Lattice Vibrations in Trigonal HgS

Trigonal HgS (cinnabar) possesses a twofold-coordinated low-symmetry structure highly unusual among AⁿB^8-n crystals. The cinnabar structure is based on close-packed helical chains, with six atoms per unit cell and D₃ symmetry. We have investigated the long-wavelength optical phonons in HgS via their interaction with light: reflectivity in the far infrared and Raman scattering in the visible. Classical-oscillator analysis of the complex reststrahlen spectra has been carried out to obtain frequencies, infrared strengths, dielectric dispersion properties, and, in addition, polariton dispersion curves for the A₂ and E modes. The Raman scattering is dominated by the A₁ lines, and the relative magnitude of the TO and LO E lines indicate that the atomic-displacement contribution to the polarizability modulation exceeds the electro-optic. Marked complementarity between Raman and infrared intensities is noted and connected to a view of the HgS lattice as a geometric perturbation on the rocksalt structure. The frequencies (given as ν in cm^-1) of the observed lattice fundamentals and their symmetry assignments are: 29(39), A₂; 45, A₁; 87(91), E; 108(147), E; 110(141), A₂; 256, A₁; 280(288), E; 333(357), A₂; and 342(350), E. (Frequencies in parentheses refer to the longitudinal representatives of the infrared-active modes.) A simple model and the observed frequencies are used to derive approximate vibrational eigenvectors for the symmetric A₁ modes, and, on the basis of electrostatic (TO-LO) and anisotropy (A₂-E) splittings as well as Raman and infrared intensities, the three eigenvectors corresponding to 108-110 cm^-1 are taken to consist largely of rigid-sublattice motions analogous to the optical modes in simple diatomic crystals such as NaCl. The effective charge of these latter vibrations is estimated as e*e=0.4.