  Self-organization on crystal surface is studied as a two dimensional spinodal
decomposition in presence of a surface stress. The elastic Green function is
calculated for a $(001)$ cubic crystal surface taking into account the crystal
anisotropy. Numerical calculations show that the phase separation is driven by
the interplay between domain boundary energy and long range elastic
interactions. At late stage of the phase separation process, a steady state
appears with different nanometric patterns according to the surface coverage
and the crystal elastic constants.
