Stability of $\gamma$ and $\delta$ 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 $\left(\omega \right)$ to an orthorhombic phase (distorted hcp, $\gamma$ phase) under a pressure of $116\pm 4\hspace{0.5em}\mathrm{GPa},$ 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 $\gamma$ phase from an $\omega$ phase, contrary to their earlier investigations showing a $\overrightarrow{\omega }\beta$ (bcc) transition in Ti at 140 GPa. Additionally, they reported another transition in Ti, a $\overrightarrow{\gamma }\delta$ (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 $\alpha \left(\mathrm{hcp}\right)\to \overrightarrow{\omega }\beta$ 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 $\gamma$ and $\delta$ phases with respect to the $\omega$ and $\beta$ structures. Our analysis predicts at 0 K the $\omega$ phase transforms to a $\beta$ phase via an intermediate $\gamma$ phase, whereas at 300 K the $\omega$ phase transforms to a $\beta$ structure directly and the $\gamma$ phase becomes the most competitive metastable structure in the pressure range of the $\beta$-phase stability. The $\delta$ phase, however, is not at all stable at any compression. This suggests that the $\gamma$ 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 $\overrightarrow{\omega }\gamma$ structural transition does not represent the phenomenon expected under hydrostatic conditions.