Solid-state materials with high ionic conduction are necessary to many technologies including all-solid-state Li-ion batteries. Understanding how crystal structure dictates ionic diffusion is at the root of the development of fast ionic conductors. Here, we show that LiTi2(PS4)3 exhibits a Li-ion diffusion coefficient about an order of magnitude higher than current state-of-the-art lithium superionic conductors. We rationalize this observation by the unusual crystal structure of LiTi2(PS4)3 which offers no regular tetrahedral or octahedral sites for lithium to favorably occupy. This creates a smooth, frustrated energy landscape resembling more the energy landscapes present in liquids than in typical solids. This frustrated energy landscape leads to a high diffusion coefficient combining low activation energy with a high pre-factor.
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