On the computational calculation of adatom, vacancy and early stage surface nucleation island free energies on the (1Â 1Â 1) copper surface

Previously, in an earlier publication we developed a general method for calculating the free energy of surfaces with an arbitrary number of excess surface atoms. In subsequent work we showed how these surfaces can be combined to produce an ad hoc grand canonical ensemble of surfaces, and constructed such an ensemble for the disordered semi-hexagonal reconstructed Glue Model Au(1 0 0) system. In this work we use the previously developed methods to calculate and construct an ensemble of surfaces for a model Embedded Atom Method Cu(1 1 1) surface and show how from this ensemble, one can calculate 'exact' formation free energies, and hence equilibrium surface concentrations of adatom and vacancy monomers, and clustered adatom and vacancy dimers, trimers and quadrimers, which form early stage 2D island formations. Results for the model Cu(1 1 1) system at 1000 K show that singular vacancies are more than twice as likely as adatoms to populate the surface. The final formation free energies at 1000 K were found to be 0.60 eV and 0.73 eV for the vacancy and adatom respectively.