<p>To facilitate the rational design of
alloy catalysts, we introduce a method for rapidly calculating the structure
and catalytic properties of a substitutional alloy surface that is in
equilibrium with the underlying bulk phase. We implement our method by developing
a way to generate surface cluster expansions that explicitly account for the
lattice parameter of the bulk structure. This approach makes it possible to
computationally map the structure of an alloy surface and statistically sample
adsorbate binding energies at every point in the alloy phase diagram. When
combined with a method for predicting catalytic activities from adsorbate binding
energies, maps of catalytic activities at every point in the phase diagram can
be created, enabling the identification of synthesis conditions likely to result
in highly active catalysts. We demonstrate our approach by analyzing Pt-rich Pt–Ni
catalysts for the oxygen reduction reaction, finding two regions in the phase
diagram that are predicted to result in highly active catalysts. Our analysis
indicates that the Pt<sub>3</sub>Ni(111) surface, which has the highest known
specific activity for the oxygen reduction reaction, is likely able to achieve
its high activity through the formation of an intermetallic phase with L1<sub>2</sub>
order. We use the generated surface structure and catalytic activity maps to
demonstrate how the intermetallic nature of this phase leads to high catalytic
activity and discuss how the underlying principles can be used in catalysis
design. We further discuss the importance of surface phases and demonstrate how
they can dramatically affect catalytic activity.</p>