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

Elastic softening in the paraelastic phases of Ba1-xSrxTiO3 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 dS ~ jT -Tcj-k with a characteristic exponent k ranging between 1.5 in SrTiO3 and 0.2 in BaTiO3. 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 Ea, which increase from SrTiO3 to BaTiO3 indicating a change from a displacive to a weakly order/disorder character of the elastic precursor. Mixed crystals of BaxSr1-xTiO3 possess intermediate behaviour. The amplitudes of the precursor elastic softening increases continuously from SrTiO3 to BaTiO3. 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 BaTiO3 with k ~ 0.2. This proves that the high temperature elastic properties of these materials are drastically affected by elastic precursor softening