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The existence of different structural forms of the same chemical element. Diamond and graphite are crystalline examples for carbon; molecular oxygen and ozone illustrate that allotropy need not consist only of different packing arrangements of identical molecules.

In crystal polymorphism, the same chemical composition has different crystal structures; for an chemical element, this is a form of allotropy. Diamond has a three-dimensional tetrahedral network of covalent bonds, giving high hardness and a wide band gap. Graphite has strongly bonded planar sheets, with weaker interactions between sheets. Sliding between sheets makes it a useful solid lubricant; mobile electronic states give good electrical conduction within the sheets. Their different properties come from different bonding and structures, despite both being carbon.

The conventional nineteenth-century answer is diamond, graphite and so-called amorphous carbon. These exhibit strikingly different physical properties while sharing the same chemical element, carbon.

Diamond is a crystalline, usually transparent form, very hard and ordinarily an electrical insulator. Its three-dimensional covalent bond network joins each carbon chemical atom to four neighbours. Graphite is a dark, soft, crystalline form with layered bonding; easy shear between layers makes it useful for marking and lubrication. Its electronic structure permits much greater electrical conductivity than that of ordinary diamond.

The historical “amorphous” class includes charcoal, coke, lampblack and soot, as well as carbon-rich materials such as gas-retort carbon. Such names describe preparation and texture as well as structure: restricted-air heating of wood gives charcoal, destructive distillation of coal gives coke, and incomplete combustion of a carbon-bearing fuel produces soot. Modern structural examination shows that these materials can contain small, imperfect graphitic regions. They are not necessarily one distinct pure allotrope. Coal itself is a chemically complex, impure carbon-rich material, rather than a pure form of the chemical element.

A common chemical connection is that pure samples of these carbon forms can yield carbon dioxide upon complete combustion in excess oxygen:Their different hardness, appearance and electrical conductivity arise from structure and impurities, rather than from being different chemical elements. This is the explanatory role of allotropy.

Modern lists also include fullerenes, carbon nanotubes and graphene. These are useful present-day extensions, not discoveries to credit to the 1867 candidate.^[ref]