Order-Disorder Behavior in the Phase Transition of PbTiO

We have quantitatively measured the temperature dependence of the local distortions of PbTiO 3 crystals below and above the structural ferroelectric phase transition using X-ray Absorption Fine Structure (XAFS) measurements. Both Pb and Ti edges were measured, providing quantitative determinations of the displacements of the atoms within the unit cell. These distortions vary little with temperature below the transition and decrease only slightly above the transition temperature. In the paraelectric phase, the Pb and Ti distortions are about 50% and 70% of the corresponding low temperature values respectively. These results show that an essential element of order-disorder is present even in this ferroelectric crystal which displays the soft mode behavior and a dielectric constant typical of displacive ferroelectrics. The presence of the local distortions suggests that the displacements should have at least two correlation length scales, one associated with the the local distortions, the..