Conductivity in Allotropic Forms of Carbon

Carbon is the atom of the periodic table that forms the greatest number of compounds. Pure carbon may also form large molecules and crystallize into a number of allotropic forms, such as 35, C o, and C70 from the large fullerene family, nano tubes (a tube-like form of a fullerene), graphite, and diamond. These substances have widely different conductivity properties. 

A crystal of C50 molecules is an insulator. This is no surprise since the interaction between the atoms belonging to different Cgo molecules is weak, while at the same time the HOMO-LUMO gap is large. The broadening of the bands due to intermolecular interactions is fairly small and hence the valence band is formed just by the HOMO, and thus completely filled. Cgo belongs to the organic semiconductors that will be discussed in Chapters 17 and 18. 

There is no energy gap at the Fermi level and this is consistent with the fact that graphite is an electric conductor. The 2p orbitals perpendicular to the molecular plane bind to form % bonds, as was described in Chapter 3. The bonds to other planes in a piece of graphite are noncovalent and weak. These bonds are of the London type, decreasing as 1/R , where R is the distance between the planes. The London forces may physically be described as due to instantaneous electronic displacements 

Diamond is sp hybridized and the valence band is filled. The band gap is large (5.4 ev) and there is no conductivity at T = 0. Diamond will be treated in Section 16.5. 

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