Expressions for the effective diffusivity in materials with interphase boundaries

Abstract

We address the problem of calculating the long-time-limit effective diffusivity in stable two-phase polycrystalline material. A phenomenological model is used where the high diffusivity interphase boundaries are treated as connected 'coatings' of the individual grains. Derivation of expressions for the effective diffusivity with segregation is made along Maxwell lines. Monte Carlo simulation using lattice-based random walks is used to test the validity of the expressions. It is shown that for the case analysed the derived expressions for the effective diffusivity are in very good agreement with simulation results. The equivalent of the Hart equation is also derived. It is shown to be in poor agreement with simulation results.

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Acknowledgments

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 Queen Elizabeth II and Professorial Fellowships.

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Correspondence to Irina V. Belova.

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Belova, I.V., Murch, G.E. Expressions for the effective diffusivity in materials with interphase boundaries. MRS Online Proceedings Library 819, 314 (2004). https://doi.org/10.1557/PROC-819-N3.14

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