Carbon nanotubes (Iijima, 1991) are currently being intensively investigated because of their remarkable electronic and mechanical properties. A multi-walled nanotubes can be thought of as graphite sheets wrapped into a coaxial seamless cylinder. In 1993, Iijima’s group as well as Bethune’s group found that the use of transition-metal catalysts could lead to nanotubes with only a single wall (Iijima, 1993; Bethune, 1993). The diameter of each freestanding single-walled carbon nanotube (SWNT) ranges from 0.7 nm to a few tens nanometers with a maximum length of about 1 μm. Although theoretical calculations have predicted the stability of a SWNT with diameter as small as 0.4 nm (Sawada, 1992), the existence of free-standing SWNTs with a diameter smaller than that of C fullerene (0.7 nm) has been in doubt for quite a while (Ajayan, 1992) because of the extreme curvature and reactivity of these structures. Smaller carbon nanotubes can exist, however, in a spatially confined environment. Carbon nanotubes with diameters of as small as 0.5 nm (Sun, 2000) and 0.4 nm (Qin, 2000) have been observed existing in the centre of multi-walled carbon nanotubes. It is still not clear, however, that whether these small nanotubes are stable in free space. Recently, we have shown that 0.4 nm-sized SWNTs can be produced by means of pyrolysing hydrocarbon molecules in 1 nm-sized channels of A1PO-5 (AFI) single crystals (Tang, 1989; Wang, 2000). These 0.4 nm-sized SWNTs have the same size of the smallest possible fullerene C (Prinz bach, 2000). They are stable inside the AFI channels but not very stable when they are in free standing.