Determining the full five-parameter grain boundary characteristics from experiments is essential for understanding grain boundaries impact on material properties, improving related models, and designing advanced alloys. However, achieving this is generally challenging, in particular at nanoscale, due to their 3D nature. In our study, we successfully determined the grain boundary characteristics of an annealed nickel-tungsten alloy (NiW) nanocrystalline needle-shaped specimen (tip) containing twins using Scanning Precession Electron Diffraction (SPED) Tomography. The presence of annealing twins in this face-centered cubic (fcc) material gives rise to common reflections in the SPED diffraction patterns, which challenges the reconstruction of orientation-specific virtual dark field (VDF) images required for tomographic reconstruction of the 3D grain shapes. To address this, an automated post-processing step identifies and deselects these shared reflections prior to the reconstruction of the VDF images. Combined with appropriate intensity normalization and projection alignment procedures, this approach enables high-fidelity 3D reconstruction of the individual grains contained in the needle-shaped sample volume. To probe the accuracy of the resulting boundary characteristics, the twin boundary surface normal directions were extracted from the 3D voxelated grain boundary map using a 3D Hough transform. For the sub-set of coherent Σ3 boundaries, the expected {111} grain boundary plane normals were obtained with an angular error of <3° for boundary sizes down to 400 nm². This work advances our ability to precisely characterize and understand the complex grain boundaries that govern material properties.
We describe a method for identifying and clustering diffraction vectors in four-dimensional (4-D) scanning transmission electron microscopy data to determine characteristic diffraction patterns from overlapping structures in projection. First, the data is convolved with a 4-D kernel, then diffraction vectors are identified and clustered using both density-based clustering and a metric that emphasizes rotational symmetries. The method works well for both crystalline and amorphous samples and in high- and low-dose experiments. A simulated dataset of overlapping aluminum nanocrystals provides performance metrics as a function of Poisson noise and the number of overlapping structures. Experimental data from an aluminum nanocrystal sample shows similar performance. For an amorphous Pd77.5Cu6Si16.5 thin film, experiments measuring glassy structure show strong evidence of 4- and 6-fold symmetry structures. A significant background arises from the diffraction of overlapping structures. Quantifying this background helps to separate contributions from single, rotationally symmetric structures vs. apparent symmetries arising from overlapping structures in projection.
Differential Phase Contrast (DPC) imaging, in which deviations in the bright field beam are in proportion to the electric field, has been extensively studied in the context of pure elastic scattering. Here we discuss differential phase contrast formed from core-loss scattered electrons, i.e. those that have caused inner shell ionization of atoms in the specimen, using a transition potential approach for which we study the number of final states needed for a converged calculation. In the phase object approximation, we show formally that differential phase contrast formed from core-loss scattered electrons is mainly a result of preservation of elastic contrast. Through simulation we demonstrate that whether the inelastic DPC images show element selective contrast depends on the spatial range of the ionization interaction, and specifically that when the energy loss is low the delocalisation can lead to contributions to the contrast from atoms other than that ionized. We further show that inelastic DPC images remain robustly interpretable to larger thicknesses than is the case for elastic DPC images, owing to the incoherence of the inelastic wavefields, though subtleties due to channelling remain. Lastly, we show that while a very high dose will be needed for sufficient counting statistics to discern differential phase contrast from core-loss scattered electrons, there is some enhancement of the signal-to-noise ratio with thickness that makes inelastic DPC imaging more achievable for thicker samples.
An innovative software with a user-friendly interface for calculation of differential phase contrast (DPC) scanning transmission electron microscopy images (integrated iDPC- and differentiated dDPC-STEM) is presented. The underlying algorithm is described and the program functionalities are demonstrated on the examples of Li5OsO6, α-Ga2O3, and LiCoO2. The software supports interpretation of DPC-STEM images, which is crucial for qualitative and quantitative analysis of crystal structures and defects.
