One of the most fascinating experimental results in fabrication of artificial nanostructures is the creation of the macroscopically ordered superlattice of Ce adatoms on Ag111 F. Silly et al., Phys. Rev. Lett. 92, 016101 2004. Here, performing kinetic Monte Carlo simulations, we study the formation of Ce superlattice at the atomic scale. It is demonstrated that the surface-state mediated long-range interaction between Ce adatoms can lead to their self-assembly into a well ordered structure. The temperature of the substrate and the concentration of Ce adatoms are shown to play a key role in this process
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