Ab initio calculation of anisotropic interfacial excess free energies

We describe a simple method to determine, from ab initio calculations, the complete orientation-dependence of interfacial free energies in solid-state crystalline systems. We illustrate the method with an application to precipitates in the Al-Ti alloy system. The method combines the cluster expansion formalism in its most general form (to model the system's energetics) with the inversion of the well-known Wulff construction (to recover interfacial energies from equilibrium precipitate shapes). Although the inverse Wulff construction only provides the relative magnitude of the various interfacial free energies, absolute free energies can be recovered from a calculation of a single, conveniently chosen, planar interface. The method is able to account for essentially all sources of entropy (arising from phonons, bulk point defects, as well as interface roughness) and is thus able to transparently handle both atomically smooth and rough interfaces. The approach expresses the resulting orientation-dependence of the interfacial properties using symmetry-adapted bases for general orientation-dependent quantities. As a by-product, this paper thus provides a simple and general method to generate such basis functions, which prove useful in a variety of other applications, for instance to represent the anisotropy of the so-called constituent strain elastic energy.