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Register a new userThe Exit-Wave Power-Cepstrum Transform for Scanning Nanobeam Electron Diffraction: Robust Strain Mapping at Subnanometer Resolution and Subpicometer Precision
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Scanning nanobeam electron diffraction (NBED) with fast pixelated detectors is a valuable technique for rapid, spatially resolved mapping of lattice structure over a wide range of length scales. However, intensity variations caused by dynamical diffraction and sample mistilts can hinder the measurement of diffracted disk centers as necessary for quantification. Robust data processing techniques are needed to provide accurate and precise measurements for complex samples and non-ideal conditions. Here we present an approach to address these challenges using a transform, called the exit wave power cepstrum (EWPC), inspired by cepstral analysis in audio signal processing. The EWPC transforms NBED patterns into real-space patterns with sharp peaks corresponding to inter-atomic spacings. We describe a simple analytical model for interpretation of these patterns that cleanly decouples lattice information from the intensity variations in NBED patterns caused by tilt and thickness. By tracking the inter-atomic spacing peaks in EWPC patterns, strain mapping is demonstrated for two practical applications: mapping of ferroelectric domains in epitaxially strained PbTiO3 films and mapping of strain profiles in arbitrarily oriented core-shell Pt-Co nanoparticle fuel-cell catalysts. The EWPC transform enables lattice structure measurement at sub-pm precision and sub-nm resolution that is robust to small sample mistilts and random orientations.
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Strain engineering enables the direct modification of the atomic bonding and is currently an active area of research aimed at improving the electrocatalytic activity. However, directly measuring the lattice strain of individual catalyst nanoparticles is challenging, especially at the scale of a single unit cell. Here, we quantitatively map the strain present in rhodium@platinum (core@shell) nanocube electrocatalysts using conventional aberration-corrected scanning transmission electron microscopy (STEM) and the recently developed technique of 4D-STEM nanobeam electron diffraction. We demonstrate that 4D-STEM combined with data pre-conditioning allows for quantitative lattice strain mapping with sub-picometer precision without the influence of scan distortions. When combined with multivariate curve resolution, 4D-STEM allows us to distinguish the nanocube core from the shell and to quantify the unit cell size as a function of distance from the core-shell interface. Our results demonstrate that 4D-STEM has significant precision and accuracy advantages in strain metrology of catalyst materials compared to aberration-corrected STEM imaging and is beneficial for extracting information about the evolution of strain in catalyst nanoparticles.
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 degrees (0.16 mrad) for orientation mapping, sensitivity at 0.04% or less for strain mapping, and improvements in computational performance are demonstrated.
We use scanning tunneling microscopy (STM) to study charge density wave (CDW) states in the rare-earth di-telluride, CeTe$_{2}$. In contrast to previous experimental and first-principles studies of the rare-earth di-tellurides, our STM measurements surprisingly detect a unidirectional CDW with $textit{q}$ ~ 0.28 $textit{a}$*, which is very close to what is found in experimental measurements of the related rare-earth tri-tellurides. Furthermore, in the vicinity of an extended sub-surface defect, we find spatially-separated as well as spatially-coexisting unidirectional CDWs at the surface of CeTe$_{2}$. We quantify the nanoscale strain and its variations induced by this defect, and establish a correlation between local lattice strain and the locally-established CDW states. Our measurements probe the fundamental properties of a weakly-bound two-dimensional Te-sheet, which experimental and theoretical work has previously established as the fundamental component driving much of the essential physics in both the rare-earth di- and tri-telluride compounds.
2D materials offer an ideal platform to study the strain fields induced by individual atomic defects, yet challenges associated with radiation damage have so-far limited electron microscopy methods to probe these atomic-scale strain fields. Here, we demonstrate an approach to probe single-atom defects with sub-picometer precision in a monolayer 2D transition metal dichalcogenide, WSe$_{2-2x}$Te$_{2x}$. We utilize deep learning to mine large datasets of aberration-corrected scanning transmission electron microscopy images to locate and classify point defects. By combining hundreds of images of nominally identical defects, we generate high signal-to-noise class-averages which allow us to measure 2D atomic coordinates with up to 0.3 pm precision. Our methods reveal that Se vacancies introduce complex, oscillating strain fields in the WSe$_{2-2x}$Te$_{2x}$ lattice which cannot be explained by continuum elastic theory. These results indicate the potential impact of computer vision for the development of high-precision electron microscopy methods for beam-sensitive materials.
The full lattice strain tensor and lattice rotations induced by a dislocation in pure tungsten were mapped using high-resolution transmission Kikuchi diffraction (HR-TKD) in a SEM. The HR-TKD measurement agrees very well with a forward calculation using an elastically isotropic model of the dislocation and its Burgers vector. Our results demonstrate that the spatial and angular resolution of HR-TKD in SEM is sufficiently high to resolve the details of lattice distortions near individual dislocations. This capability opens a number of new interesting opportunities, for example determining the Burgers vector of an unknown dislocation in a fast and straightforward way.
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