Quantitative theory of diffraction by carbon nanotubes

A quantitative theory of the kinematical diffraction of a plane wave by a carbon nanotube is developed. The formalism is based on the Cochran, Crick, and Vand theory of the diffraction by helical molecules. This leads to a closed-form expression of the diffracted amplitude produced by a single-wall tubule of arbitrary helicity, applicable to both X rays and high-energy electrons. The theory, which can be used to simulate the diffraction pattern of any multilayer nanotube, is illustrated on the case of a crystalline rope of carbon nanotubes.