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A Free-Boundary Model for Duffusion-Induced Grain Boundary Motion



P C. Fife, John W. Cahn, C M. Elliott


On the basis of a phase-field model previously proposed in Cahn et al. (acta Mater. 45, 4397-4413 (1997)) to describe the phenomenon of diffusion-induced grain boundary motion (DIGM), we present a formal asymptotic reduction to a moving free boundary problem. This problem is one of enhanced motion by curvature. The enhancement depends on the local concentration jump across the grain boundary of a solute species that is diffusing along the boundary.A rigorous theory is given for two-dimensional solutions of the free-boundary problem when there is steady motion of the grain boundary spanning a plate from face to face, solute being supplied at the faces of the plate. The motion is in the directional parallel to the face. This situation represents well known experiments designed to illustrate DIGM. The corresponding theory is also given for grain boundaries which do not span the plate, but rather trail behind the moving intersection with one of the faces, never reaching the other one.
Journal of Interfaces and Free Boundary Problems


asymptotics, diffusion, free boundary problem, grain boundary motion, motion by curvature


Fife, P. , Cahn, J. and Elliott, C. (2002), A Free-Boundary Model for Duffusion-Induced Grain Boundary Motion, Journal of Interfaces and Free Boundary Problems (Accessed June 18, 2024)


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Created December 31, 2001, Updated October 12, 2021