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X-ray refraction is analogous to visible light deflection by matter; it occurs at boundaries between different media. The main difference between visible light and X-rays is that in the latter case deflection angles are very small, from a few seconds to a few minutes of arc (i.e., the refraction index n is near to 1). Trivially but importantly, deflection of X-rays is also sensitive to the orientation of the object boundaries. These features make X-ray refraction techniques extremely suitable to a) detect defects such as pores and microcracks and quantify their densities in bulk (not too heavy) materials, and b) evaluate porosity and particle properties such as orientation, size, and spatial distribution (by mapping). While X-ray refraction techniques cannot in general image single defects, their detectability is simply limited by the wavelength of the radiation.
We thereby show the application of X-ray refraction 2D mapping (topography) and tomography to different sorts of problems in materials science and technology: 1) Sintering of SiC green bodies; 2) Porosity analysis in additively manufactured alloys; 3) Fiber de-bonding in metal and polymer matrix composites.
Such techniques, especially at the Synchrotron BESSY II, Berlin, Germany, can be used in-situ, i.e. when the specimen is subjected to temperatures or external loads. Applications of in-situ X-ray refraction radiography on aluminum alloys and composites are also shown.
The use of X-ray refraction analysis yields quantitative information, which can be directly input in kinetics, mechanical and damage models.
High-density polyethylene becomes optically transparent during tensile drawing when previously saturated with diesel fuel. This unusual phenomenon is investigated as it might allow conclusions with respect to the material behavior. Microscopy, differential scanning calorimetry, density measurements are applied together with two scanning X-ray scattering techniques: wide angle X-ray scattering (WAXS) and X-ray refraction, able to extract the spatially resolved crystal orientation and internal surface, respectively. The sorbed diesel softens the material and significantly alters the yielding characteristics. Although the crystallinity among stretched regions is similar, a virgin reference sample exhibits strain whitening during stretching, while the diesel-saturated sample becomes transparent. The WAXS results reveal a pronounced fiber texture in the tensile direction in the stretched region and an isotropic orientation in the unstretched region. This texture implies the formation of fibrils in the stretched region, while spherulites remain intact in the unstretched parts of the specimens. X-ray refraction reveals a preferred orientation of internal surfaces along the tensile direction in the stretched region of virgin samples, while the sample stretched in the diesel-saturated state shows no internal surfaces at all. Besides from stretching saturated samples, optical transparency is also obtained from sorbing samples in diesel after stretching.
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.
Modern air-liners and rotor blades of wind turbines are basically made of fiber reinforced plastics (FRP). Their failure heavily impairs the serviceability and the operational safety. Consequently, knowledge of the failure behavior under static and cyclic loads is of great interest to estimate the operational strength and to compare the performance of different materials. Ideally, the damage evolution under operational load is determined with in-situ non-destructive testing techniques. Here, we report on in-situ synchrotron X-ray imaging of tensile stress induced cracks in carbon fiber reinforced plastics (CFRP) due to inter fiber failure. An in-house designed compact-tensile testing machine with a load range up to 15 kN was integrated into the beam path. Since conventional radiographs do not reveal sufficient contrast to distinct cracks due to inter fiber failure and micro cracking from fiber bundles, the Diffraction Enhanced Imaging technique (DEI) is applied in order to separate primary and scattered (refracted) radiation by means of an analyzer crystal. In the laboratory, scanning X-ray refraction topography of CFRP has been applied long before but it comes along with several disadvantages: the long total measuring time hampers real time (in-situ) measurements and the required small beam size hinders end-to-end imaging. The introduced technique overcomes both drawbacks. Imaging and tensile test rig are run unsynchronized at the greatest possible frame rate (0.7 s-1 at 28.8 µm pixel size) and smallest possible strain rate (5.5∙10-4 s-1). For 0°/90° non-crimped fabrics (ncf) the first inter fiber cracks occurred at 380 MPa (strain 0.7 %). Prior to failure at about 760 MPa (strain 2.0 %) we observe the evolution of a nearly equidistant 1 mm grid of cracks running across the entire sample in the fully damaged state before total failure.
Modern air-liners and wind turbine rotor blades are made up primarily of fiber reinforced plastics. Failure of these materials heavily impairs the serviceability and the operational safety. Consequently, knowledge of the failure behavior under static and cyclic loads is of great interest to estimate the operational strength and to compare the performance of different materials. Ideally, the damage evolution under operational load is determined with in-situ non-destructive testing techniques. Here, we report in-situ synchrotron X-ray imaging of tensile stress induced cracks in carbon fiber reinforced plastics due to inter-fiber failure. An inhouse designed compact tensile testing machine with a load range up to 15 kN was integrated into the beamline. Since conventional radiographs do not reveal sufficient contrast to distinguish cracks due to inter-fiber failure and micro cracking from fiber bundles, the Diffraction Enhanced Imaging (DEI) technique is applied in order to separate primary and scattered (refracted) radiation by means of an analyzer crystal. This technique allows fast measurements over large fields-of-view and is ideal for in-situ investigations.
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.
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.