A 2-dimensional phase-field model which was intended to describe the dynamics of crystalline grains was analyzed. The phenomenological free energy was a function of 2 order-parameters; one of which reflected the orientational order while the other reflected the local orientation of the crystal. The gradient flow of this free energy was then considered. The solutions could be interpreted as representing ensembles of grains, in which the orientation was constant in space, separated by grain boundaries. The dynamics of the boundaries, as well as the rotation of the grains, were studied. In the limiting case of an infinitely sharp interface, the normal velocity of the boundary was proportional to its curvature and energy. Formulae were obtained for the interfacial energy and mobility, and their behavior was studied in the limit of small misorientations. The rotation rate of a grain in the sharp interface limit was calculated, and was found to depend sensitively upon the choice of model.

Sharp Interface Limit of a Phase-Field Model of Crystal Grains. A.E.Lobkovsky, J.A.Warren: Physical Review E, 2001, 63[5], 051605 (10pp)