Construction of a quartz spherical analyzer: application to high-resolution analysis of the NiKα emission spectrum

Calculating temperature-dependent X-ray structure factors of α-quartz with an extensible Python 3 package

A Python 3 software package for precise calculation of X-ray structure factors of α-quartz over a wide temperature range is presented. α-Quartz was chosen because of its practical application in high-resolution X-ray spectroscopy, but this software package can be easily extended to other crystals.

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package’s stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz.

200-mm segmented cylindrical figured crystal for von Hamos x-ray spectrometer

A von Hamos Bragg crystal spectrometer at 1C beamline of Pohang Accelerator Laboratory for x-ray emission spectroscopy (XES) is described. Diced Si crystals of different orientations ([111], [110], [100], and [311]) are glued onto a planoconcave glass substrate having 250/500 mm radius of curvature. To enhance the spectrometer efficiency, the length of the crystal analyzer is kept 200 mm. The emission spectra of Cu foil and Fe foil and elastic scattering from Al foil are measured using the von Hamos geometry in which curved crystals disperse the x-rays. Spectrometer efficiency and energy resolution are measured at various x-ray photon energies. X-rays are incident at 6.54 keV, 9.00 keV, 9.205 keV, and 11.51 keV for Si(440), Si(444), Si(800), and Si(933) crystal analyzers, respectively. The cylindrical figured analyzer is placed near 80° with respect to the sample, which gives better energy resolution. The spectrometer efficiency of the Si(444) crystal analyzer increases by ∼2 times when the length of the analyzer is increased from 100 mm to 200 mm. Furthermore, to measure Fe Kα₁, Kα₂, and K_β simultaneously, we made a mixed crystal analyzer in which alternative strips of Si[111] and Si[110] are glued onto one preshaped cylindrical substrate. The enhanced efficiency and simultaneous measurement of K_α and K_β emission lines will give an edge over in situ and time-resolved x-ray emission spectroscopy studies. The information extracted with a high efficiency spectrometer from low intensity XES emission lines will be useful for the in situ elemental characterization in catalytic reactions.

X-ray back-diffraction: can we further increase the energy resolution by tuning the energy slightly below that of exact backscattering?

X-ray beams at energies tuned slightly below that of exact backscattering (extreme conditions, where X-ray back-diffraction is almost extinguished – called residual XBD) are better focused if the experiment is carried out at lower energies in order to avoid multiple-beam diffraction effects. Following previous work by the authors [Hönnicke, Conley, Cusatis, Kakuno, Zhou, Bouet, Marques & Vicentin (2014). J. Appl. Cryst. 47, 1658–1665], herein efforts are directed towards characterizing the residual XBD beam of an ultra-thin Si 220 crystal (UTSiXTAL) at ∼3.2 keV. To achieve the residual XBD condition the UTSiXTAL was cooled from 310 to 273 K. The results indicate that under this extreme condition the energy resolution can be further improved. Issues with the energy resolution measurements due to incoming beam divergence and the ultra-thin crystal flatness are discussed.

High-energy-resolution diced spherical quartz analyzers for resonant inelastic X-ray scattering

A novel diced spherical quartz analyzer for use in resonant inelastic X-ray scattering (RIXS) is introduced, achieving an unprecedented energy resolution of 10.53 meV at the Ir L₃ absorption edge (11.215 keV). In this work the fabrication process and the characterization of the analyzer are presented, and an example of a RIXS spectrum of magnetic excitations in a Sr₃Ir₂O₇ sample is shown.

Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications

Quartz has hundreds of strong Bragg reflections that may offer a great number of choices for making fixed-angle X-ray analyzers and polarizers at virtually any hard X-ray energies with selectable resolution. However, quartz crystals, unlike silicon and germanium, are chiral and may thus appear in two different forms of handedness that are mirror images. Furthermore, because of the threefold rotational symmetry along thecaxis, the {h1h2h3L} and {h2h1h3L} Bragg reflections may have quite different Darwin bandwidth, reflectivity and angular acceptance, although they have the same Bragg angle. The design of X-ray optics from quartz crystals therefore requires unambiguous determination of the orientation, handedness and polarity of the crystals. The Laue method and single-axis diffraction technique can provide such information, but the variety of conventions used in the literature to describe quartz structures has caused widespread confusion. The current studies give detailed guidelines for design and fabrication of quartz X-ray optics, with special emphasis on the correct interpretation of Laue patterns in terms of the crystallography and diffraction properties of quartz. Meanwhile, the quartz crystals examined were confirmed by X-ray topography to have acceptably low densities of dislocations and other defects, which is the foundation for developing high-resolution quartz-based X-ray optics.