We review the experimental evidence and qualitative arguments for the existence of small highly regular rings of bonds in amorphous (a-)${\mathrm{SiO}}_2$ and selected other ${\mathit{AX}}_2$ tetrahedral glasses. The structure and vibrations of planar 3-rings and regular puckered 4-rings in a-${\mathrm{SiO}}_2$ are then modeled using Born central and noncentral forces. The vibrational coupling of these rings to the more disordered glass network is modeled by attaching a Bethe lattice at each connection. The calculated vibrational properties of the breathing modes of the rings are found to be quite consistent with the observed frequencies, linewidths, and isotope shifts of the sharp lines ${\mathit{D}}_1$ and ${\mathit{D}}_2$ seen in the Raman spectra of a-${\mathrm{SiO}}_2$. The results support the previous assignment of ${\mathit{D}}_2$ (606 ${\mathrm{cm}}^{\mathrm{-}1}$) to a planar 3-ring and ${\mathit{D}}_1$ (495 ${\mathrm{cm}}^{\mathrm{-}1}$) to a regular ring. Similar calculations for a-${\mathrm{GeO}}_2$ are consistent with the suggestion that this material contains a substantial concentration of nearly planar 3-rings. Our methods can be generalized to treat similar forms of intermediate range order in glasses having other network connectivities.

• Received 10 May 1993

DOI:https://doi.org/10.1103/PhysRevB.48.15672