 In final form 6 August 2013 Available online 15 August 2013

a b s t r a c t For (Li2S)x(P2S5)100–x glasses and Li7P3S11 glass–ceramic, which are well-known lithium superionic conductors, the conduction pathways of lithium ions were predicted and visualized by combining reverse Monte Carlo (RMC) modeling and the bond valence sum (BVS) method using synchrotron X-ray and time-of-flight neutron diffraction data. The conduction pathways of the lithium ions could be classified into two types: lithium ‘stable’ and ‘metastable’ regions. In addition, it was found that a significant relationship exists between the topology of the conduction pathways of the lithium ions and the activation energy of the electrical conduction. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The increasing demand for lithium-ion batteries (LIBs) with improved energy densities, power capacities, operation lives, and reliabilities calls for the use of solid instead of organic liquid electrolytes [1,2]. The realization of all-solid-state LIBs is critical for large-scale applications such as next-generation battery electric vehicles and plug-in hybrid electric vehicles. In particular, the Li2S–P2S5 system is a promising candidate as solid electrolyte in all-solid-state LIBs, because it exhibits high ionic conductivities at room temperature (RT) and has a wide electrochemical potential window (0–5 V vs. Li). (Li2S)x(P2S5)100x glasses can be synthesized by mechanical alloying (MA) of a stoichiometric mixture of Li2S and P2S5 [3–7]. Their ionic conductivities significantly increase with increasing Li2S content (x). For example, (Li2S)70(P2S5)30 glass exhibits a conductivity of 104 S cm1 at RT. Furthermore, (Li2S)70(P2S5)30 glass can be transformed into a Li7P3S11 metastable crystal (so-called Li7P3S11 glass–ceramic) by aging it at 260 °C. This metastable crystal exhibits an ionic conductivity of 103 S cm1 at RT. Structural studies have been conducted on the Li2S–P2S5 system by various authors, and found that the crystal structure of the Li7P3S11 glass–ceramic has P-1 symmetry within the triclinic system: a = 1.2500 nm, b = 0.6031 nm, c = 1.2530 nm, a = 102.84°, ⇑ Corresponding author. Fax: +81 72 451 2635. E-mail address: [email protected] (K. Mori). 0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.08.016

b = 113.20°, and c = 74.46° [8]. The positions of lithium ions in the (Li2S)70(P2S5)30 glass and the Li7P3S11 glass–ceramic have been precisely determined by combining neutron/X-ray Rietveld analysis and reverse Monte Carlo (RMC) modeling, respectively [9,10]. Knowing the relationship between the electrochemical properties (i.e., ionic conductivities and activation energy) and the topology of the conduction pathways of the lithium ions is very important in clarifying the lithium-ion conductive mechanism of the Li2S– P2S5 system. However, an elucidation of the conduction pathways of the lithium ions in the Li2S–P2S5 system has long been hindered by their amorphous structure. Till recently, the conduction pathways of the lithium ions were visualized by combining Rietveld analysis and the maximum entropy method (MEM) [11,12]. In this visualization methodology, high temperatures are essential for transforming the atomic motion from vibrations to diffusion. However, this approach is not applicable to glassy lithium-ion conductors. On the other hand, the conduction pathways of the lithium ions in oxide glasses (e.g., LixNa1xPO3 glass and LixRb1xPO3 glass) have been studied by combining RMC modeling and the bond valence sum (BVS) method [13–15]. In the present study, we have succeeded in predicting and visualizing the conduction pathways of the lithium ions in (Li2S)x(P2S5)100x glasses and Li7P3S11 glass–ceramic by combining RMC modeling and the BVS method using synchrotron X-ray diffraction (SXRD) and time-of-flight neutron diffraction (TOF-ND) data. Furthermore, we will discuss the relationship between the topology of the conduction pathways of the lithium

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ions and the activation energy of the electrical conduction in the Li2S–P2S5 system. 2. Experimental procedure 2.1. Synthesis 7

Li-enriched (7Li2S)x(P2S5)100x glasses (x = 50, 60, and 70) and Li7P3S11 glass–ceramic were synthesized for the SXRD and TOFND experiments. In the neutron diffraction analyses, the use of the isotope 7Li allowed the precise determination of the positions of the lithium ions because of the low absorption cross section of the lithium nucleus. Before synthesizing the (7Li2S)x(P2S5)100x glasses, P2S5 was prepared by MA of P (99.9999% purity, Mitsuwa Chemical Ind.) and S (99.99% purity, Kojundo Chemical Lab.) in the appropriate molar proportions. P and S were placed in a zirconia pot (80 cm3) with 20 zirconia balls (10 mm diameter) under a high-purity Ar gas atmosphere and then alloyed mechanically at 300 rpm for 150 h using a planetary ball-mill apparatus (P-5, Fritsch). Next, the (7Li2S)x(P2S5)100x glasses were prepared by MA of a mixture comprising P2S5 and 7Li2S (99.9% purity, Koujundo Chemical Lab.) at 300 rpm for 50 h. The 7Li7P3S11 glass–ceramic was synthesized by heating the (7Li2S)70(P2S5)30 glass at 260 °C for 2 h in a vacuum-packed borosilicate glass tube under a high-purity Ar gas atmosphere and subsequent rapid cooling to RT.

