Monte Carlo Simulations of Topological Properties in Two-Phase Polycrystalline Materials for Several Diffusion Mechanism

作     者：Rifa J. El-Khozondar Rifa J. El-Khozondar

作者机构：Physics Department Al-Aqsa University Gaza Palestine 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2020年第10卷第9期

页      面：471-491页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Monte Carlo Potts Model Topology Distribution Polycrystalline Microstructure Diffusion Mechanisms 

摘      要：Numerical simulations by means of the Monte Carlo Potts model have been provided to simulate grain structures in two-phase polycrystalline materials. The topological features in the simulated microstructure analyzed for different diffusion mechanisms over a broad range of volume fractions for both phases. The topological properties include the average number of sides, grain topology distribution and the topological size relation function. It is found that the average number of sides depends proportionally on the volume fraction. It increases as the volumes fraction increases and vice versa. Moreover, it is shown that the grain topology distribution in the self-similar growth regime can be described by time unchanged function of the relative grain size. Additionally, topological size function in the simulated microstructure can be evaluated by a quadratic function.