A new approach to multibeam X-ray diffraction using perturbation theory of scattering

Perturbations to conventional two beam X-ray diffraction arising from multibeam scattering effects have been studied theoretically. A simple analytical expression for the diffracted wave field and intensity near a multiple excitation is derived by using the perturbation theory of scattering of electromagnetic waves. Although it cannot be applied to the center of a multibeam diffraction peak, it does show explicitly the asymmetry effect observed in experiments and its phase dependence in the neighborhood of the multibeam point. A numerical calculation for the 1 Umweganregung peak on the almost-forbidden 442 reflection of silicon gives excellent agreement with experimental data and exact n-beam computer calculations based on conventional dynamical theory. From the analytical expression, a simple rule is derived for phase determination in centrosymmetric crystals. A general 'pseudo-four- beam' case where no asymmetry effect exists is also discussed as another example of the applications.