Simulated Diffraction Patterns Research Articles

A simulation of diffraction patterns using a lock-in detection code

We show that diffraction patterns can be directly simulated by a computer program implementing a lock-in algorithm. The two distinct physical topics, namely, single-slit diffraction and lock-in detection, are juxtaposed to highlight the common underlying physical principle in the context of the power spectrum of source signals arising from Fourier analysis.

Ab initio study on changing behaviors of lithium-rich layered composite cathode materials

The lithium-rich composite-layered oxide, xLi2MnO3•(1-x)LiM'O2, where M’ represents transition metals, is a promising cathode material with excellent capacity at high working voltage for lithium-ion batteries (LIBs). Nevertheless, an unusual charge-discharge feature is observed for this material with sloping and plateau regions during the initial charging. In this work, ab initio calculations based on density functional theory were employed to examine the stability of xLi2MnO3•(1-x)Li(Ni1/3Co1/3Mn1/3)O2 composite-layered cathode materials during the first charging. Optimized atomistic models for different compositions (x = 0.0, 0.3, 0.4, 0.5, 0.7, and 1) unveil a pseudo-rhombohedral or monoclinic-like structure within the solid solution phase, with simulated X-ray diffraction patterns closely matching experimental data. Using these atomistic models, the first charging process of the 0.4Li2MnO3•0.6Li(Ni1/3Co1/3Mn1/3)O2 cathode were investigated. There exists phase transition from a layered to a spinel structure. Additionally, Bader charge analysis reveals intriguing trends during the first delithiation process, where the valence states of Ni and Co gradual increase, while that of Mn almost remains unchanged. Simultaneously, significant oxidation of O is observed. This finding leads to further evaluations on oxygen vacancy formation in comparison to the energy required for delithiation. Defect formation energy calculations demonstrate that the plateau in charging curve is resulted from oxygen vacancy formation during the first charging. By empirical fitting oxygen chemical potential at μO = -1.200 eV, the calculated charging-discharging curves aligned well with experimental data during the first and second charging. Furthermore, the pathways of lithium and oxygen deintercalation are elucidated. This work contributes fundamental understandings on the xLi2MnO3•(1-x)LiM'O2 composite-layered oxides as cathode for LIBs, providing valuable guidance for further developments in high-capacity Co-lean cathode materials.

Crystallographic phase identifier of a convolutional self-attention neural network (CPICANN) on powder diffraction patterns.

Spectroscopic data, particularly diffraction data, are essential for materials characterization due to their comprehensive crystallographic information. The current crystallographic phase identification, however, is very time consuming. To address this challenge, we have developed a real-time crystallographic phase identifier based on a convolutional self-attention neural network (CPICANN). Trained on 692 190 simulated powder X-ray diffraction (XRD) patterns from 23 073 distinct inorganic crystallographic information files, CPICANN demonstrates superior phase-identification power. Single-phase identification on simulated XRD patterns yields 98.5 and 87.5% accuracies with and without elemental information, respectively, outperforming JADE software (68.2 and 38.7%, respectively). Bi-phase identification on simulated XRD patterns achieves 84.2 and 51.5% accuracies, respectively. In experimental settings, CPICANN achieves an 80% identification accuracy, surpassing JADE software (61%). Integration of CPICANN into XRD refinement software will significantly advance the cutting-edge technology in XRD materials characterization.

Theoretical Design of Strengthened Nanotwinned γ*-Boron.

The distinctive electron deficiency and unusual multicenter bonding situations of boron give rise to fascinating chemical complexity and imaginative structural polymorphism. Herein, we employ an independently developed method to construct the new twinned γ*-boron based on the well-known hardest elemental boron, γ-B28. Notably, the newly propounded γ*-boron phases exhibit considerably close energy levels with γ-B28 under ambient conditions. The simulated X-ray diffraction patterns of stable twinned structure present excellent agreement with experimental data. First-principles calculations reveal a 7.5% increase in the ideal Vickers shear strength of γ*-boron compared to γ-B28, attributed to diverse bond responses within the twinned slabs. The evaluated hardness of nanotwinned γ*-B reaches 59 GPa in consideration of the size hardening effect. Our research presents an efficient strategy for constructing new polymorphs of boron with improved mechanical properties and expands the knowledge about twinning structures of boron.

