The role of disorder in facilitating conduction in ionic lattices: insights from Monte Carlo simulations and mean-field modeling

Abstract

Solid-state batteries serve as a strong candidate for the batteries of the future due to their stability and energy density, but most current solid electrolytes suffer from slow ionic conductivity compared with liquid electrolytes. Disorder has been found to play an important role in facilitating fast ionic conduction in solid electrolytes, but there is as of yet no general understanding of how disorder acts to speed conductivity. Furthermore, for an arbitrary solid electrolyte, the extent to which added disorder will help or hinder conductivity is unknown: in some cases, added disorder will increase conductivity, but in others, too much disorder will slow conduction. As such, there is a great need for increased theoretical understanding of the effect that disorder has on conduction, as well as the development of computational tools that can probe the effects of disorder on a candidate solid electrolyte so as to optimally tune its transport properties. In this work, we seek to study the effect of disorder on conduction as well as specify a methodology for probing the effect of added disorder on a system in an approximate manner. We first consider the impact that disorder has on conduction in an idealized model of ionic hopping on a lattice with long-range interactions. We then lay out a procedure for investigating how added disorder will affect conductivity of a lattice with unknown baseline disorder, developing a mean-field model allowing for the mapping of a complex electrolyte to an effective resistor network model. Finally, we consider the problem of estimating average ionic fluxes between sites in the original lattice under limited observations of system residence times for the purpose of tuning and validating the mean-field model for a real electrolyte. This mean-field model serves as a first step toward enabling efficient exploration of the effect that added disorder will have on conductivity in complex solid electrolytes, and as such should be of general use for the automated discovery and optimization of materials.