Statistical Evaluation of the Solid-Solution State in Ternary Nanoalloys

Abstract

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.

Highly Stable and Active Solid‐Solution‐Alloy Three‐Way Catalyst by Utilizing Configurational‐Entropy Effect

“…In contrast, PdRuM catalysts that experienced degradation of the catalytic activity in the second cycle (M = Ag or Au) showed serious phase segregation into PdM and Ru even after the 2nd cycle because Ag and Au are miscible with Pd but immiscible with Ru [18,19] (Figure S12, Supporting Information). Furthermore, we performed additional characterization to verify the possible coordination environment in the most important sample, PdRuIr, by statistical analysis and Gibbs triangle representation of EDX mapping data [20] (Figures S13-S16 and Table S4, Supporting Information). The three Gibbs triangle representations of local composition distributions of PdRuIr (as-prepared, after 1st cycle, and 20th cycles) show the structural change that the three elements mix more homogeneously as TWC test cycle increases.…”

Quantitative Characterization of the Thermally Driven Alloying State in Ternary Ir–Pd–Ru Nanoparticles

“…Although the XEDS elemental maps in Figure c may qualitatively suggest the solid solution homogeneity of the nanoalloy to some extent, a quantitative description of such a nanoalloying state is highly desirable for better understanding of the controlled synthesis parameters as well as the relationship between nanoalloy composition and catalytic property under relevant operating conditions. As demonstrated in our recent study, the original XEDS maps for a relatively large group of particles can be graphically translated into a Gibbs composition triangle representation, as shown in Figure d, which statistically exhibits the local compositional variation at the sub-nanometer scale. Here the compositional data set for the ternary Ir–Pd–Ru nanoalloy (C Ir , C Pd , C Ru ) was statistically sampled from each 2D pixel (0.7 × 0.7 × l nm 3 , l is the height of a pixel column) of the XEDS maps (see Supplementary Figures S2 and S3 for the process workflow).…”

“…29 In this approach, the original composition data set (C Ir , C Pd , C Ru ) as acquired from XEDS maps was transformed using a log-ratio technique, which effectively removes the sum constraint inherent to the nature of compositional data. 25 As a result, a compositional distribution profile can be statistically described using the closed geometric mean or center g ̅ as a measure of central tendency and the centered log-ratio standard deviation (clr-SD) for compositional dispersion. The mathematical descriptions of these metrics can be found in the Materials and Methods section (Compositional Data Analysis).…”

“…16−18 To convince skeptic readers about the validity of our statistical approach, we also provided a comparison between the correlation analysis results obtained using CDA and classical statistics in Supplementary Figure S11 and Table S3, while a more comprehensive description can be found in our previous work. 25 Tracking the Local Compositional Change for Groups of NPs. Interrupted in situ heating was then applied in vacuum (∼10 −5 Pa) under two different conditions: (i) isothermal holding for 30 min at selected temperatures, i.e., RT, 300, 500, and 700 °C (Figure 2a); (ii) prolonged heating at 500 °C up to 7 h in total (Figure 2b).…”

“…%, with a focus on the local compositional evolution and related structural aspects, utilizing temperature-controlled scanning transmission electron microscopy (STEM). The use of the Gibbs composition triangles and compositional data analysis (CDA) scheme developed previously 25 allows us to better represent and statistically evaluate the alloying states of ternary nanoalloys, based on X-ray energy dispersive spectroscopy (XEDS) mapping data for large particle groups. Combining with canonical Monte Carlo (MC), molecular dynamics (MD), and density functional theory (DFT) simulations, we provide further mechanistic understanding of the observed phenomena.…”