(7Li: 1684, P: 730, and S: 2560) for the 7Li7P3S11 glass–ceramic. The atomic compositions (7Li:P:S) of the cells are consistent with the molar ratios of the respective glasses, and the number densities of atoms are the same as those obtained from solid density measurements performed using a gas pycnometer (AccuPyc1330, Shimadzu Co.). The three-dimensional structures of the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass–ceramic were illustrated using the computer program VESTA [21].

7

2.2. SXRD and TOF-ND experiments

1

Z

2p q 2r

Q max

Q fSðQ Þ  1gsinðQrÞdQ ;

According to the BVS method, the valence sAX of a bond between a cation A and an anion X is given by:

sAX ¼ exp½ðR0  RAX Þ=b;

ð2Þ

where RAX is the bond length between A and X and R0 and b are empirical parameters [22–25]. The BVS value V(A) for all bonds between A and its coordinating X within the cut-off radius Rcut-off can be estimated by:

VðAÞ ¼

X

sAX :

ð3Þ

X

The ‘softness-sensitive’ BV (softBV) parameters used for bonds between Li+ and S2 were R0 = 0.146652 nm, b = 0.0653 nm, and Rcut-off = 0.6 nm. 3. Results and discussion

The SXRD experiments were performed using a horizontal twoaxis diffractometer at the BL04B2 beam line of the SPring-8 synchrotron radiation facility [16]. The energy of the incident X-ray beam was 61.5 keV. Samples of the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass–ceramic were placed in a stainless steel cell with two KaptonÒ windows under a high-purity Ar gas atmosphere. The samples were 2 mm thick along the direction of the incident X-ray beam. The SXRD data were collected in the Q range of 1.6–260 nm1 at RT, where Q is the magnitude of the scattering vector. 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) [17]. The samples were placed in a cylindrical vanadium holder (6 mm diameter). The TOF-ND data were collected in the Q range of 4–340 nm1 using a 45° detector bank at RT. To obtain the structure factor S(Q), appropriate corrections related to polarization, multiple scattering, absorption, and incoherent scattering were applied to the SXRD and TOF-ND data. Additionally, the atomic pair distribution function g(r) of the 7Li7P3S11 glass–ceramic was calculated by means of the Fourier transformation of S(Q) as follows:

gðrÞ ¼ 1 þ

2.4. BVS method

ð1Þ

Q min

where q is the number density of atoms and r is the interatomic distance. 2.3. RMC modeling RMC modeling was performed using the computer program RMC++ [18–20]. We employed cubic RMC cells with the following properties: the RMC cell had a 4.78 nm-long edge and 5000 atoms (7Li: 1000, P: 1000, S: 3000) for the (7Li2S)50(P2S5)50 glass; the cell had a 4.66 nm-long edge and 4968 atoms (7Li: 1296, P: 864, S: 2808) for the (7Li2S)60(P2S5)40 glass; the cell had a 4.60 nm-long edge and 4998 atoms (7Li: 1666, P: 714, S: 2618) for the (7Li2S)70(P2S5)30 glass; and the cell had a 4.60 nm-long edge and 4974 atoms

S(Q) data of the (7Li2S)x(P2S5)100x glasses (x = 50, 60, and 70) and g(r) data of the 7Li7P3S11 glass–ceramic, obtained from the SXRD and TOF-ND experiments, are shown in Figure 1. Using RMC modeling, an excellent fit between observed and calculated S(Q) or g(r) values was obtained for each sample. It is worth noting that the g(r) data are employed for the RMC modeling of the 7Li7P3S11 glass–ceramic because of its crystal structure. Figure 2 shows the three-dimensional structures of the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass–ceramic, both of which comprise lithium ions and corner-shared PS4 tetrahedra. In particular, the (7Li2S)70(P2S5)30 glass and the 7Li7P3S11 glass–ceramic possess only two units, the PS4 tetrahedra and the P2S7 ditetrahedra, which agrees with the literature data [8–10]. Before studying the conduction pathways of the lithium ions in the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass–ceramic, the ionic state of each lithium ion was evaluated by the BVS method using the above mentioned softBV parameters. As a result, the BVS value of the lithium ions, BVS(Li), was determined to be close to 1+, meaning that Li+ ions travel along the conduction pathways in these solids. According to Adams [24,25], an important relationship exists between the topology of the conduction pathways of the lithium ions and areas of low BV mismatch, |DV(A)|, which can be described as follows:

j DVðAÞ j¼j BVSðAÞ  V id ðAÞ j þpðAÞ;

