Density functional study of the phase diagram and thermodynamic properties of Zr

We have investigated the structures, phonon dispersions, phase transitions and thermodynamics of Zr from first-principles calculations. At zero temperature, α-Zr transforms to ω-Zr at 0.98 GPa and then to β-Zr at 31.6 GPa. The axial ratio c/a increases with increasing pressure for α-Zr, but it is nearly invariant under compression for ω-Zr. Within the quasi-harmonic Debye model, the full phase diagram of Zr was obtained. The zero pressure phase transition from α-Zr to β-Zr occurs at 1130 K. The transition pressure from α-Zr to ω-Zr at 300 K is 2.10 GPa and the predicted triple point is at 6.35 GPa, 910 K, which is close to the experimental data. The thermal properties including the entropy, isotherm, isobar and thermal pressure in a wide range of pressure and temperature were predicted successfully.