Lattice Dynamics of Crystals of the Calcite Structure II. Dispersion Curves and Phonon Densities

Abstract

AbstractPhonon dispersion curves of the external and internal modes of trigonal CaCO3 have been calculated for some directions in the Brillouin zone. The one‐phonon density, the two‐phonon density, and the specific heat have also been determined. The results are compared with available experimental data on the specific heat and the two‐phonon absorption spectrum. The frequencies of the external modes have been calculated neglecting the internal degrees of freedom of the complex ions CO−3−, using a shell model which takes the short range interaction of nearest neighbours, the Coulomb interaction, and the polarizability of the complex ions into account. The variation of the frequencies of the internal modes with wave vector y has been determined by considering only the coupling of the transition dipoles of the complex ions. For this purpose the dipole‐dipole interaction formalism normally used at wave vector y = 0 to calculate the Davydov splitting of the internal modes is extended to wave vectors |y| ≠ 0.