Thermal Stabilization of the HCP Phase in Titanium

We have used a tight-binding model that is fit to first-principles electronic-structure calculations for titanium to calculate quasiharmonic phonons and the Gibbs free energy of the hexagonal-close-packed (hcp) and omega (ω) crystal structures. The hcp phonon dispersion agrees with experiment; the ω phonon dispersion has yet to be measured. The model predicts that the true zero-temperature ground state is the ω structure and that it is the entropy from the thermal population of phonon states which stabilizes the hcp structure at room temperature. We present a completely theoretical prediction of the temperature and pressure dependence of the hcp-ω phase transformation and show that it is in good agreement with experiment. The quasiharmonic approximation fails to adequately treat the bcc phase because the calculated phonons of this structure are not all stable.