Grain growth prediction with inclination dependence of 〈1 1 0〉 tilt grain boundary using multi-phase-field model with penalty for multiple junctions

Multi-phase-field (MPF) model with a higher-order term representing energetic penalty for multiple junctions was proposed to predict the grain growth accompanying the inclination dependence of grain boundary (GB) energy and mobility. The inclination effect was introduced on the basis of GB energy obtained from molecular dynamics (MD) simulations. The preliminary grain growth simulation of an isolated grain surrounded by Σ3 GB certified that the analytical equilibrium shape was well reproduced. The augmented higher-order term added to conventional MPF model could improve convergence and stability of numerical calculations around triple junction (TJ) region even if there exists the large GB energy gap at the TJ. Moreover, the present MPF model can realize well the Young’s relation with no GB inclination effect and further extend to the case with that effect. For the polycrystalline grain growth simulations with the GB energy distribution according to the misorientation angle of Al 〈1 1 0〉 tilt GB, Σ3 GB inclination lead the weak anisotropy characterized by Σ3{111} twin boundary. Besides, the inclination dependence can effectively drive the GBs with low GB energy like the low-angle GB during grain growth.