  Substrate strain mediated adatom density distributions have been calculated
for Cu<111> surfaces. Complemented by Monte Carlo calculations a hexagonal
close packaged adatom superlattice in a coverage range up to 0.045 ML is
derived. Conditions for the stability of the superlattice against nucleation
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 explanation of surface state mediated interactions for superstructures
found in scanning tunnelling microscopy experiments is put in question.
