GHZ ELECTRON BUNCHER COMPATIBLE WITH COMMERCIAL TEMS FOR STROBOSCOPIC IMAGING WITH SPACE-TIME RESOLUTION BETWEEN 10E-23 AND 10E-20 M∙S
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43 PARTICLE ACCELERATORS↗
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Results for “Transmission electron microscopy (TEM)”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Measuring sub-surface spatially varying thermal conductivity of silicon implanted with krypton
The thermal properties of semiconductors following exposure to ion irradiation are of great interest for the cooling of electronic devices; however, gradients in composition and structure due to irradiation often make the measurement difficult. Furthermore, the nature of spatial variations in thermal resistances due to spatially varying ion irradiation damage is not well understood. In this work, we develop an advancement in the analysis of time-domain thermoreflectance to account for spatially varying thermal conductivity in a material resulting from a spatial distribution of defects. We then use this method to measure the near-surface (≲1 μm) thermal conductivity of silicon wafers irradiated with Kr + ions, which has an approximate Gaussian distribution centered 260 nm into the sample. Our numerical analysis presented here allows for the spatial gradient of thermal conductivity to be extracted via what is fundamentally a volumetric measurement technique. We validate our findings via transmission electron microscopy, which is able to confirm the spatial variation of the sub-surface silicon structure, and provide additional insight into the local structure resulting from the effects of ion bombardment. Thermal measurements found the ion stopping region to have a nearly 50x reduction in thermal conductivity as compared to pristine silicon, while TEM showed the region was not fully amorphized. Our results suggest this drastic reduction in silicon thermal conductivity is primarily driven by structural defects in crystalline regions along with boundary scattering between amorphous and crystalline regions, with a negligible contribution being due to implanted krypton ions themselves.
36 MATERIALS SCIENCE↗
Facile hermetic TEM grid preparation for molecular imaging of hydrated biological samples at room temperature
Abstract Although structures of vitrified supramolecular complexes have been determined at near-atomic resolution, elucidating in situ molecular structure in living cells remains a challenge. Here, we report a straightforward liquid cell technique, originally developed for real-time visualization of dynamics at a liquid-gas interface using transmission electron microscopy, to image wet biological samples. Due to the scattering effects from the liquid phase, the micrographs display an amplitude contrast comparable to that observed in negatively stained samples. We succeed in resolving subunits within the protein complex GroEL imaged in a buffer solution at room temperature. Additionally, we capture various stages of virus cell entry, a process for which only sparse structural data exists due to their transient nature. To scrutinize the morphological details further, we used individual particle electron tomography for 3D reconstruction of each virus. These findings showcase this approach potential as an efficient, cost-effective complement to other microscopy technique in addressing biological questions at the molecular level.
59 BASIC BIOLOGICAL SCIENCES↗
Transmission electron microscopy of ion irradiated ODS MA956 samples
Oxide dispersion strengthened (ODS) alloys are promising candidate materials for the next generation advanced nuclear reactors due to their superior irradiation resistance and mechanical properties. To better understand the effect of irradiation on MA956, it is essential to study higher dose (50-100 dpa) samples, so that the general trend of microstructural evolution and the resulting radiation-hardening can be deduced. Currently, ion irradiations are considered the only way to achieve doses beyond ~50 dpa in a practical time frame relevant to alloy and welding development programs. This dataset contains TEM characterization results of ODS MA956 samples that were ion irradiated under different conditions: Sample #5 (1.25 dpa at 190℃); Sample #9 (50 dpa at 190℃); Sample #15 (1.25dpa under 320℃); and Sample 17 (25 dpa at 320℃). TEM characterization focused on the irradiation induced defects (dislocation lines and loops) using the on-zone axis bright field STEM technique. These data were collected using a FEI Tecnai G2 F30 S/TEM at Microscopy and Characterization Suite (MaCS) at Center for Advanced Energy Studies (CAES), Idaho Falls, ID. This project (ion irradiation and TEM studies) was supported by the U.S. Department of Energy, Office of Nuclear Energy under DOE Idaho Operations Office Contract DE-AC07-05ID14517 as part of Nuclear Science User Facilities award #18-14784 (PI: Ramprashad Prabhakaran, PNNL).
