Electron Microscopy Image Simulations Research Articles

Quantifying the thickness of WTe2 using atomic-resolution STEM simulations and supervised machine learning.

For two-dimensional (2D) materials, the exact thickness of the material often dictates its physical and chemical properties. The 2D quantum material WTe2 possesses properties that vary significantly from a single layer to multiple layers, yet it has a complicated crystal structure that makes it difficult to differentiate thicknesses in atomic-resolution images. Furthermore, its air sensitivity and susceptibility to electron beam-induced damage heighten the need for direct ways to determine the thickness and atomic structure without acquiring multiple measurements or transferring samples in ambient atmosphere. Here, we demonstrate a new method to identify the thickness up to ten van der Waals layers in Td-WTe2 using atomic-resolution high-angle annular dark-field scanning transmission electron microscopy image simulation. Our approach is based on analyzing the intensity line profiles of overlapping atomic columns and building a standard neural network model from the line profile features. We observe that it is possible to clearly distinguish between even and odd thicknesses (up to seven layers), without using machine learning, by comparing the deconvoluted peak intensity ratios or the area ratios. The standard neural network model trained on the line profile features allows thicknesses to be distinguished up to ten layers and exhibits an accuracy of up to 94% in the presence of Gaussian and Poisson noise. This method efficiently quantifies thicknesses in Td-WTe2, can be extended to related 2D materials, and provides a pathway to characterize precise atomic structures, including local thickness variations and atomic defects, for few-layer 2D materials with overlapping atomic column positions.

Role of dislocation climb on twin boundary and antiphase boundary formations in inverse-spinel MnAl2O4

The defects, e.g., stacking faults (SFs), antiphase boundaries (APBs), and twin, have been considered the critical components commonly introduced during the synthesis process of spinel oxides. In this study, employing advanced transmission electron microscopy, the formation mechanisms of twin and APBs in MnAl2O4 spinel oxide were clarified. Atomic resolution scanning transmission electron microscopy image and image simulation clarify that MnAl2O4 holds the inverse-spinel-typed structure. Detailed analysis of the twin structure reveals that the asymmetric twin structure in MnAl2O4 forms through an (Mn, Al)-containing plane missing by dislocation climb-up and then continuous shearing on {111} plane. APB forms by dislocation climb-down on an (Mn, Al)-containing {111} plane. The detailed lattice distortion induced by dislocation climb-down was analyzed by geometric phase analysis. The burgers vector for APB formation is identified as a/61̅1̅1+a/411̅0. Frank dislocation of a/61̅1̅1 climb-down and the lattice strain from introducing the extra plane brings a displacement of a/411̅0, which results in terrace-ledge-like morphology of APBs. This study provides a detailed understanding of twin and APB formation mechanisms in inverse-spinel-typed MnAl2O4.

Spatial Image Resolution Assessment by Fourier Analysis (SIRAF).

Determining spatial resolution from images is crucial when optimizing focus, determining smallest resolvable object, and assessing size measurement uncertainties. However, no standard algorithm exists to measure resolution from electron microscopy (EM) images, though several have been proposed, where most require user decisions. We present the Spatial Image Resolution Assessment by Fourier analysis (SIRAF) algorithm that uses fast Fourier transform analysis to estimate resolution directly from a single image without user inputs. The method is derived from the underlying assumption that objects display intensity transitions, resembling a step function blurred by a Gaussian point spread function. This hypothesis is tested and verified on simulated EM images with known resolution. To identify potential pitfalls, the algorithm is also tested on simulated images with a variety of settings, and on real SEM images acquired at different magnification and defocus settings. Finally, the versatility of the method is investigated by assessing resolution in images from several microscopy techniques. It is concluded that the algorithm can assess resolution from a large selection of image types, thereby providing a measure of this fundamental image parameter. It may also improve autofocus methods and guide the optimization of magnification settings when balancing spatial resolution and field of view.

Image simulation in high resolution transmission electron microscopy considering atom as an electrostatic interferometer

An alternative approach to image simulation in high resolution transmission electron microscopy (HRTEM) is introduced after a comparative analysis of the existing image simulation methods. The alternative method is based on considering the atom center as an electrostatic interferometer akin to the conventional off-axis electron biprism within few nanometers of focus variation. Simulation results are compared with the experimental images of 2D materials of MoS2, BN recorded under the optimum combination of third order spherical aberration μm and defocus 1, 4, and 8 nm and are found to be in good agreement.

