A dynamic theory for grain rotation in columnar polycrystalline microstructures was developed on the basis of the theory of diffusion-accommodated grain-boundary sliding. The driving force for rotation was the aggregate torque on the grain: the weighted sum of the energy derivatives with respect to the misorientations of all of the boundaries which made up the grain. Rotation was viewed as a sliding problem at the periphery of the grain. The required changes in the grain shape during rotation were assumed to be accommodated by diffusion; either through the grain boundaries or through the grain interiors. This model resulted in an analytical expression for the rate of rotation of a grain of arbitrary shape, as a function of the grain size and temperature. This subsumed a previous result for a regular-hexagon grain shape.

Theory of Diffusion-Accommodated Grain Rotation in Columnar Polycrystalline Microstructures. D.Moldovan, D.Wolf, S.R.Phillpot: Acta Materialia, 2001, 49[17], 3521-32