Time correlation functions of matter transport in a binary random alloy

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Abstract
The time correlation function associated with the phenomenological coefficients for matter transport in a s.c. binary random alloy with a very small vacancy content has been calculated by Monte Carlo simulation, principally for a range of concentrations all with the same atomic jump frequency ratio of ten to one. The corresponding phenomenological coefficients are in good agreement with earlier simulation results from the Einstein formulae. Three approximations to the time correlation function, which lead to well-known approximations for the phenomenological coefficients, are derived from kinetic equations and compared with the simulation results. None of these approximations is really satisfactory; even a self-consistent approximation to the solution of the kinetic equations, which leads to very accurate phenomenological coefficients, does not give a good description of the time correlation function. Simulations of such time correlation functions also allow calculations of the frequency dependence of the phenomenological coefficients. As an example, the frequency-dependent electrical conductivity is calculated from the simulation results and compared with the predictions of the three approximations.