Structural information about carbon nanotubes comes mainly from electron microscopy (EM) and electron diffraction (ED). These techniques proved to be an efficient tool and present knowledge about atomic arrangement in nanotubes, their symmetry and chirality are based on EM and ED studies. In fact EM and ED are the local probes of the structure. On the other hand there is need for characterization of spatial correlation in nanotubes as a whole. Therefore it is desirable to develop a numerical procedure for computation of powder X-ray or neutron diffraction patterns. The results of such modeling could be then compared with the experimental data and agreement between them would be a criterion for rejection of acceptation of the model. Quantitative theory of the kinematical diffraction based on the Cochran, Crick and Vand [1-3] approach developed for the chiral DNA molecules has been adopted to compute the diffraction patterns of carbon nanotubes.
In the present work we develop the direct method, which uses the Debye equation. The Cartesian coordinates of atoms building up the nanotube of given length, diameter and chirality and generated converting a planer graphene sheet into a seamless cylinder. Them all interatomic coordinates are calculated and finally the powder X-ray or neutron diffraction patterns are obtained. The results of such simulations for the zig-zag, armchair and chiral nanotubes of various size are compared with the experimental data collected using synchrotron radiation. The influence of the size on the diffraction patterns is discussed.


[1] X.-D. Fan, L.A. Bursill, Phil.Mag. A 72 (1995) 139
[2] A.A. Lucas, V.Bruyninckx, Ph. Lambin, Europhys. Let. 35 (1996) 1471
[3] Ph. Lambin, A.A. Lucas, Phys.Rev.B 56 (1997) 3571

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