First-principles calculations were used to study the effect of vacancies on the structural and electronic properties in sub-stoichiometric TiNx. The effect of vacancies upon the equilibrium volumes, bulk moduli, electronic band structures and density of states of the sub-stoichiometric phases was studied by using a full-potential linear augmented plane-wave method. A model structure of 8-atom super-cells with ordered vacancies within the N sub-lattice was used. It was found that the lattice parameters of the studied stoichiometries were smaller than that of ideal stoichiometric TiN.

First-Principles Calculations of Vacancy Effects on Structural and Electronic Properties of TiCx and TiNx. Z.Dridi, B.Bouhafs, P.Ruterana, H.Aourag: Journal of Physics - Condensed Matter, 2002, 14[43], 10237-49