Lattice Vibrations in Trigonal HgS

Trigonal HgS (cinnabar) possesses a twofold-coordinated low-symmetry structure highly unusual among $A^n{B}^{8-n}$ crystals. The cinnabar structure is based on close-packed helical chains, with six atoms per unit cell and $D_3$ 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 $A_2$ and $E$ modes. The Raman scattering is dominated by the $A_1$ 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 $\overline{\nu }$ in ${\mathrm{cm}}^{-1\mathrm{}}$) of the observed lattice fundamentals and their symmetry assignments are: 29(39), $A_2$; 45, $A_1$; 87(91), $E$; 108(147), $E$; 110(141), $A_2$; 256, $A_1$; 280(288), $E$; 333(357), $A_2$; 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 $A_1$ modes, and, on the basis of electrostatic (TO-LO) and anisotropy ($A_2-E$) splittings as well as Raman and infrared intensities, the three eigenvectors corresponding to 108-110 ${\mathrm{cm}}^{-1\mathrm{}}$ 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 $\frac{e^{*}}{e}=0.4\mathrm{}$.