Nanoparticles of Ptââ?¬â??Rh were studied by means of lattice-based Monte Carlo simulations with respect to the stability of ordered\r\nD022- and 40-phases as a function of particle size and composition. By thermodynamic integration in the semi-grand canonical\r\nensemble, 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\r\nthe lowering of the critical ordering temperature, the broadening of the compositional stability range of the ordered phases, and the\r\nnarrowing of the two-phase regions were observed and discussed in the context of complete size-dependent nanoparticle phase\r\ndiagrams. In addition, an ordered surface phase emerges at low temperatures and low platinum concentration. A decrease of platinum\r\nsurface segregation with increasing global platinum concentration was observed, when a second, ordered phase is formed\r\ninside the core of the particle. The orderââ?¬â??disorder transitions were analyzed in terms of the Warrenââ?¬â??Cowley short-range order parameters.\r\nConcentration-averaged short-range order parameters were used to remove the surface segregation bias of the conventional\r\nshort-range order parameters. Using this procedure, it was shown that the short-range order in the particles at high temperatures is\r\nbulk-like.
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