Crystal structures of Ti under high pressure: Theory

The crystal structures of a few phases of Ti such as hcp, bcc, $\ensuremath{\omega}$ (hexagonal phase) $\ensuremath{\gamma}$ (distorted hcp), $\ensuremath{\delta}$ (distorted bcc), and bcc under pressure have been studied by means of first-principles total-energy calculations in a generalized gradient approximation. Our calculations are different from calculations by Joshi et al. [Phys. Rev. B 65, 052106 (2002)] in that we have performed the full geometry optimization for hcp, $\ensuremath{\omega},\ensuremath{\gamma},$ and $\ensuremath{\delta}$ phases at each volume considered. The experimental phase sequence $\mathrm{hcp}\ensuremath{\rightarrow}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\delta}$ has been obtained, though our 0-K transition pressures are little lower than the experimental ones obtained at 300 K. The phase transition $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\delta}}\mathrm{bcc}$ was obtained at 136 GPa in contradiction to the experimental stability of $\ensuremath{\delta}$ phase up to the highest studied pressure 216 GPa. Our calculations have also shown that at the pressures higher than 170 GPa, the $\ensuremath{\delta}$ phase' parameters change in such a manner that structure obtained is bcc. This fact suggests that the $\ensuremath{\delta}$ structure observed in experiments at pressures 170 GPa and higher maybe is a consequence of nonhydrostatic stresses present in the experiments. Similar conclusion has been reached in the above-mentioned work by Joshi et al.