Comparison of the neutron, Raman, and infrared vibrational spectra of vitreous Si${\mathrm{O}}_2$, Ge${\mathrm{O}}_2$, and Be${\mathrm{F}}_2$

The inelastic neutron, Raman, and infrared vibrational spectra of vitreous Si${\mathrm{O}}_2$, Ge${\mathrm{O}}_2$, and Be${\mathrm{F}}_2$ are reported in detail and compared with one another. The neutron spectrum is shown to be a good measure of the vibrational density of states for glassy Si${\mathrm{O}}_2$ and Ge${\mathrm{O}}_2$, but a poorer measure for Be${\mathrm{F}}_2$. The density of states is shown to be split into transverse-optical—longitudinal-optical bands whose nature is revealed in the infrared and Raman spectra. Empirical selection rules are noted, including the observation that the $\mathrm{HV}$ Raman spectrum "mimics" the density of states, while the $\mathrm{HH}$ spectrum is dominated by matrix-element effects. The spectra are discussed in terms of an augmented central-force model which allows prediction of selection rules and relative densities of states. The latter allows an empirical estimate of the frequency dependence of the neutron scattering coupling coefficients, showing relatively weak scattering by acoustic modes, especially in the case of Be${\mathrm{F}}_2$ glass.