Hyper-Raman scattering analysis of the vibrations in vitreous boron oxide

Hyper-Raman scattering has been measured on vitreous boron oxide, $v-$B$_2$O$_3$. This spectroscopy, complemented with Raman scattering and infrared absorption, reveals the full set of vibrations that can be observed with light. A mode analysis is performed based on the local D$_{3h}$ symmetry of BO$_3$ triangles and B$_3$O$_3$ boroxol rings. The results show that in $v-$B$_2$O$_3$ the main spectral components can be succesfully assigned using this relatively simple model. In particular, it can be shown that the hyper-Raman boson peak arises from external modes that correspond mainly to librational motions of rigid boroxol rings.