Catenation and Allotropes of Carbon

Carbon's exceptionally strong catenation, introduced in the previous section, gives rise to several structurally very different allotropes — forms of the same element differing only in how its atoms are bonded together.

Diamond is built from carbon atoms that are each $sp^3$ hybridised and tetrahedrally bonded to four other carbon atoms by strong, purely covalent $\sigma$ bonds. This bonding pattern repeats indefinitely in all three spatial directions, producing a single, rigid, three-dimensional covalent network that extends throughout the entire crystal — in effect, a diamond crystal is one giant covalent molecule. Because every atom is locked into this dense, strongly bonded 3-D framework, diamond is exceptionally hard (the hardest known naturally occurring substance) and has an extremely high melting point. Since all four of each carbon's valence electrons are localised in fixed $\sigma$ bonds, with none delocalised, diamond does not conduct electricity. These properties make diamond valuable both as a gemstone and, industrially, as an abrasive and cutting/grinding material.

Graphite, in sharp contrast, is built from carbon atoms that are $sp^2$ hybridised and bonded to only three neighbouring carbon atoms, all lying within a single flat plane, forming an extended two-dimensional network of fused hexagonal rings. The fourth valence electron on each carbon occupies an unhybridised $p$-orbital perpendicular to this plane; these $p$-orbitals overlap sideways across the entire sheet to form a delocalised $\pi$-electron system, which is what makes graphite (unusually for a nonmetal) a good electrical conductor within each layer. Successive hexagonal sheets are stacked roughly $340\ \text{pm}$ apart and held together only by comparatively weak van der Waals forces, with no covalent bonding between layers. Because these layers can slide past one another very easily, graphite is soft, slippery and an excellent solid lubricant, and is also used as pencil "lead" and as electrodes, exploiting its conductivity.

Fullerenes are a third, structurally distinct family of carbon allotropes, discovered much more recently than diamond and graphite. The best-known member, $\text{C}_{60}$ ("buckminsterfullerene"), consists of 60 carbon atoms, all $sp^2$ hybridised, arranged in a closed, hollow, roughly spherical cage built from a network of fused 12 pentagonal and 20 hexagonal rings — geometrically identical to the pattern of panels on a football/soccer ball. Unlike diamond and graphite, which are essentially infinite covalent network solids, a fullerene is a genuine discrete molecule with a fixed, finite molecular formula, and consequently fullerenes are soluble in certain organic solvents, a property diamond and graphite do not share. …