RANDOM-WALK ANALYSIS OF THE COLLECTIVE COSINE FORMULATION OF CORRELATION-EFFECTS IN ATOM TRANSPORT IN A CONCENTRATED ALLOY

The phenomenological coefficients L(ij), which are defined in non-equi librium thermodynamics and which characterize atom transport near ther modynamic equilibrium, can be expanded in terms of so-called collectiv e cosines. A typical such quantity is [cos theta(ji)((n))] which is de fined as the average of the cosine of the angle between the direction of an initial jump of an atom of species j and a final jump of an atom of species i when there are exactly n jumps of atoms of species i fol lowing the initial j atom jump and n = 1,2, 3,.... New exact relations between the four quantities [cos theta(ji)((n))], for i,j = A, B and arbitrary n are derived for a binary random alloy of two atomic specie s (A, B) with transport by a very small concentration of vacancies. A new simplified formula for the off-diagonal coefficient L(ij),j i i, i s also derived in terms of these collective cosines. The approximate c alculation of the collective cosines by enumeration of random walks is examined; results for n = 1, 2 and 3 are in very good agreement with earlier Monte Carlo simulation results for jump frequency ratios of th e two atom components of 0.1 and 0.01.