Substrate strain mediated adatom equilibrium density distributions have been calculated for Cu<111 > surfaces using two complementing methods. A hexagonal adatom superlattice in a coverage range up to 0.045 ML is derived for repulsive short range interactions. For zero short range interactions a hexagonal superstructure of adatom clusters is derived in a coverage range about 0.08 ML. Conditions for the stability of the superlattice against formation of dimers or clusters and degradation are analyzed using simple neighborhood models. Such models are also used to investigate the dynamic of adatoms within their superlattice neighborhood. Collective modes of adatom diffusion are proposed from the analogy with bulk lattice dynamics and methods for measurement are suggested. The recently put forward explanation of surface state mediated interactions for superstructures found in scanning tunneling microscopy experiments is put in question and strain mediated interactions are proposed as an alternative.