Discreteness of nanostructures and critical dimensions of nanoclusters

Theoretical models and experimental data related to the formulation of the discreteness concept for nanoclusters and nanostructures are analysed. The discreteness is shown to be due to the existence of critical sizes of nanoclusters determined by the magic numbers of atoms and thermodynamic parameters. Such nanoclusters exhibit the highest stability in the formation of nanostructures and specific properties.