Compositions and structures of nanoparticles of trigonal symmetry D 3d : Nanotubes

• Published in: Russian journal of inorganic chemistry Vol. 53; no. 7; pp. 1088 - 1097
• Main Authors: Kustov, E. F., Nefedov, V. I., Kalinin, A. V., Karelina, M. S.
• Format: Journal Article
• Language: English
• Published: 01-07-2008
• ISSN: 0036-0236; 1531-8613
• DOI: 10.1134/S0036023608070188

A method has been developed for the determination of the structure and number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group. The formulas for calculation of the number of particles of symmetry D 3d have been reported. It has been shown that the number of atoms in trigonal shells is determined by three structurally invariant numbers and the quantum number of the group order n. All possible nanostructures of symmetry D 3d have been classified: Cc + 6z , z = 0, 1, 2, ..., where the basic shells are Cc = C6, C8, and C14. A sum rule has been obtained for the coordination numbers of the shell sites located on symmetry axes. Trigonal nanoparticles are parent ones for obtaining (3,0), (6,0), and (9,0) nanotubes of trigonal type. The general formulas of these nanotubes with icosahedral, dodecahedral, and cubic caps are N8 + 12p , N20 + 24p , and N60 + 36p (p = 1, 2, ...), respectively. The graphical constructions of all classes of trigonal nanoparticles and nanotubes are reported.