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At least 739 records · Page 41

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗

High-resolution source imaging and moment tensor estimation of acoustic emissions during brittle creep of basalt undergoing carbonation

SUMMARY As the high-frequency analogue to field-scale earthquakes, acoustic emissions (AEs) provide a valuable complement to study rock deformation mechanisms. During the load-stepping creep experiments with CO2-saturated water injection into a basaltic sample from Carbfix site in Iceland, 8791 AE events are detected by at least one of the seven piezoelectric sensors. Here, we apply a cross-correlation-based source imaging method, called geometric-mean reverse-time migration (GmRTM) to locate those AE events. Besides the attractive picking-free feature shared with other waveform-based methods (e.g. time-reversal imaging), GmRTM is advantageous in generating high-resolution source images with reduced imaging artefacts, especially for experiments with relatively sparse receivers. In general, the imaged AE locations are found to be scattered across the sample, suggesting a complicated fracture network rather than a well-defined major shear fracture plane, in agreement with X-ray computed tomography imaging results after retrieval of samples from the deformation apparatus. Clustering the events in space and time using the nearest-neighbour approach revealed a group of ‘repeaters’, which are spatially co-located over an elongated period of time and likely indicate crack, or shear band growth. Furthermore, we select 2196 AE events with high signal-to-noise-ratio (SNR) and conduct moment tensor estimation using the adjoint (backpropagated) strain tensor fields at the locations of AE sources. The resulting AE locations and focal mechanisms support our previously assertion that creep of basalt at the experimental conditions is accommodated dominantly by distributed microcracking.

58 GEOSCIENCES↗

Non-destructive Post-Transient Examination Results of the MOXTOP-1 Experiment

The MOXTOP-1 experiment has been assembled and irradiated in INL’s HFEF and TREAT facilities followed by disassembly of the experiment to enable initial post-transient examination. Results of neutron radiography of the fuel pin still in the THOR capsule were somewhat inconclusive due to the additional scatter and attenuation from the iron heat sink included in the design. Nonetheless, no obvious failure or fuel relocation could be identified in the radiography. Following disassembly of the fuel pin from the capsule, initial visual inspections were performed, and documented via images obtained through the hot cell window. No obvious signs of fuel failure were identified, indicating that the fuel pin remained intact during the transient. Some discoloration was observed near the middle of the fuel pin, likely corresponding to the fueled zone indicating that that region may have reached a relatively high temperature. Pre-transient, and post-transient profilometry of the fuel pin were performed and compared. Some additional strain displacement in the bottom portion of the fuel zone is identified, but remains well below 1%.

Mixed Oxide↗

Influence of gradation on shear behavior and pore water response of sand

Here, this paper examines the influence of particle size distribution (PSD) on the shearing behavior of sand using axisymmetric triaxial compression (ATC) testing in conjunction with 3D imaging using synchrotron micro-computed tomography (SMT). Angular sand was sieved to obtain a narrow gradation (uniform) and a wide gradation (non-uniform) with uniformity coefficients (C u ) of 1.2 and 3.0, respectively. Experiments were conducted under drained conditions and a constant effective cell pressure (σ$^{'}_3$) of 50 kPa at low and high back pressures (BP). Results of paired ATC-SMT were analyzed in terms of global constitutive behavior, strain localization, and localized flow characteristics. A new particle tracking algorithm is developed to expose strain localization. Relative particle translation gradient (RPTG) results revealed that gradation affects how early the shear band develops and a tendency for narrow gradation to exhibit varying degrees of diffused shear band at high axial strain (ε 1 ) even though a clear single shear band was observed at the peak strength. Geometric tortuosity (τ) is used as a quantitative parameter to assess flow changes and the efficiency of the flow path. Representative elementary volumes (REVs) inside and outside the shear band were analyzed and the results showed a variation in flow path characteristics where wide gradation specimens had preferential flow paths.

