Statistical estimation of atomic positions from exit wave reconstruction with a precision in the picometer range

A small-dataset-trained deep learning framework for identifying atoms on transmission electron microscopy images

To accurately identify atoms on noisy transmission electron microscope images, a deep learning (DL) approach is employed to estimate the map of probabilities at each pixel for being an atom with element discernment. Thanks to a delicately-designed loss function and the ability to extract features, the proposed DL networks can be trained by a small dataset created from approximately 30 experimental images, each with a size of 256 × 256 pixels². The accuracy and robustness of the network were verified by resolving the structural defects of graphene and polar structures in PbTiO₃/SrTiO₃ multilayers from both the general TEM images and their imitated images on which intensities of some pixels lost randomly. Such a network has the potential to identify atoms from very few images of beam-sensitive material and explosive images recorded in a dynamical atomic process. The idea of using a small-dataset-trained DL framework to resolve a specific problem may prove instructive for practical DL applications in various fields.

Machine learning in electron microscopy for advanced nanocharacterization: current developments, available tools and future outlook

In the last few years, electron microscopy has experienced a new methodological paradigm aimed to fix the bottlenecks and overcome the challenges of its analytical workflow. Machine learning and artificial intelligence are answering this call providing powerful resources towards automation, exploration, and development. In this review, we evaluate the state-of-the-art of machine learning applied to electron microscopy (and obliquely, to materials and nano-sciences). We start from the traditional imaging techniques to reach the newest higher-dimensionality ones, also covering the recent advances in spectroscopy and tomography. Additionally, the present review provides a practical guide for microscopists, and in general for material scientists, but not necessarily advanced machine learning practitioners, to straightforwardly apply the offered set of tools to their own research. To conclude, we explore the state-of-the-art of other disciplines with a broader experience in applying artificial intelligence methods to their research (e.g., high-energy physics, astronomy, Earth sciences, and even robotics, videogames, or marketing and finances), in order to narrow down the incoming future of electron microscopy, its challenges and outlook.

Comprehensive Study of Li+/Ni2+ Disorder in Ni-Rich NMCs Cathodes for Li-Ion Batteries

The layered oxides LiNixMnyCozO2 (NMCs, x + y + z = 1) with high nickel content (x ≥ 0.6, Ni-rich NMCs) are promising high-energy density-positive electrode materials for Li-ion batteries. Their electrochemical properties depend on Li+/Ni2+ cation disordering originating from the proximity of the Li+ and Ni2+ ionic radii. We synthesized a series of the LiNi0.8Mn0.1Co0.1O2 NMC811 adopting two different disordering schemes: Ni for Li substitution at the Li site in the samples finally annealed in air, and close to Ni↔Li antisite disorder in the oxygen-annealed samples. The defect formation scenario was revealed with Rietveld refinement from powder X-ray diffraction data, and then the reliability of semi-quantitative parameters, such as I003/I104 integral intensity ratio and c/(2√6a) ratio of pseudocubic subcell parameters, was verified against the refined defect concentrations. The I003/I104 ratio can serve as a quantitative measure of g(NiLi) only after explicit correction of intensities for preferred orientation. Being normalized by the total scattering power of the unit cell, the I003/I104 ratio depends linearly on g(NiLi) for each disordering scheme. The c/(2√6a) ratio appears to be not reliable and cannot be used for a quantitative estimate of g(NiLi). In turn, the volume of the R3¯m unit cell correlates linearly with g(NiLi), at least for defect concentrations not exceeding 5%. The microscopy techniques such as high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and electron diffraction tomography (EDT) allow us to study the materials locally, still, there is no proper quantitative approach for comprehensive analysis of defects. In the present work, the TEM-assisted quantitative Li+/Ni2+ disordering analysis with EDT and HAADF-STEM in six Ni-rich NMC samples with various defects content is demonstrated. Noteworthy, while PXRD and EDT methods demonstrate overall defect amounts, HAADF-STEM allows us to quantitatively distinguish regions with various disordering extents. Therefore, the combination of mentioned PXRD and TEM methods gives the full picture of Li+/Ni2+ mixing defects in Ni-rich NMCs.

