The equations for calculating diffraction profiles for bent crystals are revisited for both meridional and sagittal bending. Two approximated methods for computing diffraction profiles are treated: multilamellar and Penning-Polder. A common treatment of crystal anisotropy is included in these models. The formulation presented is implemented into the XOP package, completing and updating the crystal module that simulates diffraction profiles for perfect, mosaic and now distorted crystals by elastic bending.
The use of strongly bent crystals in spectrometers for pulses of a hard x-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared to the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, we demonstrate that spectra of the 12 keV pulses can be resolved in 440 reflection from a 20 micron thick diamond crystal bent to a radius of 10 cm.
We analyze the lineshape of x-ray diffraction profiles of GaN epitaxial layers with large densities of randomly distributed threading dislocations. The peaks are Gaussian only in the central, most intense part of the peak, while the tails obey a power law. The $q^{-3}$ decay typical for random dislocations is observed in double-crystal rocking curves. The entire profile is well fitted by a restricted random dislocation distribution. The densities of both edge and screw threading dislocations and the ranges of dislocation correlations are obtained.
Information on the lattice parameter of single crystals with known crystallographic structure allows for estimations of sample quality and composition. In many cases it is suffcient to determine one lattice parameter or the lattice spacing along a certain, high-symmetry direction, e.g. in order to determine the composition in a substitution series by taking advantage of Vegards rule. Here we present a guide to accurate measurements of single crystals with dimensions ranging from 200 $mu$m up to several millimeter using a standard powder diffractometer in Bragg-Brentano geometry. The correction of the error introduced by the sample height and the optimization of the alignment are discussed in detail. In particular for single crystals with a plate-like habit, the described procedure allows for measurement of the lattice spacings normal to the plates with high accuracy on a timescale of minutes.
Disordered heterostructures stand as a general description for compounds that are part of homologous series such as bismuth chalcogenides. In device engineering, van der Waals epitaxy of these compounds is very promising for applications in spintronic and quantum computing. Structural analysis methods are essential to control and improve their synthesis in the form of thin films. Recently, X-rays tools have been proposed for structural modeling of disordered heterostructures [arXiv:2107.12280]. Here, we further evaluate the use of these tools to study the compound Mn$_x$Bi$_2$Te$_{3+x}$ in the grazing incidence region of the reflectivity curves, as well as the effect of thickness fluctuation in the wide angle region.
X-ray scattering is one of the primary tools to determine crystallographic configuration with atomic accuracy. However, the measurement of ultrafast structural dynamics in monolayer crystals remains a long-standing challenge due to a significant reduction of diffraction volume and complexity of data analysis, prohibiting the application of ultrafast x-ray scattering to study nonequilibrium structural properties at the two-dimensional limit. Here, we demonstrate femtosecond surface x-ray diffraction in combination with crystallographic model-refinement calculations to quantify the ultrafast structural dynamics of monolayer WSe$_2$ crystals supported on a substrate. We found the absorbed optical photon energy is preferably coupled to the in-plane lattice vibrations within 2 picoseconds while the out-of-plane lattice vibration amplitude remains unchanged during the first 10 picoseconds. The model-assisted fitting suggests an asymmetric intralayer spacing change upon excitation. The observed nonequilibrium anisotropic structural dynamics in two-dimensional materials agrees with first-principles nonadiabatic modeling in both real and momentum space, marking the distinct structural dynamics of monolayer crystals from their bulk counterparts. The demonstrated methods unlock the benefit of surface sensitive x-ray scattering to quantitatively measure ultrafast structural dynamics in atomically thin materials and across interfaces.
Manuel Sanchez del Rio
,Nicolas Perez-Bocanegra
,Xianbo Shi
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(2015)
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"Simulation of X-ray diffraction profiles for bent anisotropic crystals"
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Manuel Sanchez del Rio
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