Computed tomography↗

Characterization of Humanized Mouse Model of Organophosphate Poisoning and Detection of Countermeasures via MALDI-MSI

Organophosphoate (OP) chemicals are known to inhibit the enzyme acetylcholinesterase (AChE). Studying OP poisoning is difficult because common small animal research models have serum carboxylesterase, which contributes to animals’ resistance to OP poisoning. Historically, guinea pigs have been used for this research; however, a novel genetically modified mouse strain (KIKO) was developed with nonfunctional serum carboxylase (Es1 KO) and an altered acetylcholinesterase (AChE) gene, which expresses the amino acid sequence of the human form of the same protein (AChE KI). KIKO mice were injected with 1xLD50 of an OP nerve agent or vehicle control with or without atropine. After one to three minutes, animals were injected with 35 mg/kg of the currently fielded Reactivator countermeasure for OP poisoning. Postmortem brains were imaged on a Bruker RapifleX ToF/ToF instrument. Data confirmed the presence of increased acetylcholine in OP-exposed animals, regardless of treatment or atropine status. More interestingly, we detected a small amount of Reactivator within the brain of both exposed and unexposed animals; it is currently debated if reactivators can cross the blood–brain barrier. Further, we were able to simultaneously image acetylcholine, the primary affected neurotransmitter, as well as determine the location of both Reactivator and acetylcholine in the brain. This study, which utilized sensitive MALDI-MSI methods, characterized KIKO mice as a functional model for OP countermeasure development.

2-PAM↗

Space Weathering of Olivine in Lunar Soils: A Comparison to Itokawa Regolith Samples

Regolith particles from airless bodies preserve a record of the space weathering processes that occurred during their surface exposure history. These processes have major implications for interpreting remote-sensing data from airless bodies. Solar wind irradiation effects occur in the rims of exposed grains, and impact processes result in the accumulation of vapordeposited elements and other surface-adhering materials. The grains returned from the surface of Itokawa by the Hayabusa mission allow the space weathering "style" of a chondritic, asteroidal "soil" to be compared to the lunar case. Here, we present new studies of space-weathered olivine grains from lunar soils, and compare these results to olivine grains from Itokawa. Samples and Methods: We analyzed microtome thin sections of olivine grains from the 20-45 micron fractions of three lunar soils: 71061, 71501 and 10084 (immature, submature and mature, respectively). Imaging and analytical data were obtained using a JEOL 2500SE 200kV field-emission scanning-transmission electron microscope equipped with a thin-window energy-dispersive x-ray spectrometer. Similar analyses were obtained from three Hayabusa olivine grains. Results and Discussion: We observed lunar grains showing a range of solar flare track densities (from <10(exp 9) to approx.10(exp 12)/sq cm). The lunar olivines all show disordered, highly strained, nanocrystalline rims up to 150-nm thick. The disordered rim thickness is positively correlated with solar flare track density. All of the disordered rims are overlain by a Si-rich amorphous layer, ranging up to 50-nm thick, enriched in elements that are not derived from the host olivine (e.g., Ca, Al, and Ti). The outmost layer represents impact-generated vapor deposits typically observed on other lunar soil grains. The Hayabusa olivine grains show track densities <10(exp 10)/sq cm and display disordered rims 50- to 100-nm thick. The track densities are intermediate to those observed in olivines in immature and submature lunar soils and indicate surface exposures of approx. 10(exp 5) years. The outermost few nanometers of the disordered rims on Hayabusa olivines are more Si-rich and Mg- and Fe-depleted relative to the cores of the grains and likely represent a minor accumulation of impact-generated vapors or sputter deposits. Nanophase Fe metal particles are less abundant in the Hayabusa rims compared to the rims on lunar grains. Conclusions: The Hayabusa and lunar olivine grain rims have widths and microstructures consistent with formation from atomic displacement damage from solar wind ions. The space weathering features in the Hayabusa grains are similar to those observed in olivines from immature to submature lunar soils. A major difference, however, is that the Hayabusa grains appear to lack the hypervelocity impact products (melt spherules, thick vapor deposits, and abundant nanophase Fe metal particles) that are common in lunar soil grains with a similar exposure history.

Keller, L. P.↗

CSEM, BHP, Salinity, Flow-Rate, Fiber, and Tilt Data Collected in Jan. 2022 for Proj. DE-FE0031785

This dataset consists of four directories: first directory named as EM for the controlled source electromagnetic (CSEM) survey data that are zipped per day for January 18-21, 22, 23, 24, 25, 26, 27, 28, 29, 30, and 31, 2022; second directory named as "Fiber" for the fiber optic slow-strain and microseismic data that are zipped per well; the third file that contains bottomhole pressure (BHP) and salinity and pump flow rate data during the CSEM surveys; and the fourth file that contained tiltmeter data.

