Fast Grain Mapping with Sub-Nanometer Resolution Using 4D-STEM with Grain Classification by Principal Component Analysis and Non-Negative Matrix Factorization

Abstract

Abstract

Machine learning in electron microscopy for advanced nanocharacterization: current developments, available tools and future outlook

“…Its recent success unveils unsupervised techniques as a standard for the processing of high-dimensional datasets, resembling the multimodal crystal phase mapping we described for regular STEM. [130][131][132][133][134][135] Indeed, the mapping of crystal phases and their relative rotations was tested with success in complex oxide systems (e.g., Ti 0.87 O 2 vs. Ti 2 O 3 ) and in dichalcogenide multilayers, such as MoS 2 bilayers. 100,136 Supervised ML has also been proven beneficial for 4D-STEM, as regarded in ptychography.…”

Analysis of Interpretable Data Representations for 4D-STEM Using Unsupervised Learning

“…Advances in feature representations for 4D-STEM pattern classification have been primarily limited to Bragg disks (BD) (Meng & Zuo, 2017; Pekin et al, 2017; Zeltmann et al, 2020). Recently, principal component analysis (PCA) and NMF were applied to cluster BD from polycrystalline gold nanoparticles into feature sets (Allen et al, 2021). In this work, it was shown that while both NMF and PCA have the ability to reasonably discern grains within nanoparticles, only NMF was able to output results that were directly interpretable as specific orientations due to the non-negativity constraint (Allen et al, 2021).…”

“…Recently, principal component analysis (PCA) and NMF were applied to cluster BD from polycrystalline gold nanoparticles into feature sets (Allen et al, 2021). In this work, it was shown that while both NMF and PCA have the ability to reasonably discern grains within nanoparticles, only NMF was able to output results that were directly interpretable as specific orientations due to the non-negativity constraint (Allen et al, 2021). This aligns with work in image analysis fields comparing NMF and PCA, where the sparse solution provided by NMF is more readily interpretable than the holistic output that PCA typically provides due to the presence of both additive and subtractive combinations (Lee and Seung, 1999; Guillamet et al, 2002).…”

“…This work addresses this knowledge gap by evaluating three engineered feature representations for CBED patterns within 4D-STEM datasets using the NMF approach described in prior work (Allen et al, 2021). The BD representation was analyzed due to the widespread interest and development of methods to precisely extract this feature from 4D-STEM data (Pekin et al, 2017; Han et al, 2018; Mukherjee et al, 2020; Zeltmann et al, 2020; Allen et al, 2021; Kacher et al, 2021; Yang et al, 2021). However, recovering information that is lost during the BD detection can provide an avenue for improved classification, especially for regions of a sample that may not have strong Bragg scattering.…”

High Resolution Powder Electron Diffraction in Scanning Electron Microscopy

“…More precisely, we use the individual NBD patterns just for the summation that yields the final PNBD pattern, while ignoring the specific positions and intensities of diffraction spots at each sample location. As the diffraction spots carry the information about the structure and orientation of the investigated material at a given location, the 4D-STEM/PNBD method cannot solve some special problems that are typically addressed by 4D-STEM-in-TEM methods, such as the visualization of different materials in the nanoscale (virtual imaging [28]), the identification of individual phases (structural classification [29]), the analysis of orientation of the individual nanocrystals (orientation mapping [30]), the analysis of strains of the individual nanocrystals (strain mapping [31]) and the enhancement of resolution and/or contrast of the micrographs by means of some advanced techniques (differential phase contrast or ptychography [32]). This is the price paid for the 4D-STEM/PNBD straightforwardness and simplicity.…”