Lattice dynamics of vanadium: Inelastic x-ray scattering measurements

We measured the phonon dispersions in vanadium along the principal symmetry directions using inelastic x-ray scattering. Our data complement previous results derived from thermal diffuse scattering and clearly reveal several phonon-dispersion anomalies, as well as pronounced variations of the phonon widths. Electronic structure calculations, more specifically, an analysis in terms of Fermi-surface spanning vectors allow the qualitative association of these anomalies with the topology of the Fermi surface, thus highlighting the importance of electron-phonon coupling.

Figure 1

Selected IXS spectra for the LA [1 0 0] branch at the indicated $Q$ values (given in reciprocal-lattice vector components). The experimental data are shown together with the best fit results (thin solid lines for the individual components and solid lines for the total fit). The spectra are shifted in the vertical direction for clarity, conserving the same intensity scale. The counting time per point was between 15 and 45 s.

Figure 2

Phonon dispersion for vanadium along high-symmetry directions: (a) experimental points, together with guides to the eye (dashed Bézier curves); solid lines correspond to the long-wavelength limit from ultrasonic measurements (Ref. 12) and (b) comparison of our experimental dispersion (dashed lines) with thermal diffuse scattering data (Ref. 8).

Figure 3

Line broadening (HWHM) for LA phonons along the (a)$\Gamma \text{−}H$, (b)$\Gamma \text{−}N$, and (c)$\Gamma \text{−}P\text{−}H$ directions and TA phonons along the (d)$\Gamma \text{−}P\text{−}H$ direction.

Figure 4

Phonon dispersions in vanadium and niobium (Ref. 9) compared to the FS spanning vector density (see text). The numbered shaded areas are guides to the eye associated with anomalies. The dashed lines correspond to a two-neighbor lattice dynamics model that mimics the phonon dispersion without long-range interactions. The energy scale is not retained for the $\Gamma \text{−}N$ direction.