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Abstract
The problem of calculating the long-time-limit effective diffusivity in stable two-phase polycrystalline material is addressed for the first time. We make use of a phenomenological model where the high-diffusivity interphase boundaries are treated as connected ‘coatings’ of the individual grains. The derivation of expressions for the effective diffusivity with segregation is along the lines of the analysis by Maxwell in Citation1904. Monte Carlo computer simulation using lattice-based random walks on a very fine-grained mesh is employed to test the validity of the expressions. It is shown that, for the specific cases analysed, the derived expressions for the effective diffusivity are in very good agreement with results from the simulations. Since the pattern of behaviour is not entirely clear at present, it is difficult to guide the choice for the best expression in a given case. The equivalent of the Hart equation for this problem is also derived. This equation is shown to be invariably in poor agreement with simulation results.
Acknowledgements
We wish to acknowledge support for this research from the Australian Research Council under the Large Grants and Discovery Project Grants Schemes. One of us (I.V.B.) wishes to acknowledge the award of a Queen Elizabeth II Fellowship.
Notes
‡In the type-A kinetics regime, the diffusion length is larger than the grain size (for example, Kaur et al. (Citation1995)).
† The Hart equation (Equation7) does not have this formal restriction.