Simulated Diffraction Patterns Research Articles

Enhancing deep-learning training for phase identification in powder X-ray diffractograms.

Within the domain of analyzing powder X-ray diffraction (XRD) scans, manual examination of the recorded data is still the most popular method, but it requires some expertise and is time consuming. The usual workflow for the phase-identification task involves software for searching databases of known compounds and matching lists of d spacings and related intensities to the measured data. Most automated approaches apply some iterative procedure for the search/match process but fail to be generally reliable yet without the manual validation step of an expert. Recent advances in the field of machine and deep learning have led to the development of algorithms for use with diffraction patterns and are producing promising results in some applications. A limitation, however, is that thousands of training samples are required for the model to achieve a reliable performance and not enough measured samples are available. Accordingly, a framework for the efficient generation of thousands of synthetic XRD scans is presented which considers typical effects in realistic measurements and thus simulates realistic patterns for the training of machine- or deep-learning models. The generated data set can be applied to any machine- or deep-learning structure as training data so that the models learn to analyze measured XRD data based on synthetic diffraction patterns. Consequently, we train a convolutional neural network with the simulated diffraction patterns for application with iron ores or cements compounds and prove robustness against varying unit-cell parameters, preferred orientation and crystallite size in synthetic, as well as measured, XRD scans.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document. This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

Ab initio description of bonding for transmission electron microscopy

The simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret their contrast and extract specimen features. This is especially true for high-resolution phase-contrast imaging of materials, but electron scattering simulations based on atomistic models are widely used in materials science and structural biology. Since electron scattering is dominated by the nuclear cores, the scattering potential is typically described by the widely applied independent atom model. This approximation is fast and fairly accurate, especially for scanning TEM (STEM) annular dark-field contrast, but it completely neglects valence bonding and its effect on the transmitting electrons. However, an emerging trend in electron microscopy is to use new instrumentation and methods to extract the maximum amount of information from each electron. This is evident in the increasing popularity of techniques such as 4D-STEM combined with ptychography in materials science, and cryogenic microcrystal electron diffraction in structural biology, where subtle differences in the scattering potential may be both measurable and contain additional insights. Thus, there is increasing interest in electron scattering simulations based on electrostatic potentials obtained from first principles, mainly via density functional theory, which was previously mainly required for holography. In this Review, we discuss the motivation and basis for these developments, survey the pioneering work that has been published thus far, and give our outlook for the future. We argue that a physically better justified ab initio description of the scattering potential is both useful and viable for an increasing number of systems, and we expect such simulations to steadily gain in popularity and importance.

Training artificial neural networks for precision orientation and strain mapping using 4D electron diffraction datasets

Techniques for training artificial neural networks (ANNs) and convolutional neural networks (CNNs) using simulated dynamical electron diffraction patterns are described. The premise is based on the following facts. First, given a suitable crystal structure model and scattering potential, electron diffraction patterns can be simulated accurately using dynamical diffraction theory. Secondly, using simulated diffraction patterns as input, ANNs can be trained for the determination of crystal structural properties, such as crystal orientation and local strain. Further, by applying the trained ANNs to four-dimensional diffraction datasets (4D-DD) collected using the scanning electron nanodiffraction (SEND) or 4D scanning transmission electron microscopy (4D-STEM) techniques, the crystal structural properties can be mapped at high spatial resolution. Here, we demonstrate the ANN-enabled possibilities for the analysis of crystal orientation and strain at high precision and benchmark the performance of ANNs and CNNs by comparing with previous methods. A factor of thirty improvement in angular resolution at 0.009˚ (0.16 mrad) for orientation mapping, sensitivity at 0.04% or less for strain mapping, and improvements in computational performance are demonstrated.

