Alloy surface segregation in reactive environments: First-principles atomistic thermodynamics study of Ag3Pd(111) in oxygen atmospheres
John R. Kitchin, Karsten Reuter, and Matthias Scheffler, “Alloy surface segregation in reactive environments: First-principles atomistic thermodynamics study of Ag3Pd(111) in oxygen atmospheres”, Physical Review B 77(7), 075437 (2008). https://doi.org/10.1103/physrevb.77.075437
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Question
The composition of an alloy surface usually differs from the bulk, and a reactive gas can change it further when one metal binds the gas more strongly than the other. Earlier first-principles treatments of segregation mostly focused on the bulk reservoir, or treated the environment only roughly. This paper asks how to build a framework that accounts for both the bulk alloy and the gas phase at once, and uses Ag3Pd(111) in oxygen to test which simplifications common in the literature are actually justified (Kitchin et al. 2008).
Approach
The authors extend first-principles atomistic thermodynamics to a binary alloy slab in equilibrium with an O2 gas reservoir and with the underlying bulk alloy. The surface free energy then depends on the oxygen chemical potential and on the difference between the Ag and Pd chemical potentials. Rather than computing that difference with a cluster expansion, they bracket it by two limits representing small antisite nonstoichiometries in the ordered L12 Ag3Pd bulk: a Pd-rich limit (onset of Pd phase separation) and an Ag-rich limit (onset of Ag phase separation). The width of this range equals the alloy formation energy divided by xAg(1 - xAg). Vibrational and configurational contributions are argued to be small (below about 5 and 2 meV/Ų, respectively, for temperatures below 600 K) and are neglected, so DFT total energies enter directly.
Calculations used ultrasoft pseudopotential plane-wave DFT with the PBE GGA functional, seven-layer symmetric slabs with the outer two layers relaxed, and 2x2 surface cells. The composition of the top two layers was varied from pure Ag to pure Pd (25 clean configurations), and one to four O atoms were placed in fcc hollow sites, giving 473 inequivalent structures with coverages from 0 to 1 ML. The surface free energy was then decomposed into a segregation energy term, an average O binding energy term, and a gas-phase chemical potential term so each factor could be analyzed separately.
Key findings
Computed lattice constants were 4.09 Å (Ag3Pd), 3.93 Å (Pd) and 4.14 Å (Ag), and the Ag3Pd formation energy was -0.21 eV per formula unit, giving a 0.28 eV window for the metal chemical potential difference. Under O-poor (ultrahigh-vacuum-like) conditions the most stable surface for the Pd-rich reservoir has a pure Ag first layer over a pure Pd second layer. Above an oxygen chemical potential of -0.89 eV, a 0.25 ML O structure with 75% Pd in the first layer becomes stable, and higher coverages bring fully Pd-terminated first layers, so oxygen reverses the segregation profile. For the Ag-rich reservoir the same inversion happens later (first O-covered phase at -0.68 eV), and the sequence of stable structures also changes, not just shifts. Restricting the second layer to bulk stoichiometry moved transition chemical potentials by sometimes more than 0.1 eV, which corresponds to orders of magnitude in pressure.
The dilute-impurity model for segregation (-0.31 eV for Ag in Pd, +0.24 eV for Pd in Ag) reproduces the overall trend but cannot capture the bulk reservoir and errs by several tens of meV/Ų. O binding at 0.25 ML is not a linear interpolation between Ag(111) and Pd(111): some Pd-rich alloy configurations bind O more strongly than Pd(111), and some Ag-rich ones more weakly than Ag(111). Second-layer composition changes the average binding energy by about 0.3 to 0.6 eV per O, up to about 80 meV/Ų in the surface free energy, comparable to segregation effects, whereas third-layer variations were at most 0.1 eV. Binding weakens roughly linearly with coverage, by about 1 eV on Pd-terminated and 1.5 eV on Ag-terminated surfaces between 0.25 and 1 ML. With a computed PdO formation energy of -0.86 eV, bulk oxide formation sets in at -0.86 eV (Pd-rich) and -0.65 eV (Ag-rich), just above the onset of O adsorption. The authors attribute this to the high cost of bringing scarce Pd to the surface: the Ag-rich termination binds O at only -0.13 eV, versus -1.29 eV on Pd(111).
Significance
The paper gives a general, practical recipe for predicting alloy surface composition under reaction conditions, and shows that segregation data from vacuum experiments, parent-metal adsorption energies, low-coverage binding alone, or treatments that only vary the top layer are not sufficient. It presents direct screening of ordered structures as complementary to cluster expansions, and suggests that Pd-richer Ag-Pd alloys or chemically more different pairs such as Pt-Ru may behave differently.