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10 Introduction to Carbon Materials (a) (b) o 109.5 Figure 1.6: (a) sp3 hybridisation with 109.5o angle between the four orbitals. (b) Crystal structure of diamond (two interpenetrating fcc lattices). Although they consist of the same atomic ingredient, namely carbon, the 3D graphite and diamond crystals are physically extremely different. Graphite, as described above, is a very soft material due to its layered struc- ture, whereas diamond is one of the hardest natural materials because all bonds are covalent σ bonds. The fact that all 4 valence electrons in the outer atomic shell are used in the formation of the σ bondes is also the reason for diamond being an insulator with a large band gap of 5.47 eV. In contrast to insulating diamond, the electrons in the weaker π bonds in graphite are delocalised and, thus, yield good electronic conduction properties. 1.2 Crystal Structure of Graphene and Graphite 1.2.1 Graphene’s honeycomb lattice As already mentioned in the last section, the carbon atoms in graphene con- dense in a honeycomb lattice due to their sp2 hybridisation. The honeycomb lattice is not a Bravais lattice because two neighbouring sites are not equiva- lent. Fig. 1.7 (a) illustrates indeed that a site on the A sublattice has nearest neighbours (nn) in the directions north-east, north-west, and south, whereas a site on the B sublattice has nns in the directions north, south-west, and south-east. Both A and B sublattices, however, are triangular6 Bravais lat- tices, and one may view the honeycomb lattice as a triangular Bravais lattice with a two-atom basis (A and B). The distance between nn carbon atoms is 0.142 nm, which is the average of the single (C–C) and double (C=C) 6The triangular lattice is sometimes also called hexagonal lattice. 0.357nmPDF Image | Physical Properties of Graphene
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