Ordering of atomic mono-layers on a (001) cubic crystal surface

The self-organization of a chemi-sorbed mono-layer is studied as a two dimensional ordering process in presence of surface stress. As proved previously for a single phase separation, a steady surface state is yielded from the competition between the domain boundary energy and the surface stress elastic energy. In the present letter, the resulting patterns are shown to depend on the interplay between the symmetries of both the internal layer order and the underlying crystal. For experimental relevance, our study is focussed on a (001) copper surface and we believe to enhance a route to stabilize novel surface nanostructures.