Investigation of non perfect single crystals with kinematical x-ray standing waves

The method of X-ray standing waves (XSW) is a well established technique for the determination of adsorbate or dopant atom positions in perfect crystals. It is based on the interference of incident and Bragg reflected wave, which is calculated with the dynamical theory of X-ray diffraction. In the present work a novel method is developed, that allows the application of the XSW-method to nonperfect mosaic crystals. For this purpose a theoretical and experimental investigation of X-ray standing wave formation in crystals at large deviations from the Bragg angle is performed. The Bragg scattered wave is described using the kinematical approximation, which is valid under weak diffracted beam conditions for nonperfect crystals as well as for ideal crystals. The cases of impurity atoms in the volume and on the surface are seperately treated in the frame of the ideal nonperfect crystal model. An analysis of accompanying effects shows that the influence of diffuse scattering and crystal truncation rods on the standing wave formation can be neglected. The experimental applicability of the theoretical derived formalism is verified by XSW-measurements of perfect and nonperfect crystals with known structure. The results of the measurements are in a good agreement with the theoretical values. The proposed method of kinematical X-ray standing waves is thus a new direct method for structure analysis of nonperfect crystals. (orig.)