Alloy surface segregation in reactive environments: First-principles atomistic thermodynamics study of ${\mathrm{Ag}}_3\mathrm{Pd}\left(111\right)$ in oxygen atmospheres

We present a first-principles atomistic thermodynamics framework to describe the structure, composition, and segregation profile of an alloy surface in contact with a (reactive) environment. The method is illustrated with the application to a ${\mathrm{Ag}}_3\mathrm{Pd}\left(111\right)$ surface in an oxygen atmosphere, and we analyze trends in segregation, adsorption, and surface free energies. We observe a wide range of oxygen adsorption energies on the various alloy surface configurations, including binding that is stronger than on a $\mathrm{Pd}\left(111\right)$ surface and weaker than that on a $\mathrm{Ag}\left(111\right)$ surface. This and the consideration of even small amounts of nonstoichiometries in the ordered bulk alloy are found to be crucial to accurately model the Pd surface segregation occurring in increasingly O-rich gas phases.

Figure 1

Top views of the atomic geometry of five $(2\times 2)$ surface unit-cell arrangements considered in this study. The shown configurations have a bulklike second layer composition, but a first layer composition that varies from pure Ag (I) to pure Pd (V). White colored spheres correspond to Ag atoms, whereas grey colored spheres correspond to Pd atoms. The larger spheres correspond to the first layer, and the smaller ones correspond to the second layer.

Figure 2

(Color online) Surface free energy of ${\mathrm{Ag}}_3\mathrm{Pd}\left(111\right)$ in equilibrium with a Pd-rich ${\mathrm{Ag}}_3\mathrm{Pd}$ bulk reservoir, cf. Eq. (9), as a function of oxygen chemical potential. Each line corresponds to one of the tested surface configurations, and only the few configurations that result as most stable for a range of oxygen chemical potential are drawn as dark (red) lines. Additionally shown as insets are top views of the most stable surface configurations in the same form as in Fig. 1, with adsorbed O atoms shown as dark small circles, Ag atoms as white circles, and Pd atoms as grey circles. The dependence on the oxygen chemical potential is translated into pressure scales using Eq. (5) for $T=300\mathrm{K}$ and $T=600\mathrm{K}$ (upper $x$ axes).

Figure 3

(Color online) Surface free energy ${\mathrm{Ag}}_3\mathrm{Pd}\left(111\right)$ in equilibrium with a Ag-rich ${\mathrm{Ag}}_3\mathrm{Pd}$ bulk reservoir, cf. Eq. (8), as a function of oxygen chemical potential. Each line corresponds to one of the tested surface configurations, and only the few configurations that result as most stable for a range of oxygen chemical potential are drawn as colored lines. Additionally shown as insets are top views of the most stable surface configurations in the same form as in Fig. 1, with adsorbed O atoms shown as dark small circles, Ag atoms as white circles, and Pd atoms as grey circles. The dependence on the oxygen chemical potential is translated into pressure scales using Eq. (5) for $T=300\mathrm{K}$ and $T=600\mathrm{K}$ (upper $x$ axes).

Figure 4

(Color online) Segregation energies per surface area, $E_{\mathrm{seg}}∕A_{\mathrm{surf}}$, for all clean surface configurations considered and as a function of the Ag concentration in the topmost layer. (Yellow) circles show the segregation energies for the Ag-rich bulk reservoir and (green) rhombes the segregation energies for the Pd-rich bulk reservoir. The different data points at the same topmost layer Ag concentration represent the variations due to differing Ag concentration in the second layer, and the solid circles viz. rhombes correspond to the surface configurations with nominal bulk composition in the second layer. Additionally shown by the blue line is the segregation energy estimate obtained by considering the segregation of diluted Ag impurities in Pd and diluted Pd impurities in Ag (see text).

Figure 5

(Color online) Average binding energy $E_{\mathrm{b}}$ per O atom as a function of the number of directly coordinated first-layer Ag atoms at a coverage of $\theta =0.25\mathrm{ML}$, i.e., with one O atom per $(2\times 2)$ surface unit cell. For the considered adsorption into fcc hollow sites at the close-packed (111) surface, this number of directly coordinated Ag atoms can range from zero to three. Additionally, shown as (blue) squares is the average binding energy at this coverage at the fcc sites of a $\mathrm{Pd}\left(111\right)$ surface (corresponding to zero Ag atom coordination) and of a $\mathrm{Ag}\left(111\right)$ surface (corresponding to three Ag atom coordination). The (blue) line is a guide to the eye, representing a simple linear average between the binding energy at these two parent metal surfaces.

Figure 6

(Color online) Average binding energy $E_{\mathrm{b}}$ per O atom as a function of the oxygen coverage, ranging from $0.25\mathrm{ML}$ to $1\mathrm{ML}$ [corresponding to one to four O atoms per $(2\times 2)$ surface unit cell]. Shown is only the data for surface configurations with a 100% Ag concentration in the topmost layer (yellow squares) or with a 100% Pd concentration in the topmost layer (red circles). The different data points at the same coverage correspond to surface configurations with varying second layer composition. The full Ag second layer gives the lower energies and the full Pd second layer the higher energies.