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X-ray diffraction from strongly bent crystals and spectroscopy of XFEL pulses

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 Added by Vladimir Kaganer
 Publication date 2019
  fields Physics
and research's language is English




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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.



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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 resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters, (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, and anisotropic elastic constants of the chosen crystal. Diamond, due to its unique elastic properties, can provide notably higher resolution than silicon. The results allow to optimize the parameters of bent crystal spectrometers for the hard X-ray free electron laser sources.
We present here an experimental set-up to perform simultaneously measurements of surface plasmon resonance (SPR) and X-ray absorption spectroscopy (XAS) in a synchrotron beamline. The system allows measuring in situ and in real time the effect of X-ray irradiation on the SPR curves to explore the interaction of X-rays with matter. It is also possible to record XAS spectra while exciting SPR in order to detect the changes in the electronic configuration of thin films induced by the excitation of surface plasmons. Combined experiments recording simultaneously SPR and XAS curves while scanning different parameters can be carried out. The relative variations in the SPR and XAS spectra that can be detected with this set-up ranges from 10-3 to 10-5, depending on the particular experiment.
We demonstrate that vacuum forming of 10-cm diameter silicon wafers of various crystallographic orientations under an x-ray permeable, flexible window can easily generate spherically bent crystal analyzers (SBCA) and toroidally bent crystal analyzers (TBCA) with ~1-eV energy resolution and a 1-m major radius of curvature. In applications at synchrotron light sources, x-ray free electron lasers, and laboratory spectrometers these characteristics are generally sufficient for many x-ray absorption fine structure (XAFS), x-ray emission spectroscopy (XES), and resonant inelastic x-ray scattering (RIXS) applications in the chemical sciences. Unlike existing optics manufacturing methods using epoxy or anodic bonding, vacuum forming without adhesive is temporary in the sense that the bent wafer can be removed when vacuum is released and exchanged for a different orientation wafer. Therefore, the combination of an x-ray compatible vacuum-forming chamber, a library of thin wafers, and a small number of forms having different secondary curvatures can give extreme flexibility in spectrometer energy range. As proof of this method we determine the energy resolution and reflectivity for several such vacuum-formed bent crystal analyzers (VF-BCA) in laboratory based XAFS and XES studies using a conventional x-ray tube. For completeness we also show x-ray images collected on the detector plane to characterize the resulting focal spots and optical aberrations.
We developed a new front-end application specific integrated circuit (ASIC) for the upgrade of the Maia x-ray microprobe. The ASIC instruments 32 configurable front-end channels that perform either positive or negative charge amplification, pulse shaping, peak amplitude and time extraction along with buffered analog storage. At a gain of 3.6 V/fC, 1 $mu$s peaking time and a temperature of 248 K, an electronic resolution of 13- and 10 electrons rms was measured with and without a SDD sensor respectively. A spectral resolution of 170 eV FWHM at 5.9 keV was obtained with an $^{55}$Fe source. The channel linearity was better than $pm$ 1 % with rate capabilities up to 40 kcps. The ASIC was fabricated in a commercial 250 nm process with a footprint of 6.3 mm x 3.9 mm and dissipates 167 mW of static power.
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