Piezospectroscopic Study of the Raman Spectrum of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-Quartz

Abstract

The effect of uniaxial stress on the Raman spectrum of $\ensuremath{\alpha}$-quartz is investigated at liquid-helium temperatures using a quantitative stress cryostat. Stresses up to $\ensuremath{\sim}10$ kbar were employed. The $E(\mathrm{LO}+\mathrm{TO})$ doubly degenerate Raman lines with no observable LO-TO splitting, viz., the 128-, 263-, 695-, and 1160-${\mathrm{cm}}^{\ensuremath{-}1}$ lines, split into two components when the applied compressive force $\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}$ is along a direction other than the trigonal axis. The polarization features of the stress-induced components can be explained on the basis of the reduced symmetry of the crystal under uniaxial stress. The positions of the stress-induced components of the 128-${\mathrm{cm}}^{\ensuremath{-}1}$ line are linear with stress. Degenerate perturbation theory utilizing a deformation potential linear in strain permits the stress effects for $E(\mathrm{LO}+\mathrm{TO})$ lines in different crystallographic directions of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}$ to be correlated in terms of four deformation-potential constants; these have been determined for the 128-${\mathrm{cm}}^{\ensuremath{-}1}$ line to be $a=\ensuremath{-}218$, $b=\ensuremath{-}58$, $c=\ensuremath{\mp}174$, and $d=\ifmmode\pm\else\textpm\fi{}160$ in units of ${\mathrm{cm}}^{\ensuremath{-}1}$ per unit strain. The LO components of the LO-TO doublets at 393-400, 796-805, and 1064-1232 ${\mathrm{cm}}^{\ensuremath{-}1}$ show a shift to higher frequencies, whereas the TO components remain at their zero-stress positions. The deformation-potential theory predicts a linear shift with stress for lines of ${A}_{1}$ symmetry, the shift being characterized by two deformation-potential constants. These constants have been determined to be $e=\ensuremath{-}814$ and $f=\ensuremath{-}1000$ in units of ${\mathrm{cm}}^{\ensuremath{-}1}$ per unit strain for the 205-${\mathrm{cm}}^{\ensuremath{-}1}$ line of ${A}_{1}$ symmetry. The shift of the other lines of ${A}_{1}$ symmetry, viz., the 354-, 464-, and 1081-${\mathrm{cm}}^{\ensuremath{-}1}$ lines, is less pronounced than that of the 205-${\mathrm{cm}}^{\ensuremath{-}1}$ line.