Experimental Diffraction Patterns Research Articles

Verification of a method for determining the degree of crystallinity using experimental and computer-generated powder diffraction patterns. Corrigendum

An erroneous equation and some values of related parameters in the paper by Toraya [J. Appl. Cryst. (2023), 56, 1751–1763] are corrected.

Towards measuring absolute residual stress by HR-EBSD with simulated reference patterns

The High-Resolution Electron Backscatter Diffraction (HR-EBSD) technique has drawn attention in recent years, mainly thanks to its ability to assess the elastic strain/stress state with a sub-micron spatial resolution. Each diffraction pattern is correlated with a reference one, and the strain level relative to the reference is retrieved in the procedure. Several studies have attempted to use dynamically simulated diffraction patterns as references to access absolute strain/stress states to circumvent the difficulty of finding a strain-free reference pattern, which is often inaccessible. Numerous factors need to be considered and corrected to register better experimental and simulated diffraction patterns, such as the accurate positioning of the projection center, Kikuchi band (K-band) brightness asymmetry, K-band gray level reversal, optical distortion, or non-uniform electron energy. Here, an integrated digital image correlation method is proposed to register experimental patterns to a master pattern defined on a sphere, where the difficulties with experimental patterns are, for the most part, corrected efficiently. Due to the shallow inspection depth of EBSD, the free-surface property (vanishing stress vector at the observation surface) is also adopted to reduce the degrees of freedom and enhance precision. Through several tests on high-quality experimental patterns, the proposed method proves robust and precise. Both the systematic and random errors of the residual strain results are several 10−4. The method also allows the simultaneous determination of residual stress and the projection center coordinates.

Identification of the high-pressure phases of α-SnWO4 combining x-ray diffraction and crystal structure prediction

We have characterized the high-pressure behavior of -SnWO4. The compound has been studied up to 30 GPa using a diamond-anvil cell and synchrotron powder X-ray diffraction. We report evidence of two structural phase transitions in the pressure range covered in our study, and we propose a crystal structure for the two high-pressure phases. The first one, observed around 12.9 GPa, has been obtained combining indexation using DICVOL and density-functional theory calculations. The second high-pressure phase, observed around 17.5 GPa, has been determined by using the CALYPSO code, the prediction of which was supported by a Le Bail fit to the experimental X-ray diffraction patterns. The proposed structural sequence involves two successive collapses of the unit-cell volume and an increase in the coordination number of Sn and W atoms. The room-temperature equations of state, the principal axes of compression and their compressibility, the elastic constants, and the elastic moduli are reported for -SnWO4 and for the two high-pressure phases.

Crystal Structure Determination from Powder Diffraction Patterns with Generative Machine Learning.

Powder X-ray diffraction (PXRD) is a cornerstone technique in materials characterization. However, complete structure determination from PXRD patterns alone remains time-consuming and is often intractable, especially for novel materials. Current machine learning (ML) approaches to PXRD analysis predict only a subset of the total information that comprises a crystal structure. We developed a pioneering generative ML model designed to solve crystal structures from real-world experimental PXRD data. In addition to strong performance on simulated diffraction patterns, we demonstrate full structure solutions over a large set of experimental diffraction patterns. Benchmarking our model, we predicted the structure for 134 experimental patterns from the RRUFF database and thousands of simulated patterns from the Materials Project on which our model achieves state-of-the-art 42 and 67% match rate, respectively. Further, we applied our model to determine the unreported structures of materials such as NaCu2P2, Ca2MnTeO6, ZrGe6Ni6, LuOF, and HoNdV2O8 from the Powder Diffraction File database. We extended this methodology to new materials created in our lab at high pressure with previously unsolved structures and found the new binary compounds Rh3Bi, RuBi2, and KBi3. We expect that our model will open avenues toward materials discovery under conditions which preclude single crystal growth and toward automated materials discovery pipelines, opening the door to new domains of chemistry.

On the Elusive Crystallography of Lithium-Rich Layered Oxides: Novel Structural Models.

