allotropes of carbon

Pure carbon can be the hardest natural material on Earth or the soft black smear in your pencil, the soot from a candle or a single sheet a few atoms could not be thinner. All of these are the same element, carbon, arranged differently. Different structural forms of one element are called allotropes, and carbon is the champion of them all.

The variety comes from how carbon chooses to bond. In diamond every carbon is sp3-hybridized and bonded to four neighbors in a rigid three-dimensional tetrahedral network, with no free electrons, which makes diamond extremely hard, transparent, and an electrical insulator (yet an excellent heat conductor). In graphite every carbon is sp2-hybridized and bonded to three neighbors in flat hexagonal sheets, with the leftover p electron delocalized across each sheet; the sheets are held to one another only by weak van der Waals forces, so they slide apart (graphite is a lubricant and writes on paper) and the delocalized electrons conduct electricity within a sheet. Graphene is a single such sheet; carbon nanotubes are sheets rolled into cylinders; and fullerenes such as C60 (buckminsterfullerene) are closed cages of hexagons and pentagons, a molecular soccer ball.

Carbon allotropes matter enormously: diamond for cutting and abrasives, graphite for electrodes, lubricants, and nuclear moderators, and the newer nanocarbons (graphene, nanotubes) for their record strength and electrical properties. They are also the cleanest illustration of a central idea: identical atoms can give wildly different materials purely through bonding geometry. Note that diamond and graphite are both true allotropes, but at ordinary pressure graphite is the slightly more stable form, diamond is only kinetically trapped (which is why diamonds do not turn to pencil lead on your shelf).