First Principles Evaluation of Temperature Effects on the Stability and Further Properties of Ti₂AlM-Type O-Phases with V-VIB Group Element Additions

TiAl alloys have established themselves as materials for aero-engine turbine blades. These TiAl alloys predominantly consist of the tetragonal γ-TiAl and the hexagonal α₂-Ti₃Al phase. However, to improve the damage tolerance and processability additional alloying elements like Nb or Mo are frequently added. It was found in the Ti-Al-Nb system that certain alloy compositions tend to precipitate an orthorhombic so-called O-phase with Ti₂AlNb stoichiometry. Two aspects make this phase interesting. Firstly, small amounts of it were found in some γ-TiAl-based alloys with Nb contents exceeding 8 at.%. In those systems, the O-phase could be an unwanted constituent and its content should be controlled. Secondly, the O-phase proved to be a ductile constituent in more Nb-rich and Al-leaner alloy variants, which show an attractive combination of strength and ductility in the 500 to 600 °C range. In the present work, we investigate the stability of this phase depending on temperature and variation of the ternary alloying element by first-principles methods. In addition to Nb, other elements from the groups V and VI of the periodic table like V, Ta, Mo, and W were investigated. To determine the 0 K properties of the Ti₂AlM compounds the plane wave density functional approach as implemented in the VASP software package with projector-augmented waves was used. To determine the lattice constants and energies at 0K, the energies of formation vs. volume are fitted using the Birch-Murnaghan and Morse equation of state (EOS). Two techniques describe the vibrational contribution to Helmholtz free energy: (i) the Debye model with the Debye–Grüneisen approach; and (ii) the calculation of the complete phonon spectra via the supercell method. Through a comparison of the available data from experiments with those from thermodynamic modeling, it is found that the phonon calculations, as well as the Debye model, accurately depict the thermodynamic properties of the Ti₂AlM compounds under study. The quasi-harmonic approximation (QHA) was used to calculate the lattice expansion at raised temperature for the phonon-based modeling of temperature effects. The calculated lattice parameters compare well with experimental ones from neutron scattering experiments [1,2].<br/>The main results are that (i) the equilibrium volume increases roughly linearly as a function of temperature for all ternary additions M, (ii) the bulk modulus decreases dependent on the ternary element addition in the order Mo&gt;W&gt;Ta&gt;Nb&gt;V, (iii) the bond strength follows the trend of Ti–M&gt; Ti–Al&gt; Al–M irrespective, if M is V, Nb, Ta, Mo or W, and the hybridization of Ti-<i>d</i> states, M-<i>d</i> states and Al-<i>p</i> states contributes to the bonding, and (iv) the vibrational contribution to entropy, and in turn to Gibbs energy, increases with increasing mass of the ternary addition M in the different TiAl–M compounds. The predicted thermodynamic properties provide helpful insights into the stability of different types of O-phases, especially for systems where the experimental information is lacking or less reliable.<br/><br/><br/>[1] C. Dai, <i>et al</i>. Composition and temperature dependence of α₂ phase decomposition in high Nb-containing lamellar γ-TiAl alloys: Experiments and first-principles calculations. Acta Mater. 2021, 221, 117419.<br/>[2] Hu. Q. M. <i>et al</i>. Geometric and electronic structure of Ti₂AlX (X=V, Nb, or Ta). Phys Rev B. 2003, 68, 054102.