Theory of X-ray diffraction on a lateral crystal with elastically bent lattice planes

A theory of X-ray diffraction on a lateral crystal with elastically bent lattice planes is developed within the framework of the kinematic approximation. Analytical solutions for coherent and diffuse scattering are obtained in application to high-resolution triple-axis diffractometry. The angular distribution of the intensity of coherent and diffuse scattering near a node of the reciprocal lattice are numerically simulated. It is shown that the pattern of X-ray diffraction from a crystal with a trapezoidal cross section and elastically bent lattice planes has a “butterfly” shape that was previously observed in experiment.