Phonon density of states in vanadium

Abstract

The normalized phonon density of states g(v) of vanadium is accurately determined at room temperature (294 K) from the analysis of neutron inelastic-scattering data obtained using a triple-axis crystal spectrometer with a constant momentum transfer Q = 6.5 Å−1, (1 Å = 10−10 m) a constant scattered-neutron energy of 8.0 THz, and a variable incident-neutron energy. The energy transfer in the experiment varies from −1.9 to 10.0 THz, and the energy resolution (FWHM) is 0.35 THz at the elastic position. Necessary corrections are made for background scattering, multiple scattering, multiphonon scattering, absorption and self-shielding, and for the spatial inhomogeneity of the incident beam. The resulting g(v) distribution has an average statistical precision of about 3% and is characterized by peaks at 4.9 and 6.9 THz, which we attribute to transverse and longitudinal phonons, respectively, and by a cutoff at about 8.1 THz. The peaks in our g(v) distribution are much more clearly resolved than in any previous work on vanadium. We also see a small shoulder in g(v) in the region 2–3 THz, but it is far less pronounced than in some of the earlier experiments on vanadium. Below 2 THz we find that g(v) = av2, and the observed value of a leads to a Debye temperature that is in excellent agreement with that obtained from the measured elastic cosntants of vanadium at room temperature. A theoretical g(v) distribution calculated by Clark on the basis of a nearest- and next-nearest-neighbor central force model is in generally good agreement with our results although it differs in some details. In particular, Clark's theory predicts that the transverse peak should be slightly more intense than the longitudinal peak, whereas our experimental results indicate the opposite.