Phase-field theory of grain growth in the presence of mobile second-phase particles

We have developed a phase-field model for grain growth in the presence of mobile second-phase particles. In this model, each grain and particle is represented by a unique order parameter. The grain boundaries sweep the mobile particles during grain growth. The particle velocity is taken to be proportional to the driving force arising from the curvature of the phase boundary in the neighborhood of the particle. The proportionality factor is the constitutive parameter representing the mobility of the particle. We first study the model in a one-dimensional axisymmetric setting and compare the results with theoretical calculations. We then study the interaction of a bicrystal grain boundary with a dilute distribution of particles. Finally we show the effect of particles on polycrystalline grain growth.