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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%.

X-ray diffraction tomography is an innovative method that is widely used to obtain 2D-phase-contrast diffraction images and the subsequent 3D-reconstruction of structural defects in crystals. The most frequent objects of research are linear and helical dislocations in a crystal, for which plane wave diffraction images are the most informative, since they do not contain additional interference artifacts unrelated to the images of the defects themselves. In this work, the results of modeling and analysis of 2D plane wave diffraction images of a nanodimensional Coulomb-type defect in a Si(111) thin crystal are presented based on the construction of numerical solutions of the dynamic Takagi–Taupin equations. An adapted physical expression for the elastic displacement field of the point defect, which excludes singularity at the defect location in the crystal, is used. A criterion for evaluating the accuracy of numerical solutions of the Takagi–Taupin equations is proposed and used in calculations. It is shown that in the case of the Coulomb-type defect elastic displacement field, out of the two difference algorithms for solving the Takagi–Taupin equations used in their numerical solution, only the algorithm for solving the Takagi–Taupin equations where the displacement field function enters in exponential form is acceptable in terms of the required accuracy-duration of the calculations.

This study focuses on sparse subband fusion imaging. A method based on high-precision parameter estimation of geometrical theory of diffraction (GTD) model is given. Considering the incoherence problem in each subband data, a coherent processing method is adopted in the paper. Based on an all-pole model, it makes use of the phase difference of pole and scattering coefficient between each sub-band to effectively estimate the incoherent components. After coherent processing, the high and low frequency subband data can be expressed as a uniform all-pole model. The gapped-data amplitude and phase estimation algorithm is adopted to fill up the gapped band. Finally, fusion data is gained by high precision parameter estimation of GTD-all-pole model with full-band data, such as scattering center number, scattering center type and amplitude. The experimental results of simulated data with fixed-points indicate that the resolution of one-dimensional (1D) range profile and 2D inverse synthetic aperture radar (ISAR) image based on this method is better than that of each sub-band. In this way, the validity of the proposed method is proved.

All-inorganic cesium (Cs) lead perovskites have better thermal and chemical stability than organic–inorganic hybrids. They therefore represent a hope for stability and increased performance of perovskites as absorber layers in photovoltaic solar cells. In the present work, we have deposited different layers on FTO-coated glass substrates using the one-step spin-coating method. The results of the lead substitution are presented and critically discussed. The X-ray diffraction (XRD) results show four peaks for all three samples. The main peaks of the different films are located at the 2θ angles of 26.45° and 51.50° for the Muller indices (220) and (242), respectively. These two main peaks indicate that the prepared thin films all have two preferred crystallographic orientations. Beyond these two main peaks, we have two other smaller peaks at 2θ of 33.67° and 37.70° corresponding to the Muller indices of (210) and (211), respectively. The smoother the surface of the thin films, the more light they reflect, resulting in poor light absorption by the films. It is therefore important to obtain a surface image of the prepared films, as the larger the surface image, the better the film. With this in mind, we carried out a scanning electron microscope (SEM) analysis, which gave us the surface images. Figure 3 shows the SEM images of thin CsPb 1− x Sn x I 1.5 Br 1.5 layers ( x  = 0, 0.5, and 1) grown on FTO-coated glass substrate with different [Pb]/[Sn] ratios. As can be seen from the figure, the effect of the [Pb]/[Sn] ratio is visible in the surface images of the different thin films. The smallest grain size is that of the unsubstituted CsPbI 1.5 Br 1.5 , while the largest grain size corresponds to the partially Pb-substituted layer (CsPb 0.5 Sn 0.5 I 1.5 Br 1.5 ). The fully Pb-substituted layer (CsSnI 1.5 Br 1.5 ) has an intermediate grain size. The surface images of the films show that the surfaces are well coated with grain sizes that vary greatly depending on the layer. The best grain size is that of the thin film with partial lead substitution (CsPb 0.5 Sn 0.5 I 1.5 Br 1.5 ). Regarding the UV-visible absorption of the different films, we can say that the films absorb the maximum amount of light in the wavelength range of 350–550 nm. Above 550 nm, the absorption coefficients drop significantly. The absorption coefficients of the tin-free (Sn) layer remain higher than the coefficients of the other layers throughout the UV-visible spectrum. The degradation study revealed that the Sn-free layer retains good light absorption compared to the other layers after 4 weeks of exposure to the ambient environment. The crystal structure of all the layers shows good resistance to the elements during the 4 weeks, as shown by the renewed XRD results after the 4 weeks of exposure.

