Off-center displacement of the Nb ions below and above the ferroelectric phase transition of ${\mathrm{KTa}}_{0.91}$${\mathrm{Nb}}_{0.09}$${\mathrm{O}}_3$

We have measured the off-center displacements of the Nb ions in ${\mathrm{KTa}}_{0.91}$ ${\mathrm{Nb}}_{0.09}$ ${\mathrm{O}}_3$ as a function of temperature both below and above the ferroelectric transition temperature ${\mathit{T}}_{\mathit{c}}$=85.6 K. The purpose of these measurements was to elucidate the basic nature of the ferroelectric phase transitions in mixed perovskites. The off-center displacements were determined by x-ray-absorption fine-structure (XAFS) measurements. The data were analyzed by calculating the XAFS spectra theoretically as a function of structural and other parameters and by refining these parameters to obtain the best fit with the experimental results up to the third coordination shell. In these calculations we used curved photoelectron wave functions and took into account multiple scattering up to and including, the third-order collinear scattering. It is found that these scattering contributions are both necessary and sufficient in order to account for all the scattering contributions with a total scattering path length of 8 Å or less. At 70 K the off-center displacement, relative to the oxygen octahedra, is found to be 0.145 Å in the [111] direction. These displacements change by less than 20% from 70 K to room temperature, namely, from below to far above the phase transition. These results lead to the conclusion that the magnitude of the displacements hardly changes over a very wide temperature range. Thus, the ferroelectric transition is not displacive and the main change taking place at the phase transition is from a disordered to orientationally ordered arrangement of displacements.