The electric field in crystals III. The refractivity of $\alpha$-quartz

Abstract

A calculation has been performed by using dipolar lattice sums in α-quartz to interpret the refractivities in terms of the point polarizabilities of silicon and oxygen. The details of the calculations are similar to those in the first two papers of this series which dealt with the TiO₂ structures. If quartz is taken to consist of an isotropic Si⁴⁺ ion and an O^2- ion, then the results of the present calculations show that the oxygen ion can be considered to have an axial polarizability tensor with α₀^parallel = 1.43 ų, α₀^{perpendicular} = 1.32 ų. On the other hand, the analysis does allow an interpretation in terms of neutral oxygen and silicon and it is concluded that further work is needed before the state of the atomic components in the quartz lattice is finally decided.