SELECTION RULES AND TEMPERATURE DEPENDENCE OF THE FIRST-ORDER RAMAN EFFECT IN CRYSTALS

Abstract

Starting from the most general scattering formulae, the current theory of the Raman effect in crystals is modified in such a way as to remove the well-known discrepancies between theory and experiment concerning the selection rules for calcite and similar crystals. A distinction is made between electrons in delocalized crystal orbitals and electrons in localized atomic or molecular orbitals and it is shown that only the latter produce a Raman scattering in agreement with the unmodified theory. The general formula for the scattering by delocalized electrons is analyzed and it is found that the magnitude of the components [Formula: see text] of the first-order polarizability (qi normal coordinate of the scattering lattice vibration) depends on the wave vectors Q′ and Q″ of incident and scattered light. The wave vector dependence of the first-order polarizability requires selection rules for the first-order Raman effect which do not correspond to the full symmetry of the scattering crystal but only to the symmetry operations of the group of Q = Q′ – Q″ which leave Q unchanged. These modified selection rules are shown to be compatible with experiment. The influence of mechanical anharmonicity and of polarizability derivatives of higher order on the first-order Raman effect is also discussed. It is found that these non-linear effects offer no satisfactory explanation for the great intensity of forbidden lines in the Raman spectrum of some crystals. Concerning temperature effects the non-linear terms in the intensity formulae are found to be of greater importance and are tentatively suggested as being responsible for the anomalous temperature dependence of low frequency external lattice vibrations.