Tuning the order of poly(3-alkylthiophene) derivatives ultrathin films through side-chain polarity: From a short-range ordered monolayer to a highly crystalline bilayer

In order to pave the way for the formation of ultrathin electronically conductive organic films, we explored the structure and morphology of polythiophene derivatives in situ on the water surface. By changing the side chain end-group of poly(3-hexylthiophene) (P3HT) from methyl to carboxylic acid potassium salt, we showed that the film structure is drastically changed from a highly ordered bilayer to a short-range organized monolayer. Using a comprehensive experimental approach from macroscopic length scale to molecular organization as well as simulations of diffraction patterns, the detailed structure of the crystalline P3HT bilayer was determined. Some similarities with the structure measured on thicker films deposited on solid substrates were evidenced such as the π-stacking distance, the interlayer spacing, and the edge-on conformation. Some differences were also pointed out, in particular the in-plane packing along the polymer backbones and the shift of the upper monolayer with respect to the bottom one in this direction. Such observations highlighted the influence of both the forced two-dimensional confinement and the nature of the substrate (water) on the P3HT film structure. The presence of a carboxylic acid potassium salt at the end of the side chain induced completely different behavior. Indeed, high pressures were necessary to observe a π-stacking of the thiophene units, but only short-range, and although the polymer keeps a monolayer organization independently of the pressure, a deep change in the polymer conformation was evidenced with the pressure.

Twisting two-dimensional iron sulfide layers into coincident site superlattices via intercalation chemistry.

Layered van der Waals (vdW) materials are susceptible not only to various stacking polymorphs through translations but also twisted structures due to rotations between layers. Here, we study the influence of such layer-to-layer twisting through the intercalation of ethylenediamine (EDA) molecules into tetragonal iron sulfide (Mackinawite FeS). Selected area electron diffraction patterns of intercalated FeS display reflections corresponding to multiple square lattices with a fixed angle between them, contrary to a single square lattice seen in the unintercalated phase. The observed twist angles of 49.13° and 22.98° result from a superstructure formation well described by the coincident site lattice (CSL) theory. According to the CSL theory, these measured twist angles lead to the formation of larger coincident site supercells. We build these CSL models for FeS using crystallographic group-subgroup transformations and find simulated electron diffraction patterns from the model to agree with the experimentally measured data.

Polarization- and Chaos-Game-Based Fingerprinting of Molecular Targets of Listeria Monocytogenes Vaccine and Fully Virulent Strains.

Two approaches to the synthesis of 2D binary identifiers ("fingerprints") of DNA-associated symbol sequences are considered in this paper. One of these approaches is based on the simulation of polarization-dependent diffraction patterns formed by reading the modeled DNA-associated 2D phase-modulating structures with a coherent light beam. In this case, 2D binarized distributions of close-to-circular extreme polarization states are applied as fingerprints of analyzed nucleotide sequences. The second approach is based on the transformation of the DNA-associated chaos game representation (CGR) maps into finite-dimensional binary matrices. In both cases, the differences between the structures of the analyzed and reference symbol sequences are quantified by calculating the correlation coefficient of the synthesized binary matrices. A comparison of the approaches under consideration is carried out using symbol sequences corresponding to nucleotide sequences of the hly gene from the vaccine and wild-type strains of Listeria monocytogenes as the analyzed objects. These strains differ in terms of the number of substituted nucleotides in relation to the vaccine strain selected as a reference. The results of the performed analysis allow us to conclude that the identification of structural differences in the DNA-associated symbolic sequences is significantly more efficient when using the binary distributions of close-to-circular extreme polarization states. The approach given can be applicable for genetic differentiation immunized from vaccinated animals (DIVA).

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.