CSEM↗

Window Cooling Studies and Disk Vibration Testing on a Subset of Mo-100 Disks

Production of metastable Technetium-99 (Tc-99m), a radioactive tracer that emits gamma rays, is vital to the medical imaging community. Tc-99m is extracted from the decay of Molybdenum-99 (Mo-99) which has a half-life of about 2-3 days. The work presented in this report is part of the NNSA’s mission to produce Mo-99 commercially, within the US, without the use of highly enriched uranium (HEU) in support of nonproliferation and global security. Los Alamos National Laboratory (LANL) is working with NorthStar Medical Radioisotopes (NMR) on their efforts to produce Mo-99 through the irradiation of Mo-100 targets using an electron beam. The NMR target comprises a stack of approximately 60-70 Mo-100 disks with diameter 24 mm and thickness 0.74 mm held in stainless steel laminations, each separated using 0.25 mm thick stainless-steel spacers. The symmetric target stack is housed in an Inconel vessel with two Inconel windows on either side. Two electron accelerators are used to produce 40 MeV, 3.16 µA electron beams each that penetrate the Inconel windows and irradiate the Mo-100 disks. Approximately 90% of the total 250 kW beam power is deposited in the NMR target during the irradiation process, with a smaller percentage adding up to 2.2 kW of heat deposited on the Inconel window. During irradiation, pressurized helium gas flows through thin gaps between the disks cooling the beam window, target disks, disk laminations and spacers. Both NMR and LANL have found during cold testing of the target system (no heat deposition) that the Mo 100 disks undergo significant mass loss and disk breakage due to vibrations induced by the flowing helium gas. The mass loss is not only undesirable due to monetary loss from reduced final quantities of Mo-99, but also due to the hazards associated with radioactive material trapped in the cooling lines and particle filters. The effect of flow rate and target geometry on the flow induced vibrations need to be quantified, and recommendations provided to minimize this mass loss. LANL has previously also tested NMR’s Inconel beam window by heating the window, while flowing pressurized helium, using the average heat deposited on the window. However, the NMR beam is pulsed with a duty cycle of 12.5%, which introduces oscillation in temperature around the nominal 600 °C steady state value with each pulse. Available fatigue curves for Inconel are few, established for room temperature, and they are based on mechanical strain cycles not thermally induced strain as in the NMR target. The effect of pulsed beam heating on the Inconel window therefore needs to be quantified. This report details the experiments conducted to assess the factors that lead to mass loss in the NMR target disks as well as to understand the effect of a pulsed beam on NMR’s Inconel window. This work describes LANL’s experimental characterization of the flow induced vibrations and disk mass loss in a reduced scale set-up containing 5 to 10 Mo-100 disks. We use high speed imaging, displacement measurements and microphone measurements combined with signal processing to estimate the vibration frequency of each disk. The effect of disk thickness, target fit and duration of testing on the mass loss is described. We find that in the current configuration of NMR targets, the vibrations and mass loss on the first disk are minimized, while those in the adjacent disks are highest. The microphone and high-speed image data show that increased flow rates and increased duration of testing increases vibration frequency and mass loss. The mass loss is due to both disk rotation and back and forth motion. There are visible wear marks on the disks with the highest mass loss. We also note that the current NMR window gap reduces flow induced vibrations compared to the previous smaller gaps. Improved target holders significantly reduce disk mass loss to almost negligible quantities. This work finds that the larger window to first disk gap and improved target holder geometry should allow NMR to successfully conduct irradiations with minimal mass loss. The window tests were conducted to understand the effect of a pulsed beam on both the window longevity and to estimate the window temperature and displacement during pulsing. The experiments presented here were performed at significantly low power, due to the limitations of the induction heating system. The window temperature rose to approximately 73 °C with a significantly reduced power of 45 W without beam pulsing. With a 5 Hz pulse rate, 12.5% duty cycle, the window temperature remained constant at 26 °C. These experiments will be repeated with improved coil geometry and reported in upcoming journal papers.

42 ENGINEERING↗

Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

In this work, we develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints and that minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer and a Peierls-Nabarro-like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moiré superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori and while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Å. Several applications of our model are shown, including predicting the variation of structure with twist angle and describing dislocation line tension and junction energies.

