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Polycrystals illuminated by high-energy X-rays or neutrons produce diffraction patterns in which the measured diffraction peaks encode the individual single crystal strain states. While state of the art X-ray and neutron diffraction approaches can be used to routinely recover per grain mean strain tensors, less work has been produced on the recovery of higher order statistics of the strain distributions across the individual grains. In the setting of small deformations, we consider the problem of estimating the crystal elastic strain tensor probability distribution from diffraction data. For the special case of multivariate Gaussian strain tensor probability distributions, we show that while the mean of the distribution is well defined from measurements, the covariance of strain has a null-space. We show that there exist exactly 6 orthogonal perturbations to this covariance matrix under which the measured strain signal is invariant. In particular, we provide analytical parametrisations of these perturbations together with the set of possible maximum-likelihood estimates for a multivariate Gaussian fit to data. The parametric description of the null-space provides insights into the strain PDF modes that cannot be accurately estimated from the diffraction data. Understanding these modes prevents erroneous conclusions from being drawn based on the data. Beyond Gaussian strain tensor probability densities, we derive an iterative radial basis regression scheme in which the strain tensor probability density is estimated by a sparse finite basis expansion. This is made possible by showing that the operator mapping the strain tensor probability density onto the measured histograms of directional strain is linear, without approximation. The utility of the proposed algorithm is demonstrated by numerical simulations in the setting of single crystal monochromatic X-ray scattering. The proposed regression methods were found to robustly reject outliers and accurately predict the strain tensor probability distributions in the presence of Gaussian measurement noise. [Display omitted] • Per-grain strain probability densities are extracted from X-ray diffraction data. • The presented method estimates the strain PDF from histograms of directional strain. • Gaussian strain PDFs have a closed form solutions and a known null-space. [ABSTRACT FROM AUTHOR]

Spectral X-ray Computed Tomography (CT) exploits advanced photon counting detectors (PCD) to measure a material's spectrally resolved linear attenuation coefficient (LAC) with the simultaneous spectral acquisition at multiple energy thresholds. We present a method for material classification using spectral CT. The method employs a basis material decomposition model and estimates the effective atomic number (Z eff) from the spectral LAC measurements. Basis material decomposition builds on the fact that the LAC of any material can be well approximated by a linear combination of LACs of basis materials, with known Z eff values at the extremes of the relevant Z eff range. Spectral distortions of the energy spectrum due to the physical interactions between photons and the multi-energy-bin PCD such as charge sharing and photon pileup are corrected by a spectral correction algorithm. The validation of the method has been performed with experimental data acquired with a custom laboratory instrument for spectral CT, examining "real life" phantoms with materials in the range of 6 ≤ Z eff ≤ 15. The classification performance is estimated for different numbers of projections, energy bins and basis materials in LAC decomposition. When using just 12 projections, 15 energy bins and two basis materials, the method gives a relative deviation of 2.2% for Z eff , while this deviation is 5.9% when spectral correction is not used. The classification method is now ready for use in security screening where modern spectral CT systems are employed. [ABSTRACT FROM AUTHOR]

Most metals, ceramics, semiconductors and rocks are composed of small crystals known as grains. When annealed, this polycrystalline structure coarsens, thus allowing the properties of a material to be tailored for a particular application. The mobility of grain boundaries is thought to be determined by the crystallography of the adjacent crystals, but experimental validation in bulk polycrystalline materials is lacking. Here we developed a novel fitting methodology by direct comparison of a time-resolved three-dimensional experimental data to simulations of the evolution of 1501 grains in iron. The comparison allows reduced mobilities of 1619 grain boundaries to be determined simultaneously. We find that the reduced mobilities vary by three orders of magnitude and in general exhibit no correlation with the boundary's five macroscopic degrees of freedom, implying that grain growth is governed by other factors. [ABSTRACT FROM AUTHOR]

Grain evolution in pure iron is determined in three dimensions using diffraction contrast tomography at a synchrotron source. During annealing for 75 min at 800 ∘ C , the evolution of initially 1327 grains is quantified as a function of 15 time-steps. A comprehensive statistical analysis is provided based on the equivalent radius, the number of faces and the mean width parameters of the grains. We introduce analytical relations between these parameters, validate them, and discuss their physical meaning. While the sample is fully recrystallized, the growth is found not to be self-similar, as evidenced in changes in the distributions of normalized grain size and number of faces per grain. More importantly, a strong decrease in the slope of the growth rate over the mean width of grain faces is observed, indicating a slowdown of grain growth. The data is used to determine the applicability of the isotropic MacPherson-Srolovitz theory to an anisotropic material such as iron. Geometrical properties that are averaged over the entire grain ensemble are well described by the model, but the properties and evolution of the individual grains exhibit substantial scatter. [ABSTRACT FROM AUTHOR]

