X-ray microbeam diffraction in a crystal

Abstract

Using the formalism of dynamical scattering of spatially restricted X-ray fields, the diffraction of a microbeam in a crystal with boundary functions for the incident and reflected amplitudes was studied in the case of geometrical optics and the Fresnel approximation (FA). It is shown that, for a wide front of the X-ray field, the angular distributions of the scattered intensity in the geometrical optics approximation (GOA) and the FA are approximately the same. On the other hand, it is established that, for a narrow exit slit in the diffraction scheme, it is always necessary to take into account the X-ray diffraction at the slit edges. Reciprocal-space maps and the distribution of the diffraction intensity of the microbeam inside the crystal were calculated.

X-ray Laue diffraction by sectioned multilayers. I. Pendellösung effect and rocking curves

“…However, more complete information on the structure of multilayers is provided by the use of triple-axis diffractometry (Iida & Kohra, 1979;Punegov, 2015). Therefore, the next step will be to consider the Laue diffraction in the case of restricted X-ray beams (Punegov et al, 2017;Punegov & Karpov, 2021). This will make it possible to calculate RSMs in Laue geometry, as well as compare the calculated q x and q z sections of RSMs with experimental data (Kang et al, 2005).…”

“…Such an X-ray diffraction model can be considered if only the rocking curves are analyzed. In the case where the X-ray beam incident on the multilayer is spatially restricted, it is necessary to use the two-dimensional Takagi-Taupin equations (Punegov et al, 2017;Punegov & Karpov, 2021). This approach allows one to analyze X-ray reciprocal-space maps (RSMs).…”

Two-dimensional recurrence relations and Takagi–Taupin equations. I. Dynamical X-ray diffraction by a perfect crystal

“…On the other hand, RSMs can be computed using the spatially restricted X-ray beam formalism (Punegov et al, 2017;Punegov & Karpov, 2021). For this, in the two-dimensional equations (1), it is necessary to perform the Fourier transform of the amplitudes:…”

“…The method of recurrence relations used to calculate X-ray fields inside a crystal or RSMs is always stable and gives correct results. The numerical solution of the T-T equations for describing diffraction in a perfect crystal in Fourier space is also stable (Punegov et al, 2017;Punegov & Karpov, 2021).…”

“…Both Darwin's recurrence relations and the one-dimensional T-T equations describe the dynamical diffraction of a plane (spatially unrestricted) X-ray wave; therefore, they cannot be used to calculate reciprocal-space maps (RSMs) (Iida & Kohra, 1979;Punegov, 2015). Recently, two-dimensional T-T equations have been applied to describe the dynamical diffraction of spatially restricted X-ray beams (Punegov et al, 2017;Punegov & Karpov, 2021). This approach makes it possible to simulate RSMs of perfect crystals.…”