Lattice dynamics of halogen crystals

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Abstract
We propose a lattice dynamical model of halogen crystals based on central force pair interactions between atoms. The force constants are derived by fitting the model to observed Raman and infrared frequencies at the zone centre. The phonon dispersion relations are then calculated along the symmetry directions [010] and [001]. In the case of iodine, where measured dispersion curves are available, the agreement between our calculations and the phonon frequencies measured by neutron scattering is within 10 per cent. For the cases of chlorine and bromine where neutron data are not available, phonon dispersion curves along [001] are predicted. We also present the eigenvectors of all the modes at the zone centre which clarify the existing ambiguity in the symmetry assignment in the literature. Finally, a simple procedure for evaluating the slopes of the acoustic modes at the zone centre is given based on a second order perturbation theory. As an illustration, the elastic constants along [001] direction for the three halogens are given.

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