Polymorphism of newly discovered Ti₄GaC₃: A first-principles study

The newly discovered MAX phase, Ti₄GaC₃, can exist in one of three polymorphs, α, β and γ, all with the space group P63/mmc. The Ti and Ga (underlined) atomic arrangements are, respectively, ABĀBACBC̄BC, ACĀCACAC̄AC and ABC̄BACBĀBC. Herein first-principles calculations are used to investigate the phase stabilities, electronic structures, elastic properties and compressibilities of the three polymorphs. Since the α- to γ-phase transition only involves shuffling of the A-atoms, it occurs much more easily than those to β-Ti₄GaC₃ despite the fact that the latter is thermodynamically less stable than γ-Ti₄GaC₃. For α-Ti₄GaC₃, the total density of states, TDOS, around the Fermi energy, E_f, lies in a local minimum; for the two other polymorphs, the TDOS is near a local minimum. The electrons occupy all the bonding states for α-Ti₄GaC₃, but the bonding states are partially occupied for both β- and γ-Ti₄GaC ₃. Both bond stiffness and bond angle play an important role in the compressibility. In general, with increasing pressure, all the bonds become shorter, and the rate of increase in bond stiffness also increases. The bulk moduli of the α-, β- and γ-polymorphs were calculated to be 178, 174 and 169 GPa, respectively. The corresponding theoretical densities are 5.14, 5.12 and 5.11 g cm^-3.