36 MATERIALS SCIENCE↗

Structures on Europa

Four classes of lineation patterns have been identified on Europa in the area covered by high-resolution Voyager 2 images. These include dark, wedge-shaped bands in the west-central part of the area; triple bands associated with diagonally trending, global lineations; gray concentric curvilinear bands in the southeastern part; and ridges near the terminator. The major structures appear to have been formed by tidal forces centered on the axis pointing toward Jupiter, but variations in the detail of the structural patterns may have been caused by internal forces. The older strain patterns tend to be rejuvenated by younger fractures. The most persistent rejuvenated strain patterns are the global diagonal fractures, probably formed by conjugate shear, and the straight and curvilinear fractures that apparently caused an early dichotomy in fracture patterns.

Lucchitta, B. K.↗

Shock recompaction of spall damage

Spall fracture is a high strain-rate damage phenomenon associated with shock or impulsive loading events. When a material that has been subjected to shock compression is allowed to release, rarefaction waves propagate into the sample and reduce the internal stress to zero. If multiple rarefaction waves intersect, they generate tension which, if sufficient, can nucleate voids in the material. It has been observed in several works investigating spall fracture that although the shock-wave profiles suggested spall occurred, imaging of the recovered sample revealed no voids or cracks. In this study, we aim to determine whether a second shock event could recompact existing spall damage, and if so, what form does the microstructure at the recompaction interface have? Through a series of gas-gun flyer-plate impact experiments, we demonstrate that modest shock stresses of 2 GPa–3 GPa are enough to both fully compact a damaged copper target back to a state of zero porosity and, furthermore, drive recrystallization of the interface such that there is a new bond formed where the free surfaces were brought together.

42 ENGINEERING↗

Complexity of deformation mechanism in neutron-irradiated 304L austenitic stainless steel at microstructural scale

The deformation mechanisms of neutron-irradiated 304 L stainless steel have been investigated using the in-situ electron backscattered diffraction (EBSD) technique. To decipher the role of irradiation, a detailed analysis was performed on irradiated miniature samples and compared with nonirradiated samples. Furthermore, at three levels of engineering strain, —0.0%, 4.8%, and 14.5%—microstructural features as well as EBSD were recorded at the identical location during in-situ deformation testing. Post-mortem analysis of the EBSD data revealed that the neutron-irradiated samples had higher fractions of the slip bands even at low amounts of deformation. Along with the slip bands, the neutron-irradiated sample showed the twins and martensitic phase formed almost parallel to the slip bands. In addition, the image results also indicated that the formation of twins and phases associated with the slip bands. A detailed mechanistic understanding has been investigated to identify the (111)γ planes orientation with respect to the loading direction associated with the formation of twins and martensite. The newly formed deformation twins and martensite were also found to maintain this relationship when they existed together.

304L austenitic stainless steel↗

Instrument for in situ hard x-ray nanobeam characterization during epitaxial crystallization and materials transformations

Solid-phase epitaxy (SPE) and other three-dimensional epitaxial crystallization processes pose challenging structural and chemical characterization problems. The concentration of defects, the spatial distribution of elastic strain, and the chemical state of ions each vary with nanoscale characteristic length scales and depend sensitively on the gas environment and elastic boundary conditions during growth. The lateral or three-dimensional propagation of crystalline interfaces in SPE has nanoscale or submicrometer characteristic distances during typical crystallization times. Here, an in situ synchrotron hard x-ray instrument allows these features to be studied during deposition and crystallization using diffraction, resonant scattering, nanobeam and coherent diffraction imaging, and reflectivity. The instrument incorporates a compact deposition system allowing the use of short-working-distance x-ray focusing optics. Layers are deposited using radio-frequency magnetron sputtering and evaporation sources. The deposition system provides control of the gas atmosphere and sample temperature. The sample is positioned using a stable mechanical design to minimize vibration and drift and employs precise translation stages to enable nanobeam experiments. Results of in situ x-ray characterization of the amorphous thin film deposition process for a SrTiO 3 /BaTiO 3 multilayer illustrate implementation of this instrument.

47 OTHER INSTRUMENTATION↗

An algorithm for resolving intragranular orientation fields using coupled far-field and near-field high energy $\mathrm{X}$-ray diffraction microscopy

Here, we present a novel algorithm for reconstructing spatial intragranular lattice orientation fields using both far-field and near-field high energy X-ray diffraction microscopy (HEDM) measurements. An established far-field indexing algorithm is modified to include lattice orientation distribution information (grain orientation envelopes) in addition to average grain orientations. The near-field data reduction algorithm utilizes this enriched far-field orientation data as a seed for reconstructing intragranular spatial maps of lattice orientation from the diffraction images. The primary benefit of the new algorithm is a significant decrease in the number of trial calculations that must be performed in the reconstruction process compared to existing methodologies while maintaining scalability. The resulting gains in efficiency facilitate the use of relatively modest computational resources and improve throughput at the point of measurement. We provide two example applications: volumetric orientation field reconstructions for a Ti-Al alloy both before and after the application of 3% uniaxial strain. The results showcase the efficiency of the new method and the ability to resolve subtle changes in microstructure, which are associated with incipient plastic deformation.

