Morphology of grain growth in response to diffusion induced elastic stresses: cubic systems

Abstract

In diffusion-induced recrystallization (DIR), diffusion of a misfitting solute produces coherency strains in a solid and can lead to nucleation of new grains. The local interface velocity of the newly nucleated grains depends only on the magnitude of the reduction in the elastic energy density of the coherently stressed solid ahead of the migrating grain boundary, which in turn depends only on the local interface normal of the shrinking grain. Real-space calculations of the orientation-dependent elastic energy density are outlined in general and specific results are given for cubic systems. The method of characteristics described recently by Cahn, Taylor and Handwerker is employed to obtain predictions of the evolution in grain shape with time and the range of possible limiting growth shapes in terms of the edges and corners which develop on any growing grain. When the growing grain is free of elastic strains, the possible morphologies depend on only two parameters: the elastic anisotropy α (≡2( s 11 − s 12)/ S 44), and normalized linear compressibility β( s 11 + 2 s 12)/ S 44). When the elastic anisotrophy α > 1, the morphology tends to be cuboidal, but the exact shape is found to depend on the value of the linear compressibility. For α < 1, the morphology tends to be octahedral.