Intrinsic grain boundary mobility tensor from three-dimensional interface random walk

In recent years, studies have demonstrated that the grain boundary (GB) migration is a three-dimensional (3D) process, characterized by a 3D mobility tensor. In this study, we develop a 3D interface random walk theory to extract the GB mobility and shear coupling tensors at equilibrium state based on the random walk of the GB position. Using this approach, we mathematically prove the symmetry of the GB mobility tensor in the case of overdamped GB migration. The theory and its conclusions align with molecular dynamics simulation results and disconnection analysis, and the extracted GB mobility and shear coupling tensors reflect the intrinsic GB properties, unaffected by the large driving forces in atomistic simulations. Additionally, we refined the fast adapted random walk (FAIRWalk) method, enabling efficient extraction of the GB mobility tensor from fewer simulations while maintaining high accuracy. Building on this advancement, we conducted an extensive survey of the mobility, shear coupling, and activation energy for the migration of 388 coincidence-site lattice Ni GBs in the Olmsted database. Several intriguing phenomena were observed, including temperature-induced sudden emergence, disappearance, or inversion of shear coupling; GBs with "zero" normal mobility but high shear mobility; and a non-linear relationship between activation energy and mobility. These findings challenge the traditional understanding of GB migration and warrant further investigation.