Design and investigated a novel BN polymorph in orthorhombic phase

In this work, a new BN polymorph with Pnma symmetry is proposed by RG2 and investigated by density functional theory. Pnma-II BN polymorph is shown to be dynamically and mechanically stable, and the relative enthalpy of Pnma-II BN is 0.187 eV per atom higher than that of c-BN, respectively. Mechanical properties calculations indicate that Pnma-II BN is also a potential superhard material with hardness of 49.7 GPa. The electronic band structures of Pnma-II BN show that the Pnma-II BN is a direct and ultrawide band gap semiconductor (band gap is 5.82 eV). The mechanical anisotropy of Young's modulus of Pnma-II BN and Pnma BN is greater than that of c-BN, while the mechanical anisotropy of shear modulus of Pnma-II BN in the (100), (001) plane is lower than that of c-BN. In addition, simulated X-ray diffraction patterns are provided for experimental confirmation of the predicted structures.

Theoretical design of superhard twinned BC2N

BC2N is an ideal combination of diamond and boron nitride and is expected to exhibit better mechanical properties and thermal stability than boron nitride and diamond, respectively. Recent studies raise exciting prospects of building coherent nanotwinned boundaries to improve performance of ceramics. Herein, we developed a systematic method to construct twin structures of BC2N. The newly identified nanotwinned BC2N variant (τ-BC2N) exhibits better energetic stability and higher mechanical strength than single-crystal BC2N, attributed to the optimized bonding behavior and crystal orientations induced via twinning. The simulated X-ray diffraction patterns of τ-BC2N match those reported in previous experimental data. The nanotwinned BC2N displays superior Vickers hardness of ∼140 GPa, surpassing that of diamond. The computationally tailored approach and results obtained by twin-strengthening strategies offer powerful insights for the rational design and functional optimization of nanotwinned boron–carbon–nitrogen compounds containing intricate multiatomic constituents and structures.

Parametric simulation of electron backscatter diffraction patterns through generative models

Recently, discriminative machine learning models have been widely used to predict various attributes from Electron Backscatter Diffraction (EBSD) patterns. However, there has never been any generative model developed for EBSD pattern simulation. On one hand, the training of generative models is much harder than that of discriminative ones; On the other hand, numerous variables affecting EBSD pattern formation make the input space high-dimensional and its relationship with the distribution of backscattered electrons complicated. In this study, we propose a framework (EBSD-CVAE/GAN) with great flexibility and scalability to realize parametric simulation of EBSD patterns. Compared with the frequently used forward model, EBSD-CVAE/GAN can take variables more than just orientation and generate corresponding EBSD patterns in a single run. The accuracy and quality of generated patterns are systematically evaluated. The model does not only summarize a distribution of backscattered electrons at a higher level, but also mitigates data scarcity in this field.

Deciphering the structural evolutions and electronic features of Nd3+:K2YF5 nanocrystals

Neodymium (Nd3+)-doped K2YF5 nanophosphors have attracted considerable attention due to their promising application in fiber lasers, luminescence thermometry and bioimaging. However, the structural evolutions and electronic properties of Nd3+-doped K2YF5 nanocrystals have not been comprehensively studied, which is exactly the basis of spectral formation. In this letter, the ground structure of Nd3+:K2YF5 crystals are first obtained by crystal structure prediction in conjunction with density functional theory. Our results reveal a new stable phase with Pm (No. 6) space group for the Nd3+:K2YF5 nanocrystals, and Nd3+ ions replace the position of Y3+ ions. Additionally, we have identified the presence of a local polyhedron [NdF7]4-, wherein the crystallographic site with Cs symmetry is occupied by Nd3+ ions. The excellent agreement observed between our simulated X-ray diffraction patterns and the experimental data serves as compelling evidence supporting the validity of the ground-state structure. The electronic band structure calculation of Nd3+-doped K2YF5 employing the enhanced modified Becke-Johnson methodology demonstrates a closure of the insulator band gap (4.01 eV). Our analysis of the electron localization function for Nd3+-doped K2YF5 crystal indicates a dominant ionic bond interaction between Nd and F ions. These results offer valuable insights into the structural evolution and enable the exploration of properties when encountering other rare-earth-doped materials.

