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Elastic Properties, Defect Thermodynamics, Electrochemical Window, Phase Stability, and Li+ Mobility of Li3PS4: Insights from FirstPrinciples Calculations Yanhan Yang,†,‡ Qu Wu,‡ Yanhua Cui,*,§ Yongchang Chen,∥ Siqi Shi,*,‡ Ru-Zhi Wang,*,† and Hui Yan† †

College of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, China School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China § Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621000, China ∥ Nanchang Hangkong University, Nanchang 330063, China ‡

S Supporting Information *

ABSTRACT: The improved ionic conductivity (1.64 × 10−4 S cm−1 at room temperature) and excellent electrochemical stability of nanoporous β-Li3PS4 make it one of the promising candidates for rechargeable all-solid-state lithium-ion battery electrolytes. Here, elastic properties, defect thermodynamics, phase diagram, and Li+ migration mechanism of Li3PS4 (both γ and β phases) are examined via the first-principles calculations. Results indicate that both γ- and β-Li3PS4 phases are ductile while γ-Li3PS4 is harder under volume change and shear stress than β-Li3PS4. The electrochemical window of Li3PS4 ranges from 0.6 to 3.7 V, and thus the experimentally excellent stability (>5 V) is proposed due to the passivation phenomenon. The dominant diffusion carrier type in Li3PS4 is identified over its electrochemical window. In γLi3PS4 the direct-hopping of Lii+ along the [001] is energetically more favorable than other diffusion processes, whereas in β-Li3PS4 the knock-of f diffusion of Lii+ along the [010] has the lowest migration barrier. The ionic conductivity is evaluated from the concentration and the mobility calculations using the Nernst− Einstein relationship and compared with the available experimental results. According to our calculated results, the Li+ prefers to transport along the [010] direction. It is suggested that the enhanced ionic conductivity in nanostructured β-Li3PS4 is due to the larger possibility of contiguous (010) planes provided by larger nanoporous β-Li3PS4 particles. By a series of motivated and closely linked calculations, we try to provide a portable method, by which researchers could gain insights into the physicochemical properties of solid electrolyte. KEYWORDS: Li3PS4, superionic conductor, electrochemical window, defect chemistry, ion diffusion mechanism

1. INTRODUCTION

provide the best opportunity to replace current organic liquid electrolytes.3 However, the poor Li+ conduction ability of usual SE ( 0 C22 + C33 − 2C23 > 0 C11 + C22 + C33 + 2C12 + 2C13 + 2C23 > 0

G=

(1)

Generally speaking, C11, C22, and C33 measure the resistances to the linear compressions along the [100], [010], and [001] directions, respectively, while C44, C55, and C66 have a relation to the shear resistances with respect to the (001), (010), and (001) planes, respectively.41 At first sight, both γ- and β-Li3PS4 meet the mechanical stability criteria. Furthermore, for both phases, C11, C22, and C33 are much larger than C44, C55, and C66, indicating that the resistances against uniaxial tensions are 25232

DOI: 10.1021/acsami.6b06754 ACS Appl. Mater. Interfaces 2016, 8, 25229−25242

Research Article

ACS Applied Materials & Interfaces

using smaller β-Li3PS4 particles would be a way of minimizing deformation and enhancing the ion conductivity. This would be one reason that the nanoporous β-Li3PS4 exhibits the enhancement of its ionic conductivity by 3 orders of magnitude as compared with the bulk one.12 To briefly summarize, the elastic properties of SEs are vital parameters when designing solid-state batteries, because the volume of electrode material and the electrolyte itself varies during the battery operations. This volume change would cause the instability of structure, usually accompanied by deformations or bad contact at the electrolyte/electrode interface. Because SEs could not recover these deformations, it is important to restrain deformations in the battery system. From our calculations and comparison, the sulfide electrolyte (Li3PS4) has a very small elastic modulus (E < 50 GPa, B < 40 GPa, G < 20 GPa) as compared with its oxide (Li3PO4). The smaller mechanical modulus can be predicted from the smaller atom packing density, indicating that the sulfide electrolyte is softer.49 Therefore, Li3PS4 can be fabricated through coldpressing into pellets, avoiding high-temperature treatment that would cause internal stress.5,14,16 3.3. Defect Thermodynamics and Electrochemical Window. As is well-known, point defects act as crucial roles in ionic conduction. The one with the lowest defect formation energy would contain high concentration in the solid electrolyte material, which would dominant the transport mechanism of lithium ions. In the previous study,23 the defects only involve the neutral vacancy-interstitial pair. However, the actual case is that, in the battery cycles, charged defects such as the inserted/deserted Li+ are introduced in the electrolyte inevitably. Therefore, we should analyze the thermodynamics of each possible point defect in Li3PS4 before discussing the Li+ migration mechanism. Here, we only consider the Li-associated neutral or charged point defects (listed in Table 5). Given the

