Impurity effects on grain boundary migration

Abstract

Experiments show that the impurities can drastically change grain boundary mobilities in a non-trivial manner. The most widely used type of theoretical model for impurity effects on boundary migration is a one-dimensional, continuum model, based upon several simplifying assumptions. Although several of these assumptions can be relaxed, these models cannot adequately describe realistic situations and are not quantitative. Since grain boundary mobility depends on several atomic-scale properties that are difficult to reliably extract from experiments (or calculate from a first principles method), it is not currently possible to make a quantitative comparison between theoretical models and experiment. Dynamic atomistic (MD) simulations do not provide a practical alternative because of the need to include such slow processes as long range diffusion and boundary migration. An alternative approach is based upon simple spin (extended Ising) models and kinetic Monte Carlo. This provides a concrete model against which the prediction of the continuum theory can be compared in a situation where all microscopic physical properties are known. Such simulations show that the key deficiencies of the continuum models are the assumption that intrinsic and impurity drag effects can be superimposed and not considering the mechanism of grain boundary migration. Analytical theories that address these two deficiencies are capable of reproducing the effects of impurities on boundary mobility seen in the simulations. Simple simulations provide rigorous tests against which new theories should be compared.