The problem of calculating long time-limit effective diffusivities in stable 2-phase polycrystalline materials was considered for the first time. A phenomenological model was used in which high-diffusivity interphase boundaries were treated as if they were connected coatings on individual grains. The derivation of expressions for the effective diffusivity, with segregation, paralleled a 1904 analysis by Maxwell. Monte Carlo computer simulations, using lattice-based random walks on a very fine-grained mesh, were used to test the validity of the expressions. It was shown that, for the cases analyzed, the expressions which were derived for the effective diffusivity were in very good agreement with results of the simulations. The equivalent of the Hart equation for this problem was also derived. This equation always agreed poorly with the simulation results.

The Effective Diffusivity in Polycrystalline Material in the Presence of Interphase Boundaries. I.V.Belova, G.E.Murch: Philosophical Magazine, 2004, 84[1], 17-28