py4DSTEM: A Software Package for Four-Dimensional Scanning Transmission Electron Microscopy Data Analysis

Abstract

Abstract

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

“…Due to the file size of the large field of view data set (67 GB), these computations were performed using a workstation with two Intel Xenon Silver 4114 CPUs with 512 GB RAM. For the PCA algorithm, the computation time was 55 s, whereas for the NNMF algorithm, including the class merging sequence (16 merges), it was close to 44 h. In order to speed up the NNMF computation, the size of the input data set could be reduced by using more binning and/or by using thresholding to create a 2D probability distribution of all grains and then clustering the detected Bragg disks, for example, using Voronoi cells (Savitzky et al, 2021).…”

“…This results in significantly longer computation times, yet a key benefit of NNMF is that the algorithm prohibits negative values and thus yields directly interpretable results (Lee & Seung, 1999). To date, NNMF has been employed most widely by the astrophysics community but is gaining momentum in the (S)TEM field, having been demonstrated for electron energy-loss spectrum-imaging (Nicoletti et al, 2013; Ringe et al, 2015; Shiga et al, 2016), SPED (Eggeman et al, 2015; Sunde et al, 2018; Martineau et al, 2019), and most recently also for 4D-STEM (Savitzky et al, 2021; Uesugi et al, 2021). In this work, we compare PCA and NNMF in the context of grain mapping by 4D-STEM and discuss the characteristics and relative benefits of each classification approach.…”

Anisotropic point defects in rhenium diselenide monolayers

“…The CMOS camera for recording each convergent beam electron diffraction (CBED) has 2048×2048 pixels, which is cropped and binned to 192×192 pixels to reduce the size of the 4D dataset. The CBED bright field disk was centered and the rotation of CBED was corrected by changing the direction of the scanning axis using the shadow image approach( Savitzky et al., 2021 ). 4D-STEM simulations as well as STEM-HAADF image simulations were implemented on monolayer ReSe 2 crystal model containing three types of defects, i.e., V Se , O Se and S Se , using Dr. Probe software( Barthel, 2018 ).…”

Probing Multiscale Disorder in Pyrochlore and Related Complex Oxides in the Transmission Electron Microscope: A Review

“…These include virtual imaging, structure classification followed by crystalline/semi-crystalline orientation, phase and strain mapping, as well as analyses specific to amorphous materials such as SRO/MRO analysis with STEM-PDF/RDF, and STEM-FEM. 4D-STEM has not been widely applied to pyrochlores and fluorites, fortunately there is one detailed example of its application to a pyrochlore-structured Gd 2 Ti 2 O 7 (GTO) in the literature, used to illustrate the multimodal analysis of 4D datasets using the py4DSTEM software suite ( Savitzky et al, 2021 ). In this example, a GTO single-crystal was amorphized through an irradiation treatment, then partially recrystallized through annealing.…”

“…(B) In 4D STEM, an entire 2D CBED pattern is recorded at each probe position of a 2D-STEM raster, resulting in a (C) 4D dataset, Reproduced from ( Levin et al, 2020b ). (D) The experimental setup showing a pyrochlore-structured Gd 2 Ti 2 O 7 (GTO) sample that was irradiated and subsequently annealed showing gradient in structure from fully-ordered to amorphous ( Savitzky et al, 2021 ). (E) Examples of various types of measurements that can be made in post-processing from the 4D-STEM dataset acquired in (D) .…”