Framework of compressive sensing and data compression for 4D-STEM.

Four-dimensional Scanning Transmission Electron Microscopy (4D-STEM) is a powerful technique for high-resolution and high-precision materials characterization at multiple length scales, including the characterization of beam-sensitive materials. However, the field of view of 4D-STEM is relatively small, which in absence of live processing is limited by the data size required for storage. Furthermore, the rectilinear scan approach currently employed in 4D-STEM places a resolution- and signal-dependent dose limit for the study of beam sensitive materials. Improving 4D-STEM data and dose efficiency, by keeping the data size manageable while limiting the amount of electron dose, is thus critical for broader applications. Here we introduce a general method for reconstructing 4D-STEM data with subsampling in both real and reciprocal spaces at high fidelity. The approach is first tested on the subsampled datasets created from a full 4D-STEM dataset, and then demonstrated experimentally using random scan in real-space. The same reconstruction algorithm can also be used for compression of 4D-STEM datasets, leading to a large reduction (100 times or more) in data size, while retaining the fine features of 4D-STEM imaging, for crystalline samples.

Formation and impact of nanoscopic oriented phase domains in electrochemical crystalline electrodes.

Electrochemical phase transformation in ion-insertion crystalline electrodes is accompanied by compositional and structural changes, including the microstructural development of oriented phase domains. Previous studies have identified prevailingly transformation heterogeneities associated with diffusion- or reaction-limited mechanisms. In comparison, transformation-induced domains and their microstructure resulting from the loss of symmetry elements remain unexplored, despite their general importance in alloys and ceramics. Here, we map the formation of oriented phase domains and the development of strain gradient quantitatively during the electrochemical ion-insertion process. A collocated four-dimensional scanning transmission electron microscopy and electron energy loss spectroscopy approach, coupled with data mining, enables the study. Results show that in our model system of cubic spinel MnO2 nanoparticles their phase transformation upon Mg2+ insertion leads to the formation of domains of similar chemical identity but different orientations at nanometre length scale, following the nucleation, growth and coalescence process. Electrolytes have a substantial impact on the transformation microstructure ('island' versus 'archipelago'). Further, large strain gradients build up from the development of phase domains across their boundaries with high impact on the chemical diffusion coefficient by a factor of ten or more. Our findings thus provide critical insights into the microstructure formation mechanism and its impact on the ion-insertion process, suggesting new rules of transformation structure control for energy storage materials.

The role of solid solutions in iron phosphate-based electrodes for selective electrochemical lithium extraction.

Electrochemical intercalation can enable lithium extraction from dilute water sources. However, during extraction, co-intercalation of lithium and sodium ions occurs, and the response of host materials to this process is not fully understood. This aspect limits the rational materials designs for improving lithium extraction. Here, to address this knowledge gap, we report one-dimensional (1D) olivine iron phosphate (FePO4) as a model host to investigate the co-intercalation behavior and demonstrate the control of lithium selectivity through intercalation kinetic manipulations. Via computational and experimental investigations, we show that lithium and sodium tend to phase separate in the host. Exploiting this mechanism, we increase the sodium-ion intercalation energy barrier by using partially filled 1D lithium channels via non-equilibrium solid-solution lithium seeding or remnant lithium in the solid-solution phases. The lithium selectivity enhancement after seeding shows a strong correlation with the fractions of solid-solution phases with high lithium content (i.e., LixFePO4 with 0.5 ≤ x < 1). Finally, we also demonstrate that the solid-solution formation pathway depends on the host material's particle morphology, size and defect content.

Data-driven electron microscopy: electron diffraction imaging of materials structural properties.

Transmission electron diffraction is a powerful and versatile structural probe for the characterization of a broad range of materials, from nanocrystalline thin films to single crystals. With recent developments in fast electron detectors and efficient computer algorithms, it now becomes possible to collect unprecedently large datasets of diffraction patterns (DPs) and process DPs to extract crystallographic information to form images or tomograms based on crystal structural properties, giving rise to data-driven electron microscopy. Critical to this kind of imaging is the type of crystallographic information being collected, which can be achieved with a judicious choice of electron diffraction techniques, and the efficiency and accuracy of DP processing, which requires the development of new algorithms. Here, we review recent progress made in data collection, new algorithms, and automated electron DP analysis. These progresses will be highlighted using application examples in materials research. Future opportunities based on smart sampling and machine learning are also discussed.

Cepstral scanning transmission electron microscopy imaging of severe lattice distortions.