Lithium-rich layered oxides (LRLOs) are one of the most attractive families among future positive electrode materials for the so-called fourth generation of lithium-ion batteries (LIBs). Their electrochemical performance is enabled by the unique ambiguous crystal structure that is still not well understood despite decades of research. In the literature, a clear structural model able to describe their crystallographic features is missing thereby hindering a clear rationalization of the interplay between synthesis, structure, and functional properties. Here, the structure of a specific LRLO, Li1.28 Mn0.54 Ni0.13 Co0.02 Al0.03 O2 , using synchrotron X-ray diffraction (XRD), neutron diffraction (ND), and High-Resolution Transmission Electron Microscopy (HR-TEM), is analyzed. A systematic approach is applied to model diffraction patterns of Li1.28 Mn0.54 Ni0.13 Co0.02 Al0.03 O2 by using the Rietveld refinement method considering the R m and C2/m unit cells as the prototype structures. Here, the relative ability of a variety of structural models is compared to match the experimental diffraction pattern evaluating the impact of defects and supercells derived from the R m structure. To summarize, two possible models able to reconcile the description of experimental data are proposed here for the structure of Li1.28 Mn0.54 Ni0.13 Co0.02 Al0.03 O2 : namely a monoclinic C2/m defective lattice (prototype Li2 MnO3 ) and a monoclinic defective supercell derived from the rhombohedral R m unit cell (prototype LiCoO2 ).

Similarity score for screening phase-retrieved maps in X-ray diffraction imaging - characterization in reciprocal space.

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

Based on polynomial approximation, method of reconstruction of soft X-ray and extreme ultraviolet radiation spectrum from a diffraction pattern obtained using a transmission diffraction grating

A transmission diffraction grating is a useful tool for studying spectra in the soft X-ray and extreme ultraviolet range, created by the radiation of small–sized sources, such as laser produced plasma, vacuum spark, Z-pinch, X-pinch, etc. In almost all such experiments, a distance between the source and the grating is much larger than the size of the source, so the incident wave can be considered plane with sufficient accuracy, the distance from the recording detector to the grating is also much larger than the size of the grating and, therefore, Fraunhofer diffraction takes place here and the presence of a focusing element is not required.The interpretation of the results obtained using such a grating is difficult due to the fact that different diffraction orders overlap in the registered diffraction pattern. Therefore, there is a problem of reconstruction the true spectrum from an experimental diffraction pattern. In this paper, this problem is solved by approximating the function of the radiation intensity recorded on the diffraction pattern by a polynomial. In this case, due to the properties of the transmission diffraction grating, the desired function describing the spectrum being reconstructed is also a polynomial, which can be calculated according to the developed algorithm. Both the direct conversion of the spectrum into the diffraction pattern and the reverse conversion of the diffraction pattern into the spectrum do not change the radius of convergence, since multiplication is carried out by multipliers uniformly bounded from above and below. It follows from this that minor errors in the definition of the function describing the diffraction pattern cannot lead to significant errors in the reconstructed spectrum.

Indexing high-noise electron backscatter diffraction patterns using convolutional neural network and transfer learning

The crystal orientation indexing method based on Hough transform has many “zero solution” points when indexing the crystal orientation of materials, especially those with large strains. We propose an efficient and migratable indexing method for fast and autonomous crystal orientations indexing of experimental electron backscatter diffraction (EBSD) patterns of various crystal structures by transfer learning. To better evaluate the performance of the model, the performance of the model was assessed both quantitatively based on the numerical metrics and qualitatively through the Inverse Pole Figure (IPF). The results of indexing high-noise nickel EBSD patterns show that the CNN-based indexing method could not only obtain an acceptable indexing accuracy (a mean disorientation error of 1.77° for retraining and 2.31° for transfer learning), but also reasonably index the “zero solution” points remained in the Hough transform-based indexing method. And the results of indexing other materials by transfer learning show that the CNN has strong knowledge migration capability. In addition, the interpretability of the CNN was investigated by visualizing feature maps of each convolutional layer, and the sensitivity analysis of the CNN was realized by testing masked images.

Phase Formation Mechanism and Piezoelectric Behaviour of NaNbO3 Ceramic

The solid state reaction route is adopted to synthesize NaNbO3 with the aim to examine their structural, morphological and electrical behaviour of material with sintering time. The crystal phase is formed without any secondary phase at calcination temperature 800 °C. The article shows the scope of material to be used as a sensor in piezoelectric applications. The synthesized material has been avoided to heat for longer time and has been sintered at 2 h, 4 h and 6 h. The refinement of experimental X-ray diffraction pattern displays crystallization of material in Orthorhombic phase with space group Pbcm and lattice parameters a = 5.513752 Å, b = 5.568852 Å, c = 15.52854 Å, α = β = γ = 90°. A gaussian distribution of grain size with statistical average 0.722 μm, 0.841 μm and 0.842 μm has been observed for NN02, NN04 and NN06 respectively. The NN04 shows maximum piezoelectric coefficient d33* = 110 pm V−1, piezoelectric strain 0.0021% and smallest as asymmetric factor Ys = 0.204 with respect to other investigated samples.

