Accurate Calculation of CBED Patterns for 4D STEM Using Electron Densities Calculated by Density Functional Theory.
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Oxley, Mark P.↗
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Following the Electrons: Simulation for High-Resolution STEM and CBED
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Oxley, Mark↗
Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction
Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Electron Nanocrystallography of Complex Materials and Processes
The proposed work is to develop Scanning CBED (SCBED) for the study of multi element crystals, including multiple principal elements alloys or high entropy alloys and relaxor-ferroelectric crystals. SCBED works like scanning transmission electron microscopy (STEM) but records the whole CBED at each probe position. Since CBED is a highly sensitive electron diffraction technique, SCBED combines the full benefits of CBED and STEM. Specifically, the SCBED based approach enables a quantitative determination of local atomic and electronic structures. The proposed work is thus to take advantage of SCBED for the study of complex multi-element crystals. The results from SCBED are expected to complement the methods of electron energy loss spectroscopy (EELS) near edge fine structure for probing local bonds, and X-ray and neutron scattering using the total scattering approach for probing local structure. Under the DOE BES support, we have developed SCBED to determine the structure of high entropy alloys, and we have coupled the work with in-situ compression study of dislocation dynamics to uncover the fundamental mechanisms of crystal slip.
36 MATERIALS SCIENCE↗
Atomic resolution convergent beam electron diffraction analysis using convolutional neural networks
Two types of convolutional neural network (CNN) models, a discrete classification network and a continuous regression network, were trained to determine local sample thickness from convergent beam diffraction (CBED) patterns of SrTiO 3 collected in a scanning transmission electron microscope (STEM) at atomic column resolution. Acquisition of atomic resolution CBED patterns for this purpose requires careful balancing of CBED feature size in pixels, acquisition speed, and detector dynamic range. The training datasets were derived from multislice simulations, which must be convolved with incoherent source broadening. Sample thicknesses were also determined using quantitative high-angle annular dark-field (HAADF) STEM images acquired simultaneously. The regression CNN performed well on sample thinner than 35 nm, with 70% of the CNN results within 1 nm of HAADF thickness, and 1.0 nm overall root mean square error between the two measurements. The classification CNN was trained for a thicknesses up to 100 nm and yielded 66% of CNN results within one classification increment of 2 nm of HAADF thickness. Our approach depends on methods from computer vision including transfer learning and image augmentation.
36 MATERIALS SCIENCE↗
Large Angle Rocking Beam Electron Diffraction Utilizing Electron Direct Detector
Electron diffraction of a crystal is fundamentally a function of the potential of that crystal. The intensity of electron diffraction patterns is, as a result, sensitive to the charge density of atoms and bonding inside crystals. Experimentally, the traditional method to probe this information is quantitative Convergent Beam Electron Diffraction (CBED). Quantitative CBED or QCEBD is a method which uses dynamic diffraction theory to quantify CBED intensities and to extract information about crystal structure and bonding. The sensitivity of dynamical scattering is leveraged to measure crystal symmetry and crystal structure factors. At its limit, electron structure factors are measured at high accuracy allowing access to chemical bonding information, which corroborate theoretical calculations through multipole model refinements of the experimental charge density. The primary limit to QCBED is the requirement of a non-overlapping convergent beam. This subsequently limits QCBED to crystals with small unit cells which are stable under the focused probe.
Busch, Robert↗
Point group symmetry of cadmium arsenide thin films determined by convergent beam electron diffraction
Cadmium arsenide (Cd 3 As 2 ) is one of the first materials to be discovered to belong to the class of three-dimensional topological semimetals. Reported room-temperature crystal structures of Cd 3 As 2 differ subtly in the way the Cd vacancies are arranged within its antifluorite-derived structure, which determines if an inversion center is present and if Cd 3 As 2 is a Dirac or Weyl semimetal. Here, we apply convergent beam electron diffraction (CBED) to determine the point group of Cd 3 As 2 thin films grown by molecular-beam epitaxy. Using CBED patterns from multiple zone axes, high-angle annular dark-field images acquired in scanning transmission electron microscopy, and Bloch wave simulations, we show that Cd 3 As 2 belongs to the tetragonal 4/mmm point group, which is centrosymmetric. In conclusion, the results show that CBED can distinguish very subtle differences in the crystal structure of a topological semimetal, a capability that will be useful for designing materials and thin film heterostructures with topological states that depend on the presence of certain crystal symmetries.
36 MATERIALS SCIENCE↗
High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques
Abstract 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 total data. 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.
