Cellular Automata (CA) Method for Grain Growth Modeling

The Cellular Automata (CA) method-based grain growth model is a mathematical framework for studying the evolution of crystalline structures in materials. Cellular automata provide a discrete modeling approach governed by simple rules, capable of simulating complex natural phenomena such as crystal growth. This model establishes fundamental growth rules including crystal face growth rates and grain boundary movements to simulate crystal development processes. In code implementation, the CA algorithm typically involves defining a grid structure where each cell represents a microscopic region, with state transitions determined by neighbor interactions using Moore or von Neumann neighborhoods. Key computational aspects include tracking orientation indices, calculating local energy minimization, and implementing probabilistic transition rules for recrystallization. Currently, this model is widely applied in materials science research areas such as alloy grain growth studies and investigations into strengthening mechanisms of metallic materials.