First-principles calculations have been used to study the effect of vacancies and relaxation around the vacancy sites in substoichiometric ${\mathrm{TiC}}_{1-x}.$ The effect of relaxation on phase stabilities, equilibrium volumes, and electronic structure of the substoichiometric phases was studied using a combined approach of pseudopotential plane wave and full-potential linear muffin-tin orbital methods. A relaxation away from the vacancies was found for the titanium atoms, the magnitude of which increased with vacancy concentration and the inclusion of nearest-neighbor carbon atom relaxation. The inclusion of local relaxations was found to correctly predict the off-stoichiometric equilibrium composition of titanium carbide. The anomalous volume behavior of TiC at small vacancy concentration is explained as an effect of the local relaxation of the atoms surrounding the vacancy sites, but we do not find that the lattice parameter of any of the studied stoichiometries is larger than that of ideal stoichiometric TiC.

• Received 7 July 2000

DOI:https://doi.org/10.1103/PhysRevB.63.165116