Experimental distinction of elements with similar atomic number using anomalous dispersion (δ synthesis): an application of synchrotron radiation in crystal structure analysis

A two-wavelength method (δ synthesis) which deals with the experimental distinction of elements with similar atomic number by means of single-crystal X-ray diffraction measurements is presented. This method uses the characteristic wavelength dependence of the anomalous-dispersion correction terms f′ and f′′ close to the absorption edges of the corresponding elements. In case of a properly chosen wavelength combination the resulting difference electron density map (δ map) mainly shows peaks at the positions of the 'near-edge' element. The basic mathematical formalism is described and selection rules for the determination of the optimal wavelength combination are derived. The applicability in case of mixed occupancy and/or occupancy deficiency is discussed. A series of δ maps which are based on theoretical data sets and calculated according to the formalism of the δ synthesis are shown. From this the influence of errors on the interpretation of the δ map can be estimated and the requirements on the experimental conditions can be determined. First experimental results concerning the distinction of Pb/Bi in the well known crystal structure of galenobismutite (PbBi₂S₄) are presented. They show that the δ synthesis is not only a theoretical model, but can be applied successfully in practice. For experimental reasons the applicability of the δ synthesis is restricted to elements with atomic numbers greater than Z = 22.