Effect of transition metal (M) and M–C slabs on equilibrium properties of Al-containing MAX carbides: An ab initio study

The effect of transition metal (M) and M–C slabs (n) on crystal structure and equilibrium properties of Al-containing MAX-phase carbides Mn+1AlCn (n = 1–3) was investigated. There is a linear relation between lattice parameters and Goldschmid diameter of M atoms. For a given n, c/a ratios always fall into a narrow range. The theoretical density almost increases with increasing VEC (valence electron concentration), n and d-electron shell number. In general, the formation energy and cohesive energy increase with the increase of VEC. The bond length decreases with increasing VEC. The bond length of 3d compounds is much higher than those of 4d and 5d compounds. Among M–C bonds, the lowest bond length is present in the M–C bonds with the M atoms near to Al atoms. Overall, the M–Al bond angle decreases with increasing d-electron shell number. In addition, M–C bond angles increase with increasing the corresponding M–C bond length. Overall, the total density of states at Fermi energy increases with increasing VEC and n, but decreases from 3d, 4d to 5d for M3AlC2, and M4AlC3. In addition, a weak M1–M2 bond was found in M4AlC3 with VEC = 5 and 6.