ð4Þ

where Vid(A) is the ideal ionic state of ion A (e.g., Vid(Li) = 1) and p(A) is the penalty function to avoid unphysical configurations. In general, the lithium sites with |DV(Li)| < 0.04 are considered ‘stable’ sites. Thus, to explore the lithium stable sites in the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass–ceramic, the corresponding RMC cells were divided into 250  250  250 pixels (henceforth ‘volume element’), and then, |DV(Li)| is calculated for each volume element. Notably, the volume elements around P and S atoms were excluded from the |DV(Li)| calculations. By this way, we obtained three-dimensional maps of the lithium stable sites in the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass–ceramic. The volume

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Figure 1. Reverse Monte Carlo (RMC) modeling of (a) (7Li2S)50(P2S5)50 glass, (b) (7Li2S)60(P2S5)40 glass, (c) (7Li2S)60(P2S5)40 glass, and (d) 7Li7P3S11 glass–ceramic using synchrotron X-ray and time-of-flight neutron diffraction data at room temperature. Data represented by solid lines (black) are the experimentally determined values of S(Q) and g(r) using synchrotron X-ray and time-of-flight neutron diffraction analyses. Dashed lines (red) represent the calculated ones. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Figure 2. Three-dimensional structures of (a) (7Li2S)50(P2S5)50 glass, (b) (7Li2S)60(P2S5)40 glass, (c) (7Li2S)60(P2S5)40 glass, and (d) 7Li7P3S11 glass–ceramic. In (d), the parallelepiped box with dashed lines (blue) denotes a unit cell of the Li7P3S11 glass–ceramic. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Figure 3. Three-dimensional conduction pathways of lithium ions in (a) (7Li2S)50(P2S5)50 glass; (b) (7Li2S)60(P2S5)40 glass; (c) (7Li2S)70(P2S5)30 glass; (d) 7Li7P3S11 glass– ceramic. In (d), the parallelepiped box with dashed lines (blue) denotes a unit cell of the Li7P3S11 glass–ceramic. The connected pathways (pink) obtained from the BV mismatch calculations correspond to the predicted conduction pathways of lithium ions in the solids at room temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

occupied by the lithium stable sites gradually increased with increasing x. It further increased on passing through the transformation from the (7Li2S)70(P2S5)30 glass to the 7Li7P3S11 glass–ceramic. However, the conduction pathways of the lithium ions were still unclear because the lithium stable sites did not percolate between the two edges of an individual RMC cell. When the |DV(Li)| value is increased, the lithium stable sites continued to spread further and connected with each other. Consequently, we succeeded in visualizing the connected pathways of the volume elements at the maximum value of |DV(Li)| (|DV(Li)|max, hereafter) for the (7Li2S)x(P2S5)100x glasses and the 7Li7P3S11 glass– ceramic (see Figure 3). It is worth noting that the connected pathways coincide with the predicted conduction pathways of the lithium ions around the PS4 tetrahedra at RT. In the (7Li2S)x(P2S5)100x glasses, the |DV(Li)|max value first decreased monotonically with increasing x, followed by an abrupt decrease owing to the transformation of the (7Li2S)70(P2S5)30 glass into the 7Li7P3S11 glass–ceramic (see Figure 4a). The conduction pathways of the lithium ions could be briefly classified according to two types: (I) lithium ‘stable’ regions (orange) with |DV(Li)| < 0.04 and (II) lithium ‘metastable’ regions (blue) with 0.04 6 |DV(Li)| 6 |DV(Li)|max, as shown in Figure 5. Obviously, the number and size of the lithium metastable regions was relatively reduced with increasing x and a quick drop is observed after the transformation of the (7Li2S)70(P2S5)30 glass into the 7Li7P3S11 glass–ceramic. During MA of Li2S and P2S5, Li2S molecules are incorporated into a network of the corner-shared PS4 tetrahedra, and thereby, the (Li2S)x(P2S5)100x glass is formed. In preliminary analyses using a radial distribution function (RDF) method, the coordination number of S around P was constantly four (i.e., PS4 tetrahedron),

