X-ray diffraction in a crystal with trapezoidal cross section

Within the framework of recurrence relations the dynamical X-ray diffraction in the lateral crystal with trapezoidal cross section is considered. The boundary conditions of the considered problem are described in detail. It is shown that in the recurrence relations, when the crystalline media is absent, we are also to take into account the phase change in transmitted and reflected X-ray waves. Using the obtained solution, we performed a numerical simulation of the angular distribution of the X-ray scattering intensity. Rocking curves and reciprocal space maps (RSMs) from trapezoidal crystals of different lateral width were calculated. The relative analysis of dynamical and kinematical diffraction was made. It is shown that for the trapezoidal crystals with small lateral sizes the results of kinematical and dynamical diffraction are the same. The contours of equal intensity on RSMs become narrower with increasing of lateral crystal width. The directions of the inclined stripes on kinematical and dynamical RSMs are associated with the tilt angles of the trapezoidal crystal sides relative to the lower base of the trapezoid. For large lateral size crystals the rocking curve profile matches with the shape of the reflection Darwin curve.