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

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 which alternate in length $ABABAB$ around the six sides of the island. By contrast, previous theoretical models for island faceting predict a rotating sequence of three lengths $ABCABC$ around the island. We propose a new model for the observed shapes, whose physical basis is the variation of the local arrangements of substrate atoms seen by an adsorbate atom. We map our model onto a generalized form of the two-dimensional Ising model having three- as well as two-spin interactions, and estimate using atom-embedding calculations the strengths of these interactions for Cu adsorbed on a Cu~(111) surface. We then describe a new, highly efficient Monte Carlo technique for calculating the equilibrium crystal shapes of general Ising-type models in two or three dimensions, and apply it to the model in hand. Our results do indeed show alternating facet lengths closely similar to those seen in experiments.