The growth of Cu on Ag(100) is investigated by low-temperature scanning tunneling microscopy. Exchange diffusion of Cu deposited onto Ag(100) leads to small pure Cu islands and larger islands consisting of a CuAg alloy in room temperature growth. The ratio of the different types of islands depends on terrace widths up to 100 nm. This surprisingly long-range dependence is correlated to the density of the surface alloy. We thus reveal that the exchange diffusion barrier is influenced by terrace widths far beyond quantum size confinement.