A review of methods for the accurate determination of the chiral indices of carbon nanotubes from electron diffraction patterns

The strong link between the precise molecular structure and electronic properties of single wall carbon nanotubes is well known, however the experimental investigation of these links remains a challenge. This is in part due to the difficulty in determining the structure, or chirality of individual carbon nanotubes. Performing diffraction studies within a transmission electron microscope has become arguably the most powerful technique for the accurate determination of the chirality of, not only individual single wall, but also multi-wall and small bundles of carbon nanotubes. In this paper we give an up to date review of the analytical approaches to chirality assignment. For comparison we perform each of the discussed techniques on the same diffraction pattern, obtained using standard electron diffraction techniques, and discuss the ability of each to allow for the unambiguous determination of chirality within experimental uncertainties. The aim of this review is to give guidance as to the most pragmatic approach to extracting carbon nanotube chirality from electron diffraction patterns without the need for performing complicated and time consuming simulations.