This nal chapter summarizes the presented results, states open questions and gives an outlook to future developments of X-ray dark-eld imaging.
7.1. Summary
The potential of grating-based X-ray dark-eld imaging as a new imaging modality in ma-terials research and NDT was demonstrated by means of specic application examples.
Besides providing strong imaging contrast for microstructural features, the dark-eld sig-nal also provides quantitative information about structural parameters. We pointed out this capability by deriving a theoretical framework for the dark-eld signal, which is based on well-known mathematical formalism of SAXS. Our theoretical considerations provide a direct relation of the dark-eld signal to the auto-correlation function of the sample's microstructure. By using model functions, quantitative information on the sam-ple's microstructure is extracted based on the dark-eld signal. We further developed an experimental method which allows to measure such auto-correlation functions with laboratory-based X-ray equipment and a Talbot-Lau interferometer setup. Experiments withSiO2 microspheres were carried out to validate our theoretical dark-eld framework as well as to demonstrate the feasibility of our experimental approach. Here, the micro-sphere's diameter was determined with good accuracy when compared to the manufac-turer's specications. In addition to that, short-range ordering in dense sphere suspensions was observed, and the next neighbor distance of spheres was qualitatively determined.
We further utilized the dark-eld signal's sensitivity to microstructural features to study dierent materials. At rst, building materials such as mortar and cement were studied.
Here, we presented methods for time-resolved radiography and tomography experiments and applied these techniques to study water transport in porous materials. Our results showed that temperature treatment of mortar samples inuences the material's water sorptivity. Mortar that was treated at higher temperatures takes up water faster than un-treated mortar due to an increased amount of microcracks in the heated samples. Further results revealed that water adsorption in mortar can be prevented by adding hydrophobic substances such as biolm to the mortar during mixing. Water transport is observed with strong contrast by X-ray dark-eld imaging because the intrusion of water strongly changes the scattering properties of a porous material such as mortar. Besides two-dimensional dark-eld radiography, we used time-resolved dark-eld CT to study water
7. Summary and outlook
transport in three dimensions. Here, water supply to cement by porous water-saturated limestone grains during cement hardening was presented.
Grating-based X-ray dark-eld imaging was further demonstrated to be a valuable tool for studies on cement during setting and hardening. The microstructural changes in cement paste aects the material's scattering properties. Thus, grating-based dark-eld imaging was used to study kinetics of cement hydration spatially resolved in two as well as three dimensions. The change in dark-eld signal of pure cement paste was found to follow a logistic behavior similar to ultrasound measurements[78]. Temperature variations were shown to have a strong eect on the dark-eld measurements because the chemical reac-tions causing cement hardening are temperature sensitive. While a heated cement sample shows increased reaction speed, a cooled sample displays reduced reaction speed, which is correspondingly reected in the measured dark-eld signal.
Another material class, which was studied in this work, are short ber reinforced poly-mer components. Here, the orientation sensitivity of a Talbot-Lau interferometer for scattered X-rays was exploited to study ber orientation in at SFRP samples. Fiber orientation was analyzed by XVR measurements for samples with dierent geometry and ber materials. A qualitative comparison revealed good correlation of the average struc-ture orientation measured by XVR in each pixel and the real ber orientation provided byµCT. XVR was furthermore shown to be much faster than conventional CT measure-ments, and it also provides sucient contrast between carbon bers and a carbon-based matrix to allow for orientation characterization.
7.2. Outlook
The presented application examples have illustrated the potential of grating-based X-ray dark-eld imaging as a valuable tool for materials research and NDT. Grating-based X-ray dark-eld imaging complements standard X-X-ray imaging, as it reduces the accessible structure size towards the nanometer length scale also for large objects. grating-based X-ray dark-eld imaging may therefore be benecial for studies in particular on slow dy-namical processes related to microstructural changes. Often, the probed sample volume sets boundary conditions which inuence these microstructural processes. Small sample volumes often need dedicated preparation protocols, for example in electron and X-ray microscopy. As dark-eld imaging allows to study relatively large sample volumes, while being sensitive to microstructural changes, the sample size is less restricted making in-situ experiments feasible. Research areas where such a method is potentially of great interest may include: Geological sciences, where water transport in geological materi-als is of interest, energy sciences, where structural processes in battery materimateri-als come more into focus with the rise of electrical mobility, and for example civil engineering,
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7.2. Outlook
where the need for sustainable and durable materials shifts the research focus towards the micrometer length scale. Besides qualitative studies, which benet from the dark-eld signals improved contrast for microstructures, even quantitative studies are feasible.
While quantitative studies are straight forward for simple structures such as microspheres, much more research is needed in order to extract quantitative information from dark-eld measurements on complex materials such as cement. Furthermore, some technological barriers limit the application of quantitative dark-eld imaging nowadays. The proba-ble object size is currently limited because large area gratings are not availaproba-ble in great numbers. This limits the eld of view of most grating-based imaging systems to a few centimeters. High energy applications further demand gratings with high aspect ratios of material height to grating period to provide sucient X-ray attenuation by the source and analyzer gratings. Interferometers working at mean X-ray spectrum energies of around 50 keV are easily realizable at the time, while interferometers working at energies to-wards and beyond100keV remain rare systems for now. A crucial aspect for quantitative measurements is also the period of the grating structures. Currently available grating periods limit the maximum structure size that can be quantied to 2.5−5 µm [60]. To substantially increase this length scale, smaller grating periods are necessary. Gratings of small period are more sensitive to small scattering angles which originate from structural features with a size of a few micrometers. Due to the emergence of micro-manufacturing and additive manufacturing, structures on a length scale of100 nm up to100 µm in large objects of several centimeters in size become more and more interesting to the research and engineering community [122126]. Here, quantitative grating-based X-ray dark-eld imaging has a lot potential to assist in characterization of materials and manufacturing processes.