Table 4. Calculated Bulk Modulus (B, in GPa), Shear Modulus (G, in GPa), Young’s Modulus (E, in GPa), Poisson Ratio (ν), and Anisotropic Factors (AB and AG, in %) for γ- and β-Li3PS4; Results of Li3PO4 Are Listed for Comparison44 γ-Li3PS4

β-Li3PS4

31.84 31.96 31.90 13.90 14.32 14.11 2.26 36.88 0.31 0.19 1.49

20.50 22.29 21.39 11.13 11.54 11.33 1.89 28.90 0.27 4.18 1.81

BR BV B GR GV G B/G E ν AB [%] AG [%]

γ-Li3PO4 (ref44)

72.5

40.9 1.77 103.4 0.26

B/G ratio (1.77), which is very close to the threshold of brittleness (1.75), indicating that Li3PO4 is more brittle than Li3PS4. This result agrees with our universal cognition that the oxide is usually more fragile than its sulfide. Therefore, densification is induced in sulfide electrolyte just by coldpressing. Oxide ceramics, such as Li7La3Zr2O12, should be sintered at over 1000 °C to obtain compact samples.46 Young’s modulus E measures the rigidity of the solid material. A high value means that the material is stiffer. As shown in Table 4, Young’s modulus E of γ-Li3PS4 (36.88 GPa) is relatively higher than that of β-phase (28.90 GPa), indicating that the former is stiffer than the latter. Additionally, with the increase of the E value, the covalency of a material also increases. That is why the Young’s modulus of γ-Li3PO4 (103.4 GPa) is much larger than that of Li3PS4. Poisson ratio ν evaluates the stability of a material under shearing stress. The calculated Poisson ratio of γ-Li3PS4 (0.31) is larger than that of β-Li3PS4 (0.27), thus showing that the γ-phase is more stable against the shearing situation. This is consistent with the result that γ-Li3PS4 has a larger shear modulus than β-Li3PS4. Additionally, the Poisson ratios of γ-Li3PO4 (0.26) and βLi3PS4 (0.27) are similar to each other (as shown in Table 4), which is because they have similar features in structure (Pnma). During the battery operations, Li+ ions are cycled in and out of the electrode and electrolyte materials, which would cause the generation of deformation in crystallites. Such deformations, introduced by elastic anisotropy, are important factors leading to capacity fading of the battery47 and can be evaluated by the percentage anisotropy in compressibility and shear:48 B − BR AB = V B V + BR AG =

G V − GR G V + GR

Table 5. Li-Related Point Defects Calculated in the Present Work defect

definition

VLi VLi− Lii Lii+ LiFP LiFP+ LiFP−

neutral Li vacancy negatively charged Li vacancy neutral excess interstitial Li atom positively charged excess interstitial Li ion neutral Li Frenkel pair positively charged Li Frenkel pair negatively charged Li Frenkel pair

(6)

structural complexity, there exist more than one type of interstitial site in both γ- and β-Li3PS4. Table 6 lists the optimized interstitial sites as well as the computed relative

(7)

Table 6. Optimized Parameters of Interstitial Sites in γ- and β-Li3PS4a γ-Li3PS4

where the subscripts V and R correspond to the Voigt and Reuss limits calculated above, respectively. A value of 0% identifies elastic isotropy, and a value of 100% is the largest possible anisotropy. The calculated AB and AG are also given in Table 4. Compared with other anisotropic crystals reported in ref 48, Li3PS4 is moderately anisotropic. Note that β-Li3PS4 is more anisotropic than γ-Li3PS4 both in bulk and shear factors. γ-Li3PS4 is almost isotropic in compressibility, while β-Li3PS4 has the largest anisotropic factor in this value. We suggest that

β-Li3PS4

label

position

E (eV)

label

position

E (eV)

I1 I2 II

(0.00, 0.48, 0.64) (0.00, 0.45, 0.18) (0.25, 0.00, 0.68)

0.12 0.51 0

A1 A2 B

(0.73, 0.25, 0.94) (0.77, 0.25, 0.48) (0.94, 0.25, 0.72)

0.47 0

The “II” (B) configuration energy is set to 0.0 eV in γ-Li3PS4 (βLi3PS4). Coordinates are given as fractional coordinates of the optimized perfect unit cell in Figures 1 and 2. a

