Analysis of Stress and Temperature Dependence of Fluorescence in SrTi<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Cr</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>

Abstract

We write a configurational potential for SrTi${\mathrm{O}}_{3}$ which depends on strain and the soft optic-mode coordinates whose wave vector lies at the corner of the Brillouin zone. Minimizing this potential gives the static response of the crystal to applied stress. Below the cubic-to-tetragonal transition temperature at 106\ifmmode^\circ\else\textdegree\fi{}K, uniaxial stress applied in the [111] direction induces a transition from the natural tetragonal to a trigonal phase, but transitions for [100] and [110] stresses are not found. A crystal-field calculation gives the $R$-line emission energy of ${\mathrm{Cr}}^{3+}$ impurities. The results fit the temperature-dependence anomaly found by Stokowsky and Schawlow and, within limits, the pressure dependence found by Burke and Pressley. However, pronounced discrepancies appear at stresses along the [100] and [110] directions which exceed critical values of 10 and 57 kg/${\mathrm{mm}}^{2}$, respectively, suggesting that new phases of unknown character appear. The crystal-field parameter values inferred from the comparison with experiment support the nearest-neighbor approximation for the cubic component of the crystal-field, but not for lower-symmetry components. Our calculations disagree with a reported measurement of the stress dependence of the transition temperature.