Grain-boundary migration in the presence of diffusing impurities: Simulations and analytical models

The mobilities of grain boundaries is a key factor in determining the evolution of polycrystalline microstructures. In most cases, the intrinsic boundary mobility is strongly affected by the presence of impurities. We present a series of simulations of grain-boundary migration in systems without impurities, with static impurities and with impurities that are free to diffuse. The simulations are performed within a kinetic Monte Carlo formalism based upon a simple spin model with interstitial impurities and consider the effects of bulk impurity concentration, impurity diffusivity, interaction strength and temperature. Two regimes of motion were distinguished (at low and high velocities) with a smooth transition between them under all conditions. Contrary to the classical continuum model of impurity drag, the simulation results demonstrate that attractive and repulsive impurity-grain-boundary interactions yield very different grain-boundary mobilities and the domain wall velocity never exhibits sharp jumps. A discrete model is developed that properly describes the transition between regimes and the differences between attractive and repulsive impurities.