PHONON DENSITY-OF-STATES IN VANADIUM

The normalized phonon density of states g(v) of vanadium is accurately determined at room temperature (294 K) from the analysis of neutron i nelastic-scattering data obtained using a triple-axis crystal spectrom eter with a constant momentum transfer Q = 6.5 Angstrom(-1), (1 Angstr om = 10(-10) m) a constant scattered-neutron energy of 8.0 THz, and a variable incident-neutron energy. The energy transfer in the experimen t 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 bac kground scattering, multiple scattering, multiphonon scattering, absor ption and self-shielding, and for the spatial inhomogeneity of the inc ident 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 TH z, which we attribute to transverse and longitudinal phonons, respecti vely, and by a cutoff at about 8.1 THz. The peaks in our g(v) distribu tion are much more clearly resolved than in any previous work on vanad ium. We also see a small shoulder in g(v) in the region 2-3 THz, but i t is far less pronounced than in some of the earlier experiments on va nadium. Below 2 THz we find that g(v) = av(2), 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 th e basis of a nearest- and next-nearest-neighbor central force model is in generally good y agreement with our results although it differs in some details. In particular, Clark's theory predicts that the transve rse peak should be slightly more intense than the longitudinal peak, w hereas our experimental results indicate the opposite.