Equilibrium and stability of triple junctions in anisotropic systems

When a homophase or heterophase interface involves a crystalline solid, the interfacial energy is expected to depend upon the interface–plane orientation. In this paper, the equations governing equilibrium triple-junction configurations in anisotropic systems are reviewed. These equilibrium conditions were originally derived by considering the differential change in triple-junction interfacial energy associated with a differential change in triple-junction configuration and equating it to zero. However, the derived conditions do not distinguish between a triple-junction configuration that satisfies the equilibrium conditions by residing at a local energy minimum, a local energy maximum or at a saddle point. The present paper develops stability criteria for triple junctions with and without interfaces which have anisotropic energy, which can be used to determine whether triple-junction equilibrium conditions correspond to local energy minima (stable), maxima (unstable) or saddle points. For isotropic systems, there is a single solution to the triple-junction equilibrium conditions, and it is necessarily stable. For anisotropic systems, there are multiple solutions to the triple-junction equilibrium conditions, some of which may be stable, unstable or correspond to saddle points in triple-junction interfacial energy. Microstructure features and interface lengths/areas are expected to play a role in dictating the relative energies of stable configurations.