A direct method to determine the chiral indices of carbon nanotubes

A direct method is described to determine the chiral indices (u, v) of a carbon nanotube from a nanobeam electron diffraction pattern of the nanotube with high accuracy. This method is a one-step procedure and allows rapid and precise assignment of the chiral indices of carbon nanotubes. Using a contemporary electron microscope, we have been able to achieve an accuracy that enables us to assign the chiral indices unambiguously up to the range of (30, 30), corresponding to a diameter of 4.0 nm. Examples of determination of the chiral indices for two single-walled carbon nanotubes are presented as an illustration of the method.