Formation of aeroplane-like ZnO and tetrahexahedral Pt nanocrystals: systemic symmetry and symmetry breaking during nanocrystallization

Symmetries are so involved in crystallographic detail that it is indispensable when crystal cell or lattice is mentioned. For nanocrystals, however, many are ‘systemic symmetries’, meaning that the whole structures of nanocrystal particles are symmetrical from a different view. In that case, the development of the systemic symmetry is dictated by the law of symmetry breaking; that is, nanocrystallization does, to some extent, exceed current theories associated with crystallography.