It was noted that the phenomenological coefficients, Lij, of non-equilibrium thermodynamics, which characterized atom transport near to thermodynamic equilibrium, could be expanded in terms of so-called collective cosines. A typical example was <cosji(n)>, which was defined 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 were exactly n jumps of atoms of species-i which followed the initial j-atom jump. Here, n was equal to 1, 2, 3, ... New exact relationships between the 4 quantities for i,j = A, B, and arbitrary n, were derived for a binary random alloy of 2 atomic species (A, B), in which transport involved a very small concentration of vacancies. A new simplified formula for the off-diagonal coefficient, Lij, j  i, was also derived in terms of these collective cosines. An approximate calculation of the collective cosines, via the enumeration of random walks, was considered. The results for n = 1, 2 and 3 were found to be in very good agreement with earlier Monte Carlo simulation results for jump frequency ratios (of the 2 atom components) of 0.1 and 0.01.

Z.Qin, A.R.Allnatt: Philosophical Magazine A, 1995, 71[2], 307-21