Determination of cluster binding energies on metal surfaces by statistics

Two simple formulae to determine binding energies of two-dimensional clusters on surfaces in thermal equilibrium are derived. One requires measurement of monomer and cluster populations and of the surface temperature. The cluster dissociation rate is derived and related to the atom hopping rate, allowing the theory to be extended to adatom populations that are not in chemical equilibrium. The result gives a recipe for determining dissociation energies that requires measurements of only two rates at a single temperature.