Behavior of the Electronic Dielectric Constant in Covalent and Ionic Materials

Refractive-index dispersion data below the interband absorption edge in more than 100 widely different solids and liquids are analyzed using a single-effective-oscillator fit of the form n^2-1=E₃{E₀} ({E₀^2-^2^2) }, where is the photon energy, E₀ is the single oscillator energy, and E₃ is the dispersion energy. The parameter E₃, which is a measure of the strength of interband optical transitions, is found to obey the simple empirical relationship E₃=N₂Z₀N₄, where N₂ is the coordination number of the cation nearest neighbor to the anion, Z₀ is the formal chemical valency of the anion, N₄ is the effective number of valence electrons per anion (usually N₄=8), and is essentially two-valued, taking on the "ionic" value ₈=0. 260. 04 eV for halides and most oxides, and the "covalent" value ₂=0. 370. 05 eV for the tetrahedrally bonded A^NB^8-N zinc-blende- and diamond-type structures, as well as for scheelite-structure oxides and some iodates and carbonates. Wurtzite-structure crystals form a transitional group between ionic and covalent crystal classes. Experimentally, it is also found that E₃ does not depend significantly on either the bandgap or the volume density of valence electrons. The experimental results are related to the fundamental ₂ spectrum via appropriately defined moment integrals. It is found, using relationships between moment integrals, that for a particularly simple choice of a model ₂ spectrum, viz. , constant optical-frequency conductivity with high- and low-frequency cutoffs, the bandgap parameter E₀ in the high-frequency sum rule introduced by Hopfield provides the connection between the single-oscillator parameters (E₀, E₃) and the Phillips static-dielectric-constant parameters (E₆, ₏), i. e. , ({₏) }^2=E₀E₃ and E₆^2=E₀E₀. Finally, it is suggested that the observed dependence of E₃ on coordination number and valency implies that an understanding of refractive-index behavior may lie in a localized molecular theory of optical transitions.