Simple Geometrical Aspects of Grain Growth in the Framework of Herring’s Analysis and a Disclination Model

Abstract

The time change of the area of a single grain is calculated in 2D by applying Herring’s analysis. The grain is a regular n-sided polygon with its corners representing triple junctions (TJs). The resulting change of grain area is compared to the Von Neumann–Mullins analysis, where grain boundaries (GB) are curved and angles at TJs are equilibrium angles. The rates of area change are similar with the largest deviation for triangles. For both cases of different angles at TJs polygons with n 6 grow. Pieces of evidence are provided for describing the GB-movement by disclination generation and motion due to thermal fluctuations. Thus besides energy considerations a stochastic element comes into play.