Prabhakaran, Ramprashad↗
Dynamics of Polymer Nanocapsule Buckling and Collapse Revealed by In Situ Liquid-Phase TEM
Nanocapsules are hollow nanoscale shells that have applications in drug delivery, batteries, self-healing materials, and as model systems for naturally occurring shell geometries. In many applications, nanocapsules are designed to release their cargo as they buckle and collapse, but the details of this transient buckling process have not been directly observed. In this work, we use in situ liquid-phase transmission electron microscopy to record the electron-irradiation-induced buckling in spherical 60-187 nm polymer capsules with ~3.5 nm walls. We observe in real time the release of aqueous cargo from these nanocapsules and their buckling into morphologies with single or multiple indentations. The in situ buckling of nanoscale capsules is compared to ex situ measurements of collapsed and micrometer-sized capsules and to Monte Carlo (MC) simulations. The shape and dynamics of the collapsing nanocapsules are consistent with MC simulations, which reveal that the excessive wrinkling of nanocapsules with ultrathin walls results from their large Föppl-von Kármán numbers around 10 5 . Our experiments suggest design rules for nanocapsules with the desired buckling response based on parameters such as capsule radius, wall thickness, and collapse rate.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Tensile behavior and microstructural evolution of a Fe-25Ni-20Cr austenitic stainless steel (alloy 709) from room to elevated temperatures through in-situ synchrotron X-ray diffraction characterization and transmission electron microscopy
Uniaxial tensile tests were done on Fe-25Ni-20Cr Austenitic Stainless Steel (Alloy 709) along with in-situ synchrotron measurement at different temperatures (25 degrees C, 500 degrees C, 700 degrees C and 900 degrees C). The X-Ray diffraction data was collected in-situ in order to follow the phases present as well as to derive the dislocation density as a function of strain through peak broadening analysis based on the modified Williamson-Hall method and see how trends are affected as a function of temperature. The XRD data were complemented by TEM and STEM-EDX characterization done on the post-experiment samples to observe the deformed microstructures. Finally, the paper presents a depiction of the tensile behavior of this advanced steel by interpreting the stress-strain curves and the effect of temperature through the information gained by in-situ XRD and TEM observations as well as fractography done ex-situ on the samples tested to rupture.
36 MATERIALS SCIENCE↗
STEM Characterization of Dislocation Loops in Irradiated FCC Alloys
In this study, we demonstrate the methodology systematically developed for dislocation loop (perfect and faulted loops) imaging and analysis in irradiated face-centered-cubic (FCC) alloys using scanning transmission electron microscopy (STEM). On-zone [001] STEM imaging was identified as the preferred choice for its accuracy and effectiveness based on the comparison with other dislocation loop imaging techniques including: (i) on-zone STEM imaging using other major low-index zone axes, (ii) kinematic two-beam conditions bright field imaging near the [001] zone axis in conventional TEM (CTEM) mode, and (iii) Rel-Rod CTEM dark-field (DF) imaging near the [011] zone axis. The effect of STEM collection angle on the contrast formation of dislocation loops was also investigated. The developed method was confirmed by imaging all populations of perfect and faulted loops of types a/2$\langle$110$\rangle${110} and a/3$\langle$111$\rangle${111} found in an ion irradiated Ni40Fe40Cr20 alloy. The proposed STEM-based technique can easily identify said loops with a size greater than 10 nm without any assumptions such as those commonly made using the conventional Rel-Rod CTEM-DF technique. The recommended methodology in this study is developed as a quick and convenient tool that can be generally applied to irradiated FCC-based materials due to their common crystallography.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
2D-EFICACY: Control of Metastable 2D Carbide[1]Chalcogenide Heterolayers: Strain and Moire Engineering
