Atomic structure determination of carbon nanotubes by electron diffraction

This dissertation comprises developing and applying an electron diffraction technique to determine and map the chiral indices of carbon nanotubes which dictate their chemical and physical properties. Due to the tubular geometry of carbon nanotubes, the diffraction intensity is usually elongated to form layer lines perpendicular to the tubule axis. Based on helical diffraction theory, we show that the diffraction intensity on a layer line is modulated in dominance by the Bessel functions of the lowest order and all the other Bessel functions of higher orders contribute negligibly to the diffraction intensity. By examining the peak positions of the scattering intensities on the non-equatorial principal layer lines in the electron diffraction pattern of a single-walled carbon nanotube, we can assign unambiguously the chiral indices (u,nu) of the carbon nanotube, which define its atomic structure.; A systematic procedure has been established for experimental structure determination. Electron diffraction patterns of carbon nanotubes were obtained using a modern transmission electron microscope equipped with a field emission gun. To avoid damaging the atomic structure of carbon nanotubes, the electron microscope has been operated at 80 kV above which knock-on radiation damage to the carbon nanotubes occurs. Experimentally, we have determined accurately the atomic structure of more than 200 isolated individual carbon nanotubes, and a mapping of these nanotubes in terms of their diameter, helicity and metallicity has been implemented.; We have also studied in detail the symmetry properties of electron diffraction from carbon nanotubes both theoretically and experimentally. We show that the electron diffraction pattern of a single-walled carbon nanotube always has 2mm symmetry. However, 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 the two shells of the same helicity but their chiral indices ( u,nu) have opposite evenness/oddity.; The helical electron diffraction theory has also been extended to study the structure of deformed carbon nanotubes such as elliptical and twisted carbon nanotubes. Finally, we have discussed the possibility of determining the handedness of both single-walled and multiwalled carbon nanotubes by electron diffraction.