A New Perspective on the Grain Growth Exponent Obtained in Two-dimensional Monte Carlo Simulations
Yu, Q. & Esche, S. K.
Modelling and Simulation in Materials Science and Engineering, Vol. 11, No. 6, pp. 859-862, 2003.
Abstract
The standard two-dimensional Monte Carlo method reproduces the structural self-similarity of the normal grain growth within a range of the grain radius from 3 to 15.
Grain growth exponents close to n = 0.5 can be obtained by using appropriate subsets of the simulation data in the regression analysis.
This result confirms earlier theoretical predictions of the parabolic nature of the grain growth law.
The small values for the grain growth exponent n obtained in previous studies are attributable to the following two reasons.
Firstly, it is shown in this paper that the initial grain radius at t = 0 MCS can be much larger than the nominal value of 1 that was previously used to justify the application of log-log plots of vs. t for calculating the grain growth exponent n, and for grain radii less than 15, a grain growth law including a term for the initial grain radius should thus be employed for the regression analysis.
Secondly, due to the inherent random nature of the Monte Carlo method, the obtained grain radius vs. time data fluctuate around a parabolic function.
Sometimes these local fluctuations are large enough to seriously distort the results of the regression analysis, and then subsets of the simulation data that exclude these fluctuations must be used in order to calculate satisfactory approximations for the grain growth exponent n.