Segregation profiles in ${\mathrm{Cu}}_3$Au above the order-disorder transition

The segregation at a (100) surface of ${\mathrm{Cu}}_3$Au is studied slightly above the order-disorder transition at ${\mathit{T}}_{\mathit{c}}$. Based on a semi-infinite lattice-gas model with nearest- and next-nearest-neighbor interactions, we find within mean-field theory that close to the surface and in the disordered phase the Au concentration decays exponentially towards its bulk value. The corresponding decay length Λ increases as (T-${\mathit{T}}_{\mathrm{sp}}$${)}^{\mathrm{-}1/2}$ upon approaching ${\mathit{T}}_{\mathit{c}}$, where ${\mathit{T}}_{\mathrm{sp}}$<${\mathit{T}}_{\mathit{c}}$ denotes the spinodal temperature of the order-disorder transition. Without using any adjustable parameters, we obtain theoretical predictions in good quantitative agreement with recent x-ray-scattering data from this surface.