Lattice dynamics of beryllium oxide: Inelastic x-ray scattering and ab initio calculations

The phonon-dispersion relations of the lightest wurtzite structure compound BeO have been determined from inelastic x-ray scattering (IXS) measurements and analyzed by ab initio calculations. Experimental data and calculations show good agreement and reconcile the existing controversies. The phonon linewidth of the longitudinal-optical phonon along $\Gamma \text{−}A$ reveals a marked $q$ dependence, which can be correlated with the two-phonon density of states, thus pointing toward a strong anharmonic behavior.

Figure 1

Selected IXS spectra for the in-plane polarized transverse acoustic (TA) phonons propagating along $\Gamma \text{−}M$ at the indicated $Q$ values $\left(1+\xi 1-\xi 0\right)$, given in reciprocal-lattice vector units. The experimental data are shown together with the best fit results (solid lines). The spectra are shifted along the vertical direction for clarity, conserving the same intensity scale.

Figure 2

Polar plot of the derived sound velocity data in the $a\text{−}c$ plane: experimental data (points) and fit results (solid lines). Experimental points are enumerated as given in Table .

Figure 3

IXS spectra for the longitudinal-acoustic (LA) and longitudinal-optic (LO) phonons propagating along $\Gamma \text{−}A$ at the indicated $Q$ values $\left(002+\xi \right)$, given in reciprocal-lattice vector units. The spectra are shifted along the vertical direction by 10 cps for clarity, conserving the same intensity scale.

Figure 4

Calculated intensity maps together with experimental phonon energies for $Q$ regions $\left(\xi +1\xi -21\right)$ and $\left(\xi 03\right)$ with $0\le \xi \le 0.5$. Identical symbols are attributed to the same branch.

Figure 5

Phonon dispersion for BeO along high-symmetry directions: (a) experimental points together with guides for the eye (Bézier curves); large diamonds correspond to Raman data (this work) and (b) comparison of our experimental dispersion (dashed lines) with ab initio calculation (solid lines) and INS data (Ref. 8) (empty circles).

Figure 6

(a) Dynamical structure factor $G\left(q\right)$ measured for the LO branch along the $\Gamma \text{−}A$ direction (open diamonds) compared with ab initio calculation (solid line); (b) line broadening for the same branch; (c) ab initio calculated two-phonon density of states (DOS) (weighted by thermal occupation numbers) for $\Gamma$ and $A$ points with superposed LO frequencies at $\Gamma$ and $A$ points; (d) Raman spectra taken in two different configurations as indicated in the figure.