Multivariate statistics applications in phase analysis of STEM-EDS spectrum images

Abstract

Spectrum imaging (SI) methods are displacing traditional spot analyses as the predominant paradigm for spectroscopic analysis with electron beam instrumentation. The multivariate nature of SI provides clear advantages for qualitative analysis of multiphase specimens relative to traditional gray-scale images acquired with non-spectroscopic signals, where different phases with similar average atomic number may exhibit the same intensity. However, with the improvement in qualitative analysis with the SI paradigm has come a decline in the quantitative analysis of the phases thus identified, since the spectra from individual pixels typically have insufficient counting statistics for proper quantification. The present paper outlines a methodology for quantitative analysis within the spectral imaging paradigm, which is illustrated through X-ray energy-dispersive spectroscopy (EDS) of a multiphase (Pb,La)(Zr,Ti)O(3) ceramic in scanning transmission electron microscopy (STEM). Statistical analysis of STEM-EDS SI is shown to identify the number of distinct phases in the analyzed specimen and to provide better segmentation than the STEM high-angle annular dark-field (HAADF) signal. Representative spectra for the identified phases are extracted from the segmented images with and without exclusion of pixels that exhibit spectral contributions from multiple phases, and subsequently quantified using Cliff-Lorimer sensitivity factors. The phase compositions extracted with the method while excluding pixels from multiple phases are found to be in good agreement with those extracted from user-selected regions of interest, while providing improved confidence intervals. Without exclusion of multiphase pixels, the extracted composition is found to be in poor statistical agreement with the other results because of systematic errors arising from the cross-phase spectral contamination. The proposed method allows quantification to be performed in the presence of discontinuous phase distributions and overlapping phases, challenges that are typical of many nanoscale analyses performed by STEM-EDS.