An allotrope is a variant of a substance consisting of only one type of atom. It is a new molecular configuration, with new physical properties. Substances that have allotropes include carbon, oxygen, sulfur, and phosphorous. Allotropes of a given substance will often have substantial differences between each other. For example, one allotrope of carbon, fullerene, is many times stronger and lighter than steel. An allotrope should not be confused with phase, which is a change in the way molecules relate to each other, not in the way that individual atoms bond together.

Generally one allotrope will be far more abundant than another. For example, the O2 allotrope of oxygen is far more abundant than the O3 allotrope, ozone. Phosphorous comes in at least 3 allotropic forms; red, black (or purple, or violet), white (or yellow). Red and white phosphorous are the most common, both of which consist of tetrahedrally arranged groups of four phosphorous. The tetrahedral arrangements in red phosphorous are linked into chains, whereas those in white phosphorous are separate. Black phosphorous is arranged in 2-dimensional hexagonal sheets, much like graphite. White prosphorous reacts immediately to the air, oxiding and producing phosphorus pentoxide.

Carbon is the substance with the greatest number of allotropes, with 8 discovered so far. It possesses allotropes most radically different from one another, ranging from soft to hard, opaque to transparent, abrasive to smooth, inexpensive to costly. These allotropes include the amorphous carbon allotrope, carbon nanofoam, carbon nanotube, the diamond allotrope, fullerene allotrope, graphite, lonsdaleite, and ceraphite allotrope. Coal and soot are both both forms of amorphous carbon, one of the most common carbon allotropes. Diamond is an allotrope in which atoms are linked in a 3-D crystalline network of covalent carbon bonds. Diamond, of course, is both very expensive, rare, and strong. Carbon fullerenes are among the strongest and lightest materials known. Carbon nanofoam has an extremely low density, only a few times heavier than air.

Of all the elements which exhibit allotropic properties, carbon is by far the most diverse and interesting. In fact, new allotropes for carbon atoms have been proposed, allotropes with extremely high strength/weight ratios, but synthesizing them requires techniques not yet technologically accessible.