Theory of diffusion-accommodated grain rotation in columnar polycrystalline microstructures

Abstract A dynamical theory of grain rotation in columnar polycrystalline microstructures is developed based on the theory of diffusion-accommodated grain-boundary sliding by Raj and Ashby. The driving force for rotation of any given grain is given by the aggregate torque on the grain, i.e., by the weighted sum of the energy derivatives with respect to the misorientations of all the grain boundaries delimiting the grain. Analogous to the Raj–Ashby theory, grain rotation is viewed as a sliding problem on the periphery of the grain; the necessary changes in the grain shape during rotation are assumed to be accommodated by diffusion either through the grain boundaries or through the grain interiors. Our main result is an analytic expression for the rate of rotation of a grain of arbitrary shape as a function of the grain size and temperature. This expression reduces to an earlier result of Harris et al . for the special case of a regular-hexagonal grain shape.