The Sato and Kikuchi (1971) calculation of the sodium tracer diffusion coefficient in beta-alumina, using the path probability method, was assessed using a Monte Carlo method. Two interpenetrating non-equivalent triangular sub-lattices make up the honeycomb lattice on which sodium ions were distributed subject to nearest-neighbor repulsion. The Monte Carlo results for the vacancy availability factor and the effective jump frequency factor were in excellent agreement with the calculations of Sato and Kikuchi. Results for the tracer correlation factor differed significantly because of the limitations of the pair-approximation to the path probability method.

Monte Carlo Study of Sodium Diffusion in Beta-Alumina. G.E.Murch, R.J.Thorn: Philosophical Magazine, 1977, 36[3], 517-27