A Fast Frozen Phonon Algorithm Using Mixed Static Potentials

Image simulation in electron microscopy is vital for advanced image analysis but can be prohibitively long. This is especially true when including thermal diffuse scattering through the frozen phonon method, requiring repeat simulations for a number of phonon configurations. Here a method of reducing frozen phonon simulation time is demonstrated by emulating random phonon displacements through randomly mixing a set of precalculated static potentials. This avoids excessive recalculation of atom potentials and can lead to significant time improvement. The validity and limitations of this method are also demonstrated with respect to convergent beam electron diffraction and scanning transmission electron microscopy.

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 fastimplementation of thePRISM algorithm for a decahedral 20000-atom gold nanoparticle.

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.

Scanning transmission electron microscopy image simulations of complex dislocation structures generated by discrete dislocation dynamics

Scanning Transmission Electron Microscopy Diffraction Contrast Imaging (STEM-DCI) has been gaining popularity for the identification and analysis of dislocations in crystalline materials due to its ability to supress undesirable image features that are often present in conventional TEM images. However, there does not yet exist a robust body of work demonstrating expected contrast in these imaging conditions. A novel approach for the simulation of STEM-DCI images was developed using a modified form of the scattering matrix formalism. This algorithm was used to simulate a variety of dislocation configurations generated using three-dimensional discrete dislocation dynamics.

Evidence of room-temperature shear-deformation in a Cu-Al intermetallic

Lamellar eutectics are known to evidence plastic shear in otherwise brittle intermetallics, if the lamella spacing is small enough. Here we pursue this idea of confined plasticity in intermetallics further and demonstrate room-temperature shear-deformation in a two-phase CuAl2-CuAl intermetallic nano-composite. The presence of a phase with a 3-fold symmetry is also revealed after deformation. Simulation of transmission electron microscopy images shows this to be monoclinic CuAl. These observations are made in the deformation zone underneath locations of nanoindents, of which the force-displacement curves exhibit an unusual response of continuously increasing pop-in sizes with load.

Study of Gallium-Ion-Induced Silicon Amorphization by Matching Experimental and Simulated Electron-Microscopy Images

Study of Gallium-Ion-Induced Silicon Amorphization by Matching Experimental and Simulated Electron-Microscopy Images

Multislice image simulations of sheared needle-like precipitates in an Al-Mg-Si alloy.

The image contrast of sheared needle-like precipitates in the Al-Mg-Si alloy system is investigated with respect to shear-plane positions, the number of shear-planes, and the active matrix slip systems through multislice transmission electron microscopy image simulations and the frozen phonon approximation. It is found that annular dark field scanning transmission electron microscopy (ADF STEM) images are mostly affected by shear-planes within a distance ∼6-18 unit cells from the specimen surface, whereas about 5-10 equidistant shear-planes are required to produce clear differences in HRTEM images. The contrast of the images is affected by the Burgers vector of the slip, but not the slip plane. The simulation results are discussed and compared to experimental data. LAY DESCRIPTION: Pure aluminium is too soft to be viable in most structural applications, but this may be remedied by alloying the metal with various elements. Adding small amounts of silicon and magnesium to pure aluminium allows small particles to precipitate during heat treatment. These precipitates resist plastic deformation and can increase the strength of the alloy and make it viable for a range of industrial applications, such as automotive door panels and load-bearing profiles. However, if subjected to large loads, the precipitates are sheared and the strength of the alloy changes dynamically. Designing safe products such as cars or buildings require physically based predictions on this dynamical change. Developing models that can provide such predictions depend in turn on experimental observations of the shearing process. Because the precipitates are nm long, experimental observations must be done by transmission electron microscopy. However, understanding these results sometimes require computer simulations of atomic models. In this work, we have performed image simulations of various models of sheared precipitates and compared the results with earlier experiments. The simulations indicate that certain conditions must be met for the sheared precipitates to appear different from unsheared precipitates. These conditions are most likely to be met if precipitates are sheared several times in a relatively homogeneous manner. This is important for two reasons. First, a localized shearing process would lead to large dynamical changes in precipitate strength during deformation, and in turn drastically reduce the work hardening of the alloy. Secondly, a localized shearing process would have promoted earlier fracture and failure of the alloy during deformation. Finally, our results also show how different slip directions influences the images of precipitates. In the future, these influences can be used to further understand the shearing process of these precipitates. Hence, our results can be used to improve model predictions of strength, work hardening, and fracture. In turn, this may improve alloy design and reduce the use of prototype testing in, e.g. the automotiveindustry.

