Dynamische Theorie der elastischen Elektronenbeugung unter Verwendung komplexer Atomformfaktoren

The two-beam approximation of dynamic electron diffraction in crystals is deduced from successive scattering by two-dimensional gratings. The scattering-amplitude caused by the single grating (phase-grating) is determined by the atomic scattering factors of the single atoms. The use of real atomic scattering factors leads here to the same solutions as the twobeam theory, using the Schroedinger-equation. Anomalous absorptions effects are described in the usual theory by introducing a complex lattice potential into the Schroedinger-equation, taking into account inelastic scattering. A more exact calculation of only elastic scattering by a single atom results in complex atomic scattering factors. Using the complex atomic scattering factors one can describe the anomalous absorption, if recursion-formulae for successive scattering are applied. On the other hand, the transformation to differential equations leads to results, which are not in agreement with experiments. The influence of inelastic scattering for the anomalous absorption can be neglected compared with the complex atomic scattering factors.