Paraelectric Elastic Properties of Reduced and Heterovalently Doped BaTiO₃ Single Crystals Studied by Using Brillouin Spectroscopy

The effects of rhodium (Rh) doping on the elastic properties and phase transition behaviors of reduced BaTiO₃ single crystals were investigated in the paraelectric phase by using Brillouin spectroscopy. The Rh doping induced changes in the elastic stiffness coefficients and the elastic anisotropy parameter. The degree of softening of (C₁₁ − C₁₂)/2 became more substantial with Rh doping, indicating that the polarization fluctuations were enhanced by heterovalent Rh³⁺ doping. This was supported by the much larger temperature range over which the nonzero birefringence was observed. Free charge carriers introduced by Rh doping and oxygen vacancies in the reduced BaTiO₃ and their interactions with the lattice seem to be the origin of these anomalous changes in the elastic properties.