This study investigates the impact of the surface electric field on the quantification accuracy of boron (B) implanted silicon (Si) using atom probe tomography (APT). The Si Charge-State Ratio (CSR(Si) = Si2+/Si+) was used as an indirect measure of the average apex electric field during analysis. For a range of electric fields, the accuracy of the total implanted dose and the depth profile shape determined by APT was evaluated against the National Institute of Standards and Technology Standard Reference Material 2137. The radial (non-)uniformity of the detected B was also examined. At a higher surface electric field (i.e., a greater CSR(Si)), the determined B dose converges on the certified dose. Additionally, the depth profile shape tends towards that derived by secondary ion mass spectrometry. This improvement coincides with a more uniform radial B distribution, evidenced by desorption maps. In contrast, for lower surface electric fields (i.e., a lower CSR(Si)), the B dose is significantly underestimated, and the depth profile is artificially stretched. The desorption maps also indicate a highly inhomogeneous B emission localized around the center of the detector, which is believed to be an artifact of B surface migration on the tip of the sample. For the purposes of routine investigations of semiconductor devices using APT, these results illustrate the potential origin of quantification artifacts and their severity at different operating conditions, thus providing pathways towards best practices for accurate and repeatable measurements.
Genetic algorithm (GA) and particle swarm optimisation (PSO) techniques have been integrated with the differential algebra (DA) method in charged particle optics to optimise an Einzel lens. The DA method is a robust and efficient tool for the calculation of aberration coefficients of electrostatic lenses, which makes use of nonstandard analysis for ray tracing a particle as it is subjected to the field generated by a lens. In this study, initial populations of lenses with random geometrical configurations are generated. These initial populations are then subjected to GA and PSO algorithms to alter the geometry of each lens for a set number of iterations. The lens performance is evaluated by calculating the spot size using the aberrations coefficients up to third-order generated by the DA method. Moreover, a focusing column comprising two lenses and a Wien filter was optimised using GA method.
The convergent-beam low energy electron diffraction technique has been proposed as a novel method to gather local structural and electronic information from crystalline surfaces during low-energy electron microscopy. However, the approach suffers from high complexity of the resulting diffraction patterns. We show that Convolutional Autoencoders trained on CBLEED patterns achieve a highly structured latent space. The latent space is then used to estimate structural parameters with sub-angstrom accuracy. The low complexity of the neural networks enables real time application of the approach during experiments with low latency.
Nowadays, 3D Electron Diffraction (3DED) is widely used for the structure determination of sub-micron-sized particles. In this work, we investigate the influence of the acceleration voltage on the quality of 3DED datasets acquired on BaTiO3 nanoparticles. Datasets were acquired using a wide range of beam energies, from common, high acceleration voltages (300 kV and 200 kV) to medium (120 kV and 80 kV) and low acceleration voltages (60 kV and 30 kV). It was observed that, in the integration process, Rint increases as the beam energy is reduced, which is mainly due to the increased dynamical scattering. Nevertheless, the structure was solved successfully in all cases. The structure refinement was comparable for all beam energies with small deficiencies such as negative atomic displacements for the heaviest atom in the structure, barium. Including extinction correction in the refinement noticeably improved the model for low acceleration voltages, probably due to higher beam absorption in these cases. Dynamical refinement, however, shows superior results for higher acceleration voltages, since the dynamical refinement calculations currently ignore inelastic scattering effects.
The diffraction patterns of crystalline materials with local order contain sharp Bragg reflections as well as highly structured diffuse scattering. In this study, we quantitatively show how the diffuse scattering in three-dimensional electron diffraction (3D ED) data is influenced by various parameters, including the data acquisition mode, the detector type and the use of an energy filter. We found that diffuse scattering data used for quantitative analysis are preferably acquired in selected area electron diffraction (SAED) mode using a CCD and an energy filter. In this study, we also show that the diffuse scattering in 3D ED data can be obtained with a quality comparable to that from single-crystal X-ray diffraction. As electron diffraction requires much smaller crystal sizes than X-ray diffraction, this opens up the possibility to investigate the local structure of many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.