The X‐ray reflectivity of bent perfect crystals is calculated from a model where the crystal is approximated by a stack of perfect‐crystal lamellae which have a gradually changing orientation. A computer program is developed for calculation of the reflectivity of the composite crystal from the dynamical theory of diffraction. An approximate solution is also given where an analytical formula for the reflectivity of a non‐absorbing lamella is used and the effects of absorption are calculated separately. Typically, in the Bragg case, the reflectivity curve has a steep edge and an exponentially falling slope, while in the Laue case the curve is almost rectangular if the absorption is not too large. The width of the curve is inversely proportional to the bending radius in both cases. Reflectivity curves were measured for the 111 and 400 reflections of Si with Mo Kα1 radiation. The agreement with analytical and computer calculations is good, particularly at small bending radii where the kinematical limit is approached.
A new iterative way to apply the Tikhonov regularization method for solving partial structure factors from anomalous X-ray scattering data is presented. It is used to obtain the regularized Pt-Pt partial structure factor in a complex amorphous material, platinum uridine blue, containing many atomic species, utilizing experimental anomalous wide-angle X-ray scattering data. Since only platinum has a suitable absorption edge for the measurement, the problem is very much ill-posed, and without regularization only unreliable solutions are obtained. The average Pt-Pt distances, determined from the Pt-Pt partial distribution function, are 3.0 and 5.7 A and the coordination number at 3.0 A is about 1. Accordingly, the dominating Pt-structures of Pt-uridine blue are dinuclear. The success of this method indicates that we may use anomalous scattering to obtain important, detailed information about the structure of very complex amorphous materials.
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