A complete interpretation is proposed for the pre-edge fine structure (PEFS) of the x-ray Ti K-absorption spectra for perovskite structure crystals. The interpretation is based on the results of numerous calculations performed by a modified full multiple scattering method which provides the theoretical spectra for the 3d transition metal oxides in fair agreement with experiment. It is shown that the three main peaks in the PEFS have quite different origin. The first long-wave side peak A is caused mainly by quadrupole transitions. The middle peak B is caused by the p-d mixture effect and the high intensity of it is considered to be a qualitative spectroscopic indication of ferroelectricity in the perovskite structure crystal. A simple formula is obtained which expresses the area under peak B through the lattice constants and mean-square displacement of the absorbing Ti atom from the instantaneous centre of the coordination polyhedron. The peak B area averaged over thermal atomic vibrations is determined by the three-particle atomic distribution function. The short-wave side peak C is caused by the Ti 1s electron transition to the unoccupied 3d states of the neighbouring transition metal atoms. We show that an additional peak on the short-wave side of peak C occurs if there are 4d atoms (for instance Zr atoms in the vicinity of the absorbing Ti atom in the (PZT) solid solution) within the oxygen atom octahedrons surrounding the absorbing 3d atom. The area under peak is directly determined by the average number of 4d atoms in the vicinity of the absorbing Ti one.

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X-ray absorption spectra (XAS) of Ti in crystals of Ti metal, Tic, TiN and TiO, rutile are calculated in EXAFS and XANES regions. Single, double and triple photoelectron scattering processes are included through the spherical-wave formalism and the crystalline muffin-tin (MT) potential model, which employs a Hartree-Fock exchange interaction between photoelectron and core electrons inside MT spheres. Overall agreement of the theoretical and experimental spectra is obtained on the absolute photon energy scale. This result enables one to treat the experimental XAFS without using adjustable parameter Eo.The neutral-atoms approximation is shown to be adequate for the phase-shift calculations i n m s theory for bothmetals and insulators. A comparison ofTi KxAnofTi metalcalculated bymeansofvariousexchange-correlation potentialsfor the photoelectronsinside mspheres is carried out. The best results are shown to be provided by Hartree-Fock and Dirac-Hara exchange potentials.

Temperature dependent preedge and extended x-ray absorption fine structure measurements at the Zr K edge for the perovskite-type zirconates PbZr 0.515 Ti 0.485 O 3 ͑PZT͒, PbZrO 3 ͑PZ͒, and BaZrO 3 are performed. To carry out a more accurate study of the weak reconstruction of the local atomic structure we employed a combination of two techniques: ͑i͒ analysis of the preedge fine structure, and ͑ii͒ analysis of the Fourier transform of the difference between ͑k͒ functions obtained at different temperatures. A detailed investigation of local atomic structure in the cubic phase for all the crystals is also performed. It is shown that neither the displacive nor the order-disorder model can describe correctly the changes of local atomic structure during phase transitions in PZ and PZT. A spherical model describing the local atomic structure of perovskite-type crystals suffering structural phase transitions is proposed.