Calculations of phenomenological coefficients for matter transport by the matrix method of random walk theory

Abstract

Linear response formulae for the phenomenological coefficients L AA , L AB and L BB for matter transport by single vacancies in a very dilute isotropic alloy of solute B in solvent A are studied by the matrix method of random walk theory familiar in the calculation of impurity correlation factors. A symmetry classification of vacancy jumps based on symmetry with respect to the diffusion axis is introduced and applied to the linear response formulae in order to reduce them to compact forms. For typical models these forms contain a small number of functions K ij which are linear combinations of vacancy migration Green functions for paths between sites of symmetry types i and j that do not pass through the impurity. The K ij are calculated by inversion of a certain matrix of jump probabilities. Detailed calculations are made for models with first- and second-nearest-neighbour vacancy-impurity interactions for BCC, FCC and diamond lattices. The calculations of L AB and L AA are seen to be straightforward extensions of those already familiar in the calculation of L BB and the impurity correlation factor. This suggests that extensions to other crystal structures and migration mechanisms can be made.