The experimental isolation of graphene led to the discovery of an entirely new world of two-dimensional (2D) materials in which the 2D nature often leads to emergent behaviors not seen in bulk systems. 2D transition metal dichalcogenides (TMDs) exhibit physico-chemical properties that depend on the transition metal, polymorph, thickness, and presence and type of defects. Recently, a group of thin (10-100nm) transition metal carbides (TMCs), such as Mo2C, has been synthesized that exhibit a thickness-dependent superconducting critical temperature (Tc). These thin TMCs are different from MXenes, another class of 2D materials consisting of few layers of nitrides or carbides (<5nm) produced by chemical etching and delamination. The goal of this renewal proposal is to combine experiment and computation to synthesize and elucidate the guiding principles that control the growth, orientation and strain of heterostacks of thin TMCs and TMDs composed with Nb, Ti and W. We expect to stabilize metastable hybrid phases of TMCs sandwiched between TMDs (H-TMD/Cs) with unprecedented physico-chemical properties. As part of previous DOE-funded work by the Terrones/Sinnott groups, thin (10-100 nm thick) Mo2C flakes were successfully synthesized by chemical vapor deposition (CVD). By subsequently exposing Mo2C to H2S, partial chalcogenization was achieved, resulting in heterostacks of MoCx phases and MoS2. The formation of MoS2 led to a deficiency of Mo atoms in the underlying Mo2C, resulting in an inhomogeneous phase change from α-Mo2C to γ’-MoCx and then to γ-MoC. The γ’-MoCx is a strained metastable phase and the heterostack of all three phases demonstrated an increased Tc relative to that of α-Mo2C, from 4 to 6K; its interleaved layered structure consisting of superconducting and semiconducting phases is ideal for future studies of Josephson junction series arrays. Moiré patterns in these heterostacked systems could result in new phenomena, as moiré patterns in bilayer graphene showed unconventional superconductivity and moiré excitons have been observed in twisted TMD heterobilayers. The scientific hypothesis of the proposed synergistic computational and experimental research is that orientation and strain control within confined thin metastable TMCs, sandwiched by stable phases of TMCs and layered TMDs, will depend on kinetic and thermodynamic “knobs” that include fast temperature changes, chalcogen diffusion through preferred crystallographic planes, reaction times, pressure, reactive atmosphere, precursors, and surfactants, which will also tailor properties such as superconductivity, magnetism, ferroelectricity, piezoelectricity, and catalytic performance. We will develop the guiding principles for the synthesis and stabilization of metastable H-TMD/Cs based on Nb, Ti and W. In order to validate the hypothesis, four tasks are proposed: The first task will synthesize ultra-thin TMCs based on Nb, W and Ti, by: 1) adapting the CVD method used for Mo2C, 2) plasma assisted CVD, 3) defect-mediated CVD processes, and 4) cryo-milling of carbide powders. The second task will accomplish the synthesis and basic physico-chemical characterizations of H-TMD/Cs by chalcogenization of the materials synthesized in task one, and by carbonization of TMDs. H-TMD/Cs will also be investigated for their suitability in energy conversion applications such as supercapacitors, Li and multivalent ion batteries, and electrocatalysts, topics of interest to DoE. These tasks will be carried out in close conjunction with density functional theory (DFT) calculations with insights into energetics, lattice parameters, stability, phase diagrams, band structures, and density of states of H-TMD/Cs. The third task will characterize and evaluate strain and moiré patterns at the interfaces of different H-TMD/Cs by high-resolution scanning transmission electron microscopy (HR-STEM), scanning tunneling microscopy (STM), and conductive tip atomic force microscopy. Nudged elastic band calculations with DFT will be performed to understand the chalcogen diffusion process, which will provide insights into the interfaces between different phases of TMCs and TMDs. The fourth task aims at quantifying the stability and dynamics of H-TMD/Cs by in-situ TEM and Raman studies under heating, strain, and electrical biasing. Phonon calculations using DFT will provide a basis for interpreting Raman spectra. This coherent framework involving synthesis, characterization, and computation will result in a broad scientific impact for energy related applications. The ability to develop new H-TMD/Cs will enhance a range of applications that include batteries, catalysts, switches, sensors, quantum computing components and smart coatings.
