First-principles phase transition and equation of state of titanium

The projector augmented wave method (PAW) within the Perdew–Burke–Ernzerhof (PBE) form of generalized gradient approximation (GGA) is applied to investigate the effect of hydrostatic pressure on the structures of titanium metal. In our calculations, the full geometry optimization for all the structures at each volume considered is performed. The phase sequence ω→γ→δω→γ→δ has been obtained and is in good agreement with the experimental results of Vohra et al. and Akahama et al. The obtained phase transition δ→δ→ bcc is at ca. 160.9 GPa. This conclusion is in accordance with those of Kutepov et al. and Joshi et al. The quasi-harmonic Debye model for the first time is used to predict phase diagram of α→ωα→ω and the result is in better agreement with the experimental data than those from earlier calculations at 300 K.