Phase field simulations of grain growth in two-dimensional systems containing finely dispersed second-phase particles

The pinning effect of small incoherent particles on grain growth in two-dimensional polycrystalline systems has been simulated using a phase field model. Simulations were performed for different sizes and area fractions of the second-phase particles and for two types of initial microstructure and different initial grain sizes. The grain size distribution and the number of particles located at grain boundaries were determined as a function of time. When particles are present during the nucleation of the grains, most particles are located at grain boundaries and the final mean grain radius R¯lim is predicted by R¯lim=1.28r/fa0.50, with r the radius and fa the area fraction of the particles. When particles nucleate homogeneously in a polycrystalline system with initial grain radius R¯0, many particles lie within the grains and the final grain size depends on R¯0. It was also observed that the peak of the normalized grain size distribution shifts towards smaller grain sizes due to the pinning effect. The simulation results are compared with theoretical relations, previous simulation results and experimental data for thin films from the literature.