Structure and diameter-dependent bond lengths of a multi-walled carbon nanotube revealed by electron diffraction

We report a quantitative atomic structure determination of a small diameter multi-walled carbon nanotube (MWCNT) of five walls with diameters ranging from ∼17 to 46 Å using electron diffraction. The structure was determined based on quantitative analysis of electron diffraction patterns recorded from the MWCNT. We show that the measurement is sufficiently accurate to reveal significant differences between the measured and the calculated wall diameters based on the ideal hexagonal structure of graphene and the C-C bond length of 1.421 Å. The diameter difference increases as the tube diameter decreases and is up to ∼3.8% for the innermost wall of ∼17 Å in diameter. However, the axial periodicities along the tube direction are almost the same as the ideal carbon nanotubes (CNTs) for all five walls. We fitted our experimental results by deforming the graphene unit cell. The results indicate that on average there are three different bond lengths in chiral walls and two different bond lengths in achiral walls. We expect that the experimental findings here will have a significant impact on our understanding of CNTs and carbon nanostructures in general.