QUANTITATIVE THEORY OF DIFFRACTION BY CARBON NANOTUBES

A quantitative theory of the kinematical diffraction of a plane wave b y a carbon nanotube is developed. The formalism is based on the Cochra n, Crick, and Vand theory of the diffraction by helical molecules. Thi s leads to a closed-form expression of the diffracted amplitude produc ed by a single-wall tubule of arbitrary helicity, applicable to both X rays and high-energy electrons. The theory, which can be used to simu late the diffraction pattern of any multilayer nanotube, is illustrate d on the case of a crystalline rope of carbon nanotubes.