X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

Abstract

Abstract⎯Asymmetrical Bragg diffraction in a perfect crystal with plane entrance surface is considered theoretically. In the dynamical diffraction equations the second derivatives of amplitudes in the direction, perpendicular to the diffraction plane are taken into account. Using the corresponding Green function, a general form for the amplitudes of waves in the crystal is presented. The sizes of the source in both directions as well as the source-crystal distance and non-monochromaticity of the radiation incident on the crystal are taken into account. On the basis of obtained formulas, the coherent properties of the field depending on the sizes of the source and on the width of spectrum of the incident radiation, are analized.

Dependence of X-ray asymmetrical Bragg case plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane

“…The solutions of equation (2) in the crystal can be expressed via the surface integral using the Green function for the Bragg case asymmetrical diffraction (Balyan, 2014c). We are interested in the amplitude of the reflected wave.…”

“…The general theory for the Bragg case dynamical diffraction, when two deviation parameters are taken into account, is given in the work of Balyan (2014c).…”

“…In this work, based on the general theory given by Balyan (2014c), the plane-wave rocking-curve dependence on the deviation angles in and perpendicular to the diffraction plane for the asymmetrical Bragg case is investigated. Instead of using the general theory, one may use the conventional planewave theory.…”