The problem of calculating the long-time-limit effective diffusivity in stable two-phase polycrystalline material was addressed for the first time. Use was made of a phenomenological model where the high-diffusivity interphase boundaries were treated as connected 'coatings' of the individual grains. The derivation of expressions for the effective diffusivity with segregation was along the lines of the analysis by Maxwell (1904). Monte Carlo computer simulation using lattice-based random walks on a very fine-grained mesh was employed to test the validity of the expressions. It was shown that, for the specific cases analyzed, the derived expressions for the effective diffusivity were in very good agreement with results from the simulations. Since the pattern of behavior was not entirely clear at present, it was difficult to guide the choice for the best expression in a given case. The equivalent of the Hart equation for this problem was also derived. This equation was shown to be invariably in poor agreement with 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