Deciphering the structures and electronic features of Yb3+-doped Y2O3 crystal: A theoretical perspective study

Considerable research interests have been paid to the rare-earth (RE) Yb3+-doped Y2O3 crystal which is of great potential for application as a solid-state laser because of its remarkable optoelectronic and physical properties. However, the detailed information of its microstructure is still lacking. Here, we have performed a systematically study of the structural evolution and electronic features of Yb3+-doped Y2O3 crystal by using the CALYPSO method and first-principle calculations. A novel stable phase of Yb3+-doped Y2O3 with R-3 space group has been uncovered for the first time. The obtained crystal structure indicates that the impurity Yb3+ ions are likely to substitute the Y3+ ions, forming a cage-like structure. Our simulated X-ray diffraction patterns of the lowest-energy structure show excellent agreement with the observed data, which demonstrates the accuracy of the present calculation. By analyzing the electronic band structures, we found the elimination of the insulated characters of Yb3+-doped Y2O3, resulting in an energy gap of 1.64 eV. The electron localization function and Bader charge analysis of Yb3+-doped Y2O3 are calculated and the results suggest that the Y-O bonds in Y2O3:Yb are ionic. These results can offer significant information of RE doped laser materials and serve as guides for the further investigation of such materials.

Design of a Series of Metallic BxNx+1 with Tunable Mechanical Properties.

Here a series of sp2-sp3 BxNx+1 (x = 1, 2, 3, 4, 5, 6) structures was constructed. These structures can be viewed as diamond-like BN blocks connected by single N-N bonds. Elastic constants and phonon dispersion curves confirm that all of the proposed structures are mechanically and dynamically stable. These structures all possess metallicity originating from the conductive channels formed by sp2-hybridized N atoms and adjacent sp3-hybridized B and N atoms. These structures exhibit tunable mechanical properties with a regular change in the sp2/sp3 ratio. The theoretical Vickers hardness increases and the ductility decreases as the number of diamond-like BN blocks increases, gradually approaching those of c-BN. Moreover, the convex hull at ambient pressure and 50 GPa indicates that high pressure is beneficial in the synthesis of these B-N phases. The simulated X-ray diffraction patterns of these structures were also calculated to provide more information for further experiments.

Nanostabilization of tetragonal distorted FeCo variants in ultra-thin FeCo/TiN multilayer films

Composites of ultra-thin nanolayers of FeCo/TiN with individual layer thickness of a few unit cells offer stability at elevated temperatures and exhibit defined magnetic properties which can be tuned by variying the layers thickness making them interesting candiates as components for magnetoelectric (ME) sensors. Initial studies describing the nanostructure of such thin films, however, left uncertainty about their exact crystal structure. With aberration-corrected microscopes the characterization of the local structure down to the atomic scale is possible to address the real structure with high precision. Here, by means of atomic resolution TEM imaging together with X-ray diffraction analysis, we were able to describe the nanostructure to be composed of individual layers of FeCo and TiN forming a superlattice with a defined cube-on-cube orientation relationship. The simulation of electron diffraction pattern featuring superlattice reflections on basis of structural modeling together with geometric phase analysis verified a defined orientation relationship resolving in the nanostabilization of a tetragonal distorted FeCo unit cell with c/a < 1.

Classification of crystal structures using electron diffraction patterns with a deep convolutional neural network.

Investigations have been made to explore the applicability of an off-the-shelf deep convolutional neural network (DCNN) architecture, residual neural network (ResNet), to the classification of the crystal structure of materials using electron diffraction patterns without prior knowledge of the material systems under consideration. The dataset required for training and validating the ResNet architectures was obtained by the computer simulation of the selected area electron diffraction (SAD) in transmission electron microscopy. Acceleration voltages, zone axes, and camera lengths were used as variables and crystal information format (CIF) files obtained from open crystal data repositories were used as inputs. The cubic crystal system was chosen as a model system and five space groups of 213, 221, 225, 227, and 229 in the cubic system were selected for the test and validation, based on the distinguishability of the SAD patterns. The simulated diffraction patterns were regrouped and labeled from the viewpoint of computer vision, i.e., the way how the neural network recognizes the two-dimensional representation of three-dimensional lattice structure of crystals, for improved training and classification efficiency. Comparison of the various ResNet architectures with varying number of layers demonstrated that the ResNet101 architecture could classify the space groups with the validation accuracy of 92.607%.

