Low-lying phonons in ${\text{NaBH}}_4$ studied by inelastic scattering of synchrotron radiation

Acoustic phonon dispersion has been measured in the cubic phase of ${\text{NaBH}}_4$ by the inelastic x-ray scattering (IXS) technique using single crystals of natural isotope composition at room temperature. Experimental results are compared with the compressibility data and the previously published ab initio calculations. Comparison of the elastic properties derived from the diffraction and IXS experiments indicates a non-negligible contribution (below 10%) of nonhydrostatic effects in the diffraction experiments. Strong preferred orientation in the compressed samples is also revealed by Rietveld analysis of the synchrotron powder-diffraction data.

Figure 1

(Color online) Powder-diffraction pattern collected at $p=3.64\text{GPa}$ (dots) together with the calculated and difference curves (lines). Vertical bars indicate positions of Bragg peaks.

Figure 2

Unit-cell volume as a function of pressure for the cubic phase of ${\text{NaBH}}_4$. Circles denote data points for this work while squares correspond to the data from Ref. 11.

Figure 3

Selected IXS spectra of ${\text{NaBH}}_4$ at the indicated $\xi$ values (given in reciprocal-lattice vector units) (a) for the LA [111] branch with momentum transfer $\left[2+\xi 2+\xi 2+\xi \right]$ and (b) for the TA ${\left[110\right]}_{⟨1-10⟩}$ with momentum transfer $\left[2+\xi 2-\xi 0\right]$. The spectra are shifted along the vertical direction for clarity, conserving the same intensity scale.

Figure 4

(a) IXS spectrum recorded at (310) (solid diamonds) compared to the resolution function (solid line). (b) Phonon dispersion in high-symmetry directions; experimental points (empty symbols) connected by a guide for the eyes (solid lines) are compared with the ab initio calculations (dashed lines) for the $F\overline{4}3m$ structure (Ref. 6). The estimated experimental errors are less than the symbol size.