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The ultra-low-frequency (Hz region) elastic behaviour of SrTiO3 has been examined over a wide temperature range including the cubic-tetragonal transition at Tc = 105 K and the quantum paraelectric region (T < 40 K) using a three-point-bending method. A giant elastic softening has been found in the tetragonal phase. It is explained by a model, which takes into account the motion of ferroelastic domain walls in response to the applied dynamic stress. In the quantum paraelectric regime we have detected nonlinear elastic anomalies in the real and imaginary parts of the complex Young's modulus. Our data can be consistently described if we assume that ferroelectric order is induced by the applied strain gradient, which due to flexoelectric coupling is equivalent to a homogeneous electric field. Below 25 K the induced ordered polarization clusters are frozen on the experimental timescale (11 Hz).

Results of continuous-wave resonance ͑MHz-region͒ and ultralow-frequency ͑Hz-region͒ dynamic mechanical analyzer measurements of pure KMnF 3 and mixed crystals KMn 1−x Ca x F 3 ͑x Ͻ 0.017͒ are presented in a broad temperature range including the phase-transition regions. The elastic anomalies depend strongly on the measurement frequency: The MHz-elastic constants can be well fitted by Landau theory including the difference between isothermal and adiabatic behavior. Contrary, at low frequencies ͑0.1-50 Hz͒ an elastic softening ͑superelasticity͒ due to domain-wall motion is found quite similar to that observed recently in isostructural SrTiO 3 ͓A. V. Kityk et al., Phys. Rev. B 61, 946 ͑2000͔͒. However, unlike to SrTiO 3 , for the mixed system KMn 1−x Ca x F 3 we have measured freezing of the domain-wall movement around 100 K in a certain range of concentration of Ca 2+ ions ͑x = 0.003͒. Calculating the dynamic elastic response to the ac-stress field by taking into account the motion of randomly pinned ferroelastic domain walls in KMn 1−x Ca x F 3 yields excellent agreement between theory and experiment.

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The phase transition of SrTiO3 at 105 K has been examined by studying the temperature dependence of the Young's modulus of SrTiO3 crystals along various directions. Dynamic Mechanical Analysis (DMA) at 10-140K and 10-45 Hz has been used for the experiments. The elastic behaviour is interpreted in terms of Landau theory and the DMA results are compared with ultrasonic experiments. The striking differences between the two types of data are attributed to the Occurrence of domain wall motions at low frequencies. These motions are suppressed at high frequencies (ultrasonics). We have studied the temperature behaviour of the low-frequency elastic constants of SrTi03 as function of external stress. The data analysis shows that the domain wall contribution to the elastic constants is essentially suppressed with increasing of uniaxial compression.