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Stability of γ and δ phases in Ti at high pressures

2002; American Physical Society; Volume: 65; Issue: 5 Linguagem: Inglês

10.1103/physrevb.65.052106

1095-3795

K. D. Joshi, Ghoshna Jyoti, Satish C. Gupta, S. K. Sikka,

Rare-earth and actinide compounds

Recently, Vohra and Spencer [Phys. Rev. Lett. 86, 3068 (2001)] reported that titanium metal undergoes a transition from a hexagonal phase $(\ensuremath{\omega})$ to an orthorhombic phase (distorted hcp, $\ensuremath{\gamma}$ phase) under a pressure of $116\ifmmode\pm\else\textpm\fi{}4 \mathrm{GPa},$ 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 $\ensuremath{\gamma}$ phase from an $\ensuremath{\omega}$ phase, contrary to their earlier investigations showing a $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\beta}$ (bcc) transition in Ti at 140 GPa. Additionally, they reported another transition in Ti, a $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\delta}$ (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 $\ensuremath{\alpha}(\mathrm{hcp})\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\beta}$ 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 $\ensuremath{\gamma}$ and $\ensuremath{\delta}$ phases with respect to the $\ensuremath{\omega}$ and $\ensuremath{\beta}$ structures. Our analysis predicts at 0 K the $\ensuremath{\omega}$ phase transforms to a $\ensuremath{\beta}$ phase via an intermediate $\ensuremath{\gamma}$ phase, whereas at 300 K the $\ensuremath{\omega}$ phase transforms to a $\ensuremath{\beta}$ structure directly and the $\ensuremath{\gamma}$ phase becomes the most competitive metastable structure in the pressure range of the $\ensuremath{\beta}$-phase stability. The $\ensuremath{\delta}$ phase, however, is not at all stable at any compression. This suggests that the $\ensuremath{\gamma}$ 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 $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\gamma}$ structural transition does not represent the phenomenon expected under hydrostatic conditions.