Study on topological properties in two-dimensional grain networks via large-scale Monte Carlo simulation

In order to understand the topological properties in grain networks, Monte Carlo-Potts model is employed to simulate the normal grain growth in a large scale of 10,000 × 10,000. The topological analysis of 103,849 simulated grains shows strong support to the generalized Aboav-Weaire relationship, which is consistent with the experimental observation in single-phase materials. It was found that the grain size and edge distribution in the system follow Weibull and Lognormal functions, respectively. The mean grain area is related to the edge number by a curve slightly concave upward. For different edge class n, the edge distribution in its first-nearest neighbor layer follows Lognormal function with different parameters, while the edge distributions in the neighbor layers beyond the first follow a same Lognormal function.