High-quality transition metal tellurides, especially for WTe2, have been demonstrated to be necessarily synthesized under close environments and high temperatures, which are restricted by the low formation Gibbs free energy, thus limiting the electrochemical reaction mechanism and application studies. Here, we report a low-temperature colloidal synthesis of few-layer WTe2 nanostructures with lateral sizes around hundreds of nanometers, which could be tuned the aggregation state to obtain the nanoflowers or nanosheets by using different surfactant agents. The crystal phase and chemical composition of WTe2 nanostructures were analyzed by combining the characterization of X-ray diffraction and high-resolution transmission electron microscopy imaging and elements mapping. The as-synthesized WTe2 nanostructures and its hybrid catalysts were found to show an excellent HER performance with low overpotential and small Tafel slope. The carbon-based WTe2–GO and WTe2–CNT hybrid catalysts also have been synthesized by the similar strategy to study the electrochemical interface. The energy diagram and microreactor devices have been used to reveal the interface contribution to electrochemical performance, which shows the identical performance results with as-synthesized WTe2–carbon hybrid catalysts. These results summarize the interface design principle for semimetallic or metallic catalysts and also confirm the possible electrochemical applications of two-dimensional transition metal tellurides.

Simple hydrothermal process was used to successfully produce two-dimensional (2D) MoS 2 powder flower-like nanosheets. The structure of the end product 2D-MoS 2 is altered by changing the preparation conditions of reaction time and pH value with a constant autoclave temperature. Via annealing at 500°C, all samples transfer into 2H-MoS 2 instead of 1T-MoS 2 . X-ray diffraction patterns showed that the peaks along (002) planes shifted dramatically from 14.2° to 9.4°. Field emission scanning electron microscopy and high-resolution transmission electron microscopy images revealed that the prepared samples have a flower-like structure composed of spheres of nanosheets with a good polycrystalline structure. The energy gap for pristine and annealed samples is calculated from diffuse reflectance measurements and found to be 1.3 and 0.68 eV, respectively. Differential scanning calorimeter curves showed an impressive exothermic peak at 318°C, suggesting a structural to the stable 2H-MoS 2 phase. The Brunauer–Emmett–Teller technique showed rapid decreases in the samples surface area at nearly 48 m 2  g –1 with the structural transformation.

Layered transition metal dichalcogenides (TMDs) have attracted interest due to their promise for future electronic and optoelectronic technologies. As one approaches the two-dimensional (2D) limit, thickness and local topology can greatly influence the macroscopic properties of a material. To understand the unique behavior of TMDs it is therefore important to identify the number of atomic layers and their stacking in a sample. The goal of this work is to extract the thickness and stacking sequence of TMDs directly by matching experimentally recorded high-angle annular dark-field scanning transmission electron microscope images and convergent-beam electron diffraction (CBED) patterns to quantum mechanical, multislice scattering simulations. Advantageously, CBED approaches do not require a resolved lattice in real space and are capable of neglecting the thickness contribution of amorphous surface layers. Here we demonstrate the crystal thickness can be determined from CBED in exfoliated 1T-TaS2 and 2H-MoS2 to within a single layer for ultrathin ≲9 layers and ±1 atomic layer (or better) in thicker specimens while also revealing information about stacking order—even when the crystal structure is unresolved in real space.

Timely and accurate detection and identification of cavities under urban roads is the key to road safety. Due to the inability to obtain accurate migration velocity and the difficulty of achieving complete convergence of diffraction signals of the cavity disease, traditional migration methods struggle to accurately identify and locate the subgrade cavity. This paper proposes a GPR image migration processing (TUFK method) based on 2D undecimated wavelet transform and the F–K method in accordance with the high-precision imaging of the subgrade cavity. The finite-difference forward models of subgrade cavity without and with noise are established, and the model test of cavity detection by GPR is carried out in the laboratory. Through the fine extraction and migration processing of the weak diffraction signals from the cavity, the optimal velocity required for migration is analyzed, and the TUFK method is applied to the migration process of GPR data acquired for the purpose of cavity detection. Furthermore, the proposed method is applied to the processing of GPR data acquired in the field with a cavity below the roadbed. The results show that the TUFK method can accurately extract the diffraction signals from the cavity and achieve the fine convergence of cavity diffraction signals whether in noiseless or noisy environments. Compared with the traditional Kirchhoff and F–K migration methods, this method can effectively obtain accurate migration velocity and the migration results can reflect the actual position and shape of the cavity. This study can provide a new idea and effective method for the imaging of subgrade cavity.

