Structure and energy of point defects in TiC: An ab initio study

We employ first-principles calculations to study the atomic and electronic structure of various point defects such as vacancies, interstitials, and antisites in the stoichiometric as well as slightly off-stoichiometric Ti-1-C-c(c) (including both C-poor and C-rich compositions, 0.49 <= c <= 0.51). The atomic structure analysis has revealed that both interstitial and antisite defects can exist in split conformations involving dumbbells. To characterize the electronic structure changes caused by a defect, we introduce differential density of states (dDOS) defined as a local perturbation of the density of states (DOS) on the defect site and its surrounding relative to the perfect TiC. This definition allows us to identify the DOS peaks characteristic of the studied defects in several conformations. So far, characteristic defect states have been discussed only in connection with carbon vacancies. Here, in particular, we have identified dDOS peaks of carbon interstitials and dumbbells, which can be used for experimental detection of such defects in TiC. The formation energies of point defects in TiC are derived in the framework of a grand-canonical formalism. Among the considered defects, carbon vacancies and interstitials are shown to have, respectively, the lowest and the second-lowest formation energies. Their formation energetics are consistent with the thermodynamic data on the phase stability of nonstoichiometric TiC. A cluster type of point defect is found to be next in energy, a titanium [100] dumbbell terminated by two carbon vacancies.