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X-ray refraction related interaction has received rising interest since about two decades in the field of imaging, beam shaping and analysis although being discovered a century ago. Due to refraction at interfaces in inhomogeneous media X-rays undergo natural focusing (or defocusing) of waves, revealing caustics. Such Kind of intensity patterns are well-known for visible light, but have been sparsely discussed for X-rays. The Variation of irradiation density may be predicted in case of known shapes. Analogously to light optics, the intensity distributions cover several orders of magnitude including complete extinction. The partly convergent (and divergent) caustic stripes originate from narrow zones of typical size of some 10−6 of the boundary curvature radius. For the deflection of plane wave synchrotron radiation (energy in the range of some keV to some ten keV) at rods and tubes of several μm diameter, we find good Agreement between experiments and modeling by ray tracing according to Snell’s law without additional diffraction contributions. Apart from Basic Research implications, caustics may influence the performance of irradiation technologies such as sterilization or molecular cross-linking.
In order to investigate their microcracking behaviour, the microstructures of several β-eucryptite ceramics, obtained from glass precursor and cerammed to yield different grain sizes and microcrack densities, were characterized by laboratory and synchrotron x-ray refraction and tomography. Results were compared with those obtained from scanning electron microscopy (SEM). In SEM images, the characterized materials appeared fully dense but computed tomography showed the presence of pore clusters. Uniaxial tensile testing was performed on specimens while strain maps were recorded and analyzed by Digital Image Correlation (DIC). X-ray refraction techniques were applied on specimens before and after tensile testing to measure the amount of the internal specific surface (i.e., area per unit volume). X-ray refraction revealed that (a) the small grain size (SGS) material contained a large specific surface, originating from the grain boundaries and the interfaces of TiO2 precipitates; (b) the medium (MGS) and large grain size (LGS) materials possessed higher amounts of specific surface compared to SGS material due to microcracks, which decreased after tensile loading; (c) the precursor glass had negligible internal surface. The unexpected decrease in the internal surface of MGS and LGS after tensile testing is explained by the presence of compressive regions in the DIC strain maps and further by theoretical arguments. It is suggested that while some microcracks merge via propagation, more close mechanically, thereby explaining the observed X-ray refraction results. The mechanisms proposed would allow the development of a strain hardening route in ceramics.
3D imaging techniques are very fashionable nowadays, and allow enormous progress in understanding ceramic microstructure, its evolution, and its link to mechanical, thermal, and transport properties. In this feature article, we report the use of a powerful, yet not so wide-spread, set of X-ray techniques based on refraction effects. X-ray refraction allows determining internal specific surface (surface per unit volume) in a non-destructive fashion, position and orientation sensitive, and with a nanometric detectability. While the techniques are limited by the X-ray absorption of the material under investigation, we demonstrate showcases of ceramics and composite materials, where understanding of process parameter influence or simply of microstructural parameters could be achieved in a way unrivalled even by high-resolution techniques such as electron microscopy or computed tomography.
The performance of grating interferometers coming up now for Imaging interfaces within materials depends on the efficiency (visibility) of their main component, namely the phase grating. Therefore, experiments with monochromatic synchrotron radiation and corresponding simulations are carried out. The visibility of a Phase grating is optimized by different photon energies, varying detector to grating distances and continuous rotation of the phase grating about the grid lines. Such kind of rotation changes the projected grating shapes, and thereby the distribution profiles of phase shifts. This yields higher visibilities than derived from ideal rectangular shapes. By continuous grating rotation and variation of the propagation distance, we achieve 2D visibility maps. Such maps provide the visibility for a certain combination of grating orientation and detector position. Optimum visibilities occur at considerably smaller distances than in the standard setup.
3D Crack analysis in hydrogen charged lean duplex stainless steel with synchrotron refraction CT
(2016)
Hydrogen in metals can cause a degradation of the mechanical properties, the so-called hydrogen embrittlement. In combination with internal stresses, hydrogen assisted cracking (HAC) can occur. This phenomenon is not completely understood yet. To better characterise the cracking behaviour, it is important to gain information about the evolution of the 3D crack network. For this purpose samples of lean duplex stainless steel were loaded with hydrogen by means of electrochemical charging and investigated by means of synchrotron refraction CT and SEM fractography after uniaxial tensile loading. Synchrotron refraction CT is an analyser-based imaging (ABI) technique. It uses a Si (111) single crystal as analyser, which is placed into the beam path between sample and detector. According to Bragg’s law only incident x-rays within a narrow range around the Bragg-angle are diffracted from the analyser into the detector. Hence, the analyser acts as an angular filter for the transmitted beam. This filtering allows to turn the refraction and scattering of x-rays into image contrast. Refraction occurs at all interfaces, where the density of the material changes and is more sensitive to density changes than the attenuation. Therefore, it is possible to detect smaller cracks than with classical x-ray imaging techniques, like CT, with comparable spacial resolution. It also visualises the 3D structure of the cracks and gains quantitative information about their morphology and distribution. Since cracks introduced by HAC are usually very small and have a small opening displacement, synchrotron refraction CT is expected to be well suited for imaging this cracking mechanism and can be a valuable tool to characterise the formation and the evolution of a 3D crack network.