Optimizing Nonrigid Registration for Scanning Transmission Electron Microscopy Image Series

Achieving sub-picometer precision measurements of atomic column positions in high-resolution scanning transmission electron microscope images using nonrigid registration (NRR) and averaging of image series requires careful optimization of experimental conditions and the parameters of the registration algorithm. On experimental data from SrTiO3 [100], sub-pm precision requires alignment of the sample to the zone axis to within 1 mrad tilt and sample drift of less than 1 nm/min. At fixed total electron dose for the series, precision in the fast scan direction improves with shorter pixel dwell time to the limit of our microscope hardware, but the best precision along the slow scan direction occurs at 6 μs/px dwell time. Within the NRR algorithm, the “smoothness factor” that penalizes large estimated shifts is the most important parameter for sub-pm precision, but in general, the precision of NRR images is robust over a wide range of parameters.

Recent Advances in Transmission Electron Microscopy for Materials Science at the EMAT Lab of the University of Antwerp

The rapid progress in materials science that enables the design of materials down to the nanoscale also demands characterization techniques able to analyze the materials down to the same scale, such as transmission electron microscopy. As Belgium's foremost electron microscopy group, among the largest in the world, EMAT is continuously contributing to the development of TEM techniques, such as high-resolution imaging, diffraction, electron tomography, and spectroscopies, with an emphasis on quantification and reproducibility, as well as employing TEM methodology at the highest level to solve real-world materials science problems. The lab's recent contributions are presented here together with specific case studies in order to highlight the usefulness of TEM to the advancement of materials science.

Influence of atomic site-specific strain on catalytic activity of supported nanoparticles

Heterogeneous catalysis is an enabling technology that utilises transition metal nanoparticles (NPs) supported on oxides to promote chemical reactions. Structural mismatch at the NP–support interface generates lattice strain that could affect catalytic properties. However, detailed knowledge about strain in supported NPs remains elusive. We experimentally measure the strain at interfaces, surfaces and defects in Pt NPs supported on alumina and ceria with atomic resolution using high-precision scanning transmission electron microscopy. The largest strains are observed at the interfaces and are predominantly compressive. Atomic models of Pt NPs with experimentally measured strain distributions are used for first-principles kinetic Monte Carlo simulations of the CO oxidation reaction. The presence of only a fraction of strained surface atoms is found to affect the turnover frequency. These results provide a quantitative understanding of the relationship between strain and catalytic function and demonstrate that strain engineering can potentially be used for catalyst design.

Detailed knowledge of how strain influences catalytic reactions remains elusive. Here, the authors experimentally measure the strain in supported Pt nanoparticles on alumina and ceria with atomic resolution and computationally explore how the strain affects the CO oxidation reaction.

Characterization of silver-polymer core-shell nanoparticles using electron microscopy

Silver-polymer core-shell nanoparticles show interesting optical properties, making them widely applicable in the field of plasmonics. The uniformity, thickness and homogeneity of the polymer shell will affect the properties of the system which makes a thorough structural characterization of these core-shell silver-polymer nanoparticles of great importance. However, visualizing the shell and the particle simultaneously is far from straightforward due to the sensitivity of the polymer shell towards the electron beam. In this study, we use different 2D and 3D electron microscopy techniques to investigate different structural aspects of the polymer coating.

Periodic Giant Polarization Gradients in Doped BiFeO3 Thin Films

The ultimate challenge for the development of new multiferroics with enhanced properties lies in achieving nanoscale control of the coupling between different ordering parameters. In oxide-based multiferroics, substitutional cation dopants offer the unparalleled possibility to modify both the electric and magnetic properties at a local scale. Herein it is demonstrated the formation of a dopant-controlled polar pattern in BiFeO₃ leading to the spontaneous instauration of periodic polarization waves. In particular, nonpolar Ca-doped rich regions act as spacers between consecutive dopant-depleted regions displaying coupled ferroelectric states. This alternation of layers with different ferroelectric state creates a novel vertical polar structure exhibiting giant polarization gradients as large as 70 μC cm^-2 across 30 Å thick domains. The drastic change in the polar state of the film is visualized using high-resolution differential phase-contrast imaging able to map changes in ferroelectric polarization at atomic scale. Furthermore, a periodic distortion in the Fe-O-Fe bonding angle suggests a local variation in the magnetic ordering. The findings provide a new insight into the role of doping and reveal hitherto unexplored means to tailor the functional properties of multiferroics by doping engineering.

