A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometer range (nanoscale). They are one of the allotropes of carbon. Single-walled carbon nanotubes (SWCNTs) have diameters around 0.5–2.0 nanometers, about 100,000 times smaller than the width of a human hair. They can be idealized as cutouts from a two-dimensional graphene sheet rolled up to form a hollow cylinder. Multi-walled carbon nanotubes (MWCNTs) consist of nested single-wall carbon nanotubes in a nested, tube-in-tube structure. Double- and triple-walled carbon nanotubes are special cases of MWCNT. Carbon nanotubes can exhibit remarkable properties, such as exceptional tensile strength and thermal conductivity because of their nanostructure and strength of the bonds between carbon atoms. Some SWCNT structures exhibit high electrical conductivity while others are semiconductors. In addition, carbon nanotubes can be chemically modified. These properties are expected to be valuable in many areas of technology, such as electronics, optics, composite materials (replacing or complementing carbon fibers), nanotechnology, and other applications of materials science. The predicted properties for SWCNTs were tantalizing, but a path to synthesizing them was lacking until 1993, when Iijima and Ichihashi at NEC and Bethune et al. at IBM independently discovered that co-vaporizing carbon and transition metals such as iron and cobalt could specifically catalyze SWCNT formation. These discoveries triggered research that succeeded in greatly increasing the efficiency of the catalytic production technique, and led to an explosion of work to characterize and find applications for SWCNTs. The structure of an ideal (infinitely long) single-walled carbon nanotube is that of a regular hexagonal lattice drawn on an infinite cylindrical surface, whose vertices are the positions of the carbon atoms. Since the length of the carbon-carbon bonds is fairly fixed, there are constraints on the diameter of the cylinder and the arrangement of the atoms on it.