Triple junction drag effects during topological changes in the evolution of polycrystalline microstructures

Experiments, theory and atomistic simulations show that finite triple junction mobility results in non-equilibrium triple junction angles in evolving polycrystalline systems. These angles have been predicted and verified for cases where grain boundary migration is steady-state. Yet, steady-state never occurs during the evolution of polycrystalline microstructures as a result of changing grain size and topological events (e.g., grain face/edge switching - "$T_1$" process, or grain disappearance "$T_2$" or "$T_3$" processes). We examine the non-steady evolution of the triple junction angle in the vicinity of topological events and show that large deviations from equilibrium and/or steady-state angles occur. We analyze the characteristic relaxation time of triple junction angles $\tau$ by consideration of a pair of topological events, beginning from steady-state migration. Using numerical results and theoretical analysis we predict how the triple junction angle varies with time and how $\tau$ varies with triple junction mobility. We argue that it is precisely those cases where grain boundaries are moving quickly (e.g., topological process in nanocrystalline materials), that the classical steady-state prediction of the finite triple junction mobility triple junction angle is inapplicable and may only be applied qualitatively.