Equation of Motion for a Grain Boundary

Abstract

Grain boundary (GB) migration controls many forms of microstructural evolution in polycrystalline materials. Recent theory, simulations, and experiments demonstrate that GB migration is controlled by the motion of discrete line defects or disconnections. We present a continuum equation of motion for grain boundary derived from the underlying discrete disconnection mechanism. We also present an equation of motion for the junctions where multiple grain boundaries meet - as is always the case in a polycrystal. The resulting equation of motion naturally exhibits junction drag - a widely observed phenomena in junction dynamics in solids and liquids.