Anisotropy of anomalous scattering in X-ray diffraction. II. Combining polarization-dependent transmission and diffraction, and an application to partial-structure analysis

The superposition of polarization-dependent X-ray transmission through crystals and resonant Bragg diffraction in crystals is investigated both theoretically and experimentally. The effects of anisotropic anomalous scattering (AAS) on the intensity of kinematically diffracted X-radiation emerging from an anisotropically absorbing crystal are described in a model that combines scattering in both forward and reverse directions. The model based on site-symmetry-compatible second-rank scattering-factor tensors for the absorbing atoms implies an additional intensity dependence on the rotation (Ψ) about the scattering vector h. The derived intensity function, I(h; Ψ), includes the usually factorized corrections for polarization and absorption. The model is applied to reflections in LiHSeO₃ (orthorhombic, space group P2₁2₁2₁). The systematic extinction rules for the axial reflections with odd indices can be violated by AAS. These `forbidden' reflections are then due exclusively to the partial structure of the Se `edge' atom, and a set of possible Se-atom positions can be derived from the relative intensity variations,I(h; Ψ), of only a few such `forbidden' reflections. Experimental proof was obtained by synchrotron-radiation (using DORIS II at HASYLAB/DESY) X-ray diffraction measurements at the Se K-absorption edge (E = 12.654 keV) using a large synthetic LiHSeO<sub>3</sub> crystal. Significant anisotropy of anomalous scattering was observed permitting studies of both `forbidden' (0k0, 00l) and allowed (00l) reflections. With anisotropic absorption included in the model, indications for z(Se) and y(Se) were obtained from only four 'forbidden' 00l and three 'forbidden' 0k0 reflections, respectively. The experimental values are z(Se) = 0.2375 (125) and y(Se) = 0.150 (5) compared to the true values z = 0.23316 (4) and y = 0.14709 (2).