Density Functional Theory Study of Lithium Defects in γ-Li3PS4 and Li7P3S11
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[αq] is the total energy of the structure containing defect α with charge q. Eperf is the total energy of the perfect crystal. μαbulk is the chemical potential of defect species α in the bulk phase. EFermi is the Fermi energy relative to the valence band maximum. EVBM 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 LiIx, LiI•, VLix, VLi′ were computed in γ-Li3PS4 and Li7P3S11. Both μαbulk and EFermiwere varied to evaluate the energetics of the Li defects at different conditions.
In γ-Li3PS4, Li interstitials dominate over the entire range of EFermi when μLibulk= μLi0 , where μLi0 is the chemical potential of Li in Li metal. Under this condition, transition from Li• to Lix occurs around 2.3 eV, and the formation energy remains fairly low. As the chemical potential drops, VLi′ starts to be important approximately 1 eV below μLi0.
Same calculations were performed for Li7P3S11. Again, Li interstitials dominate over the entire range of EFermi when μLibulk= μLi0 . However, the transition from Li• to Lix occurs at even lower EFermi 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.
- F. Mizuno, A. Hayashi, K. Tadanaga, and M. Tatsumisago, Advanced Materials, 17, 918 (2005).
- 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).
- N.D. Lepley, and N.A.W. Holzwarth, Journal of Electrochemical Society, 159, A538 (2012).