Simulation of transmission electron microscopy images using a generalized single-slice approach: The case of self-assembled quantum dots

Tools for numerical simulation of transmission electron microscopy (TEM) images are frequently used to provide insight about the origin of contrast features, hence, to understand and to measure correctly the properties of a material. We describe in this work a methodology for simulating the compositional-strain contrast of TEM images of large nanocrystalline heterostructures. The methodology combines finite element calculations and a generalized form of the single slice approach that takes into account also the imaging conditions. It is simple and computationally efficient and as an example of its reliability we compare experimental and simulated images of a sample of self-assembled In(Ga)As/GaAs QDs.

Extending Monte Carlo Simulations of Electron Microscopy Images and Hyperspectral Images in a User-Friendly Framework

Journal Article Extending Monte Carlo Simulations of Electron Microscopy Images and Hyperspectral Images in a User-Friendly Framework Get access Samantha Rudinsky, Samantha Rudinsky Department of Materials Engineering, McGill University. Montreal, Canada Search for other works by this author on: Oxford Academic Google Scholar Yu Yuan, Yu Yuan Department of Materials Engineering, McGill University. Montreal, Canada Search for other works by this author on: Oxford Academic Google Scholar Raynald Gauvin, Raynald Gauvin Department of Materials Engineering, McGill University. Montreal, Canada Search for other works by this author on: Oxford Academic Google Scholar Nicolas Piché, Nicolas Piché Object Research Systems. Montreal, Canada Search for other works by this author on: Oxford Academic Google Scholar Mike Marsh Mike Marsh Object Research Systems. Denver, USA Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 25, Issue S2, 1 August 2019, Pages 222–223, https://doi.org/10.1017/S1431927619001843 Published: 01 August 2019

Atomistic modelling of diamond-type SixGeyCzSn1−x−y−z crystals for realistic transmission electron microscopy image simulations

The realistic simulation of transmission electron microscopy (TEM) images requires an accurate definition of the positions of all atoms, which are linked to the mechanical properties of the material. This paper proposes an optimized atomistic modeling approach to model the lattice parameters and elastic properties of Si, Ge, diamond, alpha-tin, and related diamond alloys, with an approach compatible with systems bigger than 50000 atoms. In order to compute precisely the elastically strained SixGeyCzSn1−x−y−z diamond crystals, a dedicated parameterization of the Keating force field is provided. An original periodic boundary strategy is provided. Our tool is successfully used to interpret experimental TEM data with a reasonable accuracy and precision in a time scale about 10000 times faster than ab initio methods. The method predicts the correct lattice parameters and elastic constants of elementary compounds and alloys with a deviation inferior to 8.1%. We show that subsequent Monte-Carlo simulations predict original self-ordering effects in C in good agreement with the theory. An original approach is used to quantify the short-range and long-range order in comparison with high-resolution cross-sectional TEM experiments: the projected radial distribution function (p-RDF) appears to be a universal and very sensitive analytical tool to quantify the matching between our atomistic model and the experimental HR(S)TEM results. For our reference Si-Ge multilayer with 20 millions of atoms, a maximum broadening of 100 pm is obtained for the third-nearest neighbor (3nn) simulated peak of the p-RDF compared to the experimental one. The same value is obtained from a template matching analysis of the maximum local displacements between the projected experimental atomic positions and the corresponding simulation.

Transition-Metal Distribution in Brownmillerite Ca2FeCoO5.

Ca2Fe2-xCoxO5 (0 ≤ x ≤ 1) with higher Co content, which crystallizes in a brownmillerite-type structure, is currently one of the best oxygen-evolution-reaction (OER) catalysts. Identifying the Fe/Co occupancies at the octahedral (Oh) and tetrahedral (Td) sites in the structure is the foundation for the understanding of the role of cobalt in each site and the exploration of further improvement in the OER activity. Here, we investigate the Fe/Co distribution in Ca2FeCoO5 by means of atomic-resolution energy dispersive X-ray spectroscopy in scanning transmission electron microscopy and dynamical image simulations combined with systematic density functional theory calculations. Our careful microscopic study reveals the absence of long-range Fe/Co order within the transition-metal (TM) layers, but cobalt is slightly enriched at the Td and Oh sites in the as-synthesized (1100 °C) and 800 °C annealed for a month samples, respectively. The observed Co site preferences are interpretable from the viewpoints of TM ionic size effect and ligand field effect, which are competitive around a crossover point at a certain temperature between 800 and 1100 °C. We also elucidate that the as-synthesized sample with Co enrichment at the Td site shows the better OER activity, and the optimum annealing temperature for more OER active Ca2FeCoO5 should be higher than the crossover temperature.

