Complete characterization of an (Sb2O3)n/SWNT inclusion composite

The detailed inclusion crystallography of a one-dimensional valentinite Sb₂O₃ crystal incorporated within a helical (21, ?8) single-walled carbon nanotube (SWNT) was identified from a phase image that was recovered via a modified object wave restoration scheme. A detailed analysis of asymmetric fringe contrast in the tube walls provided strong evidence for the chiral sense of the tube itself. Due to the good agreement of the observed wall periodicity with the determined absolute focus values and power spectra obtained from single-pixel line traces along both tube walls, we were able to determine the chiral sense of the SWNT and the tilt angle of the Sb₂O₃/SWNT composite relative to the electron beam. The angle between the optimum $leftlangle {10bar 1} rightrangle $ viewing direction of the crystal fraction and the tube axis, which is aligned with the $leftlangle {4bar 12} rightrangle $ direction of the Sb₂O₃ crystal, is 78.3°. Since small deviations from this viewing direction make an insignificant difference to the observed contrast, a tube inclination of 15° is plausible for both the Sb₂O₃ crystal and the assigned (21, ?8) SWNT, which is the mirror image of a (13, 8) SWNT.