Pressure and temperature effects on the Γ and N-phonons in zirconium

The effective potentials for the E2g-phonon at the Γ point of the Brillouin zone of hcp Zr and the transverse N phonon of bcc Zr are calculated for different pressures by the frozen-phonon method. The temperature and pressure dependences of the phonon frequencies are studied within the framework of a modified pseudo-harmonic approximation. The results obtained are in good agreement with the experimental ones. The change observed in the behavior of frequencies with increasing temperature and pressure may be attributed to the peculiarities of the phase diagram of zirconium.