Fast approximate STEM image simulations from a machine learning model

Accurate quantum mechanical scanning transmission electron microscopy image simulation methods such as the multislice method require computation times that are too large to use in applications in high-resolution materials imaging that require very large numbers of simulated images. However, higher-speed simulation methods based on linear imaging models, such as the convolution method, are often not accurate enough for use in these applications. We present a method that generates an image from the convolution of an object function and the probe intensity, and then uses a multivariate polynomial fit to a dataset of corresponding multislice and convolution images to correct it. We develop and validate this method using simulated images of Pt and Pt–Mo nanoparticles and find that for these systems, once the polynomial is fit, the method runs about six orders of magnitude faster than parallelized CPU implementations of the multislice method while achieving a 1 − R2 error of 0.010–0.015 and root-mean-square error/standard deviation of dataset being predicted of about 0.1 when compared to full multislice simulations.

Comparison of different imaging models handling partial coherence for aberration-corrected HRTEM at 40–80 kV

Partial coherence of the electron waves leaving the specimen is taken into account in the high-resolution transmission electron microscopy (HRTEM) image simulation by mainly three methods - the incoherent summation approach, the transmission cross-coefficient (TCC) model, and the quasi-coherent model. In the incoherent summation approach, coherent images are calculated for each point in the effective source and summed up incoherently. The TCC is the transfer function of the microscope obtained based on the incoherent summation approach. An analytical form of the TCC can be derived by assuming a Gaussian distribution for the source radiation and for the variation of the focal length caused by the energy spread of the effective source. In the quasi-coherent model, the partial coherence effect is simplified by multiplying the wave function at the diffraction plane with the envelope functions. Envelope functions suppress the contributions to the image contrast from waves which do not propagate along the optical axis. The quasi-coherent model is usually sufficient for the image simulation of weak phase objects. This model is more computationally efficient than both the incoherent summation approach and the TCC model. For the Cs−corrected and Cc/Cs−corrected microscopes operating at 80 kV, we have compared images simulated by using the three models with the experimental images. The comparison shows that the quasi-coherent model also provides a sufficient approximation for the image simulation of high-Z materials if chromatic aberration is corrected and the samples comprise only several atomic layers. In the case of only Cs-correction, the incoherent summation approach or the TCC model needs to be employed for modelling the imaging of high-Z samples even though it is more computationally consuming.

Lorentz Transmission Electron Microscopy Image Simulations of Experimental Nano-Chessboard Observations in Co-Pt Alloys.

The magnetization configuration of a novel nano-chessboard structure consisting of L10 and L12 phases in a Co40Pt60 alloy is investigated using Lorentz transmission electron microscopy (LTEM) and micro-magnetic simulations. We show high-resolution LTEM images of nano-size magnetic features acquired through spherical aberration correction in Lorentz Fresnel mode. Phase reconstructions and LTEM image simulations are carried out to fully understand the magnetic microstructure. The experimental Fresnel images of the nano-chessboard structure show zig-zag shaped magnetic domain walls at the inter-phase boundaries between L10 and L12 phases. A circular magnetization distribution with vortex and anti-vortex type arrangement is evident in the phase reconstructed magnetic induction maps as well as simulated maps. The magnetic contrast in experimental LTEM images is interpreted with the help of magnetic induction maps simulated for various relative electron beam-sample orientations inside the TEM.

Identification of Extended Defect Atomic Configurations in Silicon Through Transmission Electron Microscopy Image Simulation

We used atomistic simulation tools to correlate experimental transmission electron microscopy images of extended defects in crystalline silicon with their structures at an atomic level. Reliable atomic configurations of extended defects were generated using classical molecular dynamics simulations. Simulated high-resolution transmission electron microscopy (HRTEM) images of obtained defects were compared to experimental images reported in the literature. We validated the developed procedure with the configurations proposed in the literature for {113} and {111} rod-like defects. We also proposed from our procedure configurations for {111} and {001} dislocation loops with simulated HRTEM images in excellent agreement with experimental images.