Verification of a method for determining the degree of crystallinity using experimental and computer-generated powder diffraction patterns

A new procedure for determining the degree of crystallinity (DOC) has been developed. It is a two-step procedure consisting of (i) the separation of the observed pattern of a partially crystallized target material into crystalline and non-crystalline parts based on the Rietveld method, and (ii) the determination of the DOC based on the Ruland method. In the latter step, a disorder factor in Gaussian form with a disorder parameter is used to redistribute the total intensity between the crystalline and non-crystalline parts. Then, the DOC and disorder parameters are optimized by minimizing the cost function under the constraint of a constant intensity distribution between the two parts irrespective of the angular interval of integration. A self-contained technique for the background/halo pattern correction has also been developed and used between the two steps. Adoption of the two-step procedure could avoid parameter correlation between 2θ-dependent functions and provide robustness. The final goal is to determine the DOC of real materials such as polyphenylene sulfide composites with crystalline and non-crystalline fillers. The present study is a first step, and its purpose is to verify the efficiency of this method. Experimental and computer-generated intensity datasets of artificially mixed patterns of known weight fractions were used for testing the procedure. The DOC could be determined routinely by the procedure presented here within an error of 1–2% for samples with DOC < 50%.

Propagation of synchrotron radiation through double microchannel plate device: Comparison of experimental data and wave-approach simulation

Since third-generation synchrotron radiation facilities are highly brilliant sources, the scattering of a partially coherent beam gives rise to strong interference effects. We present and discuss in this contribution the comparison of simulated and experimental diffraction patterns collected with an optical device made by two identical flat Micro Channel Plates (MCPs) illuminated by synchrotron radiation at different energies. The experimental patterns clearly show the increase of the density of the main peak with respect to those collected with a single flat MCP. Data demonstrate that the use of a device based on two MCPs is an ideal optical system to condense the primary radiation in a narrow intense central peak.

UnwarpCalculator: a utility to estimate intensity distribution in reciprocal space for an arbitrary 3D set of atoms

UnwarpCalculator is a command-line utility developed to calculate intensity distribution in reciprocal space. The program uses CIF syntax input files and can work either with periodic crystals or with arbitrary atomic distribution, including incommensurately modulated and defect structures. With this program the intensity can be calculated for any reciprocal space point using the three main options available, including intensity calculation at a point with (h, k, l) coordinates, intensity distribution calculation along a line in reciprocal space and building an unwarped layer pixel by pixel. The program has an interactive interface and uses a fairly simple diffraction calculation model. The tool can be used for teaching crystallography since it offers much easier options and input file creation compared with existing software for defect and diffraction pattern simulations. These features along with input files with CIF syntax allow easy use of the program even for beginners. The utility can also be applied for the interpretation of experimental diffraction patterns and comparison of calculated versus experimental diffraction images to validate crystal structure models.

Crystal structure and X-ray powder diffraction data for Lumateperone tosylate

X-ray powder diffraction data, unit-cell parameters, and space group for the Lumateperone tosylate, C24H29FN3O⋅C7H7O3S, are reported [a = 15.5848(10) Å, b = 6.0700(4) Å, c = 31.3201(14) Å, β = 96.544(5)°, V = 2943.58 Å3, Z = 4, and space group C2]. In each case, all measured lines were indexed and were consistent with the corresponding space group. The single-crystal data of Lumateperone tosylate is also reported, respectively [a = 15.626(3) Å, b = 6.0806(10) Å, c = 31.415(5) Å, β = 96.609(7)°, V = 2965.1(8) Å3, Z = 4, and space group C2]. The experimental powder diffraction pattern has been well matched with the simulated pattern derived from the single-crystal data with preferred orientation in the [002] direction (orientation coefficient = 0.75).

An approach to investigate the crystallographic unit cell of human tooth enamel.

