Three-dimensional Rh particle catalysts were prepared by heteroepitaxial growth on alpha-Al2O3 (0001),NaCl (001) and KCl (001) substrates. During the deposition, the particle structure and orientation were characterised by Reflection High Energy Electron Diffraction (RHEED). It was shown that ar sufficiently high temperatures the Rh particles conserve the symmetry of tile substrate (hexagonal in the case of alpha-Al2O3 (0001) and cubic for (001) NaCl and (001) KCl substrates). Ar lower temperatures the layers are disordered or partially disordered.