Four-dimensional Scanning Transmission Electron Microscopy Research Articles

High-speed 4-dimensional scanning transmission electron microscopy using compressive sensing techniques.

Here we show that compressive sensing allows 4-dimensional (4-D) STEM data to be obtained and accurately reconstructed with both high-speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4-D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal-to-noise ratio in the recovered phase using 0.3% of the totaldata. Lay abstract: Four-dimensional scanning transmission electron microscopy (4-D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2-dimensional signal is acquired at each 2-D probe location, equating to a 4-D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4-D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100-1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4-D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10-100 times. The acquired data is then processed to fill-in or inpaint the missing data, taking advantage of the inherently low-complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4-D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4-D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100-300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

4D-STEM Mapping of Nanocrystal Reaction Dynamics and Heterogeneity in a Graphene Liquid Cell.

Chemical reaction kinetics at the nanoscale are intertwined with heterogeneity in structure and composition. However, mapping such heterogeneity in a liquid environment is extremely challenging. Here we integrate graphene liquid cell (GLC) transmission electron microscopy and four-dimensional scanning transmission electron microscopy to image the etching dynamics of gold nanorods in the reaction media. Critical to our experiment is the small liquid thickness in a GLC that allows the collection of high-quality electron diffraction patterns at low dose conditions. Machine learning-based data-mining of the diffraction patterns maps the three-dimensional nanocrystal orientation, groups spatial domains of various species in the GLC, and identifies newly generated nanocrystallites during reaction, offering a comprehensive understanding on the reaction mechanism inside a nanoenvironment. This work opens opportunities in probing the interplay of structural properties such as phase and strain with solution-phase reaction dynamics, which is important for applications in catalysis, energy storage, and self-assembly.

Decoding Material Structures with Scanning Electron Diffraction Techniques

Recent advancements in electron detectors and computing power have revolutionized the rapid recording of millions of 2D diffraction patterns across a grid of probe positions, known as four-dimensional scanning transmission electron microscopy (4D-STEM). These datasets serve as the foundation for innovative STEM imaging techniques like integrated center of mass (iCOM) and symmetry STEM (S-STEM). This paper delves into the application of 4D-STEM datasets for diffraction analysis. We therefore use the term scanning electron diffraction (SED) instead of 4D-STEM in this review. We comprehensively explore groundbreaking diffraction methods based on SED, structured into two main segments: (i) utilizing an atomic-scale electron probe and (ii) employing a nanoscale electron probe. Achieving an atomic-scale electron probe necessitates a significant convergence angle (α > 30 mrad), leading to interference between direct and diffracted beams, distinguishing it from its nanoscale counterpart. Additionally, integrating machine learning approaches with SED experiments holds promise in various directions, as discussed in this review. Our aim is to equip materials scientists with valuable insights for characterizing atomic structures using cutting-edge SED techniques.

Direct Quantifying Charge Transfer by 4D-STEM: A Study on Perfect and Defective Hexagonal Boron Nitride.

Four-dimensional scanning transmission electron microscopy (4D-STEM) offers an attractive approach to simultaneously obtain precise structural determinations and capture details of local electric fields and charge densities. However, accurately extracting quantitative data at the atomic scale poses challenges, primarily due to probe propagation and size-related effects, which may even lead to misinterpretations of qualitative effects. In this study, we present a comprehensive analysis of electric fields and charge densities in both pristine and defective h-BN flakes. Through a combination of experiments and first-principle simulations, we demonstrate that while precise charge quantification at individual atomic sites is hindered by probe effects, 4D-STEM can directly measure charge transfer phenomena at the monolayer edge with sensitivity down to a few tenths of an electron and a spatial resolution on the order of a few angstroms.

Quantification of Hybrid Topological Spin Textures and Their Nanoscale Fluctuations in Ferrimagnets.

Noncolinear spin textures, including chiral stripes and skyrmions, have shown great potential in spintronics. Basic configurations of spin textures are either Bloch or Néel types, and the intermediate hybrid type has rarely been reported. A major challenge in identifying hybrid spin textures is to quantitatively determine the hybrid angle, especially in ferrimagnets with weak net magnetization. Here, we develop an approach to quantify magnetic parameters, including chirality, saturation magnetization, domain wall width, and hybrid angle with sub-5 nm spatial resolution, based on Lorentz four-dimensional scanning transmission electron microscopy (Lorentz 4D-STEM). We find strong nanometer-scale variations in the hybrid angle and domain wall width within structurally and chemically homogeneous FeGd ferrimagnetic films. These variations fluctuate during different magnetization circles, revealing intrinsic local magnetization inhomogeneities. Furthermore, hybrid skyrmions can also be nucleated in FeGd films. These analyses demonstrate that the Lorentz 4D-STEM is a quantitative tool for exploring complex spin textures.

