Onsager's coefficients and diffusion laws—a Monte Carlo study

Abstract

For a numerical description of multicomponent diffusion processes, the coefficients of the Onsager diffusion matrix are needed. We compare a number of models relating these parameters to experimentally accessible quantities, such as tracer diffusion coefficients. Since these models present different levels of approximation, we investigate the differences in Onsager parameters when they are determined from tracer diffusion. Moreover, we study an ideal solution alloy by Monte Carlo methods to determine the Onsager coefficients directly and using the model assumptions. Measuring atomic fluxes and site fraction gradients, our simulation method is more closely related to a real physical experiment than the usual simulation method of generalized Einstein equations. Onsager's variation principle for the calculation of the kinetic coefficients is extended and it is shown that a reasonable description, even of a simple alloy system, requires consideration of a non-diagonal dissipation matrix in the derivation of the diffusion equations.

Acknowledgement

The numerical results presented in this work were obtained using the computational resources of the Schroedinger cluster of the University of Vienna.