Robinson, Alex W.↗
Crystallographic analysis of lenticular martensite in Fe–1.0C–17Cr stainless steel by electron backscatter diffraction
The crystallography of lenticular martensite, which formed in coarse austenite grains (size about 80 μm) after subzero treatment at − 196 °C (liquid nitrogen) for different holding times, was investigated using electron backscatter diffraction (EBSD). For the sample treated with 15 min of isothermal holding, more than 50 martensite plates (with a thickness of larger than 1 μm) that formed within a coarse austenite grain were employed to obtain the pole figures. The pole figures clearly indicated that the individual plate of lenticular martensite approximately adopted the Kurdjumov–Sachs (K–S) orientation relationship with respect to the austenite matrix. For the sample treated with 30 s of isothermal holding, a few martensite plates that formed in variant pairings in a coarse austenite grain were analyzed. The results showed that zigzag couplings (including spear couplings), the major product of plate martensite, had an absolute dominance of a specific variant pair (V1/V17). The orientation gradient within a lenticular martensite plate was also measured using convergent beam electron diffraction (CBED). The evidence strongly suggests that the spread in diffracted intensity within pole figures is related to the misorientation gradient within the lenticular martensite plate. - Highlights: • The orientation relationship between lenticular martensite and austenite was investigated by pole figures via Electron Backscatter Diffraction (EBSD). • The initial stage of lenticular martensite formation was investigated, excluding interference from hard impingement. • In addition to EBSD, convergent beam electron diffraction (CBED) was used to measure the misorientation angle from the midrib to the untwinned region in lenticular martensite plate. • Zigzag couplings (including spear couplings), the major product of plate martensite, had an absolute dominance of a specific variant pair (V1/V17).
36 MATERIALS SCIENCE↗
Grains and Strains from Cepstral Analysis of 4D-STEM Nano-Diffraction Datasets
We report the availability of fast, high dynamic range pixel array detectors makes scanning convergent beam electron diffraction (CBED) a powerful tool for rapid, spatially resolved characterization of lattice structure over a wide range of length scales. However, to extract useful structural information from the large 4-dimensional datasets, especially for complex, 3D specimens, we must confront challenges with CBED intensity variations due to crystal mistilts and multiple scattering as well as challenges with precisely localizing diffracted disk centers.
36 MATERIALS SCIENCE↗
Valence Electron Distributions from Sub-Angstrom Convergent Beam Electron Diffraction
Modern aberration-corrected scanning transmission electron microscopes can acquire four-dimensional data sets (“4D STEM”) by recording convergent beam electron diffraction (CBED) patterns, using precisely positioned, sub-angstrom probes. Here, we demonstrate that these patterns can probe the site symmetry, atomic displacements, and valence electron distributions at individual atomic columns. To this end, 4D STEM CBED patterns were acquired from SrTiO 3 single crystals and compared with patterns calculated using scattering potentials derived from density functional theory. Here, we show that an aspherical valence electron charge build-up at the oxygen sites causes intensity asymmetries in the low-angle scattering portion of the patterns. Using strained SrTiO 3 films containing subtle polar displacements within nanometer-sized domains, it is shown that the high-angle scattering portion in each pattern is sensitive to atomic displacements.
36 MATERIALS SCIENCE↗
Symmetry determination on Pb-free piezoceramic 0.5Ba(Zr{sub 0.2}Ti{sub 0.8})O{sub 3}-0.5(Ba{sub 0.7}Ca{sub 0.3})TiO{sub 3} using convergent beam electron diffraction method
(1−x)(Ba(Zr{sub 0.2}Ti{sub 0.8})O{sub 3}-x(Ba{sub 0.7}Ca{sub 0.3})TiO{sub 3} (BZT-xBCT) Pb-free piezoceramic has been reported showing ultrahigh piezoelectric performance in its morphotropic phase boundary (MPB) region. However, the crystal structure characteristic for the MPB composition of BZT-xBCT is still under debate—between single orthorhombic phase and tetragonal + rhombohedral two phase mixture. In the present study, we perform the local symmetry determination on the MPB composition x = 0.5 using convergent beam electron diffraction analysis (CBED). Our CBED results from multiple zone axes suggest that there are two coexisting phases with the point group symmetries of 4 mm (tetragonal) and 3 m (rhombohedral) respectively, which agree with two phase mixture model. The strong piezoelectricity can thus be understood by considering the polarization rotation between tetragonal and rhombohedral phases by external field.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Symmetry of piezoelectric (1–x)Pb(Mg 1/3 Nb 2/3 )O₃-xPbTiO₃ (x=0.31) single crystal at different length scales in the morphotropic phase boundary region
We use probes of three different length scales to examine symmetry of (1–x)Pb(Mg 1/3 Nb 2/3 )O₃-xPbTiO₃ (PMN-xPT) single crystals in the morphotropic phase boundary (MPB) region at composition x = 0.31 (PMN-31% PT). On the macroscopic scale, x-ray diffraction (XRD) shows a mixture of strong and weak diffraction peaks of different widths. The closest match to XRD peak data is made with monoclinic Pm (M C ) symmetry. On the local scale of a few nanometers, convergent beam electron diffraction (CBED) studies, with a 1.6-nm electron probe, reveal no obvious symmetry. These CBED experimental patterns can be approximately matched with simulations based on monoclinic symmetry, which suggests locally distorted monoclinic structure. A monoclinic Cm (M A or M B )-like symmetry could also be obtained from certain regions of the crystal by using a larger electron probe size of several tens of nanometers in diameter. Thus the monoclinic symmetry of single crystal PMN-31%PT is developed only in parts of the crystal by averaging over locally distorted structure on the scale of few tens of nanometers. The macroscopic symmetry observed by XRD is a result of averaging from the local structure in PMN-31%PT single crystal. The lack of local symmetry at a few nanometers scale suggests that the polarization switching results from a change in local displacements, which are not restricted to specific symmetry planes or directions.
