Particle-grain boundary interactions: A phase field study

Abstract

A detailed phase field model is used to investigate particle-grain boundary interactions. The model takes into consideration both the curvature-driven grain boundary motion and particle migration by surface diffusion. The phase field model relaxes all the restrictive assumptions usually employed in the classical and sharp-interface models of the problem. Our 2D and 3D simulations demonstrate that the model captures all possible particle-grain boundary interactions proposed in theoretical models and observed in experiments. For high enough surface mobility, the particles move along with the migrating boundary as a quasi-rigid-body (i.e., without change in shape or size), albeit hindering its migration rate as compared to the particle-free case. For less mobile particles, the migrating boundary can separate from the particles. For the case of steady-state motion of the particles with the migrating boundary, evolution equations for the grain size were derived that predict a strong dependence of the grain growth rate on the number of particles, particle size, and surface diffusivity. For the case of boundary breakaway, the separation condition was found to agree well with predictions from theoretical calculations. However, our results show that non-uniform particle distribution promotes boundary detachment. The results also demonstrate that it is easier for a migrating boundary to separate from a spherical particle than from a cylindrical particle, and hence 2D simulations underestimate boundary breakaway.