Ordering tendencies in the binary alloys of Rh, Pd, Ir, and Pt: Density functional calculations

The binary alloys of Rh, Pd, Ir, and Pt are important because of their high catalytic potential. We report in this paper that the ${\mathrm{Rh}}_{1-x}{\mathrm{Ir}}_x$ and ${\mathrm{Rh}}_{1-x}{\mathrm{Pt}}_x$ systems, long thought to phase separate at low temperatures, actually exhibit miscibility over the entire concentration and temperature range. We find low critical ordering temperatures, indicating that long-range order is unlikely to be observed experimentally. These results are compared with previous theoretical predictions for the other binary alloys of Rh, Pd, Ir, and Pt and with calculations performed here on the ${\mathrm{Pt}}_{1-x}{\mathrm{Ir}}_x$ and ${\mathrm{Pd}}_{1-x}{\mathrm{Ir}}_x$ systems. We discuss these results and investigate the mechanisms governing ordering vs phase separating behavior in all six binaries of the $\mathrm{Rh}\text{−}\mathrm{Pd}\text{−}\mathrm{Ir}\text{−}\mathrm{Pt}$ quartet. In particular, we examine why, given the chemical similarity of all members of the quartet, three of their binaries ($\mathrm{PdIr}$, $\mathrm{PtIr}$, and $\mathrm{RhPd}$) phase separate while the remaining three ($\mathrm{RhIr}$, $\mathrm{RhPt}$, and $\mathrm{PdPt}$) order.

Figure 1

(Color online) Plot showing direct enumeration search of formation enthalpies. Every configuration with 20 or fewer atoms in the unit cell ($\approx 3\times {10}^6$ structures) was predicted based on the cluster interaction parameters. Note that all configurations possess a negative formation enthalpy. The dark circles on the convex hull indicate breaking point configurations. Also shown is the random alloy formation enthalpy curve.

Figure 2

${\mathrm{Rh}}_{1-x}{\mathrm{Pt}}_x$: Mixing enthalpies as function of concentration. For all temperatures exclusively negative enthalpies are found.

Figure 3

(Color online) Summary of the ordering behavior of all six binary alloys of Rh, Pd, Ir, and Pt. Also shown are the formation enthalpies for the random alloy at a $50\text{−}50\mathrm{at}.\%$ concentration, as determined by their respective cluster expansions (energies for the $\mathrm{PdPt}$, $\mathrm{RhPd}$, and $\mathrm{RhPt}$ systems are taken from Refs. 3, 4).

Figure 4

(Color online) Site-projected densities of states for each of the six binary alloys of the quartet in the quasirandom atomic configuration (Ref. 42). Shown are the $s$-like and $d$-like states averaged over all atoms of each type within the unit cell.