Stability of γ and δ phases in Ti at high pressures

Recently, Vohra and Spencer [Phys. Rev. Lett. 86, 3068 (2001)] reported that titanium metal undergoes a transition from a hexagonal phase (ω) to an orthorhombic phase (distorted hcp, γ phase) under a pressure of 116±4 GPa, from energy dispersive x-ray-diffraction measurements. Subsequent to this, very recently, Akahama et al. [Phys. Rev. Lett. 87, 275503 (2001)] also reported that titanium undergoes a transition to a γ phase from an (ω phase, contrary to their earlier investigations showing a (ω-->β (bcc) transition in Ti at 140 GPa. Additionally, they reported another transition in Ti, a γ-->δ (distorted bcc) transition around 140 GPa. This is unexpected, as the group-IVB elements are expected to undergo s-to-d electron transfer under pressure and thus mimic the transformation sequence α(hcp)-->ω-->β shown by these elements with increasing numbers of d electrons on alloying with d-electron-rich neighbors. This structural sequence under pressure is well established for Zr and Hf. In the present work, we carry out total energy calculations employing the full-potential linear-augmented-plane wave method to examine the stability of the γ and δ phases with respect to the ω and β structures. Our analysis predicts at 0 K the ω phase transforms to a β phase via an intermediate γ phase, whereas at 300 K the ω phase transforms to a β structure directly and the γ phase becomes the most competitive metastable structure in the pressure range of the β-phase stability. The δ phase, however, is not at all stable at any compression. This suggests that the γ phase observed in the experiments is a metastable phase that could be formed due to the shear stresses present in the experiments, and that the ω∃γ structural transition does not represent the phenomenon expected under hydrostatic conditions