Local-time formula for dissipation in solid ionic electrolytes

TL;DR

This paper derives a simplified, time-local formula for ion dissipation in solid electrolytes, reducing computational complexity while capturing key material-dependent drag effects.

Contribution

It introduces a novel time-local approximation for non-local ion-phonon interactions in crystalline solids, enabling efficient simulations.

Findings

Time-local formula accurately predicts dissipation rates.

Simplification reduces computational cost significantly.

Material properties influence the drag matrix in the model.

Abstract

When ions move through solids, they interact with the solid's constituent atoms and cause them to vibrate around their equilibrium points. This vibration, in turn, modifies the potential landscape through which the mobile ions travel. Because the present-time potential depends on past interactions, the coupling is inherently non-local in time, making its numerical and analytical treatment challenging. For sufficiently slow-moving ions, we linearize the phonon spectrum to show that these non-local effects can be ignored, giving rise to a drag-like force. Unlike the more familiar drag coefficient in liquids, the drag takes on a matrix form due to the crystalline structure of the framework. We numerically simulate trajectories and dissipation rates using both the time-local and non-local formulas to validate our simplification. The time-local formula dramatically reduces the computational cost of calculating the motion of mobile particle through a crystalline framework and clearly connects the properties of the material to the drag experienced by the particle.