Influence of lattice dynamics on lithium-ion conductivity: A first-principles study

In the context of novel solid electrolytes for solid-state batteries, first-principles calculations are becoming increasingly more popular due to their ability to reproduce and predict accurately the energy, structural, and dynamical properties of fast-ion conductors. In order to accelerate the discovery of new superionic conductors is convenient to establish meaningful relations between ionic transport and simple materials descriptors. Recently, several experimental studies on lithium fast-ion conductors have suggested a correlation between lattice softness and enhanced ionic conductivity due to a concomitant decrease in the activation energy for ion migration, $E_{a}$. In this article, we employ extensive \emph{ab initio} molecular dynamics simulations based on density functional theory to substantiate the links between ionic transport and lattice dynamics in a number of structurally and chemically distinct lithium superionic conductors. Our first-principles results show no evidence for a direct and general correlation between $E_{a}$, or the hopping attempt frequency, and lattice softness. However, we find that, in agreement with recent observations, the pre-exponential factor of lithium diffusivity, $D_{0}$, follows the Meyer-Neldel rule $\propto \exp{\left(E_{a}/\langle \omega \rangle\right)}$, where $\langle \omega \rangle$ represents an average phonon frequency. Hence, lattice softness can be identified with enhanced lithium diffusivity but only within families of superionic materials presenting very similar migration activation energies, due to larger $D_{0}$. On the technical side, we show that neglection of temperature effects in first-principles estimation of $E_{a}$ may lead to huge inaccuracies of $\sim 10$\%. The limitations of zero-temperature harmonic approaches in modeling of lithium-ion conductors are also illustrated.