Human tooth enamel (HTE) is the hardest tissue in the human body and its structural organization shows a hierarchical composite material. At the nanometric level, HTE is composed of approximately 97% hydroxyapatite [HAP, Ca10(PO4)6(OH)2] as inorganic phase, and of 3% as organic phase and water. However, it is still controversial whether the hexagonal HAP phase crystallizes in P63/m or another space group. The observance in HTE of Ca2+, Mg2+ and Na+ ions using X-ray characteristic energy-dispersive spectroscopy in the scanning electron microscope has been explained by substitutions in the HAP unit cell. Thus, Ca2+ can be replaced by Na+ and Mg2+ ions; the PO43- group can be replaced by CO32- ions; and the OH- ions can also be replaced by CO32-. A unit-cell model of the hexagonal structure of HTE is not fully defined yet. In this work, density functional theory calculations are performed to study the hexagonal HAP unit cell when substitution by OH-, CO32-, Mg2+ and Na+ ions are carried out. An approach is presented to study the crystallographic unit cell of HTE by examining the changes resulting from the inclusion of these different ions in the unit cell of HAP. Enthalpies of formation and crystallographic characteristics of the electron diffraction patterns are analysed in each case. The results show an enhancement in structural stability of HAP with OH defects, atomic substitution of Mg2+, carbonate and interstitial Na+. Simulated electron diffraction patterns of the generated structures show similar characteristics to those of human tooth enamel. Hence, the results explain the indiscernible structural changes shown in experimental X-ray diffractograms and electron diffraction patterns.

Niobium monoxide NbO single crystal growing by floating zone method

In this work, a single crystal of niobium monoxide NbO was grown by crucible-free zone melting method. Polycrystalline NbO with ordered cubic structure (sp.gr. Pm-3m) with vacancies in both metal and nonmetal sublattices served as an initial material. According to XRD data, the grown niobium monoxide NbO single crystal has predominant growth in the [111]B1 direction and contains only one ordered cubic phase NbO, its lattice constant is equal to a = 421.2 pm. The growing mechanism of the NbO single crystal was clarified, in accordance with the Kossel and Stransky theory, it was suggested that the single crystal grows layer by layer. Analysis of the Kikuchi lines geometry allowed the orientations and disorientations of single crystal to be determined to high precision. An analysis of the diffraction pattern and intersection of Kikuchi lines showed that the NbO single crystal has (111)B1 facet. The experimental Laue diffraction patterns confirmed this direction of niobium monoxide NbO single crystal growth.

Enhanced EBSD calibration accuracy based on gradients of diffraction patterns

High-resolution electron backscatter diffraction (HR-EBSD) attracts increasing attention in materials researches, and correlating simulated and experimental diffraction patterns is a major HR-EBSD branch. However, the correlation accuracy is limited by several secondary effects generally not accounted for in pattern simulations, such as the non-uniform electron energy, Kikuchi band (K-band) asymmetry or gray level reversal. Although some of these phenomena can be simulated by Monte Carlo method and dynamical simulation, the computation is highly demanding and their effects on EBSD calibration are not systematically analyzed. Recently, it has been shown that the precise locations of K-band edges were better identified using the gradient of the diffraction patterns, in particular with the presence of K-band asymmetry. In the present study, it is proposed to use a similar strategy, in Integrated Digital Image Correlation to circumvent the systematic errors, and lack of accuracy due to these asymmetry artefacts. Gray level profiles of the K-bands are analyzed to assess the correctness of image registration. High-definition experimental EBSD datasets show that crystal orientation uncertainty improves by 0.01° when using gradients. Another evidence of the enhanced calibration accuracy is the improved continuity of the calibrated projection center position at grain boundaries by about 50%. In view of these results, it is suggested to systematically use gradients of diffraction patterns in all high-resolution EBSD analyses when correlating experimental and simulated patterns.

Crystal structure and X-ray powder diffraction data of barium copper iodate Ba2Cu(IO3)6

X-ray powder diffraction data, unit-cell parameters, and space group for the barium copper iodate, Ba2Cu(IO3)6, are reported [a = 7.48540(15) Å, b = 7.51753(19) Å, c = 7.64259(17) Å, α = 98.8823(7)°, β = 95.0749(7)°, γ = 97.6297(7)°, V = 418.528(9) Å3, Z = 1, and space group P$\bar{1}$]. All measured lines are indexed and are consistent with the corresponding space group. The single-crystal diffraction data of Ba2Cu(IO3)6 are also reported [a = 7.493(3) Å, b = 7.521(6) Å, c = 7.644(5) Å, α = 98.855(18)°, β = 95.060(16)°, γ = 97.62(2)°, V = 419.3(5) Å3, Z = 1, and space group P$\bar{1}$]. The crystal structure of Ba2Cu(IO3)6 features isolated [Cu(IO3)6]4− anionic clusters separated by Ba2+ cations. The experimental powder diffraction pattern matches well with the simulated pattern derived from the single crystal data.

