Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping

Abstract

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.research papers

Simulation of X-ray diffraction in a cylindrical crystal

“…If the crystal has small lateral size, although its thickness is greater than the length of the primary extinction, diffraction can be kinematical (Punegov et al, 2014(Punegov et al, , 2016. This is also true for spatially restricted X-ray beams with small slit sizes (Punegov et al, 2017). In the case of a cylindrical crystal, with increasing node number m, the crystal thickness also changes.…”

“…X-ray radiation incident on the left side of the cylindrical crystal causes diffraction, which formally can be attributed to Laue geometry. Therefore, along with the phenomenon of primary extinction in the upper part of the crystal, the Pendellö sung effect arises (Punegov et al, 2016(Punegov et al, , 2017.…”

The dynamical theory of diffraction in a crystal modulated by a surface acoustic wave in the case of spatially restricted X-ray beams

“…. , is the coordinate in Fourier space which corresponds to the x coordinate in real space (Punegov et al, 2017;Punegov, 2018). Thus, due to the lateral modulation of the crystal lattice, a transition is made from the system of two-dimensional equations (1) to onedimensional equations for individual diffraction orders.…”

“…The previously developed theories of diffraction in crystals modulated by a SAW were considered for a spatially unrestricted plane X-ray wave [see Punegov et al (2010), and references therein]. A quantitative analysis of the structural characteristics within these theories required certain approximations, since the coherent component of the scattered intensity for a plane wave in reciprocal space is a function (Punegov et al, 2017;Punegov, 2018). On the other hand, in an experiment both the incident and reflected X-ray beams are spatially restricted by the presence of slits and collimators.…”

Solution of the Inverse Problem of X-Ray Diffraction on an Ideal Crystal Using the Differential Evolution Method

“…Расчет интенсивности рассеяния проводился в рамках динамической теории РД, расширенной на частный случая поперечно ограниченных волновых фронтов падающей и отраженной волн с учетом влияния инструментальной функции дифрактометра [4]. В этом случае интенсивность дифрагированной волны (в геометрии Брэгга) вблизи узла обратной решетки h зависит от ширины засветки поверхности кристалла l (in) x…”