A mathematical model for grain growth in thin metallic films

We use geometrical arguments based on grain boundary symmetries to introduc e crystalline interfacial energies for interfaces in polycrystalline thin f ilms with a cubic lattice. These crystalline energies are incorporated into a multi-phase field model. Our aim is to apply the multi-phase field metho d to describe the evolution of faceted grain boundary triple junctions in e pitaxially growing microstructures. In particular, we are interested in sym metry properties of triple junctions in tricrystalline thin films. Symmetri es of triple junctions in tricrystalline films have been studied in experim ents by Dahmen and Thangaraj.(6,25) In accordance with their experiments, w e find in numerical simulations that any two neighboring triple junctions b elong to different symmetry classes. We introduce a local equilibrium condi tion at triple junctions which can be interpreted as a crystalline version of Young's law. The local equilibrium condition at triple junctions is pure ly determined by the grain boundary energies. In particular no triple junct ion energies are necessary to explain which triple junctions are possible. All triple junctions observed in the experiments as well as in the simulati ons fulfil the crystalline version of Young's law. Our approach is also cap able of describing grain boundary motion in general polycrystalline thin fi lms.