Accuracy of surface strain measurements from transmission electron microscopy images of nanoparticles

Strain analysis from high-resolution transmission electron microscopy (HRTEM) images offers a convenient tool for measuring strain in materials at the atomic scale. In this paper we present a theoretical study of the precision and accuracy of surface strain measurements directly from aberration-corrected HRTEM images. We examine the influence of defocus, crystal tilt and noise, and find that absolute errors of at least 1–2% strain should be expected. The model structures include surface relaxations determined using molecular dynamics, and we show that this is important for correctly evaluating the errors introduced by image aberrations.

Picometer-scale atom position analysis in annular bright-field STEM imaging

We study the effects of specimen mistilt on the picometer-scale measurement of local structure by combing experiment and simulation in annular bright-field scanning transmission electron microscopy (ABF-STEM). A relative distance measurement method is proposed to separate the tilt effects from the scan noise and sample drift induced image distortion. We find that under a typical experimental condition a small specimen tilt (∼6 mrad) in 25 nm thick SrTiO₃ along [001] causes 11.9 pm artificial displacement between O and Sr/TiO columns in ABF image, which is more than 3 times of scan noise and sample drift induced image distortion ∼3.2 pm, suggesting the tilt effect could be dominant for the quantitative analysis of ABF images. The artifact depends on the crystal mistilt angle, specimen thickness, defocus, convergence angle and uncorrected aberration. Our study provides useful insights into detecting and correcting tilt effects during both experiment operation and data analysis to extract the real structure information and avoid mis-interpretations of atomic structure as well as the properties such as oxygen octahedral distortion/shift.

Evaluation of high-quality image reconstruction techniques applied to high-resolution Z-contrast imaging

High-quality image reconstruction techniques allow the generation of high pixel density images from a set of low-resolution micrographs. In general, these techniques consist of two main steps, namely, accurate registration, and formulation of an appropriate forward image model via some restoration method. There exist a wide variety of algorithms to cope with both stages and depending on their practical applications, some methods can outperform others, since they can be sensitive to the assumed data model, noise, drift, etc. When dealing with images generated by Z-contrast scanning transmission electron microscopes, a current trend is based on non-rigid approximations in the registration stage. In our work we aimed at reaching similar accuracy but addressing the most complex calculations in the reconstruction stage, instead of in the registration stage (as the non-rigid approaches do), but using a much smaller number of images. We review some of the most significant methods and address their shortcomings when they are applied to the field of microscopy. Simulated images with known targets will be used to evaluate and compare the main approaches in terms of quality enhancement and computing time. In addition, a procedure to determine the reference image will be proposed to minimise the global drift on the series. The best registration and restoration strategies will be applied to experimental images in order to point up the enhanced capability of this high quality image reconstruction methodology in this field.

Quantification by aberration corrected (S)TEM of boundaries formed by symmetry breaking phase transformations

The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.

Advanced electron crystallography through model-based imaging

The increasing need for precise determination of the atomic arrangement of non-periodic structures in materials design and the control of nanostructures explains the growing interest in quantitative transmission electron microscopy. The aim is to extract precise and accurate numbers for unknown structure parameters including atomic positions, chemical concentrations and atomic numbers. For this purpose, statistical parameter estimation theory has been shown to provide reliable results. In this theory, observations are considered purely as data planes, from which structure parameters have to be determined using a parametric model describing the images. As such, the positions of atom columns can be measured with a precision of the order of a few picometres, even though the resolution of the electron microscope is still one or two orders of magnitude larger. Moreover, small differences in average atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark-field scanning transmission electron microscopy images. In addition, this theory allows one to measure compositional changes at interfaces, to count atoms with single-atom sensitivity, and to reconstruct atomic structures in three dimensions. This feature article brings the reader up to date, summarizing the underlying theory and highlighting some of the recent applications of quantitative model-based transmisson electron microscopy.

