Three-dimensional evolution of interfaces under evaporation-condensation kinetics: a finite-element simulation

An interface migrates as atoms break from one grain, cross the interface and attach to the other grain at a velocity satisfied by prescribed kinetic law. We present a three-dimensional (3D) finite-element scheme to simulate migration of interfaces in materials under linear evaporation and condensation kinetics. The simulation is based upon a weak statement of classical theory. The total free energy consists of the chemical potential difference of bulk phases, the interface tension and the triple junction energy. The interfaces are discretized by the finite elements under a 3D framework. The simulation takes into account shape changes and the orientation dependence of interfaces, The present scheme is exemplified by two cases: (I)the growth and facet formation of single crystals whose evolutionary paths may bifurcate under different initial shapes; and (2) the evolution of a bicrystal him and a tricrystal film on a substrate, where the effect of multiple kinetics is demonstrated.