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ACS Applied Materials & Interfaces energies. Detailed comparison of each interstitial Li+ site is in the Supporting Information Section S3. Figures S3 and S4 show the positions of interstitial Li+ sites in γ- and β-Li3PS4, respectively. Consequently, interstitial site II is energetically favorable in γ-Li3PS4, while site B is more favorable for β phase. After analyzing the energetics of supercells with and without defects, we can obtain the dependence of Ef (i,q) and S(i,q) on the battery voltage at 300 K over the voltage range 0−5 V.12,15 Computational details on the defect thermodynamics are provided as Supporting Information Section S3. The calculated defect formation, Ef(i,q), and the corresponding defect concentration, S(i,q), of both phases of Li3PS4 are shown in Figures 3 and 4, respectively. For γ-Li3PS4, Figure 3a indicates

Figure 4. (a) Formation energies, Ef(i,q), for point defects of β-Li3PS4. (b) Defect concentrations, S(i,q), for the point defects in (a). The vertical dotted lines in (a) and (b) represent the HSE06 band gap (red) and two critical voltages (black): 0.55 V (the formation energy of Lii+ is zero) and 3.20 V (the formation energy of VLi is zero).

indicating the relatively easy Li ion migration in β-Li3PS4, which has been proved by experiments.8,11,12 In Figures 3 and 4, the formation energies of some defects (VLi and LiFP+) become negative at high voltage range, indicating these defects would form spontaneously in the system. Li3PS4 would become unstable when the voltage is above 3.65 (γ) or 3.20 (β) V. Additionally, the negative formation energies of Lii and Lii+ are also observed in the low voltage range (0−0.30 V for γ-Li3PS4 and 0−0.55 V for βLi3PS4), which would be caused by the dendritic growth of lithium during repeated deposition and dissolution cycles when using lithium metal as electrode.50 We define the stable voltage ranges for the two phases of Li3PS4 based on the defect thermodynamics (0.30−3.65 V for γ-Li3PS4 and 0.55−3.20 V for β-Li3PS4), which are narrower than the experimental measurements of 0−5 V reported by Liu et al.12 and Rangasamy et al.16 We further examine the stability of Li3PS4 assuming that it faces the inert electrode and metallic lithium, respectively. The stability of Li3PS4 facing inert electrodes is studied, adopting the method put forward by Ong et al.51 The lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) energies are obtained by calculating the density of states (DOS) of Li3PS4. The calculated DOS of Li3PS4 using GGA-PBE and hybrid functional HSE0652 are plotted in Figures S5 and S6 (Supporting Information Section S4), respectively. The band gap of Li3PS4 (both γ and β phases) is about 2.7 eV for GGAPBE and 3.7 eV for HSE06, which are also smaller than the result reported by Rangasamy et al. 15 Note that the electrochemical window obtained by this method is its upper limit, which indicates that the remarkable electrochemical stability of Li3PS4 in experimental measurement is not its intrinsic property but rather the occurrence of a passivation phenomenon.50 A similar phenomenon was also observed in Li10GeP2S12,10 which has a calculated band gap of 3.6 eV, much smaller than the reported electrochemical window (>5 V).9 To

Figure 3. (a) Formation energies, Ef(i,q), for point defects of γ-Li3PS4. (b) Defect concentrations, S(i,q), for the point defects in (a). The dotted lines in (a) and (b) represent the HSE06 band gap (red) and two critical voltages (black): 0.30 V (the formation energy of Lii+ is zero) and 3.65 V (the formation energy of VLi is zero).

that during 0−1.20 V the formation energy for Lii+ is the lowest (−0.11 to 0.45 eV). Consequently, the concentration of Lii+, ranging from 1.52 × 1024 to 4.51 × 1014 cm−3, is the highest relative to the others’ concentration at equilibrium as shown in Figure 3b. At this voltage range, electric neutrality is mainly kept by Lii+ and free electrons. Originally, Ef(Lii+) increases while Ef(VLi−) decreases with voltage. The formation energies of the two major point defects (Lii+ and VLi−) meet at ∼1.20 V and then remain equal (∼0.47 eV) from 1.20 to 3.40 V. In this voltage range, these two point defects have an equal concentration about 3.00 × 1014 cm−3 as shown in Figure 3b. Above 3.15 V, VLi contains the highest concentration and dominates the diffusion. Clearly, the diffusion carrier in γLi3PS4 changes with the battery voltage, and thus either Lii+, both Lii+ and VLi−, or VLi dominate the diffusion mechanism. The overall defects situation in β-Li3PS4 (Figure 4) is similar to that in γ-phase, but there is a tiny difference between the two phases. Lii+ and VLi− exhibit the same concentration of ∼1.84 × 1020 cm−3 with the formation energy of ∼0.12 eV, and therefore both dominate the diffusion during 0.80−3.05 V. Additionally, almost all types of defects in β-Li3PS4 have the smaller formation energies as compared with those in γ-phase, 25234


