Monte Carlo calculation of the simultaneous ionic conductivity and tracer diffusion in β-alumina

Abstract

A new Monte Carlo method is described for simultaneously calculating the charge carrier and tracer correlation factors. Application is made to β-alumina where the conduction plane is represented by a lattice gas model in which nearest-neighbour interacting sodium ions diffuse via a vacancy mechanism over two interpenetrating non-equivalent lattices. The charge carrier correlation factor is calculated from the average drift of the ions in an imposed electric field while the tracer correlation factor is calculated from the mean square displacements of tracer ions normal to the field. Results for the charge carrier correlation factor are in good agreement with the Path Probability calculations of Sato and Kikuchi (1971 a, b) but results for the tracer correlation factor differ significantly because of the limitations of the averaging procedure of the pair approximation in the Path Probability method.