Raman intensities in covalent crystals: A bond-polarizability approach

A theoretical model for the calculation of the one- and two-phonon Raman scattering intensities (far from resonance) for covalent crystals is presented. Starting from Placzek's theory, the crystal polarizability is expressed as a sum of individual bond contributions. Instead of the usual "electron-phonon" and "electron-radiation" coupling constants, the Hamiltonian for the scattering process contains the bond polarizabilities and their derivatives with respect to the bond-stretching coordinates. The numerical value of such parameters has been obtained by Maradudin and Burstein from the experimentally known elasto-optic and electrostriction constants of the crystals. The two-phonon Raman spectrum of diamond is then calculated. The intensity trend is repoduced well and a number of interesting features are discussed. A new interpretation of the anomalous sharp line at the two-phonon cutoff is given.