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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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A new method for x-ray atomic scattering factor (ASF) calculations in solids is proposedwhichenablesone toobtainimaginaryandrealpartsofthens~without Kramers-Kr6nig transformation in the anomalous dispersion region (both in XANES and EYAFS regions). Themethodproposedallowsfor the inclusionottheenvironmentalinikenceupon the ASF of the atoms in solids. Due to such influence, Asf in general becomes an anisotropic tensor. Asan example, the ASF tensor componentsofa boronatom ina hexagonal BNcrystal are calculated near the BK absorption edge. Imaginary parts of the ASF tensor components are employed to calculate the XANES which appears to be in reasonable agreement with experiment. The formulae for the intensity of x-ray diffraction from a homoatomic thin amorphous sample in a K-edge EMS region are obtained. The environmental influence upon the ASF causes the fine structure in the frequency dependence of the x-ray diffraction intensity. This fine structure together with the angular dependence of diffraction intensity is shown to provide valuable information about atomic ternary correlation functions of amorphous media.If the photon energy is close to the K absorption edge, the second term in (2) is small and the anomalous part of the ASF can be written as follows:where ro is the electron classical radius, m is the electron mass and c i s the velocity of light.