Temperature Dependence of Raman Linewidth and Shift inα-Quartz

The linewidth and frequency of the ${128-\mathrm{c}\mathrm{m}}^{-1\mathrm{}}$ and the ${466-\mathrm{c}\mathrm{m}}^{-1\mathrm{}}$ optical lattice vibrations in quartz have been measured between 5 and 300°K by means of high-resolution Raman spectroscopy. The ${128-\mathrm{c}\mathrm{m}}^{-1\mathrm{}}$ mode, which is both Raman- and infrared-active, is the lowest-lying optical vibration in quartz and shows a marked increase in lifetime at low temperatures. Utilizing available phonon dispersion spectra obtained from neutron scattering, the linewidth and shift are calculated in terms of three-phonon interactions. A simple model for the cubic anharmonicity, which includes relaxation broadening of the thermal phonons, is applied satisfactorily to the residual damping at low temperatures. The ${128-\mathrm{c}\mathrm{m}}^{-1\mathrm{}}$ LO-TO splitting, which is extremely small, is not resolved directly, but manifests itself as an observed broadening at helium temperatures.