We describe an efficient first-principles method that can be used to calculate mixing enthalpies of transition metal nitrides with B1 structure and substitutional disorder at the metal sublattice. The technique is based on the density functional theory. The independent sublattice model is suggested for the treatment of disorderinduced local lattice relaxation effects. It supplements the description of the substitutional disorder within the coherent potential approximation. We demonstrate the excellent accuracy of the method by comparison with calculations performed by means of the projector augumented wave method on supercells constructed as special quasirandom structures. At the same time, the efficiency of the technique allows for total energy calculations on a very fine mesh of concentrations which enables a reliable calculation of the second concentration derivative of the alloy total energy. This is a first step towards first-principles predictions of concentrations and temperature intervals where the alloy decomposition proceeds via the spinodal mechanism. We thus calculate electronic structure, lattice parameter, and mixing enthalpies of the quasibinary alloy c-Ti 1−x Al x N. The lattice parameter follows Vegard's law at low fractions of AlN but deviates increasingly with increasing Al content. We show that the asymmetry of the mixing enthalpy and its second concentration derivative is associated with substantial variations of the electronic structure with alloy composition. The phase diagram is constructed within the mean-field approximation.

We propose a simple theoretical description of the metal-insulator transition of rare-earth nickelates. The theory involves only two orbitals per nickel site, corresponding to the low-energy antibonding e g states. In the monoclinic insulating state, bond-length disproportionation splits the manifold of e g bands, corresponding to a modulation of the effective on-site energy. We show that, when subject to a local Coulomb repulsion U and Hund's coupling J , the resulting bond-disproportionated state is a paramagnetic insulator for a wide range of interaction parameters. Furthermore, we find that when U − 3J is small or negative, a spontaneous instability to bond disproportionation takes place for large enough J . This minimal theory emphasizes that a small or negative charge-transfer energy, a large Hund's coupling, and a strong coupling to bond disproportionation are the key factors underlying the transition. Experimental consequences of this theoretical picture are discussed.