Chirality correlation in double-wall carbon nanotubes as studied by electron diffraction

Structural correlation between two adjacent graphitic layers in double-wall carbon nanotubes (DWNTs) was systematically examined by using electron diffraction. Chiral angles and tube diameters were carefully measured, and the chiral indices of individual DWNTs were accurately determined. As a result, it was found that the interlayer distances of DWNTs were widely distributed in the range between 0.34 and $0.38\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Chiralities of the inner and outer tubes tended to be distributed at higher chiral angles, approaching $30\ifmmode^\circ\else\textdegree\fi{}$, for the tubes with diameter $D<\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. On the other hand, for the tubes with $D>\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the chiral angles were widely distributed, covering the chiral map entirely. Therefore, we consider that tubes with small diameters have a tendency to form armchair type. Correlation of chiralities between the inner and outer tubes was found to be random.