Quantitative structural analysis of individual nanotubes by electron diffraction

A general method for quantitative structure analysis of individual, cylindrical, carbon nanotubes is described here. The method is based on electron diffraction of individual nanotubes and analysis using a combination of helical diffraction theory and diffraction geometry of the underlying lattice. Experimental recording of nanotube diffraction is achieved using a nanometer-sized electron beam. Procedures are developed for 1) the measurement of chiral angles in both single- and multi-wall nanotubes and 2) structure determination based on Bessel function fitting of layer line intensity oscillations. The accuracy of the method is demonstrated for the structure determination of a single- and double-wall carbon nanotubes and partial structural analysis of a multiwall carbon nanotube. The results show that the single-, double- and incommensurate multi-wall tubes are well described by the cylindrical tube model. However, a large Debye-Waller factor in the radial direction is obtained. The method developed here is general and can be applied to other cylindrical nanotubes.