Pressure-Raman effects and vibrational scaling laws in molecular crystals: ${\mathrm{S}}_8$ and ${\mathrm{As}}_2$${\mathrm{S}}_3$

The influence of pressure on lattice vibrations in two molecular crystals, the ring-molecule elemental crystal orthorhombic sulfur and the layer-structure chalcogenide crystal ${\mathrm{As}}_2$ ${\mathrm{S}}_3$, has been measured by observations of their first-order Raman-scattering spectra at pressures to 10 kbar. Experimental results on the many Raman-active modes in each of these crystals reveal that, in contrast to network crystals, the compression-induced shifts of the optical-phonon frequencies in molecular crystals are strikingly inconsistent with the usual frequency-volume Grüneisen scaling law. Far from being frequency independent, the mode-Grüneisen parameter ${\gamma }_i=\left(\frac{{\Delta \overline{\nu }}_i}{{\overline{\nu }}_i}\right) {(-\frac{\Delta V}{V})}^{-1\mathrm{}}$ varies strongly and systematically with mode frequency ${\overline{\nu }}_i$ over the optical-phonon spectrum, falling sharply from values of order 1 at low frequencies to values of order ${10}^{-2\mathrm{}}$ at high frequencies. ${\gamma }_i$ is thus of "normal" size for external modes but is "anomalously" small for internal modes. Although we must abandon ${\overline{\nu }}_i\sim V^{-\gamma }$ (with $\gamma$ independent of $i$) for molecular crystals, the idea of a basic vibrational scaling law can be preserved in the form of the bond-stiffness-bond-length relation $k\sim r^{-6\mathrm{}\gamma }$. Here $k$ is the force constant, $r$ the bond length, and $\gamma$ the bond-scaling parameter of order unity which is presumed to apply to both intramolecular and intermolecular forces. By superimposing such a microscopic $k\left(r\right)\mathrm{}$ scaling law on a very simple model for a molecular crystal, the overall aspects of the observed behavior under pressure are well reproduced. This elementary analysis reveals, in broad agreement with experiment, that the gross behavior of ${\gamma }_i$ with ${\overline{\nu }}_i$ is roughly ${\gamma }_i\sim {\overline{\nu }}_i^{-2\mathrm{}}$ and that the range of magnitudes spanned by the observed mode-Grüneisen parameters reflects the range of force constants characterizing the solid.