A phase-field model for diffusion-induced grain-boundary motion

Abstract We model diffusion-induced grain boundary motion (DIGM) with a pair of differential equations: Download : Download high-res image (9KB) Download : Download full-size image Here u represents the concentration of solute atoms, ∅ takes the values + 1 and − 1 in the two perfect crystal grains and intermediate values in the boundary between them, τ, δ and e are constants characterizing the material, p(∅, u) is an interaction energy density, and the diffusivity D(∅) is large in the grain boundary (−1

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