Nanostructures with coherent boundaries and the local approach

Nanostructures with coherent boundaries are considered in the framework of the local approach. It is demonstrated that the use of the fiber space formalism makes it possible to derive a set of geometrical structural complexes that are building blocks of nanostructures. These complexes are determined by the specific sub-configurations of finite projective planes. It is shown that, in the case of fourfold-coordinated structures, crystalline and quasicrystalline fragments can intergrow coherently (without dangling bonds).[PUBLICATION ABSTRACT]