Symmetry of electron diffraction from single-walled carbon nanotubes

Abstract

We show that, even when the atomic structure of a single-walled carbon nanotube does not have mirror symmetry perpendicular to the tubule axis, the electron diffraction patterns of the single-walled carbon nanotube always possess 2mm symmetry. We have also analyzed the contributions of higher order Bessel functions to the intensity distribution on the layer lines and found that (a) their contributions are negligible and (b) they would not affect the symmetry of the diffraction pattern. Both experimental and simulated electron diffraction patterns of a single-walled carbon nanotube of indices (14, 9) are presented to illustrate the 2mm symmetry and to corroborate the theoretical analysis.