Kim, Kyou-Hyun↗
Synchrotron X-ray powder diffraction and convergent beam electron diffraction studies on the cubic phase of MgV{sub 2}O{sub 4} spinel
The A V{sub 2}O{sub 4} (A=Mg{sup 2+}, Zn{sup 2+}, Cd{sup 2+}) spinels are three-dimensional spin-1 frustrated systems with orbital degree of freedom, which have been known to possess intriguing orbital states causing releases of spin frustration at low temperatures. We have performed synchrotron X-ray and convergent beam electron diffraction measurements for one of these vanadates, MgV{sub 2}O{sub 4} in order to clarify its crystal structure in the high temperature cubic phase, which is regarded as an important starting point for understanding the details of the low temperature phase. We have successfully observed that the [001] zone axis convergent beam electron diffraction pattern exhibits 4mm symmetry, suggesting the space group of Fd3{sup ¯}m in the cubic MgV{sub 2}O{sub 4}. It has also been demonstrated that the crystal structure of the cubic MgV{sub 2}O{sub 4} contains VO{sub 6} octahedra elongated along the threefold rotation axis. Based on our results, we discuss the orbital states of MgV{sub 2}O{sub 4} as well as the other spinel vanadates. - Graphical abstract: Precise geometry of the VO{sub 6} octahedra in the cubic phase of MgV{sub 2}O{sub 4} spinel determined with the synchrotron powder XRD data. - Highlights: • We examined the crystal structure of the cubic phase of MgV{sub 2}O{sub 4} spinel. • We prepared the single crystal and powdered sample of MgV{sub 2}O{sub 4} with high quality. • The result of the CBED measurement agrees with the space group of Fd3{sup ¯}m in the phase. • The cubic phase has VO{sub 6} octahedra elongated along the threefold rotation axis.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Synthesis and crystal structure characterization of InGaZnO{sub 4} with a new defect structure
Single crystals of InGaZnO{sub 4} were synthesized in a sealed Pt-tube at elevated temperatures under normal pressure without flux. InGaZnO{sub 4} has a trigonal crystal system (R3{sup ¯}m; No. 166) deduced from convergent beam electron diffraction (CBED). Single crystal structure refinement from XRD data at −150 °C (a=3.275(1) Å; c=25.99(1) Å; Z=3) revealed an alternate stacking of InO{sub 6/3}{sup −} and (Ga,Zn)O{sub 4/4}{sup +} layers, iso-structural to YbFe{sub 2}O{sub 4}. The cell parameters at room temperature were refined from powder X-ray diffraction data (a=3.284(3) Å and c=26.037(3) Å). The transparent crystals have a gray-bluish color and exhibit an excess of Ga expressed by the cation ratio of In:Ga:Zn=30.2(9):39(1):31(1) determined by energy dispersive X-ray spectroscopy (EDXS). While the isovalent substitution of In{sup 3+} by Ga{sup 3+} is known, an additional aliovalent substitution of Zn{sup 2+} by Ga{sup 3+} is observed. This results in the formula (In{sub 0.9}Ga{sub 0.1})Ga{sub 1.06}Zn{sub 0.91}□{sub 0.03}O{sub 4} where 3% of the cations in 4+1 coordination are vacant due to aliovalent substitution. Further evidence of that defect structure is found in the lattice parameter a which is substantially smaller than in stoichiometric InGaZnO{sub 4}, as well as in the strong absorption in the near-IR from transitions correlated with the defect structure. The bluish color of the crystals is due to an enhanced absorption in the red of the visible spectrum. For the first time, we achieved to image InGaZnO{sub 4} at atomic resolution in the electron microscope proving a perfect periodic stacking of atomic layers. - Graphical abstract: Single crystals of InGaZnO{sub 4} have been synthesized at ambient pressure and analyzed with X-ray diffraction, electron microscopy, and optical absorption. Optical band gap and optical transmission have been determined. - Highlights: • Preparation of single crystals of InGaO{sub 3}(ZnO){sub 1} at ambient pressure for the first time. • Non-stoichiometric compound (In{sub 0.9}Ga{sub 0.1})Ga{sub 1.06}Zn{sub 0.91}□{sub 0.03}O{sub 4} with defect structure, excess of Ga, depletion of Zn. • Real structure of InGaO{sub 3}(ZnO){sub 1} imaged by high resolution TEM for the first time. • Optical band gap and transmission of InGaO{sub 3}(ZnO){sub 1} single crystal.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quantitative measurement for the microstructural parameters of nano-precipitates in Al-Mg-Si-Cu alloys
