Statistical Evaluation of the Solid-Solution State in Ternary Nanoalloys

Quantitative evaluation of the alloying state in nanoalloy systems is key to understanding their functional properties in a diverse range of applications spanning from catalysis and plasmonics to biomedicine and so forth. Here, we develop a method to statistically and visually represent the sub-nanometer local compositional distribution in ternary nanoparticles (NPs) in terms of ternary histograms and kernel density estimation analysis. Further descriptive statistics is performed within the mathematical framework of compositional data analysis to account for the constant-sum constraint and positivity inherent to the nature of compositional data. The approach has been demonstrated on several conceptual particle models and real systems, namely, Pd-Rh-Ru and Ag-Au-Pd NPs, utilizing experimental X-ray energy-dispersive spectroscopy (XEDS) maps acquired from a scanning transmission electron microscope. We regard this as a useful tool for extending to other well-known configurations such as uniformly mixed solid solutions, core-shell, or phase-decomposed clusters often encountered in other nanoalloy systems. Proposed solutions to overcome common problems associated with NPs such as low X-ray counting and XEDS spectral overlapping are also presented and discussed.