Bonding study of TiC and TiN. II. Theory

By starting with self-consistent potentials, the electronic densities and structure factors for stoichiometric TiC and TiN have been calculated with the use of the linearized-augmented-plane-wave (LAPW) method. A comparison is made with the corresponding experimental data which are presented in the preceding paper (Dunand et al.), the first paper of this series. Static displacements of titanium occur around nonmetal vacancies in the measured crystals with composition ${\mathrm{TiC}}_{0.94}$ and ${\mathrm{TiN}}_{0.99}$. Because of this nonstoichiometry, the experimental data should not be directly compared with theory, which assumes ideal NaCl structure. A sophisticated atomic model introduced in the preceding paper makes it possible to extrapolate to stoichiometric composition. These data are compared with the LAPW results and are found to agree well in the case of TiN and in TiC for the nonspherical effects around Ti; but for TiC, some discrepancies near the nuclei remain which are discussed either in terms of the model parameters used in the fit to experiment or by considering electronic effects caused by vacancies. Chemical bonding is discussed, and it consists of a combination of ionic, covalent, and metallic contributions.