Rigid-layer modes in chalcogenide crystals

In layer crystals in which the crystal unit cell is two or more layers thick, there appear very-low-frequency zone-center optical phonons in which the layers move very nearly as rigid units. Such rigid-layer modes occur as a consequence of the weakness of the interlayer bonding. Low-temperature Raman scattering experiments on crystalline ${\mathrm{As}}_2$ ${\mathrm{Se}}_3$ have uncovered the rigid-layer modes in this crystal, as well as many new intralayer modes. The latter have been used to test and extend a scaling relation connecting intralayer frequencies in ${\mathrm{As}}_2$ ${\mathrm{Se}}_3$ and ${\mathrm{As}}_2$ ${\mathrm{S}}_3$. The rigid-layer frequencies have been exploited to derive quantitative information about the interlayer forces. This has been done not only for ${\mathrm{As}}_2$ ${\mathrm{Se}}_3$ and ${\mathrm{As}}_2$ ${\mathrm{S}}_3$, but also for the other cases for which rigid-layer modes have been seen: Mo${\mathrm{S}}_2$, GaS, GaSe, and graphite. The results for the interlayer-intralayer force-constant ratio reveal a strong similarity among the chalcogenide layer crystals, despite their structural differences. In the layer chalcogenides, the shear and compressional interlayer force constants are about 60 and 20 times smaller, respectively, than the intralayer covalent-bond force constant. The contrastingly higher anisotropy factors which characterize the greater layerlike character of graphite are, respectively, approximately ${10}^3$ and ${10}^2$.