Structural and vibrational model for vitreous boron oxide

Abstract

The glass structure of ${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$ is thought to contain a large number of threefold six-member regular planar rings. The Raman spectrum shows a highly polarized and very sharp peak at 808 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. A Bethe lattice of boroxol rings is used here to investigate the vibrational density of states and the polarized Raman response. The results reproduce the experimental spectra extremely well and also explain the isotopic shifts of the modes when one substitutes $^{18}\mathrm{O}$ and $^{10}\mathrm{B}$. Through the calculation of local densities of states in boron or oxygen sites, one could obtain the participation ratio of all the modes, allowing a quantitative examination of the nature of any region in the spectrum, and a comparison with inelastic-neutron-scattering data.