CloudEMAPS: A Cloud Computing Environment for Electron Microscopy Application Simulations

Abstract

Phenomenal Simulation Modelling of X-Ray Diffraction Patterns of Pyrite Ash Bioprocessed in Acetobacter aceti Contained Media

Phenomenal profiling functions were applied for the simulation of an X-ray diffraction (XRD) pattern of pyrite ash bioprocessed in Acetobacter aceti contained growth media. The full width at half maximum (FWHM) values were estimated for each pattern of pyrite ash, and the Bragg equation was used to determine the atomic layer spacing, as well crystallite size and strain broadening were accomplished by applications of Scherrer and Williamson-Hall equations. Errors in line broadening were correlated with the FWHM equations of the generalised profiling functions, and the microstrain (&amp;lt;i&amp;gt;ε&amp;lt;/i&amp;gt;) was estimated with the relation between the integral breadth (&amp;lt;i&amp;gt;β&amp;lt;/i&amp;gt;&amp;lt;sub&amp;gt;i&amp;lt;/sub&amp;gt;) and cos&amp;lt;i&amp;gt;θ&amp;lt;/i&amp;gt;. Furthermore, the XRD pattern of a discrete peak was 3D simulated using Gaussian, Lorentzian, Pearson VII, pseudo-Voigt, and Voigt functions. The Gaussian function with a round top peak was designated the most suitable profile simulation by offering the maximum peak height, &amp;lt;i&amp;gt;I&amp;lt;/i&amp;gt;&amp;lt;sub&amp;gt;max&amp;lt;/sub&amp;gt; and tails comparable to the experimental peak.

High-precision orientation mapping from spherical harmonic transform indexing of electron backscatter diffraction patterns

The angular precision of crystal orientation determination by cross-correlating dynamically simulated electron diffraction patterns with experimental patterns via spherical harmonic analysis is investigated. The best precision found in this study is 0.016°, which approaches the level reported in the literature for other high-precision electron backscatter diffraction implementations. At this angular precision, the noise floor for geometrically necessary dislocation density calculations is found to be approximately 5×1013 m−2 at a 200 nm step size. Conventional Hough-transform indexing of the same raw patterns gave an angular precision of 0.156° and a dislocation noise floor of 6×1014 m−2, an order of magnitude larger for both parameters, albeit better than is typical for Hough indexing due to the high-quality patterns used. Experimental trade-off curves of precision versus exposure time, pattern resolution (i.e. camera binning), and analysis bandwidth are also presented, allowing for optimization of data collection and analysis rates once the desired level of precision has been determined.

Atomic structure of solute clusters in Al–Zn–Mg alloys

Scanning transmission electron microscopy imaging of Al–Zn–Mg alloys has provided new information on the atomic structures of solute rich clusters forming from a supersaturated solid solution at low temperatures. A unique unit of high Zn/Mg ratio is the fundamental cluster building block. The unit is essentially a partial substitution by Mg and Zn on the cubic aluminium cell and its surrounding truncated cube octahedral shell. A simple set of principles based on Frank–Kasper structures describes how the basic units arrange with respect to each other to form larger clusters. Density functional theory calculations, atom probe tomography and simulated diffraction patterns support the proposed atomic models. The results provide new insight into the very early stages of age-hardening in aluminium alloys.

