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It is experimentally observed that adsorbate atoms and vacancies on (111)surfaces of fcc metals cluster into islands which are approximately hexagonal,but which on closer inspection turn out to have equilibrium facets whichalternate in length $ABABAB$ around the six sides of the island. By contrast,previous theoretical models for island faceting predict a rotating sequence ofthree lengths $ABCABC$ around the island. We propose a new model for theobserved shapes, whose physical basis is the variation of the localarrangements of substrate atoms seen by an adsorbate atom. We map our modelonto a generalized form of the two-dimensional Ising model having three- aswell as two-spin interactions, and estimate using atom-embedding calculationsthe strengths of these interactions for Cu adsorbed on a Cu~(111) surface. Wethen describe a new, highly efficient Monte Carlo technique for calculating theequilibrium crystal shapes of general Ising-type models in two or threedimensions, and apply it to the model in hand. Our results do indeed showalternating facet lengths closely similar to those seen in experiments.Comment: LaTe

Model for the shapes of islands and pits on (111) surfaces of fcc metals