A finite element method for simulating interface motion - I. Migration of phase and grain boundaries

This paper describes a finite element method for simulating migration of interfaces (e.g. phase and grain boundaries) in materials. The method is built on a classical theory. Each individual grain is in an equilibrium state; interface tension and bulk phase chemical potential constitute the free energy. An interface migrates - as atoms break from one grain, cross the interface, and attach to the other grain - at a velocity proportional to the free energy reduction per unit volume of atoms crossing the interface. We express this theory in a weak statement, model the interfaces with finite elements, and update nodal positions incrementally. The variations of the free energy, associated with the virtual motions of the nodes, define the generalized forces. The weak statement connects the generalized forces and the nodal velocities with a viscosity matrix. The method takes into account large interface shape changes, interface tension anisotropy, and non-equilibrium triple junctions (if present). We illustrate the method with examples including grooving on a polycrystal surface, grain growth in a thin film, and facet formation of a single crystal particle.