Lattice dynamics of hcp Ti

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Abstract
Inelastic-neutron-scattering techniques have been used to study the lattice dynamics of hcp Ti. The phonon dispersion curves along the [001], [100], and [110] symmetry directions were determined at 295, 773, and 1054 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 room temperature this branch exhibits a dip at the zone center. These features of the phonon spectrum of hcp Ti bear a striking resemblance to those of hcp Zr and seem to be characteristic of the transition metals of column IV of the Periodic Table. The data were used to evaluate the lattice specific heat at constant pressure as a function of temperature. The calculated total specific heat, obtained by taking into account the electronic contribution, was found to agree, to within experimental uncertainties, with the results of direct specific-heat measurements.