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At least 73 records · Page 4

Applying Configurational Complexity to the 2D Ruddlesden–Popper Crystal Structure

The layered Ruddlesden–Popper crystal structure can host a broad range of functionally important behaviors. In this work, we establish extraordinary configurational disorder in a layered Ruddlesden–Popper (RP) structure using entropy stabilization assisted synthesis. A protype A 2 CuO 4 RP cuprate oxide with five cations on the A-site sublattice is designed and fabricated into epitaxial single crystal films using pulsed laser deposition. When grown on a near lattice matched substrate, the (La 0.2 Pr 0.2 Nd 0.2 Sm 0.2 Eu 0.2 ) 2 CuO 4 film features a T'-type RP structure with uniform A-site cation mixing and square-planar CuO4 units. These observations are made with a range of combined characterizations using X-ray diffraction, atomic-resolution scanning transmission electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray absorption spectroscopy measurements. It is further found that heteroepitaxial strain plays an important role in crystal phase formation during synthesis. Compressive strain over ~1.5% results in the formation of a non-RP cubic phase consistent with a Cu X 2O 4 spinel structure. The ability to manipulate configurational complexity and move between 2D layered RP and 3D cubic crystal structures in cuprate and related materials promises to enable flexible design strategies for a range of functionalities, such as magnetoresistance, unconventional superconductivity, ferroelectricity, catalysis, and ion transport.

36 MATERIALS SCIENCE↗

High–Performance NiCo 2 O 4 /Graphene Quantum Dots for Asymmetric and Symmetric Supercapacitors with Enhanced Energy Efficiency

For the sustainable growth of future generations, energy storage technologies like supercapacitors and batteries are becoming more and more common. However, reliable and high-performance materials’ design and development is the key for the widespread adoption of batteries and supercapacitors. Quantum dots with fascinating and unusual properties are expected to revolutionize future technologies. However, while the recent discovery of quantum dots honored with a Nobel prize in Chemistry, their benefits for the tenacious problem of energy are not realized yet. In this context, herein, chemical-composition tuning enabled exceptional performance of NiCo 2 O 4 (NCO)/graphene quantum dots (GQDs) is reported, which outperform the existing similar materials, in supercapacitors. A comprehensive study is performed on the synthesis, characterization, and electrochemical performance evaluation of highly functional NCO/GQDs in supercapacitors delivering enhanced energy efficiency. The high-performance, functional NCO/GQDs electrode materials are synthesized by the incorporation of GQDs into NCO. The effect of variable amount of GQDs on the energy performance characteristics of NCO/GQDs in supercapacitors is studied systematically. In-depth structural and chemical bonding analyses using X-ray diffraction (XRD) and Raman spectroscopic studies indicate that all the NCO/GQDs composites crystallize in the spinel cubic phase of NiCo 2 O 4 while graphene integration evident in all the NCO/GQDs. The scanning electron microscopy imaging analysis reveals homogeneously distributed spherical particles with a size distribution of 5–9 nm validating the formation of QDs. The high-resolution transmission electron microscopy analyses reveal that the NCOQDs are anchored on graphene sheets, which provide a high surface area of 42.27 m 2 g –1 and high mesoporosity for the composition of NCO/GQDs-10%. In addition to establishing reliable electrical connection to graphene sheets, the NCOQDs provide reliable 3D-conductive channels for rapid transport throughout the electrode as well as synergistic effects. Chemical-composition tuning, and optimization yields NCO/GQDs-10% to deliver the best specific capacitance of 3940 Fg –1 at 0.5 Ag –1 , where the electrodes retain ≈98% capacitance after 5000 cycles. The NCO/GQD-10%//AC asymmetric supercapacitor device demonstrates outstanding energy density and power density values of 118.04 Wh kg –1 and 798.76 W kg –1 , respectively. The NCO/GQDs-10%//NCO/GQDs-10% symmetric supercapacitor device delivers excellent energy and power density of 24.30 Wh kg –1 and 500 W kg –1 , respectively. These results demonstrate and conclude that NCO/GQDs are exceptional and prospective candidates for developing next-generation high-performance and sustainable energy storage devices.

