Elastic and elasto-optic constants of rutile from a Brillouin scattering study

Abstract

Brillouin scattering in rutile is studied with a triple passed scanning Fabry-Perot interferometer. By observing the spectra with large-order differences between a Brillouin component and its parent laser line, all the elastic moduli $c_{\mathrm{ij}}$ were determined with high accuracy; we obtain $c_{11}=2.674\mathrm{}\pm 0.002$, $c_{33}=4.790\mathrm{}\pm 0.002$, $c_{44}=1.233\mathrm{}\pm 0.008$, $c_{66}=1.894\mathrm{}\pm 0.015$, $c_{12}=1.808\mathrm{}\pm 0.037$, and $c_{13}=1.466\mathrm{}\pm 0.029$ in units of ${10}^{12}$ dyn/${\mathrm{cm}}^2$. Elasto-optic constants $p_{\mathrm{ijkl}}$ of rutile are deduced from an intercomparison of its Brillouin components with those of fused quartz as well as from the intensity ratios of the Brillouin components observed with a variety of scattering geometries. These constants are determined as a function of wavelength and show interesting dispersion effects. We have verified for the first time the recent prediction of Anastassakis and Burstein that $p_{\mathrm{ijkl}}\ne p_{\mathrm{jikl}}$ by obtaining $\frac{p_{\mathrm{zyzy}}}{p_{\mathrm{yzzy}}}=1.16\mathrm{}\pm 0.06$. We have also confirmed the prediction by Nelson and Lax and the observations of Nelson and Lazay regarding the inequality $p_{\mathrm{ijkl}}\ne p_{\mathrm{ijlk}}$. By measuring the Brillouin spectra and the 447-${\mathrm{cm}}^{-1\mathrm{}}$ $E_g$ Raman line under identical experimental conditions with a double monochromator, we have determined the absolute value of the single independent component characterizing the Raman tensor per unit cell, viz., $\mathrm{}\left|d\right|=22\mathrm{}\pm 2$ ${\mathrm{A}}^2$.