Improving orientation mapping by enhancing the diffraction signal using Auto-CLAHE in precession electron diffraction data

Precession electron diffraction (PED) is a powerful technique for revealing the crystallographic orientation of samples at the nanoscale. However, the quality of orientation indexing is strongly influenced by the quality of diffraction patterns. In this study, we have developed a novel algorithm called Auto-CLAHE (automatic contrast-limited adaptive histogram equalization), which automatically enhances low-intensity diffraction pattern signals using contrast-limited adaptive histogram equalization (CLAHE). The degree of enhancement is dynamically adjusted based on the overall intensity of the diffraction pattern, with greater enhancement applied to patterns with fewer spots (i.e., away from zone axes) and little or no enhancement applied to patterns with many spots (i.e., at a zone axis). By improving the visibility of low-intensity diffraction spots, Auto-CLAHE significantly improves the template matching between experimentally acquired and simulated diffraction patterns, leading to orientation maps with dramatically higher quality and lower noise. We anticipate that Auto-CLAHE provides an efficient and practical solution for preprocessing PED data, enabling higher-quality crystal orientation mapping to be routinely obtained.

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.

Convolutional Neural Networks to Assist the Assessment of Lattice Parameters from X-ray Powder Diffraction.

This article presents the development of convolutional neural networks (CNNs) for the estimation of lattice parameters in organic compounds across various crystal systems. A comprehensive collection of 92,085 organic compounds was utilized to train the CNNs, encompassing crystals with unit cells containing up to 512 atoms and a maximum unit cell volume of 8000 Å3. Simulated diffraction patterns were generated for each compound, comprising four diffraction patterns with different crystal sizes. These diffraction patterns were generated within a 2θ window of 3-60°, employing a step size of 0.02051°. Two distinct CNN architectures were developed with differing input data. The first CNN, referred to as XRD-CNN, was trained solely on diffraction patterns. In the test set, XRD-CNN demonstrated a mean absolute percentage error (MAPE) of 11.04% for unit cell vectors, 7.40% for angles, and 26.83% for unit cell volume. The second CNN, XRDElem-CNN, incorporated a binary representation of atoms within the unit cell as an additional input. XRDElem-CNN achieved improved performance, yielding MAPE values of 4.73% for unit vectors, 6.49% for angles, and 6.05% for the unit cell volume. To validate the performance of XRDElem-CNN, real diffraction patterns obtained from a conventional laboratory diffractometer (Cu Kα wavelength) were employed. Various representations of atoms within the unit cell were proposed, which were computationally efficient for evaluation with the CNNs. The assessed lattice parameters by XRDElem-CNN were validated using the Lp-search method, showing agreement with the reported values.

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.

Estimating of Fraction of Weakly Deformable Erythrocytes in a Blood Sample Based on the Method of Laser Ektacytometry and a Database of Simulated Diffraction Patterns

Estimating of Fraction of Weakly Deformable Erythrocytes in a Blood Sample Based on the Method of Laser Ektacytometry and a Database of Simulated Diffraction Patterns

Numerical Investigation of Diffraction Patterns of Small Size Apertures Using Light Sources From Xuv to The Visible Region: Simulation for The Small Size Structures

In the present work, a computer simulation program generates Fresnel diffraction patterns from small-size apertures using illumination wavelengths from extreme ultraviolet (XUV) to the visible region suggesting that it can be used to model a wide range of experimental setups. By being able to simulate diffraction patterns for such a broad range of wavelengths, the program can be used to investigate the effects of varying wavelengths and aperture size on the resulting pattern. By using a computer simulation program that can generate Fresnel diffraction patterns across a wide range of wavelengths, one can explore how different wavelengths of light interact with various aperture sizes. This allows one to investigate the effects of changing these parameters on the resulting diffraction pattern. The computer simulation program generating Fresnel diffraction patterns from square apertures by using the illumination wavelength sources from XUV to the visible region has been studied. Changing the aperture-screen distance, the illumination wavelength, and the aperture size provides a clear transition of diffraction patterns from the Fresnel to the Fraunhofer region. The diffraction patterns obtained by the Fresnel integral method have been compared with that simulated by the Fraunhofer calculation. There is a good agreement between the results. The structural similarity index (SSI) exhibits that comparing the diffraction images produced with both approaches agree.

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.