Abstract text (incl. figure legends and references)

The combination of Energy-Dispersive X-ray Spectroscopy (EDXS) and Scanning Transmission Electron Microscopy (STEM) is a rapid and robust technique for the chemical analysis of materials from microscale to nanoscale. However, suppose the sample is made of several phases that overlap in the thickness of the specimen. In that case, the technique cannot deliver an individual quantification of each phase but only an averaged composition. Many machine learning algorithms have therefore been explored to un-mix overlapping phases, among which the most promising is Non-negative Matrix Factorization (NMF) [1]. It considers that the mixture model between all individual components is linear, which applies well to EDXS in thin TEM specimens. Further, it constrains both the individual components and their weightings to be non-negative during computation, which is consistent with the physics of EDXS. Nevertheless, the effectiveness of NMF in un-mixing phases depends on the characters of the phases themselves and the signal-to-noise ratio (SNR) of the collected dataset. Under the circumstances that the concerned phases share some elements and the specimen is beam-sensitive, NMF would fail to achieve correct phase segmentation. In this paper, we seek to address this challenging case by appropriately adapting a clustering method [2] into the framework of NMF decomposition.

The sample examined is a deep Earth mantle mineral assemblage synthesized at 88 GPa and around 3000 K in a laser-heated diamond anvil cell. Figure 1(a) is the high-angle annular dark-field (HAADF) image, and Figure 1(b)-(d) are elemental maps of the assemblage. It consists of three mineral phases, Ferropericlase (i.e., a magnesium-enriched oxide), Calcium perovskite (i.e., a calcium-enriched silicate), and Bridgmanite (i.e., a magnesium-enriched silicate). Herein we name them Fp, CaPv, and Brg. The two precipitates are embedded in the matrix phase, Brg, and they overlap with each other. First, the standard NMF of scikit-learn [3] was applied, and its results are displayed in Figure 2(a)-(f). A minor phase, CaPv failed to be retrieved. The second component correctly captures the chemical features of Fp, while the first component contains much less Mg compared with the ground truth spectrum of Brg. The result is understandable since Mg is a common element shared by Brg and Fp, and the SNR of the dataset is at a low level. In contrast, the results of adapted NMF are shown in Figure 2(g)-(l). All the relevant three phases are correctly identified and segmented. Despite a few imperfections observed, the decomposed three components correctly represent phases' chemical features and their distributions.

Fig. 1. (a) The HAADF image of the mineral assemblage; (c) overlaid Mg Kα and Ca Kα elemental maps to reveal the distribution of Fp and CaPv; (b) and (d) elemental maps of Si Kα and O Kα.

Fig. 2. (a)-(c) The abundance maps, and (d)-(f) the spectra of the components of the standard NMF decomposition; (g)-(i) the abundance maps, and (j)-(l) the spectra of the components of the adapted NMF decomposition.

References:

[1] D. D. Lee, H. S. Seung, Nature 401 (6755) (1999)

[2] HW Zhang et al. International Conference on Image Processing, ICIP, 10 (2020)

[3] F Pedregosa et al. Journal of Machine Learning Research 12 (2011) 2825–2830.