X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses

X-ray beam diagnostics at the MID instrument of the European X-ray Free-Electron Laser Facility

The Materials Imaging and Dynamics (MID) instrument at the European X-ray Free-Electron Laser Facility (EuXFEL) is equipped with a multipurpose diagnostic end-station (DES) at the end of the instrument. The imager unit in DES is a key tool for aligning the beam to a standard trajectory and for adjusting optical elements such as focusing lenses or the split-and-delay line. Furthermore, the DES features a bent-diamond-crystal spectrometer to disperse the spectrum of the direct beam to a line detector. This enables pulse-resolved characterization of the EuXFEL spectrum to provide X-ray energy calibration, and the spectrometer is particularly useful in commissioning special modes of the accelerator. Together with diamond-based intensity monitors, the imager and spectrometer form the DES unit which also contains a heavy-duty beamstop at the end of the MID instrument. Here, we describe the setup in detail and provide exemplary beam diagnostic results.

Crystal bending in triple-Laue X-ray interferometry. Part I. Theory

The measured value of the (220) lattice-plane spacing of silicon 28 using scanning X-ray interferometry is essential to realize the kilogram by counting ²⁸Si atoms. An assumption made is that the measured lattice spacing is the bulk value of an unstrained crystal forming the analyser of the interferometer. However, analytical and numerical studies of the X-ray propagation in bent crystals suggest that the measured lattice spacing might refer to the analyser surface. To confirm the result of these studies and to support experimental investigations of the matter by phase-contrast topography, a comprehensive analytical model is given of the operation of a triple-Laue interferometer having the splitting or recombining crystal bent.

Crystal bending in triple-Laue X-ray interferometry. Part II. Phase-contrast topography

In a previous paper [Sasso et al. (2023). J. Appl. Cryst.56, 707-715], the operation of a triple-Laue X-ray interferometer having the splitting or recombining crystal cylindrically bent was studied. It was predicted that the phase-contrast topography of the interferometer detects the displacement field of the inner crystal surfaces. Therefore, opposite bendings result in the observation of opposite (compressive or tensile) strains. This paper reports on the experimental confirmation of this prediction, where opposite bendings were obtained by copper deposition on one or the other of the crystal sides.

Topography of bent crystals with microradian resolution in one dimension

Optimum performance in x-ray imaging and spectroscopy of plasmas with bent crystals is achievable only when the crystal reflects the x rays theoretically perfectly across its entire surface. However, typical thin quartz (101̄1) crystal samples kept flat by direct attachment to a flat substrate reflect 8 keV x rays differently across their surface, on a scale comparable to the ideal rocking curve. Additional processing improves the uniformity. Irradiation of flat crystals with collimated, monochromatic x rays in rocking curve topography shows such problems directly, with microradian resolution. Nonuniform x-ray reflection is more difficult to document for strongly bent crystals because, then, monochromatic, collimated x rays satisfy the Bragg condition only along a narrow stripe that may be too narrow to resolve with the available cameras. However, it can be resolved with a knife edge that moves through the reflected x rays with the necessary spatial precision as demonstrated here for a bent silicon crystal. This shows qualitatively similar imperfections in the reflection as flat quartz and as the bent quartz analyzers reported on previously with lower resolution.

Resolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon

The resolution function of a bent-crystal spectrometer for pulses of an X-ray free-electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness.

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, distance to a detector, and anisotropic elastic constants of the chosen crystal. The results allow the optimization of the parameters of bent-crystal spectrometers for the hard X-ray free-electron laser sources.

X-ray diffraction reveals the amount of strain and homogeneity of extremely bent single nanowires

Core-shell nanowires (NWs) with asymmetric shells allow for strain engineering of NW properties because of the bending resulting from the lattice mismatch between core and shell material. The bending of NWs can be readily observed by electron microscopy. Using X-ray diffraction analysis with a micro- and nano-focused beam, the bending radii found by the microscopic investigations are confirmed and the strain in the NW core is analyzed. For that purpose, a kinematical diffraction theory for highly bent crystals is developed. The homogeneity of the bending and strain is studied along the growth axis of the NWs, and it is found that the lower parts, i.e. close to the substrate/wire interface, are bent less than the parts further up. Extreme bending radii down to ∼3 µm resulting in strain variation of ∼2.5% in the NW core are found.