Electronic structure and energetics of ordered titanium carbides of composition Ti2C

The equilibrium geometries, formation energies, band structures, densities of states and charge densities of ordered titanium carbide phases of composition Ti2C-cubic Fd3m-Ti2C and trigonal R (3) over barm-Ti2C-were calculated self-consistently by means of the full-potential linearized augmented-plane-wave method. The trigonal phase was found to be more stable than the cubic phase by 11.6 kJ/(mole of atoms) because it enables more efficient d-d bonding between Ti d states. The cubic phase is stabilized by the relaxation of the Ti atoms next to the vacancies towards their nearest-neighbour C atoms. In agreement with experiment, the maximum of the stabilizing relaxation energy (2.8 kJ/(mole of atoms)) is found for a relaxation of 0.04 Angstrom. The formation energies are in good agreement with the available experimental values for TiC and Fd3m-Ti2C. Calculations were also performed for two tetragonal phases of composition Ti,X found experimentally for the nitride but not for the carbide. All calculated ordered Ti2C phases are found to be stable against segregation into TiC and metallic Ti.