Quantitative evaluation of particle pinning force on a grain boundary using the phase-field method

Second-phase particles are often employed to inhibit the grain growth of polycrystalline materials. We studied the interaction between a second-phase particle and a grain boundary using the phase-field method. In particular, we determined the magnitude of pinning force exerted by a particle on a grain boundary. We considered the effect of particle morphology by examining several particle shapes including spherical, ellipsoidal and cubic. The pinning forces computed from the phase-field were compared with available analytical theories for spherical and ellipsoidal particle shapes. We derived an expression for the pinning force of a grain boundary by a cubic particle and compared the prediction with phase-field simulations. The present results should be useful for evaluating the effect of particle morphology on the effectiveness of grain growth inhibition by second-phase particles.