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

TL;DR

This paper demonstrates high-throughput, sub-nanometer resolution grain mapping using 4D-STEM combined with PCA and NNMF for grain classification, enabling detailed analysis of nanoparticle catalysts.

Contribution

It introduces a fast 4D-STEM method with advanced computational analysis using PCA and NNMF for high-resolution grain mapping.

Findings

PCA and NNMF effectively classify grains in 4D-STEM data.

The method achieves sub-nanometer spatial resolution.

Potential for statistical analysis of grain orientations is discussed.

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 implemented 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.