Figure 4. Comparison of the maximum values of the BV mismatch (upper frame) and the activation energy (lower frame). (a) Maximum value of the BV mismatch |DV(Li)|max as a function of the Li2S content x for (7Li2S)x(P2S5)100x glasses (black open circles) and a Li7P3S11 glass–ceramic (red open circle). (b) Activation energy Ea as a function of x for (7Li2S)x(P2S5)100x glasses (black open squares) and the Li7P3S11 glass–ceramic (red open square). Dashed lines are visual guides. The behavior of |DV(Li)|max is quite similar to that of Ea. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Figure 5. Conduction pathways of lithium ions (enlarged for clarity). (a) (7Li2S)50(P2S5)50 glass; (b) (7Li2S)60(P2S5)40 glass; (c) (7Li2S)70(P2S5)30 glass; (d) 7Li7P3S11 glass– ceramic. Each box is 1.8 nm  1.5 nm  0.9 nm in size. In (d), the parallelepiped box with dashed lines (blue) denotes a unit cell of the Li7P3S11 glass–ceramic. The orange and blue regions indicate the lithium ‘stable’ and ‘metastable’ regions, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

although the ratio of non-bridging P–S bonds (i.e., –P=S) to bridging P–S ones (i.e., –P–S–P–) in the PS4 tetrahedral network increased with increasing x. Simultaneously, the space formed by the surrounding S atoms is deformed, which plays an important role in the lithium-ion conduction for the (Li2S)x(P2S5)100x glass, as well as for the 7Li7P3S11 glass–ceramic. Their ionic conductivities r can be expressed by the Boltzmann distribution, that is,

lnðrTÞ ¼ lnr0 

  Ea 1 ; kB T

ð5Þ

where r0 is the pre-exponential factor, Ea is the activation energy, kB is the Boltzmann constant, and T is the temperature. Since Ea corresponds to the potential barrier for the lithium ions moving along the conduction pathways, it should be strongly associated with |DV(Li)|max of the lithium metastable regions. In Figure 6, schematic diagrams represent the relationship between the topology of the conduction pathways and the potential energy profile for the lithium ions. In (Li2S)x(P2S5)100x glass with comparably low x, the conduction pathways of the lithium ions are mainly given by the lithium metastable regions with a large value of |DV(Li)|max, whereas in (Li2S)x(P2S5)100x glass with higher x and the Li7P3S11 glass–ceramic, the number and size of the lithium metastable regions is reduced and |DV(Li)|max decreases and asymptotically approaches 0.04. From this point of view, the order according to which Ea decreases can beeasily established as follows: (Li2S)50(P2S5)50 glass > (Li2S)60(P2S5)40 glass > (Li2S)70(P2S5)30 glass > Li7P3S11 glass–ceramic. In fact, this behavior of |DV(Li)|max is similar to that of Ea determined using ac four-probe measurements, as shown in Figure 4b. Thus, there is a great similarity between |DV(Li)|max and Ea. We point out that |DV(Li)|max can be utilized as an indicator for the topological optimization of the conduction pathways of the

Figure 6. Illustrations of the relationship between the topology of the conduction pathways of lithium ions and the potential energy profile. (a) (Li2S)x(P2S5)100x glass with lower x and (b) (Li2S)x(P2S5)100x glass with higher x and the Li7P3S11 glass– ceramic. The orange and blue areas correspond to the lithium ‘stable’ and ‘metastable’ regions, respectively. For each figure, the two arrows denote the migration directions of Li+ along the conduction pathway (red arrows) and the energy potential profile (pink arrows). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

lithium ions in order to obtain high ionic conductivities along with low activation energies in the Li2S–P2S5 system. To determine

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quantitatively the relationship between |DV(Li)|max and Ea, further investigations are now in progress.

for Scientific Innovation of New Generation Battery (RISING project)’ of the New Energy and Industrial Technology Development Organization (NEDO), Japan.

4. Conclusions We performed SXRD and TOF-ND analyses on 7Li-enriched (7Li2S)x(P2S5)100x glasses (x = 50, 60, and 70) and 7Li7P3S11 glass–ceramic, and succeeded in clearly visualizing the predicted conduction pathways of the lithium ions at RT by combining RMC modeling and the BVS method. The conduction pathways of the lithium ions could be briefly classified into two types: lithium ‘stable’ and ‘metastable’ regions. The lithium number and size of the metastable regions was relatively reduced with increasing x, and a concomitant quick drop in |DV(Li)|max and the activation energy Ea is observed at the transformation of the (7Li2S)70(P2S5)30 glass into the 7Li7P3S11 glass–ceramic. In addition, a great similarity between |DV(Li)|max and Ea as a function of x is revealed, thus indicating that |DV(Li)|max can be utilized as an indicator for the topological optimization of the conduction pathways of the lithium ions in order to obtain high ionic conductivities and low activation energies in the Li2S–P2S5 system. Acknowledgements The SXRD experiments were performed at BL04B2 in SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2012B1298). We thank the NOVA (BL21) group of the Materials and Life Science Facility (MLF), Japan Proton Accelerator Research Complex (J-PARC), for their help with the TOF-ND experiments. The neutron scattering experiments were approved by the Neutron Scattering Program Advisory Committee of IMSS, KEK (Proposal No. 2009S06). This work was partially supported by the ‘Research and Development Initiative

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