Pre-edge fine structure of the 3d atom K x-ray absorption spectra and quantitative atomic structure determinations for ferroelectric perovskite structure crystals

A complete interpretation is proposed for the pre-edge fine structure (PEFS) of the x-ray Ti K-absorption spectra for ATiO(3) 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 Tr Is electron transition to the unoccupied 3d states of the neighbouring transition metal atoms. We show that an additional peak C' 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 PbTixZr1-xO3 (PZT) solid solution) within the oxygen atom octahedrons surrounding the absorbing 3d atom. The area under peak C' is directly determined by the average number of 4d atoms in the vicinity of the absorbing Ti one.