The Application of the Profile Analysis of Diffraction Peaks for Determination of the Phase Relationships in the (1 – 2x)BiScO3 ⋅ xPbTiO3 ⋅ xPbMg1/3Nb2/3O3 System near the Morphotropic Phase Boundary

To determine the phase relationships in the (1 – 2x)BiScO3 ⋅ xPbTiO3 ⋅ xPbMg1/3Nb2/3O3 system near the morphotropic phase boundary, the ceramic samples for x = 0.34 and x = 0.46 were studied by the XRD method. The profiles of nine regions of the XRD patterns were analyzed using the WinFit software program. In both cases, the best agreement with the experimental data was observed when additional phases with the cubic symmetry were introduced. Simulation of the full X-ray diffraction patterns of the samples using the Le Bail method showed that the samples under study contained two phases: the main phase with a cubic (a = 4.0432 A) (x = 0.34) and a tetragonal (a = 3.9963 A, c = 4.0580 A) (x = 0.46) unit cell and an additional one. The additional phases with broad diffraction peaks can be considered to be cubic ones with the unit cell parameters a = 4.045 A and a = 4.017 A, respectively.

Body centered cubic carbon BC14: An all- sp3 bonded full-fledged pentadiamond

We report on the finding of a hard carbon structure in body centered cubic $(I{2}_{1}3)$ symmetry that possesses an extremely high bulk modulus (386 GPa) and Vickers hardness (60 GPa) comparable to that of $c$-BN and diamond. This carbon phase has a 14-atom primitive cell in an all-${sp}^{3}$ bonding network comprising five-membered rings, making it a truly full-fledged pentadiamond. Total energy calculations show that it is more stable than the previously reported diamondlike six-membered-ring bonded BC8 and BC12 carbon phases. Electronic band structure calculations show that it is an insulator with an indirect band gap of 5.64 eV. Simulated x-ray diffraction patterns and lattice parameters provide an excellent match to the previously unexplained distinct diffraction peaks found in carbon soot. The present results establish a distinct type of carbon phase and offer insights into its outstanding structural, mechanical, and electronic properties.

X-ray Diffraction Study of Deformational Evolution of Stacking Faults in Nanocrystalline Metals

The evolution of stacking faults (SF) during the mechanical activation (MA) of metals with a different energy of SF (γ): Co (7 mJ/m2), Cu (45 mJ/m2), Ni (125 mJ/m2),—was studied by X-ray diffraction analysis using (i) a complex for processing diffraction patterns and (ii) simulation of crystal diffraction patterns (DIFFaX). The study was performed to understand the connection of the evolution mentioned with plastic deformation mechanisms and depending on grain size. The values ​​of the energy yields of stacking faults (G) upon MA for nanocrystalline Co and Cu are in agreement with the values of ​​ γ for these metals in the coarse crystalline state (the lower the γ, the higher the G). The increased G for nanocrystalline nickel is associated with the effect of impurities. When decreasing the sizes of Co, Cu, and Ni crystallites in the course of MA to 30, 77, and 60 nm respectively, the maximum G are observed, which is a consequence of deformation by the mechanism of the generation of partial Shockley dislocations by nanograin boundaries and their sliding in the grain body with the formation of SF. A scheme of the deformation-induced shear transformation in nanocrystalline cobalt is proposed.

Structure and properties of amorphous uranium dioxide

Amorphous uranium dioxide (UO2) has been modelled on the atomic scale using a combination of quantum mechanical (density functional theory) and classical forcefield methods (molecular dynamics and reverse Monte-Carlo). The atomic scale structure of the amorphous state has been predicted and is presented in the form of simulated X-ray diffraction patterns, pair correlation functions and bond angle distributions. These are shown to be consistent with the experimental patterns previously reported. To enable accurate calculation of the energies and magnetic properties, using quantum mechanics, reverse Monte-Carlo was used to generate reduced cells from larger molecular dynamic melt-quenches. This allowed density functional theory energy minimisation for structures consistent with the amorphous state. Building on this, the material's propensity to deviate from stoichiometry, the magnetic structure and amorphous UO2 surface energy were computed. Non-stoichiometry is accommodated more readily in the amorphous system than in crystalline UO2. This indicates that deviations from stoichiometry in fuel (for example as a result of operation) will be accommodated at amorphous phases, if present, leaving a more stoichiometric crystalline phase – impacting processes including fission gas mobility, melting points and a number of other safety relevant properties. The magnetic structure of bulk amorphous UO2 is predicted to be a spin-glass, unlike crystalline UO2 which has anti-ferromagnetic ordering at 0 K. The surface energy of amorphous UO2 is computed to be 0.79 Jm−2, which is similar to the experimentally observed surface energy of grain boundary bubbles in UO2 and comparable to the surface energies reported for crystalline UO2. Results are pertinent to ongoing efforts to understand the nature of grain boundaries in nuclear fuels, to model fission gas release from them, radiation induced amorphization and the impact of dopants and impurities on nuclear fuel's manufacture and in-reactor behaviour.

