Annotated Bibliography of Electron Diffraction from Nanotubes


This bibliography is intended to provide a comprehensive coverage of literature in chronological order on this subject and comments are welcome on any omission of important papers or misunderstanding of the cited literature.

S. Iijima, Helical mirotubules of graphitic carbon. Nature 354, 56 (1991).

First paper reporting the observation of nanotubes and electron diffraction pattern showing helical structure of the multiwalled nanotubes.

S. Iijima and T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter. Nature 363, 603 (1993).

Observation of single-walled carbon nanotubes and show evidence of helical structure using electron diffraction. Helicity is equaled to the twist angle observed in the electron diffraction pattern. 2mm symmetry is observed.

X.F. Zhang, X.B. Zhang, G. Van Tendeloo, S. Amelinckx, M. Op de Beeck, and J. Van Landuyt, Carbon nano-tube; their formation process and observation by electron microscopy. J. Cryst. Growth 130, 368 (1993).

A systematic study of multiwalled carbon nanotubes using electron imaging and electron diffraction.

X.B. Zhang, X.F. Zhang, S. Amelinckx,  G. Van Tendeloo, J. Van Landuyt, The reciprocal space of carbon tubes: a detailed interpretation of the electron diffraction effects. Ultramicroscopy 54, 237 (1994).

Geometrical discussion of electron difffraction from carbon nanotubes in the reciprocal space.

L.-C. Qin, Electron diffraction from cylindrical nanotubes. J. Mater. Res. 9, 2450 (1994).

Helical diffraction theory is formulated to account analytically in closed form for the scattering amplitude from nanotubes.

A.A. Lucas, V. Bruyninckx, and Ph. Lambin, Calculating the diffraction of electrons or x-rays by carbon nanotubes. Europhys. Lett. 35, 355 (1996).

Helical diffraction theory is formulated using different symbols showing equivalent results as Qin 1994.

L.-C. Qin, T. Ichihashi, and S. Iijima, On the measurement of helicity of carbon nanotubes. Ultramicroscopy 67, 181 (1997).

Cylindrical correction is shown to be necessary which can lead to errors as large as 80% if uncorrected.

J.M. Cowley, P. Nikolaev, A. Thess, and R.E. Smalley, Electron nano-diffraction study of carbon single-walled nanotube ropes. Chem. Phys. Lett. 265, 379 (1997).

Observation of [10,10] nanotubes using nanodiffraction in STEM.

L.-C. Qin, S. Iijima, H. Kataura, Y. Maniwa, S. Suzuki, and Y. Achiba, Helicity and packing of single-walled carbon nanotubes studied by electron nanodiffraction. Chem. Phys. Lett. 268, 101 (1997).

Shows helicity distribution in single-walled carbon nanotubes produced by laser evaporation is rather uniform instead of all [10,10].

Ph. Lambin and A.A. Lucas, Quantitative theory of diffraction by carbon nanotubes. Phys. Rev. B 56, 3571 (1997).

Helical diffraction theory incorporating the atomic positions of carbon atoms in a nanotube.

L.-C. Qin, Measuring the true helicity of carbon nanotubes. Chem. Phys. Lett. 297, 23 (1998).

Proposes a scheme for correcting cylindrical effects. Order of dominant Bessel functions is derived geometrically.

S. Amelinckx, A.A. Lucas, and Ph. Lambin, Electron diffraction and microscopy of nanotubes. Rep. Prog. Phys. 62, 1471 (1999).

A review article summarizing the authors' results. Comprehensive on the geometrical interpretation of the electron diffraction patterns of carbon nanotubes.

L.-C. Qin, Helical diffraction from tubular structures. Mater. Characterization 44, 407 (2000).

A systematic procedure incorporating cylindrical correction is given for measuring helicity from electron diffraction patterns.

M. Gao, J.M. Zuo, R.D. Twesten, I. Petrov, L.A. Nagahara, and R. Zhang, Structure determination of individual single-wall carbon nanotubes by nanoarea electron diffraction. Appl. Phys. Lett. 82, 2703 (2003).

Establishes a procedure to obtain helicity from the ratio of layer line spacings.

J.M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L.A. Nagahara, Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300, 1419 (2003).

Using a crystallographic method (over sampling) to obtain the atomic structure of a double-walled carbon nanotube.

Z. Liu and L.-C. Qin, Symmetry of electron diffraction from single-walled carbon nanotubes. Chem. Phys. Lett. 400, 430 (2004).

2mm symmetry is always present in electron diffraction patterns of single-walled carbon nanotubes and shows that there is only one order of Bessel function that is dominating the scattering intensities on the layer lines.

Z. Liu and L.-C. Qin, Breakdown of 2mm symmetry in electron diffraction from multiwalled carbon nanotubes. Chem. Phys. Lett. 402, 202 (2004).

Shows that the 2mm symmetry can breakdown in the electron diffraction patterns of multiwalled carbon nanotubes due to coherent interference between waves from different shells when they overlap on the same layer lines.

Z. Liu and L.-C. Qin, A direct method to determine the chiral indices of carbon nanotubes. Chem. Phys. Lett. 408, 75 (2005).

Establishes a procedure to measure the chiral indices [u,v] of carbon nanotubes using the relationship I1=|Jv(ƒÎdR)|2, I2=|Ju(ƒÎdR)|2, and I3=|Ju+v(ƒÎdR)|2.

L.-C. Qin, Electron diffraction from carbon nanotubes. Rep. Prog. Phys. 69, 2761 (2006).

A review article on the electron diffraction from carbon nanotubes with a detailed treatment of electron scattering.

L.-C. Qin, Determination of the chiral indices (n,m) of carbon nanotubes by electron diffraction. Phys. Chem. Chem. Phys. 9, 31 (2007).

An up to date summary of advances on the measurement of chiral indices using electron diffraction.


Lu-Chang Qin
Department of Physics & Astronomy
University of North Carolina at Chapel Hill