25 ENERGY STORAGE↗

Clathrate XI K 58 Zn 122 Sb 207 : A New Branch on the Clathrate Family Tree

Abstract The compositional screening of K‐Zn‐Sb ternary system aided by machine learning, rapid exploratory synthesis using KH salt‐like precursor and in situ powder X‐ray diffraction yielded a novel clathrate type XI K 58 Zn 122 Sb 207 . This clathrate consists of a 3D Zn‐Sb framework hosting K + ions inside polyhedral cages, some of which are reminiscent of known clathrate types while others are unique to this structure type. The complex non‐centrosymmetric structure in the tetragonal space group was solved by means of single crystal X‐ray diffraction as a 6‐component twin due to pseudocubic symmetry and further confirmed by high‐resolution synchrotron powder X‐ray diffraction and state‐of‐the‐art scanning transmission electron microscopy. The electron‐precise composition of this clathrate yields narrow‐gap p ‐type semiconductor with extraordinarily low thermal conductivity due to displacement or “rattling” of K cations inside oversized cages and as well as to twinning, stacking faults and antiphase boundary defects.

Cox, Tori↗

Clathrate XI K 58 Zn 122 Sb 207 : A New Branch on the Clathrate Family Tree

Abstract The compositional screening of K‐Zn‐Sb ternary system aided by machine learning, rapid exploratory synthesis using KH salt‐like precursor and in situ powder X‐ray diffraction yielded a novel clathrate type XI K 58 Zn 122 Sb 207 . This clathrate consists of a 3D Zn‐Sb framework hosting K + ions inside polyhedral cages, some of which are reminiscent of known clathrate types while others are unique to this structure type. The complex non‐centrosymmetric structure in the tetragonal space group was solved by means of single crystal X‐ray diffraction as a 6‐component twin due to pseudocubic symmetry and further confirmed by high‐resolution synchrotron powder X‐ray diffraction and state‐of‐the‐art scanning transmission electron microscopy. The electron‐precise composition of this clathrate yields narrow‐gap p ‐type semiconductor with extraordinarily low thermal conductivity due to displacement or “rattling” of K cations inside oversized cages and as well as to twinning, stacking faults and antiphase boundary defects.

Cox, Tori↗

Three-dimensional structure of buried heterointerfaces revealed by multislice ptychography

Here, we report on the three-dimensional (3D) structure determination of a twisted hexagonal boron nitride (h-BN) heterointerface from a single-view dataset using multislice ptychography. We identify the buried heterointerface between two twisted h-BN flakes with a lateral resolution of 0.57 Å and a depth resolution of 2.5 nm. The latter represents a significant improvement (∼2.7 times) over the aperture-limited depth resolution of incoherent imaging modes, such as annular-dark-field scanning transmission electron microscopy. This improvement is attributed to the diffraction signal extending beyond the aperture edge, with the depth resolution set by the curvature of the Ewald sphere. Future advancements in this approach could enhance the depth resolution to the subnanometer level and enable the identification of individual dopants, defects, and color centers in twisted heterointerfaces and other materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Detection of defects in atomic-resolution images of materials using cycle analysis

The automated detection of defects in high-angle annular dark-field Z-contrast (HAADF) scanning-transmission-electron microscopy (STEM) images has been a major challenge. Here, we report an approach for the automated detection and categorization of structural defects based on changes in the material’s local atomic geometry. The approach applies geometric graph theory to the already-found positions of atomic-column centers and is capable of detecting and categorizing any defect in thin diperiodic structures (i.e., “2D materials”) and a large subset of defects in thick diperiodic structures (i.e., 3D or bulk-like materials). Despite the somewhat limited applicability of the approach in detecting and categorizing defects in thicker bulk-like materials, it provides potentially informative insights into the presence of defects. The categorization of defects can be used to screen large quantities of data and to provide statistical data about the distribution of defects within a material. This methodology is applicable to atomic column locations extracted from any type of high-resolution image, but here we demonstrate it for HAADF STEM images.

36 MATERIALS SCIENCE↗

Atomic electron tomography in three and four dimensions

Atomic electron tomography (AET) has become a powerful tool for atomic-scale structural characterization in three and four dimensions. It provides the ability to correlate structures and properties of materials at the single-atom level. With recent advances in data acquisition methods, iterative three-dimensional (3D) reconstruction algorithms, and post-processing methods, AET can now determine 3D atomic coordinates and chemical species with sub-Angstrom precision, and reveal their atomic-scale time evolution during dynamical processes. In this work, we review the recent experimental and algorithmic developments of AET and highlight several groundbreaking experiments, which include pinpointing the 3D atom positions and chemical order/disorder in technologically relevant materials and capturing how atoms rearrange during early nucleation at four-dimensional atomic resolution.

