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

• 作者: Rifa J. El-Khozondar
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Monte Carlo Potts Model Topology Distribution POLYCRYSTALLINE MICROSTRUCTURE Diffusion Mechanisms
• 年，卷（期）: llsxjzyw_2020,（9）
• 页码范围: 471-491
• 页数: 21页
• 分类号: O18

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 </span><span style="font-family:Verdana;">and</span><span style="font-family:Verdana;"> the topological size relation function. It is found that the average number of sides depends proportionally on the volume fraction. It increases as the </span><span style="font-family:Verdana;">volumes</span><span style="font-family:Verdana;"> fraction increases and vice versa. Moreover, it is shown that the grain topology distribution in the self-similar growth regime can be described by </span><span style="font-family:Verdana;">time</span><span style="font-family:Verdana;"> unchanged function of the relative grain size. Additionally, topological size function in the simulated microstructure can be evaluated by a quadratic function.