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

Abstract

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, Al5Ti3 along with Al5Ti3′, Al11Ti7 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 Al5Ti3′, Al11Ti7 and Al3Ti2 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 Al11Ti7 LPSs at their respective concentrations. The calculations of single-crystal elastic constants of Al5Ti3, 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 Al5Ti3 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.