Rotation-induced grain growth and stagnation in phase-field crystal models

Polycrystalline microstructures are typically formed by thermal processes such as quenching or annealing of melts, through the nucleation and growth of grains of different crystallographic orientation. Since these microstructures have a controlling role on the large scale material properties, it is crucial to understand their formation and late stage evolution. Here we consider the grain growth and stagnation in polycrystalline microstructures using a phase-field crystal model. We identify a transition from a grain growth stagnation upon deep quenching below the melting temperature $T_{m}$ to a continuous coarsening at shallower quenching near $T_{m}$. We find that the grain evolution is mediated by local grain rotations. In the deep quenching regime, the grain assembly typically reaches a metastable state where the kinetic barrier for recrystallization across boundaries is too large and grain rotation with subsequent coalescence or boundary motion is infeasible. For quenching near $T_{m}$ the grain growth depends on the average rate of grain rotation, and follows a power-law behavior with time, with a scaling exponent that depends on the quenching depth.