It was noted that the coefficients of the Onsager diffusion matrix were needed for the numerical description of multi-component diffusion processes. A number of models relating these parameters were compared with experimentally accessible quantities such as tracer diffusion coefficients. Since these models represented differing levels of approximation, the differences in Onsager parameters which were deduced from tracer diffusion were investigated. An ideal solution alloy was studied by using Monte Carlo methods to determine the Onsager coefficients directly. By measuring atomic fluxes and site fraction gradients, these simulations were more closely related to a real physical experiment than was the usual simulation method involving generalized Einstein equations. Onsager's variational principle for the calculation of kinetic coefficients was extended, and it was shown that a reasonable description -  even of a simple alloy system - required consideration of a non-diagonal dissipation matrix in the derivation of the diffusion equations.

Onsager’s Coefficients and Diffusion Laws - a Monte Carlo Study. M.A.Hartmann, R.Weinkamer, P.Fratzl, J.Svoboda, F.D.Fischer: Philosophical Magazine, 2005, 85[12], 1243-60