Formation of a New Dynamical Mode in $\alpha$-Uranium Observed by Inelastic X-Ray and Neutron Scattering

Phonon dispersion curves were obtained from inelastic x-ray and neutron scattering measurements on $\alpha$-uranium single crystals at temperatures from 298 to 573 K. Both measurements showed a softening and an abrupt loss of intensity in the longitudinal optic branch along $[00\zeta ]$ above 450 K. Above the same temperature a new dynamical mode of comparable intensity emerges along the $[01\zeta ]$ zone boundary with energy near the top of the phonon spectrum. The new mode forms without a structural transition but coincides with an anomaly in the mechanical deformation behavior. We argue that the mode is an intrinsically localized vibration and formed as a result of a strong electron-phonon interaction.

Figure 1

Raw data offset for clarity: (a) IXS and (b) INS. The geometry in reciprocal space is shown as an inset in each frame, with $\mathit{Q}$ designating the scattering vector and $\mathit{q}$ the phonon wave vector.

Figure 2

Inelastic intensities derived from fits to the raw data shown in Fig. 1, and corrected for the thermal factor ($⟨n⟩+1$), where $⟨n⟩$ is the Bose-Einstein thermal factor. Each data set is normalized to the count time and the IXS data is multiplied by a scale factor for comparison with the relative changes in the INS data.

Figure 3

Data showing a new mode emerge near 14 meV at high temperature, together with the softening of the mode at about 11 meV. Data are offset for clarity. The phonon wave vector $\mathit{q}$ is at a zone boundary.

Figure 4

Partial summary of the phonon dispersion data (left panels) with a comparison to phonon DOS extracted from a time-of-flight (TOF) neutron scattering measurement [2] (right panel). The dispersion data points shown are all from modes polarized along $[00\zeta ]$. Right: Brillouin zone for $\alpha$-uranium indicating the notation used for the high symmetry directions and the locations of the measured anomalies (see text).

Figure 5

Heat capacity of uranium determined by direct measurement [20] and calculated by summing the contribution from the phonon DOS and the electrons ($C_{\mathrm{el}}+C_{\mathrm{ph}}$), see text.