2-Dimensional materials↗
2D-EFICACY: Control of Metastable 2D Carbide Chalcogenide Heterolayers: Strain and Moire Engineering
The experimental isolation of graphene led to the discovery of an entirely new world of two-dimensional (2D) materials in which the 2D nature often leads to emergent behaviors not seen in bulk systems. 2D transition metal dichalcogenides (TMDs) exhibit physico-chemical properties that depend on the transition metal, polymorph, thickness, and presence and type of defects. Recently, a group of thin (10-100nm) transition metal carbides (TMCs), such as Mo 2 C, has been synthesized that exhibit a thickness-dependent superconducting critical temperature (Tc). These thin TMCs are different from MXenes, another class of 2D materials consisting of few layers of nitrides or carbides (<5nm) produced by chemical etching and delamination. The goal of this renewal proposal is to combine experiment and computation to synthesize and elucidate the guiding principles that control the growth, orientation and strain of heterostacks of thin TMCs and TMDs composed with Nb, Ti and W. We expect to stabilize metastable hybrid phases of TMCs sandwiched between TMDs (H-TMD/Cs) with unprecedented physico-chemical properties. As part of previous DOE-funded work by the Terrones/Sinnott groups, thin (10-100 nm thick) Mo 2 C flakes were successfully synthesized by chemical vapor deposition (CVD). By subsequently exposing Mo 2 C to H 2 S, partial chalcogenization was achieved, resulting in heterostacks of MoCx phases and MoS 2 . The formation of MoS 2 led to a deficiency of Mo atoms in the underlying Mo 2 C, resulting in an inhomogeneous phase change from α-Mo 2 C to γ’-MoCx and then to γ-MoC. The γ’-MoCx is a strained metastable phase and the heterostack of all three phases demonstrated an increased Tc relative to that of α-Mo 2 C, from 4 to 6K; its interleaved layered structure consisting of superconducting and semiconducting phases is ideal for future studies of Josephson junction series arrays. Moiré patterns in these heterostacked systems could result in new phenomena, as moiré patterns in bilayer graphene showed unconventional superconductivity and moiré excitons have been observed in twisted TMD heterobilayers. The scientific hypothesis of the proposed synergistic computational and experimental research is that orientation and strain control within confined thin metastable TMCs, sandwiched by stable phases of TMCs and layered TMDs, will depend on kinetic and thermodynamic “knobs” that include fast temperature changes, chalcogen diffusion through preferred crystallographic planes, reaction times, pressure, reactive atmosphere, precursors, and surfactants, which will also tailor properties such as superconductivity, magnetism, ferroelectricity, piezoelectricity, and catalytic performance. We will develop the guiding principles for the synthesis and stabilization of metastable H-TMD/Cs based on Nb, Ti and W. In order to validate the hypothesis, four tasks are proposed: The first task will synthesize ultra-thin TMCs based on Nb, W and Ti, by: 1) adapting the CVD method used for Mo 2 C, 2) plasma assisted CVD, 3) defect-mediated CVD processes, and 4) cryo-milling of carbide powders. The second task will accomplish the synthesis and basic physico-chemical characterizations of H-TMD/Cs by chalcogenization of the materials synthesized in task one, and by carbonization of TMDs. H-TMD/Cs will also be investigated for their suitability in energy conversion applications such as supercapacitors, Li and multivalent ion batteries, and electrocatalysts, topics of interest to DoE. These tasks will be carried out in close conjunction with density functional theory (DFT) calculations with insights into energetics, lattice parameters, stability, phase diagrams, band structures, and density of states of H-TMD/Cs. The third task will characterize and evaluate strain and moiré patterns at the interfaces of different H-TMD/Cs by high-resolution scanning transmission electron microscopy (HR-STEM), scanning tunneling microscopy (STM), and conductive tip atomic force microscopy. Nudged elastic band calculations with DFT will be performed to understand the chalcogen diffusion process, which will provide insights into the interfaces between different phases of TMCs and TMDs. The fourth task aims at quantifying the stability and dynamics of H-TMD/Cs by in-situ TEM and Raman studies under heating, strain, and electrical biasing. Phonon calculations using DFT will provide a basis for interpreting Raman spectra. This coherent framework involving synthesis, characterization, and computation will result in a broad scientific impact for energy related applications. The ability to develop new H-TMD/Cs will enhance a range of applications that include batteries, catalysts, switches, sensors, quantum computing components and smart coatings.
2-Dimensional Materials↗
Structure of the (110) Ln ScO 3 ( Ln =Gd,Tb,Dy) surfaces
The surface reconstruction on the (110) surface of LnScO 3 (Ln=Gd,Tb,Dy) has been investigated using x-ray photoelectron spectroscopy, atomic force microscopy, and transmission electron diffraction coupled with higher-level density-functional theory methods. The experimental techniques generate constraints on the surface chemistry and structure that are used to inform the theoretical comparison of a number of potential surface structures. The resulting structure is then compared to experimental aberration-corrected transmission electron microscopy results using multislice simulation. The surfaces of both single-crystalline substrates and hydrosauna synthesized nanoparticles exhibit a Sc-rich double layer with a Sc 3 O 4 termination.
