Coulomb effects in disordered solids

We develop a general theory to calculate the vibrational response functions for disordered solids (such as glasses and disordered crystalline alloys) in the presence of long-range Coulomb forces. The longitudinal εₗ({ω}) and transverse εₜ({ω}) dielectric functions are shown to be related by εₗ({ω})/ε_∞=2-ε_∞/εₜ( {ω}), where ε_∞ is the high-frequency electronic response. The Lyddane-Sachs-Teller relation is generalized for use in such systems. We derive sum rules involving moments that should be useful in interpreting experimental data. A general formulation is also set up for the density of states {ρ}(ω²) and the neutron scattering law S(k,{ω}). These general results are illustrated by calculating these response functions for a model AX₂ glass that roughly corresponds to vitreous silica. A periodic random network with 1536 ions in each supercell is constructed. The response functions are found using the equation-of-motion method with the Coulomb sums included explicitly using the Ewald method. The (bare) transverse response shows a rather broad optic peak whereas the longitudinal response (which is sensitive to the depolarizing field) has a sharper response at a higher frequency.