Scientific instruments for material characterization have recently been improved to yield big data. For instance, scanning transmission electron microscopy (STEM) allows us to acquire many diffraction patterns from a scanning area, which is referred to as four-dimensional (4D) STEM. Here we study a combination of 4D-STEM and a statistical technique called non-negative matrix factorization (NMF) to deduce sparse diffraction patterns from a 4D-STEM data consisting of 10,000 diffraction patterns. Titanium oxide nanosheets are analyzed using this combined technique, and we discriminate the two diffraction patterns from pristine TiO2 and reduced Ti2O3 areas, where the latter is due to topotactic reduction induced by electron irradiation. The combination of NMF and 4D-STEM is expected to become a standard characterization technique for a wide range materials.

中文翻译：

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四维扫描透射电子显微镜大数据挖掘的非负矩阵分解

最近改进了用于材料表征的科学仪器以产生大数据。例如，扫描透射电子显微镜 (STEM) 允许我们从扫描区域获取许多衍射图案，这被称为四维 (4D) STEM。在这里，我们研究了 4D-STEM 和称为非负矩阵分解 (NMF) 的统计技术的组合，以从由 10,000 个衍射图案组成的 4D-STEM 数据推断稀疏衍射图案。使用这种组合技术分析氧化钛纳米片，我们区分原始 TiO2 和还原 Ti2O3 区域的两个衍射图，其中后者是由于电子辐射引起的拓扑还原。