Electron diffraction from cylindrical nanotubes

Electron diffraction intensities from cylindrical objects can be conveniently analyzed using Bessel functions. Analytic formulas and geometry of the diffraction patterns from cylindrical carbon nanotubes are presented in general forms in terms of structural parameters, such as the pitch angle and the radius of a tubule. As an example the Fraunhofer diffraction pattern from a graphitic tubule of structure [18,2] has been simulated to illustrate the characteristics of such diffraction patterns. The validity of the projection approximation is also discussed.