Rejuvenation as the origin of planar defects in the CrCoNi medium entropy alloy

High or medium- entropy alloys (HEAs/MEAs) are multi-principal element alloys with equal atomic elemental composition, some of which have shown record-breaking mechanical performance. However, the link between short-range order (SRO) and the exceptional mechanical properties of these alloys has remained elusive. The local destruction of SRO by dislocation glide has been predicted to lead to a rejuvenated state with increased entropy and free energy, creating softer zones within the matrix and planar fault boundaries that enhance the ductility, but this has not been verified. Here, we integrate in situ nanomechanical testing with energy-filtered four-dimensional scanning transmission electron microscopy (4D-STEM) and directly observe the rejuvenation during cyclic mechanical loading in single crystal CrCoNi at room temperature. Surprisingly, stacking faults (SFs) and twin boundaries (TBs) are reversible in initial cycles but become irreversible after a thousand cycles, indicating SF energy reduction and rejuvenation. Molecular dynamics (MD) simulation further reveals that the local breakdown of SRO in the MEA triggers these SF reversibility changes. As a result, the deformation features in HEAs/MEAs remain planar and highly localized to the rejuvenated planes, leading to the superior damage tolerance characteristic in this class of alloys.

Four-Dimensional Scanning Transmission Electron Microscopy: Part II, Crystal Orientation and Phase, Short and Medium Range Order, and Electromagnetic Fields

Abstract Four-dimensional scanning transmission electron microscopy (4D-STEM) is a spatially resolved electron diffraction technique that records the electron scattering distribution at each point of the electron beam raster, thereby producing a four-dimensional dataset. This second installment of this series presents applications of 4D-STEM, including measurements of crystal orientation and phase, short- and medium-range order, and internal electromagnetic fields.

Valence-Ordered Thin-Film Nickelate with Tri-component Nickel Coordination Prepared by Topochemical Reduction.

The metal-hydride-based "topochemical reduction" process has produced several thermodynamically unstable phases across various transition metal oxide series with unusual crystal structures and nontrivial ground states. Here, by such an oxygen (de-)intercalation method we synthesis a samarium nickelate with ordered nickel valences associated with tri-component coordination configurations. This structure, with a formula of Sm9Ni9O22 as revealed by four-dimensional scanning transmission electron microscopy (4D-STEM), emerges from the intricate planes of {303}pc ordered apical oxygen vacancies. X-ray spectroscopy measurements and ab initio calculations show the coexistence of square planar, pyramidal, and octahedral Ni sites with mono-, bi-, and tri-valences. It leads to an intense orbital polarization, charge-ordering, and a ground state with a strong electron localization marked by the disappearance of ligand-hole configuration at low temperature. This nickelate compound provides another example of previously inaccessible materials enabled by topotactic transformations and presents an interesting platform where mixed Ni valence can give rise to exotic phenomena.

Rotational position error correction in ptychography.

Accurate determination of scan positions is essential for achieving high-quality reconstructions in ptychographic imaging. This study presents and demonstrates a method for determining the rotation angle of the scan pattern relative to the detector pixel array using diffraction data. The method is based on the Fourier-Mellin transform and cross-correlation calculation. It can correct rotation errors up to 60deg. High-quality reconstructions were obtained for visible light and electron microscopy datasets, and intricate structures of samples can be revealed. We believe that this refinement method for rotary position errors can be valuable for improving the performance of ptychographic four-dimensional scanning transmission electron microscopy.

Twisted epitaxy of gold nanodisks grown between twisted substrate layers of molybdenum disulfide.

We expand the concept of epitaxy to a regime of "twisted epitaxy" with the epilayer crystal orientation between two substrates influenced by their relative orientation. We annealed nanometer-thick gold (Au) nanoparticles between two substrates of exfoliated hexagonal molybdenum disulfide (MoS2) with varying orientation of their basal planes with a mutual twist angle ranging from 0° to 60°. Transmission electron microscopy studies show that Au aligns midway between the top and bottom MoS2 when the twist angle of the bilayer is small (<~7°). For larger twist angles, Au has only a small misorientation with the bottom MoS2 that varies approximately sinusoidally with twist angle of the bilayer MoS2. Four-dimensional scanning transmission electron microscopy analysis further reveals a periodic strain variation (<|±0.5%|) in the Au nanodisks associated with the twisted epitaxy, consistent with the Moiré registry of the two MoS2 twisted layers.

