The first-order Raman spectrum of $\ensuremath{\alpha}$-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 $\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}$ was applied along the trigonal axis $\stackrel{^}{z}$, along the binary axis $\stackrel{^}{x}$, or along ${\stackrel{^}{z}}^{\ensuremath{'}}=(\frac{1}{\ensuremath{\surd}2})(\ensuremath{-}\stackrel{^}{y}+\stackrel{^}{z})$. 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-${\mathrm{cm}}^{\ensuremath{-}1}$ $E$ 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 ${\mathrm{cm}}^{\ensuremath{-}1}$ were measured to be 1.25 \ifmmode\pm\else\textpm\fi{} 0.09, 2.39 \ifmmode\pm\else\textpm\fi{} 0.10, and -3.02 \ifmmode\pm\else\textpm\fi{} 0.45 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively, for the phonon wave vector, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ along $\stackrel{^}{y}$; 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-${\mathrm{cm}}^{\ensuremath{-}1}$ lines were just resolved at liquid-helium temperature for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\parallel}\stackrel{^}{y}$. 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-${\mathrm{cm}}^{\ensuremath{-}1}$ line.
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