First-principles study of bulk ordering and surface segregation in Pt-Rh binary alloys

Abstract

The cluster expansion technique in conjunction with first-principles calculations has been applied in Monte Carlo simulations to derive the configurational thermodynamics of the bulk and (111) surface of Pt-Rh alloys. Lattice-dynamics calculations reveal that the vibrational contribution to Pt-Rh bulk phase stability is fairly negligible. Calculated short-range-order parameter, ground state, and ordering transition temperature ${T}_{c}$ of bulk ${\mathrm{Pt}}_{50}{\mathrm{Rh}}_{50}$ are in satisfactory agreement with experimental values in the literature. Calculated composition profiles of the (111) surface at $T=1373\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ show the enrichment of Pt at the top layer and Pt depleted at the second layer for the entire composition, which is in agreement with experimental observations. At low temperatures, a significant difference is found in the temperature dependence of the layer composition profile between ${\mathrm{Pt}}_{25}{\mathrm{Rh}}_{75}$ and ${\mathrm{Pt}}_{50}{\mathrm{Rh}}_{50}$. While Pt composition of the ${\mathrm{Pt}}_{25}{\mathrm{Rh}}_{75}$ subsurface shows positive temperature dependence, that of ${\mathrm{Pt}}_{50}{\mathrm{Rh}}_{50}$ has a minimum at $T\ensuremath{\sim}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The former can be qualitatively interpreted by taking account of the on-site energy only. The latter is due to the occurrence of sublayer-confined phase transition from $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ order to disorder alloys.