Temperature dependence of the normal vibrational modes of hcp Zr

Abstract

Inelastic-neutron-scattering techniques have been used to study the temperature dependence of the normal vibrational modes of hcp Zr. The phonon spectra along the [001], [100], and [110] symmetry directions were determined at 295, 773, and 1007 K. The [001] LO branch and a selected number of phonons of other branches were determined also at 5.5 K. As the temperature decreases we observe a rather large increase in the frequencies of all but the [001] LO branch. The zone-center mode of the [001] LO branch softens appreciably and at 5.5 K this branch exhibits a dip at the zone center reminiscent of the anomalous dispersion of the corresponding branch of technetium at room temperature. The data were used to evaluate the lattice specific heat at constant pressure as a function of temperature. The calculated total specific heat at constant pressure, obtained by taking into account the electronic contribution, was found to be consistent, to within experimental uncertainties, with the results of specific-heat measurements. We propose an explanation for the softening of the zone-center mode of the [001] LO branch and the large increase in the frequencies of the other modes with decreasing temperature which is based on the electronic structure of Zr.