Phonon dispersions in niobium determined by x-ray transmission scattering

Quasielastic x-ray scattering from thermally populated phonons in crystalline niobium was recorded using a charge-coupled device over a large angular range. The patterns, displayed on a logarithmic intensity scale, reveal rich features. Theoretical patterns based on a lattice dynamics calculation are generated, and a least-squares simultaneous fit of these patterns recorded at several incidence angles yields phonon dispersion relations over the entire reciprocal space. The dispersions along high-symmetry directions are generally in good accordance with available neutron scattering data.