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.