Measuring Lattice Strain in Three Dimensions through Electron Microscopy

The three-dimensional (3D) atomic structure of nanomaterials, including strain, is crucial to understand their properties. Here, we investigate lattice strain in Au nanodecahedra using electron tomography. Although different electron tomography techniques enabled 3D characterizations of nanostructures at the atomic level, a reliable determination of lattice strain is not straightforward. We therefore propose a novel model-based approach from which atomic coordinates are measured. Our findings demonstrate the importance of investigating lattice strain in 3D.

High-precision scanning transmission electron microscopy at coarse pixel sampling for reduced electron dose

Determining the precise atomic structure of materials’ surfaces, defects, and interfaces is important to help provide the connection between structure and important materials’ properties. Modern scanning transmission electron microscopy (STEM) techniques now allow for atomic resolution STEM images to have down to sub-picometer precision in locating positions of atoms, but these high-precision techniques generally require large electron doses, making them less useful for beam-sensitive materials. Here, we show that 1- to 2-pm image precision is possible by non-rigidly registering and averaging a high-angle dark field image series of a 5- to 6-nm Au nanoparticle even though a very coarsely sampled image and decreased exposure time was used to minimize the electron dose. These imaging conditions minimize the damage to the nanoparticle and capture the whole nanoparticle in the same image. The high-precision STEM image reveals bond length contraction around the entire nanoparticle surface, and no bond length variation along a twin boundary that separates the nanoparticle into two grains. Surface atoms at the edges and corners exhibit larger bond length contraction than atoms near the center of surface facets.

Atomic-scale mapping of dipole frustration at 90° charged domain walls in ferroelectric PbTiO3 films

The atomic-scale structural and electric parameters of the 90° domain-walls in tetragonal ferroelectrics are of technological importance for exploring the ferroelectric switching behaviors and various domain-wall-related novel functions. We have grown epitaxial PbTiO3/SrTiO3 multilayer films in which the electric dipoles at 90° domain-walls of ferroelectric PbTiO3 are characterized by means of aberration-corrected scanning transmission electron microscopy. Besides the well-accepted head-to-tail 90° uncharged domain-walls, we have identified not only head-to-head positively charged but also tail-to-tail negatively charged domain-walls. The widths, polarization distributions, and strains across these charged domain-walls are mapped quantitatively at atomic scale, where remarkable difference between these domain-walls is presented. This study is expected to provide fundamental information for understanding numerous novel domain-wall phenomena in ferroelectrics.

Atomic structure of quantum gold nanowires: quantification of the lattice strain

Theoretical studies exist to compute the atomic arrangement in gold nanowires and the influence on their electronic behavior with decreasing diameter. Experimental studies, e.g., by transmission electron microscopy, on chemically synthesized ultrafine wires are however lacking owing to the unavailability of suitable protocols for sample preparation and the stability of the wires under electron beam irradiation. In this work, we present an atomic scale structural investigation on quantum single crystalline gold nanowires of 2 nm diameter, chemically prepared on a carbon film grid. Using low dose aberration-corrected high resolution (S)TEM, we observe an inhomogeneous strain distribution in the crystal, largely concentrated at the twin boundaries and the surface along with the presence of facets and surface steps leading to a noncircular cross section of the wires. These structural aspects are critical inputs needed to determine their unique electronic character and their potential as a suitable catalyst material. Furthermore, electron-beam-induced structural changes at the atomic scale, having implications on their mechanical behavior and their suitability as interconnects, are discussed.

Atomic-scale measurement of structure and chemistry of a single-unit-cell layer of LaAlO3 embedded in SrTiO3

A single layer of LaAlO3 with a nominal thickness of one unit cell, which is sandwiched between a SrTiO3 substrate and a SrTiO3 capping layer, is quantitatively investigated by high-resolution transmission electron microscopy. By the use of an aberration-corrected electron microscope and by employing sophisticated numerical image simulation procedures, significant progress is made in two aspects. First, the structural as well as the chemical features of the interface are determined simultaneously on an atomic scale from the same specimen area. Second, the evaluation of the structural and chemical data is carried out in a fully quantitative way on the basis of the absolute image contrast, which has not been achieved so far in materials science investigations using high-resolution electron microscopy. Considering the strong influence of even subtle structural details on the electronic properties of interfaces in oxide materials, a fully quantitative interface analysis, which makes positional data available with picometer precision together with the related chemical information, can contribute to a better understanding of the functionality of such interfaces.

