Lattice Dynamics of Yttrium at 295 K

Abstract

Phonon-dispersion curves along the [$10\overline{1}0$], [$11\overline{2}0$], and [0001] symmetry directions of the hcp metal yttrium have been measured by inelastic neutron scattering using the triple-axis neutron spectrometer at the Ames Laboratory Research Reactor. The dispersion curves are not strikingly different from those of other hcp metals with a similar $\frac{c}{a}$ ratio. A careful search has been made for Kohn-type anomalies, and evidence for two such anomalies has been obtained. A modified axially symmetric force-constant model has been used to fit the phonon frequencies, and it has been found that although forces acting normally to the basal plane are not large beyond first neighbors, forces acting parallel to the basal plane are long-ranged, and interactions up to at least sixth neighbors have to be taken into account. The fitting has been done in a linear manner using Fourier analyses of the dispersion curves and other linear constraints such as the elastic constants. A frequency-distribution function has been calculated and used to calculate the specific heat and anisotropic Debye-Waller factor. Good agreement is obtained on comparison with the experimental data.