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Figure 5. (a−g) Li−P−S grand potential phase diagrams at different voltages. The equilibrium phases with Li3PS4 are noted in black (stable) and red (unstable), respectively. The insert in (g) shows the enlarged convex hull near Li3PS4. x equals NP/(NP + NS), where Ni is the number of atoms for the element i in each phase.

examine the phase equilibria of Li3PS4 with Li during operations of battery cycles. Similar approaches were applied in the Li−Ge−P−S system.10 Computational details are summarized in Supporting Information Section S5. We list the obtained phase equilibria of Li3PS4 in equilibrium with

explore this interfacial passivation, we examine the phase equilibria of Li3PS4 when it faces metallic lithium. Employing the approach proposed by Ong et al.,53 we construct the lithium grand potential phase diagrams of the Li− P−S system at different battery voltages (V) in Figure 5 to 25235


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voltage is very close to the threshold (0.30−0.55 V) when the formation energy of Lii+, which is obtained by the defect thermodynamics calculations, becomes negative. It is predicted that the formation of Li2S protects the solid electrolyte Li3PS4 from further decompositions under low battery voltage. A similar reaction was also predicted by Lepley et al.23 In Li-CFx batteries, micron level textural changes were observed at the cycled Li/β-Li3PS4 interface according to the SEM images,15 indicating the formation of a thin buffer layer during the battery cycles. Another experimental work about Li10GeP2S12 reported the formation of Li2S and Li3P directly at the interface of Li10GeP2S12/Li using in situ X-ray photoelectron spectroscopy (XPS) and time-resolved electrochemical measurements.55 However, with the addition of solid oxide filler (e.g., Li6ZnNb4O14), nanocrystalline β-Li3PS4 shows no significant interfacial reactions with metallic lithium.56 When the battery voltage is >2.32 V, P2S5 and S would generate at the interface, accompanied by the delithiation, which similarly prevents the decomposition of Li3PS4. Recent theoretical work by Zhu et al. predicted similar phase equilibria for Li3PS4 and other solid electrolytes.57,58 We suggest that the electrochemical window obtained by this method is its lower limit. In summary, we obtain three different electrochemical windows of Li3PS4: 3.35 V for γ-Li3PS4 and 2.65 V for βphase obtained from the defect thermodynamics calculations; 3.7 V obtained from the HOMO and LUMO calculations (the upper limit); and 0.6 V obtained from Li−P−S grand potential phase diagram (the lower limit). The stability of solid

metallic Li and the corresponding voltage range in Table 7. The total energies and the normalized grand potentials of each phase in the Li−P−S system at different voltages are listed in Tables S2 and S3. Table 7. Phase Equilibrium of Li3PS4 with Metallic Li and the Corresponding Voltage Range voltage range (V)

phase equilibrium

0−0.87 0.88−0.93 0.94−1.17 1.18−1.50 1.51−1.71 1.72−2.31 >2.32

Li2S, Li3P Li2S, LiP Li2S, Li3P7 Li2S, LiP7 Li2S, P Li3PS4 P2S5, S

In Figure 5, the horizontal and vertical coordinates denote the ratio of P and S atoms in each phase (a constant value for each species) and the grand potential (varies with the voltage), respectively. For each voltage, we construct the convex hull (solid black line in each figure), making sure that all the other potential points are above it.54 According to our results, the intrinsic stable range of Li3PS4 is limited in 1.72−2.31 V (corresponds to −3.62 to −4.21 eV of μLi). With the loss of battery voltage from 1.71 to 0 V, Li3PS4 decomposes to Li2S and LixPy (e.g., LiP7, Li3P7, and Li3P), as shown in Figure 5(a− e). When the electrode voltage is 1.75), whereas the bulk modulus, shear modulus, Young’s modulus, and Poisson ratio of γ-Li3PS4 are all larger than those of β-Li3PS4, indicating that the former could resist larger stress and strain. To achieve the electrochemical window, we calculate the DOS of Li3PS4 and construct the Li−P−S grand potential phase diagram in a wide lithium chemical potential range. The obtained electrochemical window of Li3PS4 ranges from 0.6 to 3.7 V. Therefore, the excellent stability of Li3PS4 in experiments is due to the

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Author Contributions

Y.Y. and Q.W. contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Nature Science Foundation of China (Grant nos. 51622207, 51372228, 25240


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21363016, U1630134, and U1430104), Shanghai Pujiang Program of China (Grant no. 14PJ1403900), Laboratory of Precision Manufacturing Technology, China Academy of Engineering Physics (Grant no. ZZ13007), the Project of China Academy of Engineering Physics (Grant no. 2013A030214), the Young Scholar Science Foundation of Jiangxi Province (Grant no. 20142BAB216030), and the Natural Science Foundation of Jiangxi Province (Grant no. 20151BAB203047). All the computations were performed on the high-performance computing platform of Shanghai University.

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