We perform first-principles calculations and Monte Carlo sampling to investigate the structures of ternary PdRuM (M = Pt, Rh, or Ir) nanoparticles (NPs) with respect to three different spherical shapes. The morphologies include hexagonal close-packed (hcp), truncated-octahedral (fcc), and icosahedral (Ih, fcc) shapes with 57, 55, and 55 atoms, respectively. The calculations show that the atomic position is dominant in determining the stability of the ternary NPs. For bare ternary NPs, Pd and Ru atoms favor a location on the vertex sites and the core, respectively, which can be understood by the surface energy of the corresponding slab models. For single-crystalline NPs, the binary shell could be either a solid solution or a segregation alloy depending on composition and morphology. However, polycrystalline Ih NPs only form segregated binary shells surrounding the Ru core. Such configurations tend to minimize the surface lattice to gain more energy from the d orbital of the transition metals. In addition to the bare NPs, we study the oxidized ternary NPs. The results show that the Ru atoms penetrate outwards from the core to the surface reducing the oxidation formation energy. Furthermore, oxygen adsorption facilitates Pt, Pd, and Pd penetration into the PdRuPt, PdRuRh, and PdRuIr NPs, respectively. Most of the oxide shells are a solid solution, except for the PdRuRh NP with an Ih shape, which is found to be in a segregation shell. The free energy calculation reveals that the pure hcp NPs are thermodynamically unstable under oxygen-rich conditions. This work clearly demonstrates the structural trends of small ternary NPs and their oxidation, unveiling that the structural trends can be understood by the surface formation energy and the interplay between adsorbent and adsorbing oxygen atoms.
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