Direct observation of strong surface reconstruction in partially reduced nickelate films

The polarity of a surface can affect the electronic and structural properties of oxide thin films through electrostatic effects. Understanding the mechanism behind these effects requires knowledge of the atomic structure and electrostatic characteristics at the surface. In this study, we use annular bright-field imaging to investigate the surface structure of a Pr0.8Sr0.2NiO2+x (0 < x < 1) film. We observe a polar distortion coupled with octahedral rotations in a fully oxidized Pr0.8Sr0.2NiO3 sample, and a stronger polar distortion in a partially reduced sample. Its spatial depth extent is about three unit cells from the surface. Additionally, we use four-dimensional scanning transmission electron microscopy (4D-STEM) to directly image the local atomic electric field surrounding Ni atoms near the surface and discover distinct valence variations of Ni atoms, which are confirmed by atomic-resolution electron energy-loss spectroscopy (EELS). Our results suggest that the strong surface reconstruction in the reduced sample is closely related to the formation of oxygen vacancies from topochemical reduction. These findings provide insights into the understanding and evolution of surface polarity at the atomic level.

Local atomic stacking and symmetry in twisted graphene trilayers.

Moiré superlattices formed by twisting trilayers of graphene are a useful model for studying correlated electron behaviour and offer several advantages over their formative bilayer analogues, including a more diverse collection of correlated phases and more robust superconductivity. Spontaneous structural relaxation alters the behaviour of moiré superlattices considerably and has been suggested to play an important role in the relative stability of superconductivity in trilayers. Here we use an interferometric four-dimensional scanning transmission electron microscopy approach to directly probe the local graphene layer alignment over a wide range of trilayer graphene structures. Our results inform a thorough understanding of how reconstruction modulates the local lattice symmetries crucial for establishing correlated phases in twisted graphene trilayers, evincing a relaxed structure that is markedly different from that proposed previously.

Direct observation of charge density and electronic polarization in fluorite ferroelectrics by 4D-STEM

&lt;p&gt;The fluorite ferroelectrics is extremely promising for memory applications due to the silicon compatibility and the robust ferroelectricity with decreasing size. However, the direct observation of local electronic polarization remains elusive, thereby hindering the comprehension of the atomic-scale origin of ferroelectricity. Here, we directly map the real-space charge density of the ZrO&lt;sub&gt;2&lt;/sub&gt; nanocrystal in its polar, nonpolar, as well as interphase regions with sub-?ngstr?m resolution by four-dimensional scanning transmission electron microscopy (4D-STEM). Based on the variation of the electric dipole moments, we analyze the electronic contribution to the total spontaneous polarization, which reaches a maximum of 17.8%. In comparison to the continuous polarization in conventional ferroelectric units, the local polarization profile looks like a maple leaf edge at the tetragonal-orthorhombic phase interface, which suggests a gradual increase in the electronic polarization and the covalent nature of the Zr-O bond. We validate these findings with 4D-STEM simulations and calculations based on density functional theory. These findings provide atomic insights into the bonding nature and phase transition feature in fluorite oxides, and unravel the likely origin of ferroelectricity in ferroelectrics.&lt;/p&gt;

In-Plane Ferrielectric Order in van der Waals β'-In2Se3.

van der Waals ferroic materials exhibit rich potential for implementing future generation functional devices. Among these, layered β'-In2Se3 has fascinated researchers with its complex superlattice and domain structures. As opposed to ferroelectric α-In2Se3, the understanding of β'-In2Se3 ferroic properties remains unclear because ferroelectric, antiferroelectric, and ferroelastic characteristics have been separately reported in this material. To develop useful applications, it is necessary to understand the microscopic structural properties and their correlation with macroscopic device characteristics. Herein, using scanning transmission electron microscopy (STEM), we observed that the arrangement of dipoles deviates from the ideal double antiparallel antiferroelectric character due to competition between antiferroelectric and ferroelectric structural ordering. By virtue of second-harmonic generation, four-dimensional STEM, and in-plane piezoresponse force microscopy, the long-range inversion-breaking symmetry, uncompensated local polarization, and net polarization domains are unambiguously verified, revealing β'-In2Se3 as an in-plane ferrielectric layered material. Additionally, our device study reveals analogous resistive switching behaviors of different types owing to polarization switching, defect migration, and defect-induced charge trapping/detrapping processes.

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. 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.

