Zinc phosphide (Zn 3 P 2 ) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping of the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel "perturbation extrapolation" is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn 3 P 2 and act as "electron sinks," nullifying the desired doping and lowering the Fermi-level back toward the p-type regime. This is consistent with experimental observations of both the tendency of conductivity to rise with phosphorus partial pressure, and with current partial successes in n-type doping in very zinc-rich growth conditions.

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We describe a simple method to determine, from ab initio calculations, the complete orientationdependence 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.