Longitudinal and Transverse Optical Lattice Vibrations in Quartz

The vibrational Raman spectrum of quartz has been obtained by means of argon laser excitation. Vibrations ascribed by earlier investigators to multiphonon processes are shown to be longitudinal components of the doubly degenerate species-$E$ vibrations. The frequency splittings observed between the longitudinal and transverse components of each species-$E$ mode are shown to agree very well with the values calculated using classical oscillator theory. The frequency and symmetry of each of the vibrations in $\ensuremath{\alpha}$-quartz are correlated with those of $\ensuremath{\beta}$-quartz. A discussion of the complications introduced by birefringence and anisotropy is also presented. It is shown that frequency splittings between longitudinal and transverse vibrations due to electrostatic forces are in some cases much greater for quartz than the frequency shifts due to the anisotropy of the short-range interatomic forces, contrary to what has been concluded previously in the literature.