Geometric origin of particle and dislocation dynamics during grain boundary migration

Abstract

Grain boundaries are complex defects in polycrystalline systems and their migration has a key role in determining the properties of such solids. Understanding grain boundary motion in terms of both particle and dislocation dynamics remains a central problem. Here we establish a fundamental geometric principle governing grain boundary migration at the microscopic level: particles preferentially transition between grains at specific lattice equivalence points identified through a refined O-lattice construction. We validate this principle using loop-shaped grain boundaries in two-dimensional colloidal crystals created with holographic optical tweezers and computer simulations. Building on this principle, we develop a geometric framework that accurately predicts the microscopic dynamics of both particles and dislocations during grain boundary migration. Our results shed light on the microscopic mechanism of grain boundary migration and reveal the intrinsic connection between the dynamics of particles and dislocations.