Resonant powder X-ray diffraction

Synchrotron radiation provides a wide choice of wavelengths for diffraction experiments, enabling resonant (anomalous scattering) effects to be exploited for most elements with atomic numbers >20. Rietveld analysis of resonant X-ray diffraction profiles may be used to study different valence states of the absorbing element and to resolve disordered structures. These resonant powder experiments are usually performed at an X-ray energy 0-20 eV below the elemental absorption edge, giving rise to a large negative value of f, the real anomalous dispersion coefficient. Two common disorder problems can be solved by Rietveld analysis of resonant diffraction data. Elements with very similar atomic numbers can be contrasted, e.g. the Fe/Ni distribution over four sites in the oxoborate FeNi2(BO3)O-2 has been determined using a single resonant pattern collected at the Fe R edge. A second problem is to distinguish between different cation substitution models, such as in the 90 K superconductor 'Tl2Ba2CuO6' where a deficiency of scattering at the Tl site could be due to vacancy formation or substitution by Cu. Simultaneously fitting the structural model to resonant patterns collected at the Cu K and Tl L(III) edges shows that Cu substitution, not vacancy formation occurs. In complex materials containing many cations, a series of resonant diffraction patterns collected at each accessible edge can be used to analyse the composition of the structure site by site. A study of the 120 K superconductor (Tl0.5Pb0.5)Sr2Ca2Cu3O9 at the TI L(III), Pb L(III), Sr K, and Cu K edges has been used to identify and quantify the substituents at each site, giving the composition (Tl0.60Pb0.40)(Sr1.60Ca0.40) (Ca1.93Tl0.07)Cu3O9. More detailed information such as site-resolved XANES and EXAFS features can be obtained by measuring diffraction peak intensities at a series of energies across an absorption edge. These DAFS (Diffraction Anomalous Fine Structure) experiments are made practicable by the development of intense new synchrotron sources and energy dispersive detectors.