Ab-initio study of long-period superstructures and anti-phase boundaries in Al-rich γ-TiAl (L1₀)-based alloys

In this work, we report first-principles investigation of structural stability of all experimentally observed ordered long-period superstructures (LPSs), viz., r-Al₂Ti, h-Al₂Ti, Al₅Ti ₃ along with Al₅Ti₃′, Al ₁₁Ti₇ and Al₃Ti₂ LPSs, which are observed only as short-range ordered clusters at nanoscale level in Al-rich TiAl-based alloys. We adopt a procedure based on space-filling tiling arrangement of ordered Ti₂Al, Ti₃Al, Ti₄Al motifs and their combination along with a symmetry analysis programme to determine the unit cell and the crystallographic information of Al ₅Ti₃′, Al₁₁Ti₇ and Al ₃Ti₂ LPSs in terms of L₁₀ fcc unit cell. First-principles calculations are performed to further refine these crystallographic parameters (Wyckoff positions and lattice parameters) obtained from the above procedure. Moreover, it is found that the family of five LPSs have subgroup-supergroup relationships with γ-TiAl (Sp. gr. P4/mmm) and among themselves. Further, we find the inherent stability of r-Al₂Ti + γ-TiAl and 2Al₅Ti₃ + γ-TiAl phase mixtures at 0 K compared to isomolecular Al₃Ti₂ and Al ₁₁Ti₇ LPSs at their respective concentrations. The calculations of single-crystal elastic constants of Al₅Ti ₃, Al₁₁Ti₇, Al₃Ti₂ and Al₅Ti₃′ LPSs show all these four structures are mechanically stable. We also calculate antiphase boundary (APB) formation energies for two types of APBs, viz., type-A and type-C in ordered Al ₅Ti₃ LPS using the supercell approach. The relaxed APB energies for type-A and type-C APBs are 15.44 and 124.16 mJ/m², respectively.