Phase field simulation of grain growth in three dimensional system containing finely dispersed second-phase particles

Phase field simulations of grain growth in three-dimensional polycrystalline systems containing finely dispersed second-phase particles were executed. Simulations were performed with various volume fractions of the second-phase particles. The fraction of particles located at grain boundaries were evaluated. The limiting grain size 〈Rlim〉 is predicted by 〈Rlim〉 = 1.42r/f0.870, with r the radius and f the volume fraction of the particles. The simulation results are compared with Zener type relations and previous simulation results.