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Abstract: It is shown that the intensities of electron diffraction from a commensurate multiwalled carbon nanotube are sensitive to the angle of rotation of the nanotube about its axis. This dependence is usable to measure the handedness of the commensurate graphene shells of multiwalled carbon nanotubes. The period of intensity oscillation of the scattering intensity for graphene shells of the same handedness is much larger than that for nanotube shells of opposite handedness. By examining the angular dependence of the scattering intensities, the relative handedness, having the same or opposite handedness, of the commensurate shells can, therefore, be determined. [Copyright &y& Elsevier]

Abstract: 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 4.0nm. Examples of determination of the chiral indices for two single-walled carbon nanotubes are presented as an illustration of the method. [Copyright &y& Elsevier]

Abstract: A quantitative method for the structural determination by electron diffraction of nanotubes of elliptical cross-section is developed as a general case while the cylindrical nanotubes are treated as a special class. We found that the chiral indices of a carbon nanotube can always be measured from the electron diffraction pattern regardless if the nanotube is circular or elliptical. An experimental electron diffraction pattern from a partly-deformed carbon nanotube is also analyzed. Assisted with numerical simulations, it is determined that the observed carbon nanotube has chiral indices (15,7) with 8° tilt relative to the horizontal plane and eccentricity of 0.553. [Copyright &y& Elsevier]

Abstract: Electron diffraction patterns of single-walled carbon nanotubes always have 2mm symmetry regardless if the nanotubes themselves have such symmetry. We here show that, for the case of multiwalled carbon nanotubes, the 2mm symmetry can break down when coherent interferences of the electron waves from two different shells take place such as when two shells of the same helicity but their chiral indices (u,v) have opposite evenness/oddity. Both an experimental electron diffraction pattern and analytic analysis are presented to demonstrate the conditions under which the 2mm symmetry breaks down in the electron diffraction patterns of multiwalled carbon nanotubes. [Copyright &y& Elsevier]

We report a method that allows direct, systematic, and accurate determination of the atomic structure of multiwalled carbon nanotubes by analyzing the scattering intensities on the nonequatorial layer lines in the electron diffraction pattern. Complete structure determination of a quadruple-walled carbon nanotube is described as an example, and it was found that the intertubular distance varied from 0.36 nm to 0.5 nm with a mean value of 0.42 nm. [ABSTRACT FROM AUTHOR]