Advanced electron microscopy for advanced materials

The idea of this Review is to introduce newly developed possibilities of advanced electron microscopy to the materials science community. Over the last decade, electron microscopy has evolved into a full analytical tool, able to provide atomic scale information on the position, nature, and even the valency atoms. This information is classically obtained in two dimensions (2D), but can now also be obtained in 3D. We show examples of applications in the field of nanoparticles and interfaces.

Direct observation of ferrielectricity at ferroelastic domain boundaries in CaTiO3 by electron microscopy

High-resolution aberration-corrected transmission electron microscopy aided by statistical parameter estimation theory is used to quantify localized displacements at a (110) twin boundary in orthorhombic CaTiO(3). The displacements are 3-6 pm for the Ti atoms and confined to a thin layer. This is the first direct observation of the generation of ferroelectricity by interfaces inside this material which opens the door for domain boundary engineering.

High precision measurements of atom column positions using model-based exit wave reconstruction

In this paper, it has been investigated how to measure atom column positions as accurately and precisely as possible using a focal series of images. In theory, it is expected that the precision would considerably improve using a maximum likelihood estimator based on the full series of focal images. As such, the theoretical lower bound on the variances of the unknown atom column positions can be attained. However, this approach is numerically demanding. Therefore, maximum likelihood estimation has been compared with the results obtained by fitting a model to a reconstructed exit wave rather than to the full series of focal images. Hence, a real space model-based exit wave reconstruction technique based on the channelling theory is introduced. Simulations show that the reconstructed complex exit wave contains the same amount of information concerning the atom column positions as the full series of focal images. Only for thin samples, which act as weak phase objects, this information can be retrieved from the phase of the reconstructed complex exit wave.

A method to determine the local surface profile from reconstructed exit waves

Reconstructed exit waves are useful to quantify unknown structure parameters such as the position and composition of the atom columns at atomic scale. Existing techniques provide a complex wave in a flat plane which is close to the plane where the electrons leave the atom columns. However, due to local deviation in the flatness of the exit surface, there will be an offset between the plane of reconstruction and the actual exit of a specific atom column. Using the channelling theory, it has been shown that this defocus offset can in principle be determined atom column-by-atom column. As such, the surface roughness could be quantified at atomic scale. However, the outcome strongly depends on the initial plane of reconstruction especially in a crystalline structure. If this plane is further away from the true exit, the waves of the atom columns become delocalized and interfere mutually which strongly complicates the interpretation of the exit wave in terms of the local structure. In this paper, we will study the delocalization with defocus using the channelling theory in a more systematic way.

Resolving the structure of active sites on platinum catalytic nanoparticles

Accurate understanding of the structure of active sites is fundamentally important in predicting catalytic properties of heterogeneous nanocatalysts. We present an accurate determination of both experimental and theoretical atomic structures of surface monatomic steps on industrial platinum nanoparticles. This comparison reveals that the edges of nanoparticles can significantly alter the atomic positions of monatomic steps in their proximity, which can lead to substantial deviations in the catalytic properties compared with the extended surfaces.

Order, disorder and structural modulations in Bi-Fe-W-O-Br Sillén-Aurivillius intergrowths

Transmission electron microscopy observations on a new complex oxybromide with nominal composition Bi(4)Fe(1/3)W(2/3)O(8)Br, heated at high temperature, reveal the transformation of its basic structure yielding two types of crystals. The first crystal type shows ordered and disordered extended defects leading to a new family of intergrowths between one Sillén block and n Aurivillius blocks and occasionally between one Aurivillius block and n Sillén blocks. The second type presents a compositionally modulated structure, determined by electron diffraction, with an average composition Bi(4)Fe(1/2)W(1/2)O(8 - delta)Br and unit-cell parameters a = (1/gamma) 3.8, b = 3.8, c = 14.5 A (gamma = 0.10-0.15) in the superspace group Immm[(1 - gamma)00] no. 71.1.