  Using Monte Carlo simulation method in the canonical ensemble, we have
studied the commensurate-incommensurate transition in two-dimensional finite
mixed clusters of Ar and Kr adsorbed on graphite basal plane at low
temperatures. It has been demonstrated that the transition occurs when the
argon concentration exceeds the value needed to cover the peripheries of the
cluster. The incommensurate phase exhibits a similar domain-wall structure as
observed in pure krypton films at the densities exceeding the density of a
perfect $(\sqrt{3}\times\sqrt{3})R30^\circ$ commensurate phase, but the size of
commensurate domains does not change much with the cluster size. When the argon
concentration increases, the composition of domain walls changes while the
commensurate domains are made of pure krypton. We have constructed a simple
one-dimensional Frenkel-Kontorova-like model that yields the results being in a
good qualitative agreement with the Monte Carlo results obtained for
two-dimensional systems.
