Microscopic theory of ionic motion in solids

TL;DR

This paper develops a microscopic theoretical framework for ionic motion in solids, linking thermal fluctuations, drag, and diffusion to estimate ionic conductivities and aid in designing solid electrolytes.

Contribution

It introduces a tensorial microscopic theory of ionic transport in solids based on a solid-state Hamiltonian and non-equilibrium path integral formalism.

Findings

Derived a relation between force variance and friction tensor.

Formulated ionic mobility in terms of crystal potential profiles.

Provides a basis for designing solid electrolyte materials.

Abstract

Drag and diffusion of mobile ions in solids are of interest for both purely theoretical and applied scientific communities. This article proposes a theoretical description of ion drag in solids that can be used to estimate ionic conductivities in crystals, and forms a basis for the rational design of solid electrolyte materials. Starting with a general solid-state Hamiltonian, we employ the non-equilibrium path integral formalism to develop a microscopic theory of ionic transport in solids in the presence of thermal fluctuations. As required by the fluctuation-dissipation theorem, we obtain a relation between the variance of the random force and friction. Because of the crystalline nature of the system, however, the two quantities are tensorial. We use the drag tensor to write down the formula for ionic mobility, determined by the potential profile generated by the crystal's ions.