  In this paper we investigate by means of first-principles density functional
theory calculations the (111) surface of the Ag-Cu alloy under varying
conditions of pressure of the surrounding oxygen atmosphere and temperature.
This alloy has been recently proposed as a catalyst with improved selectivity
for ethylene epoxidation with respect to pure silver, the catalyst commonly
used in industrial applications. Here we show that the presence of oxygen leads
to copper segregation to the surface. Considering the surface free energy as a
function of the surface composition, we construct the convex hull to
investigate the stability of various surface structures. By including the
dependence of the free surface energy on the oxygen chemical potential, we are
able compute the phase diagram of the alloy as a function of temperature,
pressure and surface composition. We find that, at temperature and pressure
typically used in ethylene epoxidation, a number of structures can be present
on the surface of the alloy, including clean Ag(111), thin layers of copper
oxide and thick oxide-like structures. These results are consistent with, and
help explain, recent experimental results.
