Electronic structure of substoichiometric carbides and nitrides of zirconium and niobium

The electronic structures of ${\mathrm{ZrC}}_{\mathrm{x}}$, ${\mathrm{ZrN}}_{\mathrm{x}}$, ${\mathrm{NbC}}_{\mathrm{x}}$, and ${\mathrm{NbN}}_{\mathrm{x}}$ for several concentrations x were investigated by means of the Korringa-Kohn-Rostoker coherent-potential approximation and the Korringa-Kohn-Rostoker Green’s-function methods. The influence of vacancies on the electronic structure of these compounds is quite similar to the case of substoichiometric carbides and nitrides of 3d metals: near the minimum in the density of states between the nonmetal p and the metal d subbands additional ‘‘vacancy peaks’’ appear, and (except for ${\mathrm{ZrC}}_{\mathrm{x}}$) the Fermi energy is lowered. It is argued that similar properties may be expected for other d- and f-metal carbides, pnictides, and chalcogenides.