The refractive indices of calcite and aragonite

Abstract

1. The two crystalline forms of calcium carbonate, calcite and aragonite, have been analyzed by X-ray methods, and they both display strong double refraction. It is therefore of interest to see whether the large difference in the refractive indices for light polarized in different planes can be explained by the atomic arrangements in the crystals. The electron theory of dielectric media supposes that the atoms of the medium become polarized under the influence of an external electric field. The positive and negative components of the atom suffer a relative displacement, which is equivalent to the development of an electric doublet placed at or near the centre of the atom. The moment of the doublet is proportional to the strength of the electric field in its immediate neighbourhood, the constant of proportionality being characteristic of the atom considered. The local field which causes the polarization of the atom may for convenience be divided into two parts, the first being the force arising from charges in the field, including the doublets of the polarized medium not in the immediate neighbourhood of the atom, the second being the force arising from the doublets in its immediate neighbourhood. In isotropic media, such as liquids or amorphous solids, the average effect of the neighbouring doublets will be same what-ever the direction of the electric field which causes polarization. In Crystals of lower symmetry than that of the cubic system, this will not be the case. The influence of the neighbouring doublets on an atom will depend on the orientation of the electric field with reference to the crystal axes; this will be the case both for the alternating fields of a wave train as well as for a steady field. The effective dielectric constant will therefore depend upon the direction of the electric vector of the waves, and since the velocity of light is inversely proportional to the square root of the dielectric constant, the crystal will display double refraction.