Monte Carlo evaluation of the diffusion correlation factor in concentrated lattices and comparison with an improved theory.

Abstract

A theoretical discussion of the difficulty inherent in obtaining an accurate estimate of the tracer diffusion correlation factor in concentrated, single-component systems from Monte Carlo data involving relatively short runs is given. The theory is tested on the available Monte Carlo data of Murch, who used runs lasting approximately 50 Monte Carlo steps per particle (MCS/p). To avoid these difficulties, new precision Monte Carlo data, collected from runs lasting 500 MCS/p, are supplied. The relevant estimates for the diffusion correlation factor are compared with those supplied by a properly renormalized version of the earlier theory, which also includes the small but noticeable effects of spatial constraints on the scattering of a coupled tracer-vacancy pair. The agreement between the improved theory and the numerical estimates is within the overall precision, 2 parts per thousand, of the new Monte Carlo experiments.