Affiliations: Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ, USA
Correspondence:
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Corresponding author: Sven K. Esche, Stevens Institute of Technology, Department of Mechanical Engineering, Castle Point on Hudson, Hoboken, NJ 07030, USA. Tel.: +1 201 216 5559; Fax: +1 201 216 8315; E-mail: SEsche@stevens.edu.
Abstract: Monte Carlo (MC) Potts models have been widely used to study various microstructural phenomena. The efficiency and accuracy of the method is very critical in order to apply it to industrially relevant engineering problems. This paper provides new insights into the conventional MC (CMC) 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 significantly affects the microstructural evolution leading to low grain growth exponents. We show 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 CMC algorithm is partially responsible for the lower values of the grain growth exponent. A three-parameter nonlinear regression analysis is used 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.
Keywords: Monte Carlo method, Potts model, grain growth, regression analysis, growth kinetics
