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

Frances I Allen; Thomas C Pekin; Arun Persaud; Steven J Rozeveld; Gregory F Meyers; Jim Ciston; Colin Ophus; Andrew M Minor

doi:10.1017/S1431927621011946

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

Microsc Microanal. 2021 Aug;27(4):794-803. doi: 10.1017/S1431927621011946.

Authors

Frances I Allen^{1

2}, Thomas C Pekin^{1

2}, Arun Persaud³, Steven J Rozeveld⁴, Gregory F Meyers⁴, Jim Ciston², Colin Ophus², Andrew M Minor^{1

2}

Affiliations

¹ Department of Materials Science and Engineering, UC Berkeley, Berkeley, CA94720, USA.
² National Center for Electron Microscopy, Molecular Foundry, LBNL, Berkeley, CA94720, USA.
³ Accelerator Technology and Applied Physics Division, LBNL, Berkeley, CA94720, USA.
⁴ Core R&D - Analytical Sciences, The Dow Chemical Company, Midland, MI48674, USA.

PMID: 34169813
DOI: 10.1017/S1431927621011946

Abstract

High-throughput grain mapping with sub-nanometer spatial resolution is demonstrated using scanning nanobeam electron diffraction (also known as 4D scanning transmission electron microscopy, or 4D-STEM) combined with high-speed direct-electron detection. An electron probe size down to 0.5 nm in diameter is used and the sample investigated is a gold–palladium nanoparticle catalyst. Computational analysis of the 4D-STEM data sets is performed using a disk registration algorithm to identify the diffraction peaks followed by feature learning to map the individual grains. Two unsupervised feature learning techniques are compared: principal component analysis (PCA) and non-negative matrix factorization (NNMF). The characteristics of the PCA versus NNMF output are compared and the potential of the 4D-STEM approach for statistical analysis of grain orientations at high spatial resolution is discussed.

Keywords: 4D-STEM; NNMF; PCA; grain orientation mapping; scanning nanobeam electron diffraction.