On the Accuracy of Monte Carlo Potts Models for Grain Growth
Yu, Q., Nosonovsky, M. & Esche, S. K.
Journal of Computational Methods in Sciences and Engineering, Vol. 8, No. 4-6, pp. 227-243, 2008.
Abstract
Monte Carlo Potts models have been widely used in scientific studies of various microstructural phenomena.
In order to successfully apply the Monte Carlo method for solving industrially relevant engineering problems, the efficiency and accuracy of the method is very critical.
This paper provides some new insights into the conventional Monte Carlo algorithm for grain growth.
It was believed earlier that an unphysical finite-size effect is likely to dominate the simulated grain growth in small grain size regimes and that the decrease of the probability for successful reorientation attempts also significantly affects the microstructural evolution.
Here, it is shown that the simulated grain growth is affected by the decrease of this probability only in the very early stage, and furthermore that no such unphysical finite-size effect is observed.
Alternatively, the strong random nature of the conventional Monte Carlo algorithm is identified to be partially responsible for the lower values of the grain growth exponent.
A three-parameter nonlinear regression analysis is appropriate in order to obtain the classical power-law grain-growth kinetics with a more accurate growth exponent.
Therefore, large lattice systems are not required for accurate modeling of the microstructure evolution, which reduces the computing time considerably, especially for three-dimensional applications.