Using LAMMPS to shed light on Haven’s ratio: Calculation of Haven’s ratio in alkali silicate glasses using molecular dynamics

Abstract

Haven and Verkerk studied the diffusion of ions in ionic conductive glasses with and without an external electric field to better understand the mechanisms behind ionic conductivity. In their work, they introduced the concept now known as Haven’s ratio (HR), which is defined as the ratio of the tracer diffusion coefficient (Dself) of ions to the diffusion coefficient from steady-state ionic conductivity (Dσ), calculated by the Nernst–Einstein equation. Dσ can be challenging to obtain experimentally because the number of charge carriers has to be implied, a subject still under discussion in the literature. Molecular dynamics (MD) allows for direct measurement of the mean squared displacement (r2) of diffusing cations, which can be used to calculate D, avoiding the definition of a charge carrier. Using MD, the authors have calculated the r2 of three alkali ions (Li, Na, and K) at different temperatures and concentrations in silicate glass, with and without the influence of an electric field. Results found for HR generally fell close to 0.6 at lower concentrations (x = 0.1) and close to 0.3 at higher concentrations (x = 0.2 and 0.3), comparable to the literature, implying that the electric field introduces new mechanisms for the diffusion of ions and that MD can be a powerful tool to study ionic diffusion in glasses under external electric fields.