Ab-initio analysis of stability of ω-phase in Ti, Zr and Hf under high pressure

The unusual occurrence of ω phase (a three atom simple hexagonal structure) prior to β (bcc) phase under high pressure in group IV transition metals Ti, Zr and Hf has been analyzed through first principles electronic band structure calculations. The analysis of band structure of ω and β phases in the w stability regime suggest that the opening of band gap at the Fermi level in ω phase lowers the total energy of this phase relative to β, and stabilizes the ω phase. Additionally, the extension of band gap near Fermi level is largest in Ti followed by Hf and then Zr suggesting that ω phase is most stable in Ti and least in Zr, in line with the experimental observations. Further, the density of states of ∼ 0.33, 0.4 and 0.5, respectively at Fermi energy for ω phase relative to β phase in Ti, Hf and Zr indicates that the lowering in energy for ω is highest in Ti and lowest in Zr.