Ordering tendencies in Pd-Pt, Rh-Pt, and Ag-Au alloys

Bimetallic Pt-Pd nano-catalyst: size, shape and composition matter

The goal of this work is to understand how the phase diagram (PHAD) of the platinum-palladium (Pt-Pd) alloy changes with size and shape and how it correlates with catalytic properties. By using nano-thermodynamics, the size and shape effects on the PHAD of Pt-Pd nanoparticles were determined theoretically. The PHAD of some nanoparticles (sphere, tetrahedron, octahedron, decahedron, cube, cuboctahedron and rhombic dodecahedron) exhibits a congruent melting point that becomes more and more pronounced when the size decreases. At the right of the congruent melting point i.e. close to the Pt-rich side, the coexistence region exhibits a contraction while an expansion is noticed at larger palladium concentrations. From the Gibbs free energy analysis, the stability of all the considered shapes has been determined versus temperature and composition. Furthermore, the surface segregation was also calculated and it is shown that the surface segregation is reversed at very small sizes. Indeed, below a critical size, Pd does not segregate anymore at the surface like it normally does for larger nanoparticles; but Pt does. The critical size range has been determined for each considered shape; and within this range Pt and Pd co-exist at the surface. Finally, the most catalytically active shapes are predicted to be the tetrahedron and the cube in agreement with the available experimental data and other theoretical results.

Unveiling stable group IV alloy nanowires via a comprehensive search and their electronic band characteristics

By means of density functional theory calculations, the cluster expansion method, and Monte Carlo simulations, we identify the stable spatial configurations (ground states) for [100] CSi, GeSi, and SnSi alloy nanowires (NWs) across compositions. In particular, we find that stable configurations of GeSiNWs and SnSiNWs exhibit core-shell segregation tendencies, while those of CSiNWs favor ordering. Moreover, we show compositional ranges where the band gaps are expected to vary linearly with composition, allowing predictable band gap fine-tuning. We also predict composition ranges where the spatial separation of near-band gap states are imminent, making it possible for electron-hole charge separation. By addressing both the issues of stability and the compositional trend of electronic band structure, our work should prove useful for designing alloy NWs of smaller dimensions.

Size-dependent phase diagrams of metallic alloys: A Monte Carlo simulation study on order-disorder transitions in Pt-Rh nanoparticles

Nanoparticles of Pt-Rh were studied by means of lattice-based Monte Carlo simulations with respect to the stability of ordered D0(22)- and 40-phases as a function of particle size and composition. By thermodynamic integration in the semi-grand canonical ensemble, phase diagrams for particles with a diameter of 7.8 nm, 4.3 nm and 3.1 nm were obtained. Size-dependent trends such as the lowering of the critical ordering temperature, the broadening of the compositional stability range of the ordered phases, and the narrowing of the two-phase regions were observed and discussed in the context of complete size-dependent nanoparticle phase diagrams. In addition, an ordered surface phase emerges at low temperatures and low platinum concentration. A decrease of platinum surface segregation with increasing global platinum concentration was observed, when a second, ordered phase is formed inside the core of the particle. The order-disorder transitions were analyzed in terms of the Warren-Cowley short-range order parameters. Concentration-averaged short-range order parameters were used to remove the surface segregation bias of the conventional short-range order parameters. Using this procedure, it was shown that the short-range order in the particles at high temperatures is bulk-like.

First-principles study of phase equilibria in Cu-Pt-Rh disordered alloys

Phase stability of Cu-Pt-Rh ternary disordered alloys is examined by a combination of cluster expansion techniques and Monte Carlo statistical simulation based on first-principles calculation. The sign of pseudo-binary ECIs indicates that neighboring Cu and Pt strongly prefer unlike-atom pairs, Pt and Rh weakly prefer unlike-atom pairs, and Cu and Rh atoms prefer like-atom pairs, indicating that the ternary alloy retains the ordering tendency of the constituent binary alloys. The formation energy of a random alloy at T = 1200 K exhibits a negative sign for a wide range of Pt-rich compositions, while at Pt-poor compositions of x≤0.25, the formation energy has a positive value. Calculated affinities for the random alloy show the variety of energetically favored bonds for the alloy: Cu-Pt bonds in both first-and second-nearest neighbor (1-NN and 2-NN) are energetically preferred for all the composition range, the Pt-Rh bond in 1-NN is preferred at Pt-rich compositions, the Pt-Rh in 2-NN and Rh-Cu in 1-NN bonds are unfavored for all compositions, and the Rh-Cu bond in 2-NN is unfavored for Pt-poor compositions. We elucidate that the ordering tendency of 1-NN and 2-NN Cu-Pt, 2-NN Pt-Rh and 1-NN Cu-Rh atoms in constituent binary alloys is retained for the whole composition range of Cu-Pt-Rh ternary alloys, while that of 1-NN Pt-Rh and 2-NN Cu-Rh atoms significantly depends on composition.