Solids that are also liquids: elastic tensors of superionic materials

Superionics are fascinating materials displaying both solid- and liquid-like characteristics: as solids, they respond elastically to shear stress; as liquids, they display fast-ion diffusion at normal conditions. In addition to such scientific interest, superionics are technologically relevant for energy, electronics, and sensing applications. Characterizing and understanding their elastic properties is, e.g., urgently needed to address their feasibility as solid-state electrolytes in all-solid-state batteries. However, static approaches to elasticity assume well-defined reference positions around which atoms vibrate, in contrast with the quasi-liquid motion of the mobile ions in fast ionic conductors. Here, we derive the elastic tensors of superionics from ensemble fluctuations in the isobaric-isothermal ensemble, exploiting extensive Car-Parrinello simulations. We apply this approach to paradigmatic Li-ion conductors, and complement with a block analysis to compute statistical errors. Static approaches sampled over the trajectories often overestimate the response, highlighting the importance of a dynamical treatment in determining elastic tensors in superionics.