Model study of the vacancy formation trend of Nb carbides, nitrides and oxides

Based on a two-centre tight-binding model the vacancy formation trend is studied for Nb-X (X=C, N, O) compounds by comparison of averaged band energies. These are obtained by averaging the band energies of Nb and X valence states with respect to the number of Nb and X atoms in the unit cell. Only d states at the Nb sites and p states at the X sites are included in the Hamiltonian. The vacancies are described by removing bonds (hoppings=0) of the ordered Nb4X4 compound of rock-salt crystal structure in order to get ordered Nb4X3, Nb3X4 and Nb3X3 compounds. The model describes reasonably well the trend as found by experiment.