With a genetic algorithm, the lowest-energy structures of adatom clusters on a series of metal fcc (001) surfaces are determined. The atomic interactions are modeled by the realistic model potentials including embedded-atom method potential, surface-embedded-atom method potential, and Rosato-Guillopé-Legrand potential. The results show that the adatom clusters of sizes $n=6,9,\dots ,36\mathrm{}$ have the same structures on the different surfaces. Their special stability indicates that they are magic number clusters. For clusters of other sizes, the structures are generally different on the different surfaces. The change of the cluster structure with surfaces can be interpreted in terms of the relative interaction range and the compensation effect from the adatom-substrate interaction. When the interaction range becomes long and/or the compensation effect becomes strong, the shape of the lowest-energy structure tends to change from square to rectangle or even to one-dimensional chain.

• Received 17 September 2003

DOI:https://doi.org/10.1103/PhysRevB.69.165421