Structure of Icosahedral Nanoobjects

The structure of nanoparticles is probably the most important problem for physicists and chemists dealing with the nanostate of matter. The structure of many nanoparticles synthesized over the last decade is so unusual from the standpoint of classical crystallography that many authors describe it in literary rather than in rigorous scientific terms. The basic structural (for the most part, geometric) principles of the nanostate are formulated. The nanoparticle structure is determined in the framework of the local approach, which includes the paradigm of structural blocks with the use of non-Euclidean geometry concepts (the curved-space approximation) and locally minimal manifolds and takes into account the possibility of coherently joining fragments with different (incompatible in crystals) symmetry elements. The formulated principles are used to explain the structure of nanoparticles of different types, in particular, icosahedral nanoparticles.