Elastic precursor effects during Ba_{1−x}Sr_{x}TiO_{3} ferroelastic phase transitions

Elastic softening in the paraelastic phases of Ba_{1−x}Sr_{x}TiO_{3} is largest near the transition temperatures and decreases on heating smoothly over extended temperature ranges. Softening extends to the highest measured temperature (850 K) for Ba-rich compounds. The temperature evolution of the excess compliance of the precursor softening follows a power law δS∝|T−T_{C}|^{−κ} with a characteristic exponent κ ranging between 1.5 in SrTiO_{3} and 0.2 in BaTiO_{3}. The latter value is below the estimated lower bounds of displacive systems with three orthogonal soft phonon branches (0.5). An alternative Vogel-Fulcher analysis shows that the softening is described by extremely low Vogel-Fulcher energies E_{a}, which increase from SrTiO_{3} to BaTiO_{3} indicating a change from a displacive to a weakly order-disorder character of the elastic precursor. Mixed crystals of Ba_{x}Sr_{1−x}TiO_{3} possess intermediate behavior. The amplitude of the precursor elastic softening increases continuously from SrTiO_{3} to BaTiO_{3}. Using power-law fittings reveals that the elastic softening is still 33% of the unsoftened Young's modulus at temperatures as high as 750 K in BaTiO_{3} with κ≃ 0.2. This proves that the high-temperature elastic properties of these materials are drastically affected by precursor softening.