The Thermal Stability of Asymmetric Separated Configurations inside Alloy Nanoparticles: Atomic-Scale Modeling of Pd–Ir Nanophase Diagrams

Abstract

Compared to alloy bulk phase diagrams, the experimental determination of phase diagrams for alloy nanoparticles (NPs), which are useful in various nanotechnological applications, involves significant technical difficulties, making theoretical modeling a feasible alternative. Yet, being quite challenging, modeling of separation nanophase diagrams is scarce in the literature. The task of predicting comprehensive nanophase diagrams for Pd−Ir face-centered cubic-based three cuboctahedra is facilitated in this study by combining the computationally efficient statistical-mechanical Free-energy Concentration Expansion Method, which includes short-range order (SRO) with coordination-dependent bond-energy variations as part of the input and with rotationally symmetric site grouping for extra efficiency. This nanosystem has been chosen mainly because of the very small atomic mismatch that simplifies the modeling, e.g., in the assessment of vibrational entropy contributions based in this work on fitting to the Pd−Ir experimental bulk critical temperature. This entropic effect, together with SRO, leads to significant destabilization of low-T Quasi-Janus (QJ) asymmetric configurations of the NP core, which transform to symmetric partially mixed nanophases. First-order and second-order intracore transitions are predicted for dilute and intermediate-range compositions, respectively. Caloric curves computed for the former case yield the NP-size dependent transition latent heat, and in the latter case critical temperatures exhibit a specific scaling behavior. The computed separation diagrams and intracore solubility diagrams reflect enhanced elemental mixing in smaller QJ nanophases. In addition to these diagrams, the revealed near-surface compositional variations are likely to be pertinent to the utilization of Pd−Ir NPs, e.g., in catalysis.