Abstract
A way has been developed to measure the unit-cell parameters of a single crystal just from an energy scan with X-rays, even when the exact energy of the X-rays is not well defined due to an error in the pitch angle of the monochromator. The precision of this measurement reaches da/a ∼ 1 × 10-5. The method is based on the analysis of diffraction losses of the beam, transmitted through a single crystal (the so-called `glitch effect'). This method can be easily applied to any transmissive X-ray optical element made of single crystals (for example, X-ray lenses). The only requirements are the possibility to change the energy of the generated X-ray beam and some intensity monitor to measure the transmitted intensity. The method is agnostic to the error in the monochromator tuning and it can even be used for determination of the absolute pitch (or 2θ) angle of the monochromator. Applying the same method to a crystal with well known lattice parameters allows determination of the exact cell parameters of the monochromator at any energy.
Highlights
Effective optics are crucial to fully reveal the potential of fourth-generation synchrotron sources
compound refractive lenses (CRLs) have since undergone development and adaptation for current and even new generations of synchrotron sources [MAX-IV (Tavares et al, 2014), European Synchrotron Radiation Facility (ESRF)-EBS (ESRF, 2015–2022), PETRA IV (PETRA IV, 2019), SPring-8-II (Tanaka, 2016)], and X-ray free-electron lasers (XFELs) (Pellegrini, 2012) such as LCLS (Emma et al, 2010) and the European XFEL (Altarelli, 2011)
We have demonstrated a method to determine UC parameters of any single crystal with a cubic cell using its spectra of glitches
Summary
Effective optics are crucial to fully reveal the potential of fourth-generation synchrotron sources. As we will demonstrate in this work, the proposed method can be used in a reciprocal way – to determine the absolute pitch angle of the monochromator This is important for any application that requires exact knowledge of the absolute X-ray energy, especially for an experiment requiring changing energy (like spectroscopy). 2. Experimental observation of X-ray glitches in transmission geometry We performed several X-ray spectroscopy measurements at the BM31 Swiss–Norwegian Beamlines (SNBL) of the European Synchrotron Radiation Facility (ESRF), France (Polikarpov et al, 2018; Zhang et al, 2019). To eliminate the glitches caused by the monochromator as well as to compensate the refills of the synchrotron ring with electrons, the transmitted intensity was normalized by the incident intensity (I1/I0) and by its smoothed version (to compensate for the change in absorption by the sample with X-ray energy as well as different efficiency of the beamline and the ion chambers). Ð7Þ a where hkl is a dimensionless vector made of the corresponding h, k, l Miller indices
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