Numerical analysis of the vertex models for simulating grain boundary networks

Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical distributions is extremely complex and is strongly influenced by topological changes in the network. This work is an attempt to elucidate the role of these changes by conducting a thorough numerical investigation of one of the simplest types of grain growth simulation models, called vertex models. While having obvious limitations in terms of its ability to represent realistic systems, the vertex model enables full control over topological transitions and retains essential geometric features of the network. We formulate a self-consistent vertex model and investigate the role of microscopic parameters on the mesoscale network behavior. This study sheds light onto several important questions, such as how statistics are affected by the choice of temporal and spatial resolution and rules governing topological changes. Statistical analysis of the data produced by the simulation is performed for both isotropic and anisotropic grain boundary energy.