Phonon dispersion curves of bcc Ba

Abstract

Large single crystals of bcc Ba were grown and were used to study the lattice dynamics of this divalent metal by inelastic neutron scattering. The phonon dispersion curves were measured, at room temperature, along the [ξ00], [ξξ0], and [ξξξ] symmetry directions. Along the [ξ00] symmetry direction, the frequencies of the longitudinal dispersion curve were found to be lower than those of the transverse branch, a surprising result in view of the relatively simple electronic structure of this metal. This anomalous feature of the dispersion curves was attributed to the hybridization of the free-election-like states with the d bands, which in this metal are only slightly above the Fermi level. To provide support for this interpretation, the frequencies of the longitudinal and transverse branches along the [ξ00] direction were evaluated at the middle of the zone (ξ=(1/2)) with use of first-principles frozen-phonon techniques. The results of these calculations are in good agreement with the experimental data and, in addition, clearly demonstrate that the observed anomaly is sensitive to the position of the d bands relative to the Fermi level. The data were used to evaluate the elastic constants, the phonon density of states, and the lattice specific heat of Ba.