Piezospectroscopy of the Raman spectrum ofα-quartz

The first-order Raman spectrum of $\alpha$-quartz, consisting of four totally symmetric $A_1$ lines, four $E$ lines with "unresolved" LO-TO components, and four LO-TO split $E$ doublets, have been investigated under uniaxial stress. A compressive force $\overrightarrow{\mathrm{F}}$ was applied along the trigonal axis $\hat{z}$, along the binary axis $\hat{x}$, or along ${\hat{z}}^{\prime }=\left(\frac{1}{\surd 2}\right)(-\hat{y}+\hat{z})$. All splittings and/or shifts were found to be linear in stress and hence describable in terms of a linear-deformation-potential theory. From measurements using these three force directions the two deformation-potential constants characterizing each $A_1$ and the four constants characterizing each $E$ line have been deduced. The extreme sharpness of the 128-${\mathrm{cm}}^{-1\mathrm{}}$ $E$ line at liquid-helium temperature allowed a Fabry-Perot interferometer to be used in the study of its behavior. The LO-TO splittings of the $E$ lines at 263, 695, and 1160 ${\mathrm{cm}}^{-1\mathrm{}}$ were measured to be 1.25 ± 0.09, 2.39 ± 0.10, and -3.02 ± 0.45 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively, for the phonon wave vector, $\overrightarrow{\mathrm{q}}$ along $\hat{y}$; the LO-TO splittings are comparable to the observed linewidths at liquid-helium temperature and were deduced from the zero-stress intercepts of the least-squares fits characterizing the stress dependence of the components. The LO-TO splittings of the 695- and 1160-${\mathrm{cm}}^{-1\mathrm{}}$ lines were just resolved at liquid-helium temperature for $\overrightarrow{\mathrm{q}}\parallel \hat{y}$. The LO-TO splittings calculated from the reststrahlen spectra for all eight $E$ lines are in satisfactory agreement with those measured in the present Raman study, even as to the unusual negative sign for the splitting of the 1160-${\mathrm{cm}}^{-1\mathrm{}}$ line.