High energy 2D X-ray powder diffraction experiments are widely used for lattice strain measurement. The 2D to 1D conversion of diffraction patterns is a necessary step used to prepare the data for full pattern refinement, but is inefficient when only peak centre position information is required for lattice strain evaluation. The multi-step conversion process is likely to lead to increased errors associated with the ‘caking’ (radial binning) or fitting procedures. A new method is proposed here that relies on direct Digital Image Correlation analysis of 2D X-ray powder diffraction patterns (XRD-DIC, for short). As an example of using XRD-DIC, residual strain values along the central line in a Mg AZ31B alloy bar after 3-point bending are calculated by using both XRD-DIC and the conventional ‘caking’ with fitting procedures. Comparison of the results for strain values in different azimuthal angles demonstrates excellent agreement between the two methods. The principal strains and directions are calculated using multiple direction strain data, leading to full in-plane strain evaluation. It is therefore concluded that XRD-DIC provides a reliable and robust method for strain evaluation from 2D powder diffraction data. The XRD-DIC approach simplifies the analysis process by skipping 2D to 1D conversion, and opens new possibilities for robust 2D powder diffraction data analysis for full in-plane strain evaluation.

Three different algorithms, as implemented in three different computer programs, were put to the task of extracting direct space lattice parameters from four sets of synthetic images that were per design more or less periodic in two dimensions (2D). One of the test images in each set was per design free of noise and, therefore, genuinely 2D periodic so that it adhered perfectly to the constraints of a Bravais lattice type, Laue class, and plane symmetry group. Gaussian noise with a mean of zero and standard deviations of 10 and 50% of the maximal pixel intensity was added to the individual pixels of the noise-free images individually to create two more images and thereby complete the sets. The added noise broke the strict translation and site/point symmetries of the noise-free images of the four test sets so that all symmetries that existed per design turned into pseudo-symmetries of the second kind. Moreover, motif and translation-based pseudo-symmetries of the first kind, a.k.a. genuine pseudo-symmetries, and a metric specialization were present per design in the majority of the noise-free test images already. With the extraction of the lattice parameters from the images of the synthetic test sets, we assessed the robustness of the algorithms’ performances in the presence of both Gaussian noise and pre-designed pseudo-symmetries. By applying three different computer programs to the same image sets, we also tested the reliability of the programs with respect to subsequent geometric inferences such as Bravais lattice type assignments. Partly due to per design existing pseudo-symmetries of the first kind, the lattice parameters that the utilized computer programs extracted in their default settings disagreed for some of the test images even in the absence of noise, i.e., in the absence of pseudo-symmetries of the second kind, for any reasonable error estimates. For the noisy images, the disagreement of the lattice parameter extraction results from the algorithms was typically more pronounced. Non-default settings and re-interpretations/re-calculations on the basis of program outputs allowed for a reduction (but not a complete elimination) of the differences in the geometric feature extraction results of the three tested algorithms. Our lattice parameter extraction results are, thus, an illustration of Kenichi Kanatani’s dictum that no extraction algorithm for geometric features from images leads to definitive results because they are all aiming at an intrinsically impossible task in all real-world applications (Kanatani in Syst Comput Jpn 35:1–9, 2004 ). Since 2D-Bravais lattice type assignments are the natural end result of lattice parameter extractions from more or less 2D-periodic images, there is also a section in this paper that describes the intertwined metric relations/holohedral plane and point group symmetry hierarchy of the five translation symmetry types of the Euclidean plane. Because there is no definitive lattice parameter extraction algorithm, the outputs of computer programs that implemented such algorithms are also not definitive. Definitive assignments of higher symmetric Bravais lattice types to real-world images should, therefore, not be made on the basis of the numerical values of extracted lattice parameters and their error bars. Such assignments require (at the current state of affairs) arbitrarily set thresholds and are, therefore, always subjective so that they cannot claim objective definitiveness. This is the essence of Kenichi Kanatani’s comments on the vast majority of computerized attempts to extract symmetries and other hierarchical geometric features from noisy images (Kanatani in IEEE Trans Pattern Anal Mach Intell 19:246–247, 1997 ). All there should be instead for noisy and/or genuinely pseudo-symmetric images are rankings of the relative likelihoods of classifications into higher symmetric Bravais lattice types, Laue classes, and plane symmetry groups.