Atomic Structure Modeling of Li-P-S Solid Electroryte Glass with RMC and DFT Calculations

Introduction

                   Li₂S-P₂S₅ glass has been attracted attention as the solid electrolyte for lithium ion battery because of its high ionic conductivity and wide electrochemical potential window. It is known that the ratio of Li₂S and P₂S₅ affects Li-ion conductivity, and suggested that the atomic structure is related to Li ion conductivity. Atomic structures of Li₂S-P₂S₅ glasses calculated by Reverse Monte Carlo (RMC) modeling previously reported.^1,2RMC calculation results in structures satisfying the requirement for experimental data in totality, however, its local structure might have unreasonable configuration.

                   In this study, we calculated reasonable Li₃PS₄, Li₇P₃S₁₁ and Li₄P₂S₇glass structure using combination of RMC calculations and density functional theory (DFT) calculations.

Method

                   Cubic cell whose lattice constant is about 22.5 Å and number of atoms is 567 were used for the initial structure of Li₇P₃S₁₁ glass structure. Density is equal to experimental result. Li atoms, PS₄ and P₂S₇molecules were randomly allocated in the cell.

At first, RMC calculation was performed for the initial random structure. RMC calculation was carried out for the two structure-factor data S(Q) of Li₇P₃S₁₁ glass using RMC++ code. S(Q) data were obtained from neutron diffraction and X-ray diffraction. Secondly, DFT calculation was performed for RMC structure using VASP code. In DFT part, internal atomic positions optimized until residual forces become less than 0.02 eV/Å. These RMC and DFT calculations were repeated until the difference of atomic structures between RMC and DFT become to be less than 0.1 Å.

                   For comparison, smaller cells, 10 types of 325-atom cells and 100 types of 105-atom cells were calculated in the same way.

Results and Discussion

                   The structures calculated by RMC had good agreement with S(Q) in any cases as shown in Fig. 1, however, the densities of states are obviously different. While the last RMC structure had about 1.5 eV band gap (shown in blue line in Fig. 2), the 1st RMC structure was metallic (shown in red line in Fig. 2). The largest difference between 1st and last RMC structure is configuration of Li atoms. Figure 3 shows the pair distribution function of Li and Li. The last RMC g(r) is flat around 1, which means that Li atoms exist homogeneously in the cell. In contrast, the 1st RMC g(r) has a peak at 2.5 Å which is equal to the constraint distance between Li atoms setup condition in RMC. This suggests that Li configuration does not affect to the S(Q) in this system even if neutron diffraction is considered. Figure 4 shows the relative energies of Li₇P₃S₁₁ based on Li₂S and P₂S₅ energies against band gaps. The energies of glass structures are higher than crystal and lower than the mixture of Li₂S and P₂S₅. Most energy fell within 0.03 eV/atom and band gaps fell within 0.6 eV.

                   In summary, the combination of RMC and DFT calculation results proper atomic structures satisfying experimental data within satisfactory accuracy.

Acknowledgment

This work was supported by the RISING project of the New Energy and Industrial Technology Development Organization (NEDO).

References

[1] Y. Onodera, et al. Journal of Physics: Conference Series 340(2012) 012058.

[2] K. Mori, et al. Chemical Physics Letters 584 (2013) 113.