Lattice Dynamics of Terbium

The frequency-wave-vector dispersion relation for the normal modes of vibration of terbium at room temperature has been measured by means of slow-neutron inelastic scattering techniques. The triple-axis spectrometer at the Oak Ridge high flux isotope reactor was used, mostly in the constant-$Q$ mode of operation. Phonon frequencies for wave vectors along the principal symmetry directions have been determined and, in addition, measurements of phonon frequencies along the boundaries of the Brillouin zone and along a more general direction are reported. The data have been fitted with a Born-von Kármán force model which includes interactions out to the eighth nearest neighbor. The interactions have been assumed to be general (tensor) out to the fourth neighbor and axially symmetric beyond. The model has been used to calculate a frequency distribution function $g\left(\nu \right)$ and related quantities such as the lattice specific heat and Debye temperature.