For the first time we present direct 2D imaging of refracted X-rays without any discrimination of the Primary radiation. X-refraction works in analogy to visible light optics: X-rays are entirely deflected at interfaces where discontinuities of (electron) density occur. This is demonstrated at the example of inner and outer surfaces of model samples of well-defined geometry (fibres, capillaries, and monodisperse micro particles). The samples are scanned through a 50 μm monochromatic (20 keV) pencil beam. In order to warrant a sufficient angular resolution a 2D detector (pixel size 7 μm) is placed 3 m downstream of the sample. Scanning the sample in micron steps allows for detecting local changes of interface / surface orientation directly in two dimensions. At the actual angular resolution of about 3 seconds of arc (scattering vector increments Δk = 10-3 nm-1) and 50 μm spatial resolution (scanning) the material’s inner surfaces (with nanometer separation) can be characterized even at sampling rates below 1 second per frame. Moreover, our technique is suited to directly determine particle diameters of up to 250 nm by means of diffraction fringes. Some potential applications to technical submicron structures are discussed.
X-ray dark field imaging
(2014)
A new kind of enhanced contrast X-ray imaging of weakly absorbing materials in dark field mode is presented.
Samples such as plastics and biological tissue are a perpetual challenge for radiographic imaging. Recent innovative approaches such as Diffraction Enhanced Imaging (DEI), “phase contrast”, grating interferometry (Talbot-Lau), or Refraction Enhanced Imaging (REI) have in common that they yield enhanced contrast based on deflected X-rays.
Here, we introduce a REI modification, which works with a slightly bent single crystal reflecting in Bragg geometry. The samples are placed upstream of the thin crystal within a parallel synchrotron beam. The crystal’s curvature creates a dark-field stripe in the transmission image, similar to the inverse of a Darwin-Prins rocking curve of plane crystals. The reflection condition is met better or worse as a steady function of incidence position.
Refracted beam portions of sample interfaces appear bright on black stripes. The entire image is finally synthesized by multiple dark-field stripes. The technique is an alternative to the mentioned techniques. We demonstrate the technique’s advantage by examples of biological and technical microstructures.
Evaluating porosity in cordierite diesel particulate filter materials, part 1 X-ray refraction
(2013)
Bi-continuous porous ceramics for filtration applications possess a particularly complicated microstructure, with porosity and solid matter being intermingled. Mechanical, thermal, and filtration properties can only be precisely estimated if the morphology of both solid matter and porosity can be quantitatively determined. Using x-ray absorption and refraction, we quantitatively evaluate porosity and pore orientation in cordierite diesel particulate filter ceramics. Porosity values turn out to agree with mercury intrusion measurements, while pore orientation factors agree with published crystallographic texture data.
The relevance of nano sized structures and interfaces in upcoming technologies requires new non-destructive Xray
techniques exploiting attenuation as well as scattering. In the course of driving the resolution and the contrast
of modern radiography into micro and nano metre dimension the inevitable scattering effects require increased
attention. Several radiologists interpret the observed edge artefacts simply by 'phase contrast' due to different
X-ray path lengths within the sample and others refer to Fresnel scattering. The ultra small angle scattering is of
high intensity and may reach the level of the primary beam. We present monochromatic synchrotron
measurements on rather simply shaped objects (such as plates and cylinders) which prove clearly the dominance
of refraction intensity over total reflection and coherent small angle scattering. The refraction conditions hold for
angles of incidence of several degrees to the surface, but typical deflection angles range from several seconds to
minutes of arc. Additionally to the concept of 'phase contrast' of the primary beam its deflection becomes the
essential issue. The appropriate removal of the attenuation contribution enables the imaging of inner surfaces and
interfaces by refraction scanning topography. The presented measurements of reference particles demonstrate the
reliability of laboratory refraction scanners applying X-ray tubes.