Development of the Statistical Theory of Grain Growth for the General Case of Non-Uniform Grain Boundaries and Textures

Abstract

The development of analytical investigation of curvature driven grain growth processes will be reviewed and ordered by subsequently introducing the parameters grain size, number of sides and crystallographic orientation for characterising the grains. Then by applying all three parameters, i.e. for the case of non-uniform grain boundaries and textures, a statistical theory of grain growth is derived from first principles without additional heuristic assumptions. For transparency sake, the derivation of the present paper are given only for the 2-dimensional case, for some simulations at the end of the paper, however, the expressions resulting for three dimensions are used since they are more important for applications. They show that nonuniformity of grain boundary energy or mobility may lead to dramatic changes of the grain growth behaviour which may assume very different forms depending on the occurring grain boundary mobility and energy.