Interpretation of electron diffraction from carbon nanotube bundles presenting precise helicity

The structure of bundles of carbon nanotubes produced by catalytic chemical vapor deposition has been studied by electron diffraction. The experimental results were analyzed with the kinematical theory of diffraction. An interpretation of the diffraction patterns demonstrates unambiguously that some bundles are made of double-walled carbon nanotubes, and not single-walled nanotubes as previously reported in Phys. Rev. B 64, 125425 (2001). In this previous work, we have focused our attention on bundles presenting one or two helicities. The interpretation of our diffraction data based on the assumption of double-walled nanotubes is shown to fit remarkably with experiment. In the present paper, the detailed analysis of an electron diffraction pattern from a small bundle exhibiting two helicities is made and we deduced the most probable wrapping indices of the two tubes constituting the double-walled nanotubes.

Figure 1

(a) SAED pattern of a bundle exhibiting precise helicities and (b) magnification of the equatorial line labeled A in (a) (Ref. 11).

Figure 2

Experimental equatorial line profiles recorded with different exposure times.

Figure 3

Comparison between the experimental equatorial line profile and the computed equatorial line profiles (a) for a $(\rho =4.4\mathrm{\AA })@(\rho =7.7\mathrm{\AA })$ DWNT bundle, (b) for a $(\rho =5.9\mathrm{\AA })@(\rho =9.2\mathrm{\AA })$ DWNT bundle, (c) for a SWNT bundle with tubes of $\rho =7.7\mathrm{\AA }$, and (d) for a SWNT bundle with tubes of $\rho =9.2\mathrm{\AA }$. The computed profiles are average spectra over all the 2D crystal orientations in the continuum theory. Each bundle is made of 13 nanotubes (DWNT or SWNT).

Figure 4

Experimental equatorial line profile compared with the computed EL profile for different small bundles of DWNT’s.

Figure 5

Comparison of two simulated patterns of a bundle of 13 (11,0)@(16,6) DWNT’s computed at normal incidence (a) and for a tilt angle of 15° (b).

Figure 6

Experimental intensity profile of the “layer line” $\mathrm{E}+\mathrm{F}$ compared with the corresponding layer lines for different angle tilts of 0°, 5°, 10°, 15°, 20°, 25° simulated with a bundle of 13 (11,0)@(16,6) DWNT’s.

Figure 7

Experimental profiles of layer lines C and D compared with the corresponding simulated profiles of layer lines for two bundles constituted, respectively, of (11,0)@(16,6) DWNT’s and (8,3)@(19,0) DWNT’s with a tilt angle of 15°. The large central peak of the experimental spectrum is due to the unscattered beam.