A Finite Energy Bandwidth-Based Diffraction Simulation Framework for Thermal Processing Applications

We present a novel finite energy bandwidth-based diffraction simulation framework to aid the analysis of x-ray diffraction patterns gathered during in situ advanced manufacturing processes. The framework generates two-dimensional diffraction patterns that simulate the effects of x-ray energy distributions typical of monochromating optics, and uses microstructure and temperature fields from thermal processing simulations as input. As a demonstration of the capabilities of the framework, we model diffraction associated with selective laser melting of the nickel-based superalloy Inconel 625, employing a finite element thermal model for the input. The simulated diffraction patterns correspond to material volumes exhibiting large temperature gradients consistent with complex thermal processing environments, and we illustrate their utility for interpreting in situ data.

CloudEMAPS: A Cloud Computing Environment for Electron Microscopy Application Simulations

The rapid progress in the performance of today's sophisticated transmission electron microscopes also demands computational and educational tools capable of simulating the intricacy of electron image formation. The tools ideally should be widely accessible to the microscopy community and capable of covering both the breadth and depth demanded by modern materials science. Here, a cloud-based microscopy simulation platform, called cloudEMAPS and powered by cloud computing and modern server-client web programming architecture, is described. Compared to the current desktop solutions for electron microscopy simulations, cloud computing offers the unique advantages of on-demand, data sharing, high-performance computation and internet easy access using the state-of-the-art web infrastructure. This article will demonstrate these advantages using examples of interactive simulations of electron diffraction patterns and aberration-corrected electron optics.

Combining crystal structure prediction and simulated spectroscopy in pursuit of the unknown nitrogen phase ζ crystal structure

The structure of nitrogen phase $\ensuremath{\zeta}$ remains unknown decades after it was first observed spectroscopically, despite numerous experimental and theoretical investigations. The present computational study performs crystal structure prediction using ab initio random structure searching and density functional theory to identify candidate structures. These candidates are then analyzed for consistency with experiment in terms of their simulated x-ray diffraction patterns and Raman spectra. While none of the structures generated here is a clear match for the phase-$\ensuremath{\zeta}$ experimental data, several of the candidates do exhibit features in common with the experiments and could provide an interesting starting point for future studies. The techniques here also rule out several candidate $\ensuremath{\zeta}$ nitrogen structures that have been identified previously. Finally, one of the structures might be considered a candidate for phase $\ensuremath{\kappa}$, whose structure is also unknown.

SVAT4: a computer program for visualization and analysis of crystal structures.

SVAT4 is a computer program for interactive visualization of three-dimensional crystal structures, including chemical bonds and magnetic moments. A wide range of functions, e.g. revealing atomic layers and polyhedral clusters, are available for further structural analysis. Atomic sizes, colors, appearance, view directions and view modes (orthographic or perspective views) are adjustable. Customized work for the visualization and analysis can be saved and then reloaded. SVAT4 provides a template to simplify the process of preparation of a new data file. SVAT4 can generate high-quality images for publication and animations for presentations. The usability of SVAT4 is broadened by a software suite for simulation and analysis of electron diffraction patterns.