36 MATERIALS SCIENCE↗

Surface Ruptures and Building Damage of the 2003 Bam, Iran, Earthquake Mapped by Satellite Synthetic Aperture Radar Interferometric Correlation

We use the interferometric correlation from Envisat synthetic aperture radar (SAR) images to map the details of the surface ruptures related to the 26 December 2003 earthquake that devastated Bam, Iran. The main strike-slip fault rupture south of the city of Bam has a series of four segments with left steps shown by a narrow line of low correlation in the coseismic interferogram. This also has a clear expression in the field because of the net extension across the fault. Just south of the city limits, the surface strain becomes distributed over a width of about 500 m, probably because of a thicker layer of soft sedimentary material.

Synthetic Aperture Radar (SAR)↗

Assessment of Ultrasound Devices to Protect the Health of Astronauts in the New Era of Space Exploration: A Literature Review

Microgravity and radiation of space create harsh physiological strains on astronauts with significant damaging effects on cardiovascular and musculoskeletal systems among others. It is necessary to utilize medical technologies that can effectively monitor chronic and acute alterations to astronauts’ health statuses on spacecrafts. Future missions to distant planetary bodies will result in longer exposure to damaging environmental factors and limit crew access to healthcare resources and maintenance devices; thus, even greater logistical and quality considerations must be made. Remarkable advancements in ultrasound technology have created new powerful portable imaging devices and a potential chip-based alternative to piezoelectric crystals that are used in nearly all ultrasound devices. This literature review will investigate new commercial and prototypal ultrasound medical devices on their potential effectiveness in austere environments such as space. The accuracy, versatility, and practicality of each device will be compared to each other as well as the current technological gold standards of health monitoring used in traditional healthcare settings. Assessment of new ultrasound technology in this literature review will provide guidance to future missions by space agencies regarding the most optimal medical devices to protect astronauts and, therefore, enable further exploration of distant planets and solar systems.

Parag Vyas↗

Machine Learning Driven Contouring of High-Frequency Four-Dimensional Cardiac Ultrasound Data

Automatic boundary detection of 4D ultrasound (4DUS) cardiac data is a promising yet challenging application at the intersection of machine learning and medicine. Using recently developed murine 4DUS cardiac imaging data, we demonstrate here a set of three machine learning models that predict left ventricular wall kinematics along both the endo- and epi-cardial boundaries. Each model is fundamentally built on three key features: (1) the projection of raw US data to a lower dimensional subspace, (2) a smoothing spline basis across time, and (3) a strategic parameterization of the left ventricular boundaries. Model 1 is constructed such that boundary predictions are based on individual short-axis images, regardless of their relative position in the ventricle. Model 2 simultaneously incorporates parallel short-axis image data into their predictions. Model 3 builds on the multi-slice approach of model 2, but assists predictions with a single ground-truth position at end-diastole. To assess the performance of each model, Monte Carlo cross validation was used to assess the performance of each model on unseen data. For predicting the radial distance of the endocardium, models 1, 2, and 3 yielded average R2 values of 0.41, 0.49, and 0.71, respectively. Monte Carlo simulations of the endocardial wall showed significantly closer predictions when using model 2 versus model 1 at a rate of 48.67%, and using model 3 versus model 2 at a rate of 83.50%. These finding suggest that a machine learning approach where multi-slice data are simultaneously used as input and predictions are aided by a single user input yields the most robust performance. Subsequently, we explore the how metrics of cardiac kinematics compare between ground-truth contours and predicted boundaries. We observed negligible deviations from ground-truth when using predicted boundaries alone, except in the case of early diastolic strain rate, providing confidence for the use of such machine learning models for rapid and reliable assessments of murine cardiac function. To our knowledge, this is the first application of machine learning to murine left ventricular 4DUS data. Future work will be needed to strengthen both model performance and applicability to different cardiac disease models.

4D ultrasound↗

Revealing the three-dimensional arrangement of polar topology in nanoparticles

In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