Super-resolution electron ptychography of low dimensional materials at 30 keV: Beyond the detector limit

We demonstrate that electron ptychographic phase reconstruction can recover spatial frequencies higher than those directly recorded in the experimental electron diffraction patterns. This ability to recover high angle information from the oversampled low angle information allows an annular detector to be inserted which partially shadows a lower pixelated detector to simultaneously record a conventional annular dark field image and a ptychographic dataset. We apply this approach to 30 keV imaging of monolayer molybdenum disulfide and achieve an Abbe limited resolution of 1.2 ± 0.1Å in our reconstructions.

High Proton Conductivity of the UiO-66-NH2-SPES Composite Membrane Prepared by Covalent Cross-Linking.

A sulfonated poly(ethersulfone) (SPES)-metal-organic framework (MOF) film with excellent proton conductivity was synthesized by anchoring UiO-66-NH2 to the main chain of the aromatic polymer through the Hinsberg reaction. The chemical bond was formed between the amino group in MOFs and the -SO2Cl group in chlorosulfonated poly(ethersulfones) to conduct protons in the proton channel of the membrane, making the membrane have excellent proton conductivity. UiO-66-NH2 is successfully prepared as a result of the consistency of the experimental and simulated powder X-ray diffraction (PXRD) patterns of MOFs. The existence of absorption peaks of characteristic functional groups in Fourier transform infrared (FTIR) spectra proved the successful preparation of SPES, PES-SO2Cl, and a composite film. The results of the AC impedance test indicate that the composite film with a 3% mass fraction has the best proton conductivity of 0.215 S·cm-1, which is 6.2 times higher than that of the blended film without a chemical bond at 98% RH and 353 K. To our knowledge, there are rarely any reports on the preparation of a composite membrane by directly linking MOFs and the membrane matrix with chemical bonds. This work provides a good way to synthesize the highly conductive proton exchange film.

Pseudotetrahedral C2-symmetrical Co/Zn(II)-achiral Schiff base complexes with Δ/Λ-chirality induction at-metal as a racemic mixture

Reaction of achiral Schiff base ligands 1-((X-phenylimino)methyl)naphthalen-2-ol {X = 2-ethyl (HL1) or 4-methyl (HL2)} with cobalt(II) or zinc(II) acetate provided the corresponding bis[1-((X-phenylimino)methyl)naphthalen-2-olato-k2N,O]cobalt(II) or zinc(II) {X = 2-ethyl: M = Co (1) and Zn (2) or X = 4-methyl: M = Co (3) and Zn (4)} complexes. The molecules crystallize in the centrosymmetric space groups R–3 (1) and P–1 (3 or 4). Molecular structures determinations showed coordination of two molecules of the N,O-chelate ligands to the metal ion and formation of pseudotetrahedral complexes with C2-symmetry. Furthermore, coordination of two unsymmetrical achiral N,O-chelates induces Λ/Δ-chirality at the metal atom as a racemic mixture in the centrosymmetric space groups. Structural analyses further reveal that incorporation of 2-ethyl (1) or 4-methyl (3 or 4) group on the N-bound phenyl ring leads to an increase of both the O1-M-O2 and N1-M-N2 bond angles on going from 1 to 3 or 4, with the N1-M-N2 angle increasing to a much greater extent. The fair matching of the experimental and simulated powder X-ray diffraction patterns confirms the phase purity of bulk microcrystalline sample. Differential scanning calorimetry (DSC) results suggest an irreversible phase transformation from solid crystals to isotropic-liquids and subsequent thermal stability of the complexes. Cyclic voltammograms indicate a quasi-reversible two one electron charge transfer processes for 1 or 3 in N,N-dimethylformamide (DMF). Optimized geometry and excited state properties by density functional theory (DFT) and time dependent-density functional theory (TD-DFT) calculations correspond well to the experimental results.