Lattice dynamics in the [alpha]-phase of the IVB transition elements
Inelastic neutron scattering techniques have been used to study the temperature dependent lattice dynamics of the group IVB transition elements, titanium (Ti) and hafnium (Hf), in the hcp ((alpha)) phase. In these studies the dispersion curves as well as their temperature dependence were investigated in order to obtain information about the temperature dependence of the thermophysical properties of these elements as well as the change with temperature of the electronic response to the nuclear motions. The results show a significant softening of the phonon modes as the temperature is increased for all branches of the dispersion curves except the 001LO zone-center mode. This mode increases in frequency with increasing temperature. These features of the dispersion curves of Ti and Hf bear a striking resemblance to the other IVB element, Zr;The data for hcp Ti and hcp Hf 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 rather well with direct specific heat measurements. The unusual temperature dependence of the LO001 zone center mode and the large decrease in the frequencies of the other modes with increasing temperature for the IVB elements is explained on the basis of their unique electronic structure near the Fermi surface.