Effects of tensile stress on the R lines of Cr(3+) in a sapphire fiber

Review: Coefficients for Stress, Temperature, and Composition Effects in Fluorescence Measurements of Alumina

The numerical coefficients linearly relating the effects of stress (including pressure), temperature, and composition to shifts in the energies of the Cr-related fluorescence in alumina (Al₂O₃) are reviewed. The primary focus is the shift of the R₁ and R₂ "ruby" fluorescence lines under conditions typical for stress determination in polycrystalline Al₂O₃. No significant experimental difference in the R₁ and R₂ responses is observed for hydrostatic stress (or pressure) conditions (average shift coefficient of about 7.6 cm^-1/GPa), changes in temperature (about 0.140 cm^-1/K), or variations in composition (about 120 cm^-1/mass fraction of Cr). There are significant differences in the R₁ and R₂ responses for nonhydrostatic stress conditions. In particular, for uniaxial stress along the a and c directions in the Al₂O₃ crystal, the R₁ piezospectroscopic tensor coefficients (about 3.0 cm^-1/GPa and 1.6 GPa cm^-1/GPa, respectively) differ considerably, whereas the R₂ coefficients (about 2.6 cm^-1/GPa and 2.3 GPa cm^-1/GPa, respectively) do not. Measurements of the piezospectroscopic tensor coefficients are shown to have interlaboratory relative consistency of about 4 % extending over 30 years, and are consistent with the scalar high-pressure measurements. Measurements of the temperature coefficients are shown to have interlaboratory relative consistency less than 1 % extending over 60 years. Fluorescence-based measurements of stress in polycrystalline Al₂O₃, although requiring temperature adjustment, are shown to have a relative uncertainty of about 2.5 %.