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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
E.W. Hart, Acta Metall., 5, 597 (1957).
A.J. Mortlock, Acta Metall., 8, 132 (1960).
I. Kaur, Y. Mishin and W. Gust, Fundamentals of Grain and Interphase Boundary Diffusion (Wiley, 1995).
I.V. Belova and G.E. Murch, J. Phys. Chem. Solids, 64, 873 (2002).
I.V. Belova and G.E. Murch, J. Metastable Nanocrystalline Materials, 19, pp 25–34 (2004).
I.V. Belova and G.E. Murch, Interface Science, 11, 91 (2003).
J.C. Maxwell 1904, Treatise on Electricity and Magnetism, 3rd Ed. (Clarendon Press, 1904).
J.R. Kalnin, E.A. Kotomin and J. Maier, J. Phys. Chem. Solids, 63, 449 (2002).
A.D. Brailsford and K.G. Major, Brit. J. Appl. Phys., 15, 313 (1964).
A. Einstein, Ann. Physik, 17, 549 (1905).
G.E. Murch, Diffusion in Crystalline Solids, edited by G.E. Murch and A.S. Nowick (Academic Press, 1984) pp 379–427.
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.
About this article
Cite this article
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