X-ray Diffraction Microtomography Research Articles

Comprehensive Recovery of Point Defect Displacement Field Function in Crystals by Computer X-ray Diffraction Microtomography

In the case of the point defect in a crystal, the inverse Radon’s problem in X-ray diffraction microtomography has been solved. As is known, the crystal-lattice defect displacement field function f(r) = h·u(r) determines phases − (±h)-structure factors incorporated into the Takagi–Taupin equations and provides the 2D image patterns by diffracted and transmitted waves propagating through a crystal (h is the diffraction vector and u(r) is the displacement field crystal-lattice-defects vector). Beyond the semi-kinematical approach for obtaining the analytical problem solution, the difference-equations-scheme of the Takagi–Taupin equations that, in turn, yield numerically controlled-accuracy problem solutions has been first applied and tested. Addressing the inverse Radon’s problem solution, the χ2-target function optimization method using the Nelder–Mead algorithm has been employed and tested in an example of recovering the Coulomb-type point defect structure in a crystal Si(111). As has been shown in the cases of the 2D noise-free fractional and integrated image patterns, based on the Takagi–Taupin solutions in the semi-kinematical and difference-scheme approaches, both procedures provide the χ2-target function global minimum, even if the starting-values of the point-defect vector P1 is chosen rather far away from the reference up to 40% in relative units. In the cases of the 2D Poisson-noise image patterns with noise levels up to 5%, the figures-of-merit values of the optimization procedures by the Nelder–Mead algorithm turn out to be high enough; the lucky trials number is 85%; and in contrast, for the statistically denoised 2D image patterns, they reach 0.1%.

3D imaging of complex materials: the case of cement

AbstractAbsorption-based X-ray micro-tomography (X-μCT) provides fundamental in-situ information on the 3D microstructure of complex multiphase materials such as cements. However, since the phases present in a hydrating cement paste may be characterized by similar values of the attenuation coefficient, leading to low absorption contrast between different crystalline or amorphous phases, micro-structural interpretation can be equivocal. 3D phase mapping by X-ray diffraction micro-tomography proved to be a successful technique for investigating the spatial distribution of the products in the paste during the hydration process, in a totally non-invasive mode and with enhanced phase selectivity compared to absorption tomography. Phase-selective maps, in the case of crystalline phases, can be extracted from single Bragg peaks or from the Rietveld-refined scale factor. However, even poorly crystalline and/or amorphous phases present in the cement paste, such as calcium silicate hydrates, can be successfully mapped by the use of selected portions of the measured powder data containing the relevant scattering of the phase. The reconstructed maps can be directly modeled by multifractal analysis and compared with computer-generated distributions.

Towards three-dimensional quantitative reconstruction of cement microstructure by X-ray diffraction microtomography

Quantitative characterization of the microstructure of cement-based materials is of fundamental importance for assessing the performance and durability of the final products. However, accessing the three-dimensional microstructural information of hydrating cement pastes without introducing any perturbation is not trivial. Recently, a novel non-invasive method based on X-ray diffraction computed microtomography (XRD-CT) has been applied to cement-based materials, with the aim of describing the three-dimensional spatial distribution of selected phases during the hydration of the cement paste. This paper illustrates a method based on XRD-CT, combined with Rietveld-based quantitative phase analysis and image processing, which provides quantitative information relative to the distribution of the various phases present in the studied samples. In particular, it is shown how this method allows the estimation of the local volume fraction of the phase ettringite within a hydrating cement paste, and construction of a three-dimensional distribution map. Application of this method to the various constituents of a cementitious material, or, more generally, of a composite polycrystalline material, may provide a non-invasive tool for three-dimensional microstructural quantitative characterization.

Microstructural mapping of C60 phase transformation into disordered graphite at high pressure, using X-ray diffraction microtomography

An extended use of synchrotron-based X-ray diffraction microtomography (XRD-µCT) to study simultaneously the phase distribution and microstructure in phase-transformation processes is proposed. This three-dimensional non-invasive imaging approach has been applied to understand the phase transformation of C60 rhombohedral polymer (C60R) into disordered graphite (DG) at high pressure and high temperature. The heterogeneous sample was synthesized (5 GPa, 1100 K) using a Paris–Edinburgh cell and selective image reconstructions were achieved for all different phases present in this sample. The XRD-µCT analysis evidences elongated DG domains with a fiber texture where nested (002)DGplanes show ±70° preferential orientation relative to the compression axis. In contrast C60R domains are found to be small and spotty, preferentially in the middle of the sample. The parent and product phases are mutually interpenetrative and exhibit a crystallographic relationship. This study evidences that formation of (002)DGplanes occurs parallel to {111}C60Cpseudo-cubic planes. Among these four possible alignments, uniaxial pressure favors one [111]C60Cdirection. Transmission electron microscopy observations validate these nondestructive XRD-µCT results.

X-ray diffraction microtomography (XRD-CT), a novel tool for non-invasive mapping of phase development in cement materials

A recently developed synchrotron-based imaging technique, X-ray diffraction microtomography (XRD-CT), has been applied here for the first time to a complex system, the hydrating Portland cement paste, in order to monitor the evolution of microstructure and phase formation with a 3D non-invasive imaging approach. The ettringite-XRD-peak-based image reconstructions, combined with transmission microtomography (X-microCT) images, allowed to assess the ubiquitous distribution of this phase, which appears early in the hydration process and showed its preferential concentration in the relatively less compact regions of the paste. The comparison of greyscale histograms for cement pastes after 9 and 58 h from hydration showed an increase of ettringite content with age, in agreement with the quantitative Rietveld analysis of the sum patterns. By renormalizing the greyscale histograms to the relative weight fraction, as obtained from Rietveld refinements, a new technique which allows estimation of phase contents with spatial resolution has been developed. The results achievable by combining XRD-CT, X-microCT and Rietveld appear very promising to provide experimental snapshots of the cement hydration process to be compared with results obtained from computer simulations.

X-ray diffraction microtomography using synchrotron radiation

The X-ray diffraction computed tomography technique is based on the interference phenomena of the coherent scatter. For low-momentum transfer, it is most probable that the scattering interaction will be coherent. A selective discrimination of a given element in a scanned specimen can be realized by fixing the Bragg angle which produces an interference peak and then, to carry out the computed tomography in the standard mode. The image reconstructed exalts the presence of this element with respect to other ones in a sample. This work reports the feasibility of a non-destructive synchrotron radiation X-ray diffraction imaging technique. This research was performed at the X-ray Diffraction beam line of the National Synchrotron Light Laboratory (LNLS) in Brazil. The coherent scattering properties of different tissue and bone substitute materials were evaluated. Furthermore, diffraction patterns of some polycrystalline solids were studied due to industrial and environmental human exposure to these metals. The obtained diffraction patterns form the basis of a selective tomography technique. Preliminary images are presented.

51726 X-ray diffraction microtomography : Measurement Science and Technology, Vol. 4, No. 1, pp. 83–87 (1993)

51726 X-ray diffraction microtomography : Measurement Science and Technology, Vol. 4, No. 1, pp. 83–87 (1993)

X-ray diffraction microtomography

A table-top system has been developed for tomographic imaging of the internal structure of objects of low mass density at sub-millimetre resolution. Images are based on the X-ray diffraction properties of constituent materials, and are reconstructed from tomographic data using summation-filtered back-projection. Typical images are presented, the apparatus used for data acquisition is described, and the application of summation-filtered back-projection is discussed.