Interaction of Elastic Strain with the Structural Transition of Strontium Titanate

Second-order displacive transitions of a type often observed in crystals of perovskite structure are analyzed by means of a phenomenological model employing optical soft-mode and elastic-strain coordinates. Relations connecting spontaneous distortion, soft-mode vibrational frequencies, and elastic constants of a tetragonal low-temperature phase are derived. These relations are found to be consistent with existing x-ray, neutron, EPR, Raman, Brillouin, and ultrasonic data for SrTi${\mathrm{O}}_{3}$. From these data, it is inferred that properties of SrTi${\mathrm{O}}_{3}$ are isotropic to a considerable degree and that, of the small anisotropy which determines the symmetry of the low-temperature phase, interaction with strain contributes a large portion. Under certain assumptions, the soft-mode force constant inferred from the data appears to vary fairly smoothly through the transition temperature. Discontinuities in the specific heat and the temperature-derivative of the restoring-force coefficient amounting to 1.3% in SrTi${\mathrm{O}}_{3}$ and about 8% in LaAl${\mathrm{O}}_{3}$ are predicted.