A method to determine material parameters by comparing the evolution of experimentally determined 3D microstructures to simulated 3D microstructures is proposed. The temporal evolution of a dendritic solid-liquid mixture is acquired in situ using x-ray tomography. Using a time step from these data as an initial condition in a phase-field simulation, the computed structure is compared to that measured experimentally at a later time. An optimization technique is used to find the material parameters that yield the best match of the simulated microstructure to the measured microstructure in a global manner. The proposed method is used to determine the liquid diffusion coefficient in an isothermal Al-Cu alloy. However, the method developed is broadly applicable to other experiments in which the evolution of the three-dimensional microstructure is determined in situ. We also discuss methods to describe the local variation of the best-fit parameters and the fidelity of the fitting. We find a liquid diffusion coefficient that is different from that measured using directional solidification. [ABSTRACT FROM AUTHOR]

The development of energy resolving photon counting detectors (PCD) has paved the way to spectral X-ray Computed Tomography (CT), with which one can simultaneously extract the energy dependence of a material's linear attenuation coefficient (LAC). Spectral CT has proved to be an advanced technique to classify materials based on their physical properties such as electron density (ρ e) and effective atomic number (Z eff). However, the application of spectral CT may be hindered by the poor image reconstruction quality when used for material identification in security screening where rapid scanning is required. Image reconstruction from few projections or low radiation exposure time would enable rapid scanning. The reconstruction quality for each energy bin may also be degraded since the division of photon counts into multiple energy bins naturally leads to higher noise levels. In this work, we explore how to perform accurate spectral CT reconstructions from such data, and propose L ∞ norm-based vectorial total variation (L ∞ -VTV) regularization that uses correlations between multiple energy bins. Using experimental data acquired with a custom laboratory instrument for spectral CT, the L ∞ -VTV is tested on "real life" phantoms consisting of materials in the range of 6 ≤ Z eff ≤ 15. For material classification from only 7 projections, the L ∞ -VTV gives the relative deviations of 3.5% for ρ e and 2.4% for Z eff , whereas the total nuclear variation (TNV) of another state-of-the-art joint reconstruction and the total variation (TV) yield those of 3.4% and 3.1%, and 3.8% and 4.2%, respectively. The L ∞ -VTV is now ready for use in security screening. • A joint reconstruction algorithm with L infinity norm improves image reconstruction. • The algorithm is robust to few projections and/or low photon counts. • Using correlations between multiple energy bins enhances material identification. • L infinity norm in the algorithm leads to suppression of outliers in gradient magnitudes. • High noise levels in specific energy bins can be alleviated using unaffected bins. [ABSTRACT FROM AUTHOR]

• 3D X-ray diffraction yields per-grain strain, texture, twin relations and structure. • Applicable to a broad scope of functional polycrystalline materials. • Demonstrated by application to a kesterite (CZTS) thin film solar cell. • CZTS is a technologically interesting case with complex phase composition. • 3DXRD may detect and characterize secondary phases not otherwise distinguishable. [Display omitted] The non-destructive structural characterization of individual grains in thin-films photovoltaics based on polycrystalline materials is a powerful tool for revealing important details of the microstructure of solar cell absorbers. Here, we use three-dimensional X-ray diffraction (3DXRD) to obtain statistics on the phase, size, orientation and strain tensors of the grains, as well as their twin relations in Cu 2 ZnSnS 4 (CZTS) absorbers. Moreover, this powerful approach allows the non-ambiguous determination of phases with distinct optical and electrical properties but similar lattice parameters, such as CZTS and ZnS. Our analysis over cumulative statistics of nearly 600 grains in polycrystalline CZTS reveals that a fraction of 2.5% corresponds to the ZnS secondary phase. Statistics of the strain distribution in the polycrystalline CZTS layer indicate an average tensile stress in the plane of the film of ~70 MPa and a compressive stress along the normal to the film of ~145 MPa. We found that 41% of the total number of grains in CZTS absorbers are Σ3 twins. We calculate the frequency of the six types of Σ3 boundaries, revealing that the 180° rotation along the axis<221>is the most frequent. Accessing the microstructure opens the possibility to study its influence on the properties of the film, such as bandgap variations due to strain or the role of twin boundaries in the charge transport mechanisms. [ABSTRACT FROM AUTHOR]

We present a method for material classifications in spectral X-ray Computed Tomography (SCT) taking advantage of energy-resolving 2D detectors to simultaneously extract the energy dependence of a material's linear attenuation coefficient (LAC). The method employs an attenuation decomposition presented by Alvarez et al., and estimates system-independent material properties of electron density (ρ e) and effective atomic number (Z eff), independent of the scanner, from the energy-dependent LAC measurements. The method uses a spectral correction algorithm and the energy range is truncated to exclude bins with photon starvation and spectral distortion present even after correction of detector response. A novel technique of energy bin selection is used for optimized classification performance. The method is tested against another SCT classification method called SRZE for inspecting materials in the range of 6 ≤ Z eff ≤ 23. Our method aims at an increase in the speed of pot processing workflow after the data acquisition, and it achieves explicitly up to 32 times better time efficiency for the reconstruction with comparable accuracy for a range of materials important in threat detection. • Just two spectral detector energy bins needed for accurate material identification. • Correction of the spectral detector response is required for accurate classification. • The low- to high-energy threshold are optimized above 100 keV. • Non-overlapping energy bins improve classification performance. [ABSTRACT FROM AUTHOR]