Atomic transport in a random alloy from the moments of time correlation functions

Abstract

The phenomenological coefficients for matter transport in a random binary alloy can all be calculated from the time integral of a single time correlation function C(t). Exact expressions for the coefficients (moments) in the Taylor exparkion of C(t) in powers of t have been calculated for terms up to t ⁴. The moments have been used to construct approximations for C(t)) and for the phenomenological coefficients by means of the Mori continued-fraction representation of the Laplace transform, by a method based on a result in the Kirkwood transport theory of liquids, and by means of Pade approximants. The results have been compared with earlier Monte Carlo simulation values. For the first two methods the predictions of phenomenological coefficients are better than those of the path probability expressions of Sat0 and coworkers but do not approach the remarkable accuracy of the Manning theory. The inadequacies of our results arise because the approximate time correlation functions are smaller than the Monte Carlo results at long times.