Central force model for the high frequency vibrational bands of glasses

We have set up a simple model for the high frequency vibrational modes of A_nX_m glasses (i.e. those modes which are probed most easily in infrared absorption and Raman scattering experiments). This model involves using only nearest neighbor central forces and is a generalization of previous work by Sen and Thorpe for AX₂ glasses in which the vibrational spectrum is derived from the connectivity matrix of the structure. Simple algebraic expressions are obtained for the band edges and applied to the spectra of glassy GeS₂, GeO₂ and P₂O₅. The dominant features of the spectra are associated with particular band edges in the central force model, taking due account of selection rules governing polarized Raman scattering in network glasses. Errors to be expected from the omission of non-central forces and long-range Coulomb forces are discussed.