We review the experimental evidence and qualitative arguments for the
existence of small highly regular rings of bonds in amorphous (a-)SiO2
and selected other AX2 tetrahedral glasses. The structure and vibrati
ons of planar 3-rings and regular puckered 4-rings in a-SiO2 are then
modeled using Born central and noncentral forces. The vibrational coup
ling of these rings to the more disordered glass network is modeled by
attaching a Bethe lattice at each connection. The calculated vibratio
nal properties of the breathing modes of the rings are found to be qui
te consistent with the observed frequencies, linewidths, and isotope s
hifts of the sharp lines D1 and D2 seen in the Raman spectra of a-SiO2
. The results support the previous assignment of D2 (606 cm-1) to a pl
anar 3-ring and D1 (495 cm-1) to a regular ring. Similar calculations
for a-GeO2 are consistent with the suggestion that this material conta
ins 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.