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

Microscopic theory of ionic motion in solids