30 DIRECT ENERGY CONVERSION↗

Thin-film TaAs: Developing a platform for Weyl semimetal devices

MX monopnictide compounds (M = Nb,Ta, X = As,P) are prototypical 3D Weyl semimetals (WSMs) that have been shown in bulk single crystal form to have potential for a wide variety of novel devices due to topologically protected band structures and high mobilities. However, very little is known about thin-film synthesis, which is essential to enable device applications. We synthesize TaAs(001) epilayers by molecular beam epitaxy on GaAs(001) and provide an experimental phase diagram illustrating conditions for single-phase, single-crystal-like growth. We investigate the relationship between nanoscale defects and electronic structure using angle-resolved photoemission spectroscopy, kelvin probe force microscopy, and transmission electron microscopy. Our results provide a roadmap and platform for developing 3D WSMs for device applications.

36 MATERIALS SCIENCE↗

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material’s detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure–function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials’ intrinsic atomic and near atomic-length scale. Finally, we conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular beam epitaxy and crystal structure of majority a -plane-oriented and substrate-strained Mn 3 Sn thin films grown directly on sapphire (0001)

The Kagome antiferromagnet Mn 3 Sn has garnered much attention due to the presence of exciting properties such as anomalous Hall and Nernst effects. This paper discusses the synthesis of crystalline Mn 3 Sn thin films, prepared on Al 2 O 3 (0001) substrates at 453 ± 5°C using molecular beam epitaxy. The growth is monitored in situ using reflection high energy electron diffraction and measured ex situ using x-ray diffraction, Rutherford back-scattering, and cross-sectional scanning transmission electron microscopy. Our analysis shows the in-plane lattice constants of a 1,M = 4.117 ± 0.027 Å and a 2,M = 4.943 ± 0.033 Å, which is a very unexpected result when compared to the bulk a-plane Mn 3 Sn. This indicates a strain in the film and makes it challenging to provide a straightforward explanation. In an effort to explain our results, we discuss two possible orientation relationships between the Mn 3 Sn films and the sapphire substrates. Samples prepared under these conditions appear to have smooth surfaces locally, but overall the film has a 3D island morphology. First-principles calculations provide atomic models of the Mn 3 Sn (112¯0) lattice on Al 2 O 3 (0001) high symmetry sites, indicating that the L3-R90° is the most stable configuration. A detailed discussion of the experimental data and theoretical results, as well as strain effects, is provided.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evidence of hexagonal germanium grains on annealed monolayer MoS 2

Growing three-dimensional (3D) materials on two-dimensional (2D) van der Waals surface has shown its effectiveness in overcoming materials incompatibility for stacking transferrable membranes toward advanced device manufacturing. Herein, we demonstrate that the nucleation of hexagonal germanium (Ge) grains within a continuous crystalline film, which has been unfeasible through traditional epitaxy techniques, is realized by chemical vapor deposition on top of n-type monolayer molybdenum disulfide (MoS 2 ) substrates. Suggested by quantum molecular dynamics calculation, the hexagonal Ge nucleation is thermodynamically preferable to cubic Ge when growing on monolayer MoS 2 with sulfur vacancies. The strained hexagonal Ge grains have been confirmed by transmission electron microscopy analyses from both real space and reciprocal space. Scanning probe microscopy shows that the hexagonal Ge film possesses higher reflectivity in infrared spectral range, implying a higher carrier concentration resulted from the narrower band gap, as compared to cubic Ge.

36 MATERIALS SCIENCE↗

Three-Dimensional Ultrastructure of Arabidopsis Cotyledons Infected with Colletotrichum higginsianum

We used serial block-face scanning electron microscopy (SBF-SEM) to study the host–pathogen interface between Arabidopsis cotyledons and the hemibiotrophic fungus Colletotrichum higginsianum. By combining high-pressure freezing and freeze-substitution with SBF-SEM, followed by segmentation and reconstruction of the imaging volume using the freely accessible software IMOD, we created 3D models of the series of cytological events that occur during the Colletotrichum–Arabidopsis susceptible interaction. We found that the host cell membranes underwent massive expansion to accommodate the rapidly growing intracellular hypha. As the fungal infection proceeded from the biotrophic to the necrotrophic stage, the host cell membranes went through increasing levels of disintegration culminating in host cell death. Intriguingly, we documented autophagosomes in proximity to biotrophic hyphae using transmission electron microscopy (TEM) and a concurrent increase in autophagic flux between early to mid/late biotrophic phase of the infection process. Occasionally, we observed osmiophilic bodies in the vicinity of biotrophic hyphae using TEM only and near necrotrophic hyphae under both TEM and SBF-SEM. Overall, we established a method for obtaining serial SBF-SEM images, each with a lateral ( x-y) pixel resolution of 10 nm and an axial ( z) resolution of 40 nm, that can be reconstructed into interactive 3D models using the IMOD. Application of this method to the Colletotrichum–Arabidopsis pathosystem allowed us to more fully understand the spatial arrangement and morphological architecture of the fungal hyphae after they penetrate epidermal cells of Arabidopsis cotyledons and the cytological changes the host cell undergoes as the infection progresses toward necrotrophy. [Formula: see text] Copyright © 2024 The Author(s). This is an open access article distributed under the CC BY 4.0 International license .

