Coulomb effects in disordered solids

Abstract

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 ${\epsilon }_l$(ω) and transverse ${\epsilon }_t$(ω) dielectric functions are shown to be related by ${\epsilon }_l$(ω)/${\epsilon }_{\infty }$=2-${\epsilon }_{\infty }$/${\epsilon }_t$( ω), where ${\epsilon }_{\infty }$ 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(${\omega }^2$) and the neutron scattering law S(k,ω). These general results are illustrated by calculating these response functions for a model ${\mathrm{AX}}_2$ 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.