This thesis presents a systematic study of the application of DAFS to determine site-specific local structural and chemical information in complex materials, and the first application of state-of-the-art theoretical XAFS calculations using the computer program FEFF to model DAFS data. In addition, the iterative dispersion analysis method, first suggested by Pickering, et al., has been generalized to accommodate the off-resonance anomalous scattering from heavy atoms in the unit cell. The generalized algorithm KKFIT was applied to DAFS data from eight (00L) reflections of the high-T_{c} superconductor YBa_{2}Cu_{3}O_{7-d} to obtain the weighted complex resonant scattering amplitudes f_{w}(Q,E). The fine-structure functions chi_{w}(Q,E) isolated from the f_{w}(Q,E) are linear combinations of the individual site fine structure functions chi_{w}(Q,E)= Sum_{i} W_{i,Q}chi_{i}(E) from the two inequivalent Cu sites, added together according to the structure factor for the Cu sublattice. The chi_{w}(Q,E) were fit en masse using the XAFS analysis program FEFFIT under a set of constraints on the coefficients W_{i,Q} based on the structure factor for kinematic scattering. The W_{i,Q} determined by FEFFIT were used to obtain the fully separated complex resonant scattering amplitudes f(E) for the two Cu sites. |
The theoretical connection between DAFS and XAFS is used to justify the application of state-of-the-art theoretical XAFS calculations to DAFS analysis. The polarization dependence of DAFS is described in terms of individual virtual photoelectron scattering paths in the Rehr-Albers separable curved-wave formalism. Polarization is shown to be an important factor in all DAFS experiments. Three experimental constraints are found necessary for obtaining site-separated f(E) from DAFS data by linear inversion of the W_{i,Q} matrix and KKFIT isolated f_{w}(Q,E): 1) The diffraction must be confined to a plane perpendicular to the incident photon polarization axis; 2) The sublattice of resonant sites must have a center of symmetry parallel to the diffraction wavevector transfer; and 3) The projected density of the resonant sites onto the scattering plane must be separable. Analysis methods based on FEFF, rather than direct linear inversion, lift the first restriction; methods that do not rely on the iterative dispersion analysis lift the second restriction. Special attention was paid to demonstrating the reliability of the analysis methods for determining the complex amplitude from measured intensity data. The KKFIT algorithm was tested extensively on mocked-up DAFS data calculated by FEFF. The reliability tests showed that KKFIT accurately reproduces the input function f(E). |