Sharp Interface Limit of a Phase-Field Model of Crystal Grains
A E. Lobkovsky, James A. Warren
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a function of a complex order parameter whose amplitude reflects the orientational order. Its phase is the predominant local orientation of the crystal. We consider the gradient flow of this free energy. Solutions can be interpreted as ensembles of grains (in which the phase of the order parameter is approximately constant in space) separated by grain boundaries. We study the dynamics of the boundaries as well as the rotation of the grains. In the limit of the infinitely sharp interface, the normal velocity of the boundary is proportional to both its curvature and itsenergy. We obtain explicit formulas for the interfacial energy and mobility and study their behavior in the limit of a small misorientation. We calculate the rate of rotation of a grain in the sharp interface limit and find that it depends sensitively on the choice of the model.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
and Warren, J.
Sharp Interface Limit of a Phase-Field Model of Crystal Grains, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=850051
(Accessed November 30, 2023)