We present a review of experimental and theoretical results on the nucleation and growth of single-walled nanotubes, with particular emphasis on the growth of nanotube bundles emerging from catalyst particles obtained from evaporation-based elaboration techniques. General results are first discussed. Experiments strongly suggest a root-growth process in which carbon, dissolved at high temperatures in catalytic particles, segregates at the surface at lower temperatures to form tube embryos and finally nanotubes through a nucleation and growth process. A theoretical analysis of the reasons carbon does not always form graphene sheets to wrap the particles suggests analogies with other surface or interface instabilities, in particular, with those found in epitaxial growth. In the second part, detailed experimental results for nickel-rare earth metal catalysts are presented. By using various electron microscopy techniques, it is shown that carbon and the rare earth metal co-segregate at the surface of the particle and form carbide platelets, providing nucleation sites for nanotubes growing in directions perpendicular to the surface. A simple theoretical model is then presented in which the role of the rare earth metal is just to transfer electrons from metal to carbon. The graphene sheet is shown to become unstable; pentagons and heptagons are favored, which can explain the occurrence of local curvatures and of tube embryos. Finally, a brief discussion of some recent atomistic models is given.
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