Theory of diffusion-accommodated grain rotation in columnar polycrystalline microstructures

A dynamical theory of grain rotation in columnar polycrystalline microstruc tures is developed based on the theory of diffusion-accommodated grain-boun dary 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 th e grain boundaries delimiting the grain. Analogous to the Raj-Ashby theory. grain rotation is viewed as a sliding problem on the periphery of the grai n; 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 rat e 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-hexaggonal grain shape. (C) 2001 Pub lished by Elsevier Science Ltd on behalf of Acta Materialia Inc.