Dispersion Relation of an OH-Stretching Vibration from Inelastic X-Ray Scattering

We show that recent advances now allow us to measure the wave vector dependence of OH-stretching frequencies at energies around 400 meV by inelastic x-ray scattering using ID28@ESRF. We found a large, unexpected dispersion when we measured the dispersion relations of the hydrogen stretching frequencies of diaspore, $\alpha$-AlOOH, where the hydrogen atoms participate in a hydrogen bond of intermediate strength. We can account for this behavior with density functional perturbation theory calculations and a simple model based on H-H interactions.

Figure 1

The structure of diaspore. We use a setting in space group Pbnm, with $a=4.401\AA$, $b=9.421\AA$, $c=2.845\AA$ [6]. Black, gray, and light gray spheres represent Al, O, and H-atoms, respectively. Dashed lines indicate hydrogen bonds.

Figure 2

Prediction of the dispersion relation of the OH-stretching vibrations along high symmetry directions in the BZ from DFPT calculations.

Figure 3

Based on DFPT calculations, dynamical structure factors and hence IXS spectra were predicted in order to optimize the measurement strategy.

Figure 4

Exprimentally determined (points) and predicted (lines) phonon spectra of diaspore at $(2.500)$ and $(2.50\overline{1})$ from inelastic x-ray scattering and DFPT, respectively.

Figure 5

Left: Spectrum measured at $(2.50-\text{}1)$, which is dominated by an OH-stretching vibration having an energy of 374 meV. Total counting time was 2040 s per step. Right: Spectrum measured at $(2.500)$, which is dominated by an OH vibration having an energy of 357 meV. Total counting time was 1380 s per step.

Figure 6

Eigenvectors of the phonons at the BZ boundary at $(0.500)$, showing that during the high frequency vibration (left) the hydrogen remain at a constant distance, while during the low frequency motion (right) the hydrogens move further apart.

Figure 7

Dispersion of the OH-stretching frequencies along a low symmetry direction. The left vertical line corresponds to $(0.500)$, the right vertical line to $(00-\text{}0.333)$.