Diffraction from quasi one-dimensional crystals and nanotubes

Abstract

Intensity distribution for diffraction from arbitrary quasi one-dimensional crystal is calculated with the help of symmetry classification of such systems onto 15 conformation classes. Characteristic features of patterns are discussed. In particular, carbon nanotubes are single-orbit systems generated by the fifth family line groups. It is shown how the identification of single-wall tubes can be performed in two steps: at first we reconstruct the line group from the pattern, and afterwards the chirality indices are found easily due to the bi-unique correspondence of the single-wall carbon nanotubes and their symmetry groups. A comment on the diffraction from double- and multi-wall nanotubes is made. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.