Nature of the ferroelectric phase transition in PbTiO₃

We have measured quantitatively the temperature dependence of the local distortions of PbTiO₃ crystals below and above the structural ferroelectric phase transition, using x-ray absorption fine-structure (XAFS) measurements. Two probe atoms, Pb and Ti, were used. The results were analyzed by fitting parametrized theoretical XAFS spectra to the experimental results. These measurements provide quantitative ‘‘distortion parameters’’ defined as the difference between the distance of the probe to its nearest neighbor measured in the actual structure and that in a centrosymmetric structure with the same unit cell dimensions. At low temperatures the Pb-edge spectra were fit using four shells and included single, double, and triple scattering configurations. The high-temperature fits included only two shells. The Ti-edge spectra were fitted with the first shell only. The Pb and Ti distortions vary relatively little with temperature below the transition and decrease faster near the transition temperature. Above the transition temperature, the Pb and Ti distortions at the peaks of their distortion distribution function (DDF’s) are both more than 70% of the corresponding low-temperature values. These results show that an essential element of order-disorder is present even in this nominally pure ferroelectric crystal which displays a soft mode and a dielectric constant typical of displacive-type ferroelectrics. The presence of the local distortions suggests that the displacements should have at least two correlation length scales, one associated with the local distortions, the other with the order parameter.