Collective correlation effects in solid-state diffusion

Abstract

Collective correlation factors are the correlated part of the phenomenological coefficients of irreversible thermodynamics. It is shown that collective correlation factors can be expressed in a manner similar to tracer correlation factors, that is they are associated with the collective cosines of the angle between successive jumps. These collective cosines can be determined by following a step-by-step walk of a vacancy. Illustrative calculations are performed on a binary random alloy with a vanishingly small concentration of vacancies in a simple-cubic lattice to an approximation that the vacancy will become random after six jumps. The results are found to fall between the data predicted by Manning and by Sato and coworkers over a large concentration region and for various exchange frequency ratios. When CA → 1, the present study gives the exact value for collective correlation factor for a pure system and, when CA → 0 and ω_A = ω_B, the present result is coincident with the known value for f₀ for the same number of vacancy jumps.