Density Functional Theory Study of Lithium Defects in γ-Li3PS4 and Li7P3S11

Lithium thiophosphates are promising candidates for the solid electrolyte material for all-solid-state batteries.^1,2 Lithium ion conduction mechanisms in these materials are focus of intense research, but they are still poorly understood, and there is a strong need for both theoretical and experimental studies. Recently, Lepley and Holzwarth studied Li defects in selected Li thiophosphates and phosphates using the density functional theory (DFT). Further examining the migration mechanisms of Li atom, they concluded that a Frenkel pair is the most stable defect with the lowest migration barrier in Li₇P₃S₁₁. Unfortunately, there was no discussion about the absolute scale of the defect formation energies. Therefore, the relative stability of different defects was not justified. In this work, we performed DFT calculations to determine dominant lithium defects present in γ-Li₃PS₄ and Li₇P₃S₁₁and revisited the migration mechanisms of Li-ions.

γ-Li₃PS₄ and Li₇P₃S₁₁ are representative crystalline structures of Li-P-S compound used in solid-state batteries. Their unit cell structures are shown in Fig. 1. γ-Li₃PS₄ is the most stable polymorph of Li₃PS₄ at room temperature and atmospheric pressure. Its unit cell structure is simple, and each atomic species are uniquely coordinated. Li₇P₃S₁₁is well-known for its high ionic conductivity. Although it is slightly unstable, it is stabilized by the entropic contribution and retains the meta-stable structure. Because of these reasons, these two materials are ideal for studying the Li-ion conduction mechanisms in crystalline Li-P-S compounds. 

Quite generally, defect formation energy of defect α with charge q is defined by the following expression:

 E_f[α^q]=E[α^q]-E_perf+ μ_α^bulk+q·(E_Fermi+E_VBM+dV)

 E[α^q] is the total energy of the structure containing defect α with charge q. E_perf is the total energy of the perfect crystal. μ_α^bulk is the chemical potential of defect species α in the bulk phase. E_Fermi is the Fermi energy relative to the valence band maximum. E_VBM is the position of the valence band maximum in the perfect crystal. dV is the shift in the valence band maximum due to the presence of the defect. Using this expression, the defect formation energies of Li_I^x, Li_I^•, V_Li^x, V_Li′ were computed in γ-Li₃PS₄ and Li₇P₃S₁₁. Both μ_α^bulk and E_Fermiwere varied to evaluate the energetics of the Li defects at different conditions.

In γ-Li₃PS₄, Li interstitials dominate over the entire range of E_Fermi when μ_Li^bulk= μ_Li⁰ , where μ_Li⁰ is the chemical potential of Li in Li metal. Under this condition, transition from Li^• to Li^x occurs around 2.3 eV, and the formation energy remains fairly low. As the chemical potential drops, V_Li′ starts to be important approximately 1 eV below μ_Li⁰.

Same calculations were performed for Li₇P₃S₁₁. Again, Li interstitials dominate over the entire range of E_Fermi when μ_Li^bulk= μ_Li⁰ . However, the transition from Li^• to Li^x occurs at even lower E_Fermi and formation energy than in γ-Li₃PS₄.

In this paper, we report the defect formation energies of Li defects evaluated under a variety of different conditions in these two structures. Migration mechanisms of the Li-ions in these materials are also investigated, and implication for the battery application will be discussed. 

1. F. Mizuno, A. Hayashi, K. Tadanaga, and M. Tatsumisago, Advanced Materials, 17, 918 (2005).
2. N. Kamaya, K. Homma, Y. Yamakawa, M. Hirayama, R. Kanno, M. Yonemura, T. Kamiyama, Y. Kato, S. Hama, K. Kawamoto, and A. Mitsui, Nature Materials, 10, 682 (2011).
3. N.D. Lepley, and N.A.W. Holzwarth, Journal of Electrochemical Society, 159, A538 (2012).