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Expressions for the effective diffusivity in materials with interphase boundaries

Published online by Cambridge University Press:  15 March 2011

Irina V. Belova and
Graeme E. Murch
Irina V. Belova
Affiliation:
Diffusion in Solids Group, School of Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia
Graeme E. Murch
Affiliation:
Diffusion in Solids Group, School of Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia
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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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