Ab initio geometry optimization and ground state properties of layered ternary carbides Ti₃MC₂ (M = Al, Si and Ge)

The crystal structures of all layered ternary carbides called '312' phases including Ti₃AlC₂, Ti₃SiC₂ and Ti₃GeC₂ have been fully optimized by means of ab initio total-energy calculations. The equilibrium lattice parameters, the atomic positions in the unit cell and interatomic distances have been determined. The differences between the calculated and the measured lattice constants are generally less than 1%. It is also shown that c/a of the hexagonal lattices decreases from Ti₃AlC₂ to Ti₃GeC₂. The calculated bulk moduli are 190 GPa for Ti₃AlC₂, 202 GPa for Ti₃SiC₂ and 198 GPa for Ti₃GeC₂, respectively, which are comparable to that of TiC. The electronic structures reveal that the Ti(1, 2) and C atoms form a strong Ti(2)-C-Ti(1)-C-Ti(2) covalent bond chain, while the bonding between Ti(2) and M (M = Al, Si, Ge) is relatively weak. The strong Ti(2)-C-Ti(1)-C-Ti(2) covalent bond chain corresponds to the high strength and modulus, while the metallic bond corresponds to the metallic conductivity of these ternaries.