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 disorder-induced 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 $c\text{−}{\mathrm{Ti}}_{1-x}{\mathrm{Al}}_x\mathrm{N}$. 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.

• Received 22 June 2006

DOI:https://doi.org/10.1103/PhysRevB.75.045123