Biochemistry & Molecular Biology↗

Enhancing Oxygen Stability in Low-Cobalt Layered Oxide Cathode Materials by Three-Dimensional Targeted Doping

In this project, we propose to develop a new concept and a generic platform that can lead to the greatly enhanced stabilization of all high-energy cathode materials, and in particular high-nickel (Ni) and low-cobalt (Co) oxides. The new concept is a 3D doping technology that hierarchically combines surface and bulk doping. We will use surface doping to stabilize the surface of primary particles and also introduce dopants in the bulk to further enhance oxygen stability, conductivity, and structural stability in low-Co oxides under high voltage and deep discharging operating conditions. This new concept not only will deliver a low-cost, high-energy cathode but also will provide a generic method that can stabilize all high-energy cathodes. The proposed novel 3D doping approach is poised to resolve some longstanding challenges in fundamental doping effects on battery materials as well as to reduce Li-ion batteries’ cost and improve their safety, energy density, and lifetime. To tackle this problem, we have formed a highly complementary multi-university/national labs/industry team to enable a doping-central and systematic investigation of low-Co materials and create a knowledge base for many electrode materials to be used in advanced electric vehicles. The successful execution of the proposed project relies on five components that can be carried out by the complementary team members: (1) a theoretical investigation of the surface and bulk stabilizing dopants (Persson), (2) a precise synthesis of materials with targeted doping (Lin and Xin), (3) development of electrolytes for high-Ni low-Co oxides (Xu), (4) multi-scale characterization of the structures and their interfaces by scanning transmission electron microscopy (SEM) and synchrotron X-ray imaging and spectroscopy tools (Xin and Lin), and (5) pouch cell-level integration (Fan). The UCI-led project will enable a doping-central and systematic investigation of low-Co materials and create a knowledge base for many electrode materials to be used in advanced electric vehicles.

25 ENERGY STORAGE↗

Low-Cost, Efficient and Durable High Temperature Wireless Sensors by Direct Write Additive Manufacturing for Application in Fossil Energy Systems

In-situ monitoring of physical parameters in fossil energy (FE) systems is challenging because of their high operating temperatures and oxidizing environments. This research aims utilize Aerosol Jet (AJ) nanoparticle printing, an advanced additive manufacturing method, to fabricate high temperature sensors for FE applications. Sensor films were fabricated by the AJ printing method with an excellent control over film microstructure and properties, in addition to creating less waste. Printing of six different materials, namely, silver (Ag), nickel (Ni), nickel-chromium (NiCr) alloy, copper (Cu), copper-nickel (CuNi), and carbon nanotubes (CNTs) was carried out for their evaluation of as sensor films. The films were then characterized using impedance spectroscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), x-ray diffraction (XRD), and x-ray photoelectron spectroscopy (XPS). Film microstructure was correlated with the sensor electrical and mechanical behavior at different temperatures (24-500 °C) and frequencies (0.02 - 300 kHz). This knowledge was then used to fabricate, test, and characterize strain and temperature sensors for high temperature applications. The strain sensors were shown to have a very low thermal strain up to 500 °C and a 57% higher gauge factor compared to the commercially available counterparts. This enhance performance was attributed to the inherent porosity in the sensor films that allowed the films to exhibit a metamaterial-like behavior when deformed. The AJ printed temperature sensors were shown to have the highest Seebeck coefficient amongst all the film-based temperature sensors. In addition, fundamental aspects of crystal structure and phase transformations in Ba(Fe0.7Ta0.3)O3-δ (BFTO), a high temperature sensor material, was investigated along with 3D printed antennas that can transmit sensor signals at high temperatures. Two PhD students, one from first generation college-going underrepresented minority community (URM), two postdoctoral fellows, and several masters and undergraduate students were supported by this award. This work opens up the possibility of realizing low-cost high-performance sensor devices using advanced manufacturing techniques for high temperature FE applications.

