Carbon is capable of forming many allotropes (structurally different forms of the same element) due to its valency. Well-known forms of carbon include diamond and graphite. In recent decades, many more allotropes have been discovered and researched, including ball shapes such as buckminsterfullerene and sheets such as graphene. Larger-scale structures of carbon include nanotubes, nanobuds and nanoribbons. Other unusual forms of carbon exist at very high temperatures or extreme pressures. Around 500 hypothetical 3‐periodic allotropes of carbon are known at the present time, according to the Samara Carbon Allotrope Database (SACADA). Atomic carbon and diatomic carbon Under certain conditions, carbon can be found in its atomic form. It can be formed by vaporizing graphite, by passing large electric currents to form a carbon arc under very low pressure: in vacuum arc. It is extremely reactive, but it is an intermediate product used in the creation of carbenes. Diatomic carbon can also be found under certain conditions. It is often detected via spectroscopy in extraterrestrial bodies, including comets and certain stars. Diamond Diamond is a well-known allotrope of carbon. The hardness, extremely high refractive index, and high dispersion of light make diamond useful for industrial applications and for jewellery. Diamond is the hardest known natural mineral. This makes it an excellent abrasive and makes it hold polish and luster extremely well. No known naturally occurring substance can cut or scratch diamond, except another diamond. In diamond form, carbon is one of the costliest elements. The crystal structure of diamond is a face-centred cubic lattice having eight atoms per unit cell to form a diamond cubic structure. Each carbon atom is covalently bonded to four other carbons in a tetrahedral geometry. These tetrahedrons together form a 3-dimensional network of six-membered carbon rings in the chair conformation, allowing for zero bond angle strain. The bonding occurs through sp3 hybridized orbitals to give a C-C bond length of 154 pm.

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Graphene
Graphene (ˈgræfiːn) is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds. Each atom in a graphene sheet is connected to its three nearest neighbors by σ-bonds and a delocalised π-bond, which contributes to a valence band that extends over the whole sheet.
Synthetic diamond
Lab-grown diamond (LGD; also called laboratory-grown, laboratory-created, man-made, artisan-created, artificial, synthetic, or cultured diamond) is diamond that is produced in a controlled technological process (in contrast to naturally formed diamond, which is created through geological processes and obtained by mining). Unlike diamond simulants (imitations of diamond made of superficially similar non-diamond materials), synthetic diamonds are composed of the same material as naturally formed diamonds – pure carbon crystallized in an isotropic 3D form – and share identical chemical and physical properties.
Amorphous carbon
Amorphous carbon is free, reactive carbon that has no crystalline structure. Amorphous carbon materials may be stabilized by terminating dangling-π bonds with hydrogen. As with other amorphous solids, some short-range order can be observed. Amorphous carbon is often abbreviated to aC for general amorphous carbon, aC:H or HAC for hydrogenated amorphous carbon, or to ta-C for tetrahedral amorphous carbon (also called diamond-like carbon).
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