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https://doi.org/10.1111/j.1151-2916.1996.tb08568.x

has been cited by the following article:

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

  AUTHORS: Rifa J. El-Khozondar

  KEYWORDS: Monte Carlo Potts Model, Topology Distribution, Polycrystalline, Microstructure, Diffusion Mechanisms

  JOURNAL NAME: Advances in Pure Mathematics, Vol.10 No.9, September 8, 2020

  ABSTRACT: 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.