36 MATERIALS SCIENCE↗
Tailoring Solution-Processable Li Argyrodites Li6+xP1-xMxS5I (M = Ge, Sn) and Their Microstructural Evolution Revealed by Cryo-TEM for All-Solid-State Batteries
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99 GENERAL AND MISCELLANEOUS↗
Corrosion behavior of a series of combinatorial physical vapor deposition coatings on SiC in a simulated boiling water reactor environment
Here, the simulated boiling water condition corrosion properties of multilayer and combinatorial physical vapor deposition metal coatings (Zr, Cr, and/or Ti) deposited on a SiC f -SiC composite were investigated. Various compositions within the ternary system were corroded to the most suitable composition preventing underlying SiC f -SiC from further attack. Mass measurements and visual observations were conducted to identify which coatings formed protective oxides and which coatings spalled. Transmission electron microscopy was conducted to observe the microstructure of the physical vapor deposition metal layer before and after corrosion as well as identify the oxide which were forming.
36 MATERIALS SCIENCE↗
Deep learning-based noise filtering toward millisecond order imaging by using scanning transmission electron microscopy
Application of scanning transmission electron microscopy (STEM) to in situ observation will be essential in the current and emerging data-driven materials science by taking STEM’s high affinity with various analytical options into account. As is well known, STEM’s image acquisition time needs to be further shortened to capture a targeted phenomenon in real-time as STEM’s current temporal resolution is far below the conventional TEM’s. However, rapid image acquisition in the millisecond per frame or faster generally causes image distortion, poor electron signals, and unidirectional blurring, which are obstacles for realizing video-rate STEM observation. Here we show an image correction framework integrating deep learning (DL)-based denoising and image distortion correction schemes optimized for STEM rapid image acquisition. By comparing a series of distortion corrected rapid scan images with corresponding regular scan speed images, the trained DL network is shown to remove not only the statistical noise but also the unidirectional blurring. This result demonstrates that rapid as well as high-quality image acquisition by STEM without hardware modification can be established by the DL. The DL-based noise filter could be applied to in-situ observation, such as dislocation activities under external stimuli, with high spatio-temporal resolution.
47 OTHER INSTRUMENTATION↗
Electron inelastic mean free path in water
Liquid phase transmission electron microscopy (LPTEM) is rapidly developing as a powerful tool for probing processes in liquid environments with close to atomic resolution. Knowledge of the water thickness is needed for reliable interpretation and modelling of analytical studies in LPTEM, and is particularly essential when using thin liquid layers, required for achieving the highest spatial resolutions. Furthermore, the log-ratio method in electron energy-loss spectroscopy (EELS) is often applied in TEM to quantify the sample thickness, which is measured relative to the inelastic mean free path ( λ IMFP ). However, λ IMFP itself is dependent on sample material, the electron energy, and the convergence and divergence angles of the microscope electronoptics. Here, we present a detailed quantitative analysis of the λ IMFP of water as functions of the EELS collection angle ( β ) at 120 keV and 300 keV in a novel nanochannel liquid cell. We observe good agreement with earlier studies conducted on ice, but find that the most widely used theoretical models significantly underestimate λ IMFP of water. We determine an adjusted average energy-loss term E m, water , and characteristic scattering angle θ E, water that improve the accuracy. The results provide a comprehensive knowledge of the λ IMFP of water (or ice) for reliable interpretation and quantification of observations in LPTEM and cryo-TEM studies.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Atomistic observation on diffusion-mediated friction between single-asperity contacts
Super-lubricity, a sliding regime in which friction almost vanishes, has been well-documented with the advent of atomic force microscopy (AFM) and molecular dynamics (MD) simulation due to its enormous implications for manufacturing micro-/nano-electromechanical systems (MEMS/NEMS). Nevertheless, the atomistic mechanisms for super-lubricious behaviors are still elusive, primarily due to a lack of direct observation of interface at atomic resolution during frictional process. Here by using in situ high-resolution transmission electron microscopy (HRTEM) coupled with AFM, we report diffusion-mediated formation of a loosely-packed interfacial layer between two metallic asperities at infinitesimal normal forces, which is responsible for the sliding regime, super-lubricity exhibiting ultra-low friction forces and continuous sliding. By contrast, the loosely-packed interfacial layer vanishes along with the super-lubricity, leading to typical stick-slip friction. Additionally, in situ TEM observation and MD simulations reveals the crucial role that atom diffusion plays in atomic friction, and provides new insights into the fundamental mechanisms of super-lubricity.
