Intercalation of Al into MC (M = Ti, V, Cr)

The energetics of point defects and twins in MCx (x < 1, M = Ti, V, Cr, space group F m 3 ¯ m ) was studied using density functional theory. Our goal is to contribute towards understanding the underlying atomic mechanisms enabling the Al intercalation into MCx. As the valence electron concentration is increased by substituting Ti in TiCx with V and further with Cr, the energy of formation for C vacancies is decreased. This may be understood based on the electronic structure. Upon increasing the valence electron concentration, the bonding becomes less ionic and more covalent. In covalent crystals, directional bonding may be rearranged and local relaxation is observed upon vacancy creation, while this gives rise to repulsive Coulomb forces in ionic crystals, and hence the energy of formation is expected to decrease as the valence electron concentration of M is increased. The difference between the energy of formation for an Al substitution at a C site and a C vacancy, the migration energy for Al, the point defect ordering energy, and the twin boundary energy may be overcome, for instance, during vapor phase condensation. These results may be of general relevance for the formation of MAX phases (space group P63/mmc) at low temperatures.