Rings in central-force network dynamics

Abstract

The central-force network dynamics model for glasses is extended to treat networks involving small regular rings of bonds. In particular, band-limit formulas are obtained for an ${A}_{2}{X}_{3}$ glass consisting of regular puckered six-membered ${A}_{3}{X}_{3}$ rings. The special case of planar rings is compared with observations on vitreous ${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$. This continuous random network of "boroxol" rings shows improved agreement with experiment over a model not containing rings. The remaining discrepancies illustrate the need to include noncentral forces in the network dynamics of $v$-${\mathrm{B}}_{2}$${\mathrm{O}}_{3}$.