First-principles studies of typical long-period superstructures Al5Ti3, h-Al2Ti and r-Al2Ti in Al-rich TiAl alloys

First-principles calculations are performed to study the structural stabilities, electronic and elastic properties of typical long-period superstructures Al5Ti3, h-Al2Ti and r-Al2Ti in Al-rich TiAl alloys together with γ-TiAl. The obtained lattice parameters by relaxation of crystalline cells are in good agreement with the experimental data. The calculated formation enthalpies show that r-Al2Ti has the highest structure stability from energetic point of view, and then followed by h-Al2Ti, Al5Ti3 and γ-TiAl. The electronic density of states and charge density distribution indicate that due to strong hybridization between Al-2p and Ti-3d, there is a strong directional bonding between Ti and Al atoms. The elastic constants are calculated, suggesting that these structures are mechanically stable. Bulk modulus B, shear modulus G, Young’s modulus E and Poison’s ratio ν of polycrystalline materials are derived from the elastic constants. By several criteria, elastic anisotropies are analyzed, showing that these structures possess different degree of anisotropies.