The concept of a spatial-velocity hodograph is introduced to describe quantitatively the extrusion of a carbon tubule from a catalytic particle. The conditions under which a continuous tubular surface can be generated are discussed in terms of this hodograph, the shape of which determines the geometry of the initial nanotube. The model is consistent with all observed tubular shapes and explains why the formation process induces stresses that may lead to "spontaneous" plastic deformation of the tubule. This result is due to the violation of the continuity condition, that is, to the mismatch between the extrusion velocity by the catalytic particle, required to generate a continuous tubular surface, and the rate of carbon deposition.

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PACK 81.10 -Methods of crystal growth and purification. methods).

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A model that postulates a mixture of scroll-shaped and concentric, cylindrical graphene sheets is proposed to explain the microstructure of graphite multishell nanotubes grown by arc discharge. The model is consistent with the observed occurrence of a relatively small number of different chiral angles within the same tubule. The model explains clustering in a natural way and is consistent with the observation of asymmetric (0002) lattice fringe patterns and with the occurrence of singular fringe spacings larger than c/2 (c is the c parameter of graphite) in such patterns. Anisotropic thermal contraction accounts for the 2 to 3 percent increase in the c parameter of nanotubes, compared with bulk graphite, but is too small to explain the singular fringe spacings. The model also explains the formation of multishell closure domes. Nucleation is attributed to the initial formation of a fullerene "dome."