On the relationship between refractive index and density for SiO2 polymorphs

Abstract

The Gladstone-Dale law (specific refraction) and the Drude law (molecular refraction) for silica polymorphs, at “sodium light” (λ D =0.5893 μm), are derived from simple atomic properties of SiO2 complex (atomic weight, first ionization potential). The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) v 0 of elementary electron oscillators (in energy units, hv) is identified with the band gap E G of a solid; on the other hand, this E G -gap is identified with the single ionization potential $$\tilde U$$ of non-free atoms. For $$\tilde U$$ =E G =10.2 eV (energy gap of quartz, see Nitsan and Shankland 1976b) the Gladstone-Dale law, or specific refraction, is (n−1)/ρ=0.208 cm3/g, where n and ρ are the refractive index and the density of medium, respectively. According to empirical data, the average value of the specific refraction of pure SiO2 polymorphs (except stishovite-high density phase of silica) is (〈n〉−1)/ρ=0.207±0.001 (〈n〉 denotes the mean refractive index of crystal). For stishovite the Drude law (n 2−1)/ρ=0.542 cm3/g is valid under an assumption that the first ionization potential $$\tilde U$$ =E G ≈9 eV; this result is good agreement with the empirical value (〈n〉2−1)/ρ=0.536 cm3/g.