Ab initiogeometry 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 Ti 3 AlC 2 , Ti 3 SiC 2 and Ti 3 GeC 2 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 Ti 3 AlC 2 to Ti 3 GeC 2 . The calculated bulk moduli are 190 GPa for Ti 3 AlC 2 , 202 GPa for Ti 3 SiC 2 and 198 GPa for Ti 3 GeC 2 , 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.