Phase separation transitions inside Pd-Ir nanoparticles: modeling size-dependent phase diagrams & finite-size scaling Micha Polak and Leonid Rubinovich Department of Chemistry, Ben-Gurion University of the Negev, Israel Only few theoretical predictions of equilibrium phase separation diagrams of alloy nanoparticles (NPs) have been reported so far (and probably no experimental diagrams), despite their relevance to several practical applications. In this study, we employed the statistical-mechanical Free-energy Concentration Expansion Method (FCEM [1]), which includes short-range order, combined with coordination-dependent bond-energy variations [2] as part of the input, and with rotationally-symmetric site or layer grouping [3] for extra efficiency. This semi-analytical methodology enables to separate and elucidate different contributions to the thermal stability of nano-phases. The Pd-Ir system, having a very small atomic mismatch, was chosen mainly in order to simplify the modeling, e.g., in the assessment of vibrational entropy effects, which are found to be quite substantial. Free-energy minimalization for twenty-two Pd-Ir cuboctahedra consisting of 147 up to 49,049 atoms furnished at low temperatures Quasi-Janus configurations consisting of asymmetrically separated cores below surface- segregated Pd. The cores transform sharply at higher temperatures to mixed multi-shell configurations. The dependence of the corresponding critical temperature (at equiatomic composition) on the NP size obeys finite-size scaling with correlation-length exponent ν=0.97±0.07, consistently with reports for surface constrained nano- structures. The complete size-dependence of Pd-Ir nano-phase diagrams were computed for 147-10,179 atom NPs. In particular, for the small size NPs, the miscibility gaps span significantly lower temperatures compared to the bulk gap, but this deviation becomes lesser for larger NPs. The predicted ranges of thermal stability, as well as variations obtained in the near-surface compositions, are likely to be pertinent to the use of Pd-Ir nanoparticles, e.g., in heterogeneous catalysis. References 1. M. Polak and L. Rubinovich, “The interplay of surface segregation and atomic order in alloys”,Surface Science Reports, 38, 127 (2000). 2. L. Rubinovich and M. Polak, “Prediction of distinct surface segregation effects due to coordination-dependent bond-energy variations in alloy nanoclusters”, Phys. Rev. B 80, 045404 (2009). 3. M. Polak and L. Rubinovich, “Thermally-induced chemical-order transitions in medium-large alloy nanoparticles predicted using a coarse-grained layer model”, Phys. Chem. Chem. Phys., 17, 28211 (2015).
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