Grain Growth in Large-Scale Molecular Dynamics Simulation: Linkage between Atomic Configuration and von Neumann-Mullins Relation

Abstract

Grain growth in nanometer scale is closely investigated with a combination of a large-scale molecular dynamics (MD) simulation and a comprehensive post-analysis technique. The volume change of grains is directly estimated for all grains in two-dimensional and three dimensional grain growths. For the two-dimensional grain growth, grains with seven and more neighboring grains generally grow larger, whereas those with five and less neighboring grains shrink and some of them disappear within the timescale of the simulation. The result agrees with the von Neumann–Mullins relation. For the three-dimensional grain growth, threshold number of neighboring grains is estimated to be approximately 14, which is close to many of reported values from previous experiments and simulations. An extended model of the von-Neumann-Mullins relation for the three-dimensional grain growth is derived based on the MacPherson-Srolovitz model, from which the threshold number of neighboring grains is estimated to be 14.7. Using the von Neumann–Mullins relation, grain boundary mobility is estimated to be in the order of 10 × 10^-9 m⁴J^-1s^-1, which is within the range of reported values. Results and discussion derived from the large-scale MD simulation basically agree with the classical theory, which proofs the validity of simulation results from the statistical point of view, whereas most of present MD studies still limits the discussion to the local structure around of particular grain boundaries due to the size limitation. The quantitative discussion based on the large-scale MD simulation is largely attributable to the rapid progress in high-performance computational environments.