Elastic precursor effects during Ba1-xSrxTiO3 ferroelastic phase transitions

Elastic softening in the paraelastic phases of Ba1-xSrxTiO3 is largest near the transition temperatures anddecreases on heating smoothly over extended temperature ranges. Softening extends to the highest measuredtemperature (850 K) for Ba-rich compounds. The temperature evolution of the excess compliance of theprecursor softening follows a power law ?S ? |T - Tc|^-? with a characteristic exponent ? ranging between1.5 in SrTiO3 and 0.2 in BaTiO3. The latter value is below the estimated lower bounds of displacive systemswith three orthogonal soft phonon branches (0.5). An alternative Vogel-Fulcher analysis shows that the softeningis described by extremely low Vogel-Fulcher energies Ea, which increase from SrTiO3 to BaTiO3 indicatinga change from a displacive to a weakly order-disorder character of the elastic precursor. Mixed crystalsof BaxSr1-xTiO3 possess intermediate behavior. The amplitude of the precursor elastic softening increasescontinuously 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 ? ~ 0.2. This proves thatthe high-temperature elastic properties of these materials are drastically affected by precursor softening.