42 ENGINEERING↗
Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments
We discuss the need to understand materials exposed to overlapping extreme environments such as high temperature, radiation, or mechanical stress. When these stressors are combined there may be synergistic effects that enable unique microstructural evolution mechanisms to activate. Understanding of these mechanisms is necessary for the input and refinement of predictive models and critical for engineering of next generation materials. The basic physics and underlying mechanisms require advanced tools to be investigated. The in situ ion irradiation transmission electron microscope (I 3 TEM) is designed to explore these principles. To quantitatively probe the complex dynamic interactions in materials, careful preparation of samples and consideration of experimental design is required. Particular handling or preparation of samples can easily introduce damage or features that obfuscate the measurements. There is no one correct way to prepare a sample; however, many mistakes can be made. The most common errors and things to consider are highlighted within. The I 3 TEM has many adjustable variables and a large potential experimental space, therefore it is best to design experiments with a specific scientific question or questions in mind. Experiments have been performed on large number of sample geometries, material classes, and with many irradiation conditions. The following are a subset of examples that demonstrate unique in situ capabilities utilizing the I 3 TEM. Au nanoparticles prepared by drop casting have been used to investigate the effects of single ion strikes. Au thin films have been used in studies on the effects of multibeam irradiation on microstructure evolution. Zr films have been exposed to irradiation and mechanical tension to examine creep. Ag nanopillars were subjected to simultaneous high temperature, mechanical compression, and ion irradiation to study irradiation induced creep as well. These results impact fields including: structural materials, nuclear energy, energy storage, catalysis, and microelectronics in space environments.
47 OTHER INSTRUMENTATION↗
Creep properties of advanced austenitic steel 709 determined through short experiments under in-situ neutron diffraction followed by TEM characterization
Here in this study, the creep mechanisms at play in Alloy 709 (Fe-20Cr-25Ni) are investigated by performing short-term creep-type tests under in-situ neutron diffraction experiments. Short tests are performed in the temperature range of 500 to 900 °C under constant load with a load ranging from 50 to 150 MPa. The creep exponent and activation energy are determined using the Bird-Mukherjee-Dorn relation and compared to that obtained from conventional longer creep tests from the literature. Scanning transmission electron microscopy (S/TEM) of the post-creep microstructure indicates that interaction of dislocations with precipitates are a dominant mechanism at play. Furthermore, local elemental mapping indicated chemical segregation at grain boundaries and formation of complex precipitates.
36 MATERIALS SCIENCE↗
Finding simplicity: unsupervised discovery of features, patterns, and order parameters via shift-invariant variational autoencoders *
Abstract Recent advances in scanning tunneling and transmission electron microscopies (STM and STEM) have allowed routine generation of large volumes of imaging data containing information on the structure and functionality of materials. The experimental data sets contain signatures of long-range phenomena such as physical order parameter fields, polarization, and strain gradients in STEM, or standing electronic waves and carrier-mediated exchange interactions in STM, all superimposed onto scanning system distortions and gradual changes of contrast due to drift and/or mis-tilt effects. Correspondingly, while the human eye can readily identify certain patterns in the images such as lattice periodicities, repeating structural elements, or microstructures, their automatic extraction and classification are highly non-trivial and universal pathways to accomplish such analyses are absent. We pose that the most distinctive elements of the patterns observed in STM and (S)TEM images are similarity and (almost-) periodicity, behaviors stemming directly from the parsimony of elementary atomic structures, superimposed on the gradual changes reflective of order parameter distributions. However, the discovery of these elements via global Fourier methods is non-trivial due to variability and lack of ideal discrete translation symmetry. To address this problem, we explore the shift-invariant variational autoencoders (shift-VAEs) that allow disentangling characteristic repeating features in the images, their variations, and shifts that inevitably occur when randomly sampling the image space. Shift-VAEs balance the uncertainty in the position of the object of interest with the uncertainty in shape reconstruction. This approach is illustrated for model 1D data, and further extended to synthetic and experimental STM and STEM 2D data. We further introduce an approach for training shift-VAEs that allows finding the latent variables that comport to known physical behavior. In this specific case, the condition is that the latent variable maps should be smooth on the length scale of the atomic lattice (as expected for physical order parameters), but other conditions can be imposed. The opportunities and limitations of the shift VAE analysis for pattern discovery are elucidated.
97 MATHEMATICS AND COMPUTING↗