We have calculated the effective cluster interactions (ECI) which govern the ordering of Ir adatoms on the Ir(111) surface. The computations are based on a tight-binding Hamiltonian in which no adjustable or experimentally determined parameters were introduced. Both atoms adsorbed in ‘bulk’ sites (i.e. continuing the fee lattice) and those in ‘surface’ sites (i.e. producing hep stacking) are considered. We use this formalism to determine the relative stability of various adsorption sites and cluster shapes at zero temperature. The overall trends are in excellent agreement with the experimental results found by Ehrlich and co-workers. Next, we employ these ECI in Monte Carlo simulations of the kinetics of domain growth and evolution. Specifically we analyze the effect of diffusion barriers and the competition between the ordering tendencies of the system and entropic effects. Typical ‘snapshots’ in a range of temperatures and coverages are discussed.