Domain-dependent strain and stacking in two-dimensional van der Waals ferroelectrics

Van der Waals (vdW) ferroelectrics have attracted significant attention for their potential in next-generation nano-electronics. Two-dimensional (2D) group-IV monochalcogenides have emerged as a promising candidate due to their strong room temperature in-plane polarization down to a monolayer limit. However, their polarization is strongly coupled with the lattice strain and stacking orders, which impact their electronic properties. Here, we utilize four-dimensional scanning transmission electron microscopy (4D-STEM) to simultaneously probe the in-plane strain and out-of-plane stacking in vdW SnSe. Specifically, we observe large lattice strain up to 4% with a gradient across ~50 nm to compensate lattice mismatch at domain walls, mitigating defects initiation. Additionally, we discover the unusual ferroelectric-to-antiferroelectric domain walls stabilized by vdW force and may lead to anisotropic nonlinear optical responses. Our findings provide a comprehensive understanding of in-plane and out-of-plane structures affecting domain properties in vdW SnSe, laying the foundation for domain wall engineering in vdW ferroelectrics.

Large bi-axial tensile strain effect in epitaxial BiFeO3 film grown on single crystal PrScO3

A BiFeO3 film is grown epitaxially on a PrScO3 single crystal substrate which imparts ~ 1.45% of biaxial tensile strain to BiFeO3 resulting from lattice misfit. The biaxial tensile strain effect on BiFeO3 is investigated in terms of crystal structure, Poisson ratio, and ferroelectric domain structure. Lattice resolution scanning transmission electron microscopy, precession electron diffraction, and X-ray diffraction results clearly show that in-plane interplanar distance of BiFeO3 is the same as that of PrScO3 with no sign of misfit dislocations, indicating that the biaxial tensile strain caused by lattice mismatch between BiFeO3 and PrScO3 are stored as elastic energy within BiFeO3 film. Nano-beam electron diffraction patterns compared with structure factor calculation found that the BiFeO3 maintains rhombohedral symmetry, i.e., space group of R3c. The pattern analysis also revealed two crystallographically distinguishable domains. Their relations with ferroelectric domain structures in terms of size and spontaneous polarization orientations within the domains are further understood using four-dimensional scanning transmission electron microscopy technique.

Using Scanning Transmission Electron Microscopy (STEM) to Study Oxides and Future Outlook on 4D-STEM

Oxides can host a variety of physical properties including metallicity, ferroelectricity, piezoelectricity and superconductivity. As lattice structures or defects at nanoscale are responsible for exhibiting certain properties, scanning transmission electron microscopy becomes an important characterization tool for oxides. Here we first introduce what oxides are, and proceed to show several examples where microscopy can aid our understanding of oxides. Moreover, with the development of electron microscopy detectors, the concept of four-dimensional scanning transmission electron microscopy will be briefly introduced. Examples using this method and its future outlook will be discussed further.

(Invited) Understanding Strain and Deformation in 2D Materials Via 4D-STEM and Cryo-EM

Strain and deformations play a critical role in the mechanical, electrical, and chemical properties of two-dimensional (2D) materials due to their atomic thinness. This presentation will discuss using the state-of-the-art transmission electron microscopy (TEM) techniques to study the strain and deformations in 2D materials. First, the speaker will introduce the study of strain relaxation in epitaxial lateral heterojunctions of 2D transition metal dichalcogenides (TMD) using nano-beam four-dimensional scanning TEM (4D-STEM)1. By developing an unsupervised learning approach, we were able to accelerate and automate the method for more general users2. In addition, the speaker will also present the direct visualization of the floppiness of 2D DNA origami using cryo-EM. The work uncovers flexible arms in 2D cross tiles, as well as clusters and stacks, which may potentially affect the assembly of DNA origami3. Han, Y. et al. Strain Mapping of Two-Dimensional Heterostructures with Subpicometer Precision. Nano Letters 18, 3746–3751 (2018).Shi, C. et al. Uncovering material deformations via machine learning combined with four-dimensional scanning transmission electron microscopy. Npj Comput Mater 8, 114 (2022).Ni, H. et al. Direct visualization of floppy two-dimensional DNA origami using cryogenic electron microscopy. Iscience 25, 104373 (2022).

Measurement of Atomic Modulation Direction Using the Azimuthal Variation of First-Order Laue Zone Electron Diffraction.

We show that diffraction intensity into the first-order Laue zone (FOLZ) of a crystal can have a strong azimuthal dependence, where this FOLZ ring appears solely because of unidirectional atom position modulation. Such a modulation was already known to cause the appearance of elliptical columns in atom-resolution images, but we show that measurement of the angle via four-dimensional scanning transmission electron microscopy (4DSTEM) is far more reliable and allows the measurement of the modulation direction with a precision of about 1° and an accuracy of about 3°. This method could be very powerful in characterizing atomic structures in three dimensions by 4DSTEM, especially in cases where the structure is found only in nanoscale regions or crystals.