Theory of the Photoelastic Effect of Cubic Crystals

Abstract

The theory of Ewald and Born of the double refraction of crystals is applied to the calculation of the photoelastic properties of $D$ lattices. Only in special cases, as for instance in KCl for pressure parallel [111], is the effect determined by the anisotropy of the Lorentz and Coulomb forces. In these cases the photoelastic data determine the ratio $\frac{R_{\mathrm{Cl}}}{R_{\mathrm{K}}}$ of the ionic refractions. Satisfactory agreement with all observations can be reached by assuming that the elastic deformations produce optical anisotropy of the atoms. Introducing this assumption in the Ewald-Born theory leads to an explanation of the change of the index of refraction with the density, and of the different photoelastic properties of NaCl, KCl, Ca${\mathrm{F}}_2$ and diamond. The photoelastic constants of other crystals are predicted. It is shown that the "cavity" method of Lorentz and Bragg gives the same Lorentz force as the theory of Born and Ewald. The calculations of the photoelastic effect by Herzfeld and Banerjee are incorrect and incomplete.