Anisotropy of anomalous scattering in X-ray diffraction. III. `Forbidden' axial reflections in space groups up to orthorhombic symmetry

Abstract

Kinematic single-crystal X-ray diffraction of totally polarized radiation is investigated for the presence of AAS (anisotropy of anomalous scattering). The developed model allows a clear distinction between geometric and structural aspects of the scattering. The former incorporates essentially an extension of the conventional polarization correction, the latter leads to a generalized structure factor. Both aspects are combined in the description of a structure-factor tensor that is defined in the diffractometer system and consists of a complex linear combination of six real basic tensors uniquely defining the dependence of a reflection intensity on both the scattering angle 2Θ and the azimuthal setting ψ of the crystal. The complex coefficients of that structure-factor expansion are determined by the crystal structure, including the anisotropy of at least one atomic scattering factor. Under the limiting conditions of purely σ-polarized radiation and one `edge atom' per asymmetric unit, effects of AAS on the systematically extinct (`forbidden') axial reflections in all monoclinic and orthorhombic space groups are studied. The compilation of the results offers both a concise survey over 23 unique cases of relevant symmetry and a practical guide to designing diffraction experiments. One possible application of FRED (forbidden reflection near-edge diffraction) is partial-structure determination, i.e. the location of an anisotropically resonant scattering `edge atom' from the intensity variations l(h, ψ). The method requires only AAS and a few reflections whose intensities are measured at selected azimuthal settings.