The spontaneous strain in in the quantum paraelectric regime: the dependence on sample preparation

The temperature dependence of the spontaneous strain in has been studied using triple-axis diffractometers of high momentum-space resolution for synchrotron radiation with energies above 100 keV. In the temperature range from 40 to 80 K the experimental data are in excellent agreement with a Landau theory taking into account the quantum mechanical zero-point fluctuations. At temperatures below 40 K a difference between experiment and theory of about 4% occurs which is considered as an indication for a novel phase in the quantum paraelectric regime. The difference between the fitted theory and the experimental data is nearly the same for all of the samples investigated; the biggest difference is observed in the fit parameter describing the theoretical saturation value of the spontaneous strain at zero temperature. In absolute numbers the measured spontaneous strain is strongly sample dependent, i.e. flux-grown, float-zone-grown and Verneuil-grown crystals show differences in the spontaneous strain of about 30% at 10 K. On the other hand, only small variations are observed in samples which were subjected to different heat treatments, which determine the number of oxygen vacancies.