Vertex models for two-dimensional grain growth

Abstract

We develop two-dimensional vertex models which are expected to capture the essential ingredients of the long-time behaviour of two-dimensional grain growth and permit efficient large-scale computer simulations. Such simulations are carried out starting with the initial 24 000 randomly chosen Voronoi cells. We confirm the 1/2 power law for the growth of average grain size. We also find the normalized grain-size distribution and the edge number distribution which exhibit stationary behaviour at long times except for small-amplitude oscillatory behaviour for the latter.