Calculating the diffraction of electrons or X-rays by carbon nanotubes

The theory developed by Cochran, Crick and Vand for the diffraction of X-rays by helical biological molecules has been used to compute the diffraction patterns of monolayer or multilayer carbon nanotubes. By describing a single-wall chiral tubule as a set of regular carbon helices, its exact, kinematical diffraction amplitude is obtained in closed form. The theory is illustrated by computer simulations which faithfully reproduce the observed intensity patterns of transmission electron diffraction from multilayer nanotubes.