A coherent set of model equations for various surface and interface energies in systems with liquid and solid metals and alloys.

In this paper first a generally valid model is derived from the two fundamental equations of Gibbs for temperature and composition dependences of all types of interfacial energies. This general model is applied here to develop a coherent set of particular model equations for surface tension of liquid metals and alloys, for surface energy of solid metals and alloys, for high-angle grain boundary energy in metals and alloys, for solid/liquid interfacial energy in metals and alloys, for liquid/liquid interfacial energy in alloys and for solid/solid interfacial energy in metals and alloys. The latter case is sub-divided into models on coherent, incoherent and semi-coherent interfaces with the same phases and with different phases on the two sides of the interface. Model parameters are given here as an example for the 111 plane of fcc metals and alloys. For other crystal planes or other crystal structures the model parameters should be adjusted, while the model equations remain the same. The method is demonstrated on various surface and interfacial energies of pure Au, on solid/liquid interfacial energy in the AlCu system, on different types of solid/solid interfacial energies in the AuNi system, on solid/solid, solid/liquid and liquid/liquid interfacial energies in the AlPb system and on the coherent, incoherent and semi-coherent interfacial energies between ordered and disordered fcc phases in the Ni-rich part of the NiAl system. The ability of this method is demonstrated to predict surface and interface transition along free surfaces and grain boundaries and also negative interfacial energies in nano-systems.