Ion implantation, specified by parameters like ion energy, ion fluence, ion
flux and sub-strate temperature, has become a well-established tool to
synthesize buried low-dimensional nanostructures. In general, in ion beam
synthesis the evolution of nanostructures is determined by the competition
between ballistic and thermodynamic effects. A kinetic 3D lattice
Monte-Carlo model is introduced, which allows for a proper incorporation of
collisional mixing and phase separation within supersaturated
solid-solutions. It is shown, that for both the ballistically and
thermodynamically dominated regimes, the Gibbs-Thomson relation is the key
ingredient in understanding nanocluster evolution. Various aspects of
precipitate evolution during implantation, formation of ordered arrays of
nanophase domains by focused ion implantation and compound nanocluster
synthesis are discussed.