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A Mathematical Formulation for Interfacial Diffusion, Incorporating Deviation from the Classical Random Walk Theory

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Abstract:

Fisher’s model for grain boundary diffusion considers the lattice and the grain boundary on the same basis by presuming the validity of Fick’s second law for both cases, despite the significant structural differences between them. Recent studies [1-3] have, however, shown that grain boundary diffusion is profoundly different from lattice diffusion. We propose an alternative mathematical formulation that incorporates these structural differences and consequently models grain boundary diffusion phenomena more accurately than Fisher’s model. This is achieved by considering possible deviations from the classical random walk for solute atoms diffusing through grain boundaries. This formalism can also be applied to surface diffusion and triple junction diffusion.

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Periodical:

Defect and Diffusion Forum (Volume 266)

Pages:

63-71

DOI:

https://doi.org/10.4028/www.scientific.net/DDF.266.63

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Online since:

September 2007

Authors:

N.S. Raghavan, A.H. King

Keywords:

Anomalous Diffusion, Fick's Law, Fractional Diffusion Equation, Grain Boundary Diffusion, Random Walk, Sub-Diffusion, Super- Diffusion

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© 2007 Trans Tech Publications Ltd. All Rights Reserved

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