We describe theoretical calculations applying a 2D Frenkel-Kontorova (
FK) model to the heteroepitaxial system Cu on Ru(1000). The experiment
ally observed variation of structure with layer thickness is simulated
by scaling the adatom-adatom interaction. The minimum energy configur
ations are in exceptional agreement with recent scanning tunneling mic
roscopy results showing four distinct structures as a function of thic
kness. These metal on metal films present a new realization of the FK
model which complements previous investigations of rare gas adsorption
on graphite.