The development of four-dimensional (4D) scanning transmission electron microscopy (STEM) using fast detectors has opened-up new avenues for addressing some of longstanding challenges in electron imaging. One of these challenges is how to image severely distorted crystal lattices, such as at a dislocation core. Here we develop a new 4D-STEM technique, called Cepstral STEM, for imaging disordered crystals using electron diffuse scattering. In contrast to analysis based on Bragg diffraction, which measures the average and periodic scattering potential, electron diffuse scattering can detect fluctuations caused by crystal disorder. Local fluctuations of diffuse scattering are captured by scanning electron nanodiffraction (SEND) using a coherent probe. The harmonic signals in electron diffuse scattering are detected through Cepstral analysis and used for imaging. By integrating Cepstral analysis with 4D-STEM, we demonstrate that information about the distortive part of electron scattering potential can be separated and imaged at nm spatial resolution. We apply the technique to the analysis of a dislocation core in SiGe and lattice distortions in a high entropy alloy.

Training artificial neural networks for precision orientation and strain mapping using 4D electron diffraction datasets.

Techniques for training artificial neural networks (ANNs) and convolutional neural networks (CNNs) using simulated dynamical electron diffraction patterns are described. The premise is based on the following facts. First, given a suitable crystal structure model and scattering potential, electron diffraction patterns can be simulated accurately using dynamical diffraction theory. Secondly, using simulated diffraction patterns as input, ANNs can be trained for the determination of crystal structural properties, such as crystal orientation and local strain. Further, by applying the trained ANNs to four-dimensional diffraction datasets (4D-DD) collected using the scanning electron nanodiffraction (SEND) or 4D scanning transmission electron microscopy (4D-STEM) techniques, the crystal structural properties can be mapped at high spatial resolution. Here, we demonstrate the ANN-enabled possibilities for the analysis of crystal orientation and strain at high precision and benchmark the performance of ANNs and CNNs by comparing with previous methods. A factor of thirty improvement in angular resolution at 0.009˚ (0.16 mrad) for orientation mapping, sensitivity at 0.04% or less for strain mapping, and improvements in computational performance are demonstrated.

Lattice strain mapping using circular Hough transform for electron diffraction disk detection.

Scanning Electron NanoDiffraction (SEND) is a powerful and versatile technique for lattice strain mapping in nano-devices and nano-materials. The measurement is based on Bragg diffraction from a local crystal volume. However, the resolution and precision of SEND are fundamentally limited by the uncertainty principle and scattering that govern electron diffraction. Here, we propose to measure lattice strain using a focused probe and circular Hough transform to locate the position of non-uniform diffraction disks. Methods for fitting a 2D lattice to the detected disks for strain calculation are described, including error analysis. We demonstrate our technique on a FinFET device for strain mapping at the spatial resolution of 1 nm and strain precision of ∼3×10-4. Using this and simulations, the experimental parameters involved in data acquisition and analysis are thoroughly investigated to construct an optimum strain mapping strategy using SEND.

Studies of x-ray localization and thickness dependence in atomic-scale elemental mapping by STEM energy-dispersive x-ray spectroscopy using single-frame scanning method.

The delocalization of x-ray signals limits the spatial resolution in atomic-scale elemental mapping by scanning transmission electron microscopy (STEM) using energy-dispersive x-ray spectroscopy (EDS). In this study, using a SrTiO3 [001] single crystal, we show that the x-ray localization to atomic columns is strongly dependent on crystal thickness, and a thin crystal is critical for improving the spatial resolution in atomic-scale EDS mapping. A single-frame scanning technique is used in this study instead of the multiple-frame technique to avoid peak broadening due to tracking error. The strong thickness dependence is realized by measuring the full width at half maxima (FWHM) as well as the peak-to-valley (P/V) ratio of the EDS profiles for Ti K and Sr K + L, obtained at several crystal thicknesses. A FWHM of about 0.16 nm and a P/V ratio of greater than 7.0 are obtained for Ti K for a crystal thickness of less than 20 nm. With increasing crystal thickness, the FWHM and P/V ratio increases and decreases, respectively, indicating the advantage of using a thin crystal for high-resolution EDS mapping.

Fast Atomic-Scale Elemental Mapping of Crystalline Materials by STEM Energy-Dispersive X-Ray Spectroscopy Achieved with Thin Specimens.

Elemental mapping at the atomic-scale by scanning transmission electron microscopy (STEM) using energy-dispersive X-ray spectroscopy (EDS) provides a powerful real-space approach to chemical characterization of crystal structures. However, applications of this powerful technique have been limited by inefficient X-ray emission and collection, which require long acquisition times. Recently, using a lattice-vector translation method, we have shown that rapid atomic-scale elemental mapping using STEM-EDS can be achieved. This method provides atomic-scale elemental maps averaged over crystal areas of ~few 10 nm2 with the acquisition time of ~2 s or less. Here we report the details of this method, and, in particular, investigate the experimental conditions necessary for achieving it. It shows, that in addition to usual conditions required for atomic-scale imaging, a thin specimen is essential for the technique to be successful. Phenomenological modeling shows that the localization of X-ray signals to atomic columns is a key reason. The effect of specimen thickness on the signal delocalization is studied by multislice image simulations. The results show that the X-ray localization can be achieved by choosing a thin specimen, and the thickness of less than about 22 nm is preferred for SrTiO3 in [001] projection for 200 keV electrons.