20 FOSSIL-FUELED POWER PLANTS↗

Iridium Incorporation into MnO 2 for an Enhanced Electrocatalytic Oxygen Evolution Reaction

Here, we have investigated the structure and activity of electrocatalysts for the oxygen evolution reaction (OER) that had low loadings of Ir incorporated into the 2D layered MnO 2 , (birnessite, nominally δ-MnO 2 ) and the 3D MnO 2 (pyrolusite, β-MnO 2 ). The Ir-incorporated β-MnO 2 (Ir/β-MnO 2 ) electrocatalysts were prepared for the first time via a thermally induced phase transition of δ-MnO 2 containing 16-22 wt% Ir. This phase transition of δ-MnO 2 to β-MnO 2 was facilitated by the presence of Ir in the structure, as both Ir in IrO 2 and Mn in β-MnO 2 could adopt a thermodynamically favored rutile structure. Extended X-ray absorption fine structure (EXAFS) of Ir/β-MnO 2 showed that the catalyst consisted of Ir substituted into the crystalline β-MnO 2 lattice. 22 wt% Ir/β-MnO 2 (60 μg Ir cm $\ ^{-2}_{geo}$) exhibited an OER overpotential (η) of 337 mV, lower than the η for commercial IrO 2 . This η was constant for 6 h, at 10 mA cm $\ ^{-2}_{geo}$ in 0.5 M H 2 SO 4 . EXAFS, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and X-ray absorption near edge structure (XANES) showed that 22 wt% Ir/β-MnO 2 had a strained structure containing ~41% Mn 3+ , an OER active species, along with a modified Ir bond covalency consisting of both Ir-O-Ir and Ir-O-Mn.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Defect detection in atomic-resolution images via unsupervised learning with translational invariance

Abstract Crystallographic defects can now be routinely imaged at atomic resolution with aberration-corrected scanning transmission electron microscopy (STEM) at high speed, with the potential for vast volumes of data to be acquired in relatively short times or through autonomous experiments that can continue over very long periods. Automatic detection and classification of defects in the STEM images are needed in order to handle the data in an efficient way. However, like many other tasks related to object detection and identification in artificial intelligence, it is challenging to detect and identify defects from STEM images. Furthermore, it is difficult to deal with crystal structures that have many atoms and low symmetries. Previous methods used for defect detection and classification were based on supervised learning, which requires human-labeled data. In this work, we develop an approach for defect detection with unsupervised machine learning based on a one-class support vector machine (OCSVM). We introduce two schemes of image segmentation and data preprocessing, both of which involve taking the Patterson function of each segment as inputs. We demonstrate that this method can be applied to various defects, such as point and line defects in 2D materials and twin boundaries in 3D nanocrystals.

36 MATERIALS SCIENCE↗

Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy

Abstract One approach to three-dimensional structure determination using the wealth of scattering data in four-dimensional (4D) scanning transmission electron microscopy (STEM) is the parallax method proposed by Ophus et al. (2019. Advanced phase reconstruction methods enabled by 4D scanning transmission electron microscopy, Microsc Microanal25, 10–11), which determines the scattering matrix and uses it to synthesize a virtual depth-sectioning reconstruction of the sample structure. Drawing on an equivalence with a hypothetical confocal imaging mode, we derive contrast transfer and point spread functions for this parallax method applied to weakly scattering objects, showing them identical to earlier depth-sectioning STEM modes when only bright field signal is used, but that improved depth resolution is possible if dark field signal can be used. Through a simulation-based study of doped Si, we show that this depth resolution is preserved for thicker samples, explore the impact of shot noise on the parallax reconstructions, discuss challenges to making use of dark field signal, and identify cases where the interpretation of the parallax reconstruction breaks down.

3D imaging↗

Discovering invariant spatial features in electron energy loss spectroscopy images on the mesoscopic and atomic levels

Over the last two decades, Electron Energy Loss Spectroscopy (EELS) imaging with a scanning transmission electron microscope has emerged as a technique of choice for visualizing complex chemical, electronic, plasmonic, and phononic phenomena in complex materials and structures. The availability of the EELS data necessitates the development of methods to analyze multidimensional data sets with complex spatial and energy structures. Traditionally, the analysis of these data sets has been based on analysis of individual spectra, one at a time, whereas the spatial structure and correlations between individual spatial pixels containing the relevant information of the physics of underpinning processes have generally been ignored and analyzed only via the visualization as 2D maps. Here, we develop a machine learning-based approach and workflows for the analysis of spatial structures in 3D EELS data sets using a combination of dimensionality reduction and multichannel rotationally invariant variational autoencoders. This approach is illustrated for the analysis of both the plasmonic phenomena in a system of nanowires and in the core excitations in functional oxides using low loss and core-loss EELS, respectively. The code developed in this manuscript is open sourced and freely available and provided as a Jupyter notebook for the interested reader.

36 MATERIALS SCIENCE↗