The lattice dynamics of niobium I. Measurements of the phonon frequencies

Abstract

Measurements of the frequencies of the normal modes of vibration of niobium at 296 °K have been made by inelastic neutron scattering techniques. Results are presented for several hundred phonons with wave vectors at general positions in the [11, macron0] reciprocal lattice plane. The phonon dispersion relations in symmetry directions agree well with the previous work of Nakagawa and Woods. The measured frequencies cannot be fitted well by tensor force-constant models even when the range of the forces extends to tenth-nearest neighbours, but the critical points in the phonon density of states derived from the eighth-neighbour model agree with those observed in superconducting tunnelling experiments, and the calculated Debye temperature also agrees quite well with measured values.