The role of disorder in structural phase transitions in perovskite ferroelectrics

Since the 1960's, there have been two competing models for describing structural phase transitions in the ABO3 perovskite ferroelectrics. In the displacive model of the soft mode, the order parameter is determined by the local displacements that vanish in theparaelectric phase. In the alternative order-disorder model, the order parameter is determined by the average of the local displacements, and the displacements persist in the paraelectric phase on the local scale. Although there is much evidence indicating that the local structure in theparaelectric phase of the perovskite ferroelectrics is different than the average structure, there has been a strong reluctance to abandon the displacive model.; X-ray scattering measurements from paraelectric BaTiO3 and KNbO3 reveal diffuse sheets of scattering in reciprocal space that are indicative of structural disorder. However, the diffuse sheets have also been explained by the presence of the soft mode in order to reconcile the displacive model. As a result, the origin of the diffuse sheets is still a matter of debate. In order to shed new light on this unsettled controversy, we have carried out a synchrotron x-ray scattering study of PbTiO3. This system has the same soft mode as BaTiO3 and KNbO3, but the local structure is distinctly different. If the diffuse sheets are caused by the soft mode, then we expect to find the same diffuse sheets in paraelectric PbTiO3. If the diffuse sheets are caused by the local distortions, then we expect to find something different in the diffuse scattering signature of PbTiO3. Indeed, we find that diffuse x-ray scattering from the local structure of paraelectric PbTiO3 is broad and featureless, in stark contrast to the diffuse sheets that are observed in BaTiO3 and KNbO3. A quantitative analysis of the thermal diffuse scattering indicates that the soft mode contribution is negligible in all three perovskites and the difference in the diffuse scattering from PbTiO3 is due to the different disordering of their local structures. This is in agreement with the finding that local distortions in the perovskite ferroelectrics persist above the phase transition, but lose their long-range correlation.