Size, number density and volume fraction of nano-precipitates are important microstructural parameters controlling the strengthening of materials. In this work a widely accessible, convenient, moderately time efficient method with acceptable accuracy and precision has been provided for measurement of volume fraction of nano-precipitates in crystalline materials. The method is based on the traditional but highly accurate technique of measuring foil thickness via convergent beam electron diffraction. A new equation is proposed and verified with the aid of 3-dimensional atom probe (3DAP) analysis, to compensate for the additional error resulted from the hardly distinguishable contrast of too short incomplete precipitates cut by the foil surface. The method can be performed on a regular foil specimen with a modern LaB{sub 6} or field-emission-gun transmission electron microscope. Precisions around ± 16% have been obtained for precipitate volume fractions of needle-like β″/C and Q precipitates in an aged Al-Mg-Si-Cu alloy. The measured number density is close to that directly obtained using 3DAP analysis by a misfit of 4.5%, and the estimated precision for number density measurement is about ± 11%. The limitations of the method are also discussed. - Highlights: •A facile method for measuring volume fraction of nano-precipitates based on CBED •An equation to compensate for small invisible precipitates, with 3DAP verification •Precisions around ± 16% for volume fraction and ± 11% for number density.
36 MATERIALS SCIENCE↗
Practical aspects of diffractive imaging using an atomic-scale coherent electron probe
Four-dimensional scanning transmission electron microscopy (4D-STEM) is a technique where a full two-dimensional convergent beam electron diffraction (CBED) pattern is acquired at every STEM pixel scanned. Capturing the full diffraction pattern provides a rich dataset that potentially contains more information about the specimen than is contained in conventional imaging modes using conventional integrating detectors. In this work, using 4D datasets in STEM from two specimens, monolayer MoS 2 and bulk SrTiO 3 , we demonstrate multiple STEM imaging modes on a quantitative absolute intensity scale, including phase reconstruction of the transmission function via differential phase contrast imaging. Finally, practical issues about sampling (i.e. number of detector pixels), signal-to-noise enhancement and data reduction of large 4D-STEM datasets are emphasized.
36 MATERIALS SCIENCE↗
High throughput crystal structure and composition mapping of crystalline nanoprecipitates in alloys by transmission Kikuchi diffraction and analytical electron microscopy
Statistically significant crystal structure and composition identification of nanocrystalline features such as nanoparticles/nanoprecipitates in materials chemistry and alloy designing using electron microscopy remains a grand challenge. In this paper, we reveal that differing crystallographic phases of nanoprecipitates in alloys can be mapped with unprecedented statistics using transmission Kikuchi diffraction (TKD), on typical carbon-based electron-transparent samples. Using a case of multiphase, multicomponent nanoprecipitates extracted from an improved version of 9% chromium Eurofer-97 reduced-activation ferritic-martensitic steel we show that TKD successfully identified more than thousand M 23 C 6 , MX, M 7 C 3 , and M 2 X ( M =Fe, Cr, W, V, Ta; X = C, N) nanoprecipitates in a single scan, something that is currently unachievable using a transmission electron microscope (TEM) without incorporating a precision electron diffraction (PED) system. Precipitates as small as ~20–25 nm were successfully phase identified by TKD. We verified the TKD phase identification using high-resolution transmission electron microscopy (HRTEM) and convergent beam electron diffraction (CBED) pattern analysis of a few precipitates that were identified by TKD on same sample. TKD study was combined with state-of-art analytical scanning transmission electron microscopy (STEM)-energy dispersive X-ray (EDX) spectroscopy and multivariate statistical analysis (MVSA) which provided the complete crystal structure and distinct chemistries of the precipitates in the steel in a high throughput automated way. This technique should be applicable to characterizing any multiphase crystalline nanoparticles or nanomaterials. Furthermore the results highlight that combining phase identification by TKD with analytical STEM and modern data analytics may open new pathways in big data material characterization at nanoscale that may be highly beneficial for characterizing existing materials and in designing new materials.
36 MATERIALS SCIENCE↗