Ideal and real structures of different forms of carbon, with some remarks on their geological significance

Carbon is found in nature in a huge variety of allotropic forms and recent research in materials science has encouraged the development of technological materials based on nanocarbon. Carbon atoms with sp(2) or sp(3) hybridization can be thought of as building blocks. Following a bottom-up approach, we show how graphene and diamond molecules are built up and how their properties vary with size, reaching an upper limit with bulk graphite and diamond. Carbon atoms with sp(2) hybridization give rise to an impressive number of different materials, such as carbon nanotubes, graphene nanoribbons, porous carbon and fullerene. As in any crystalline phase, the crystal structures of natural carbon allotropes (i.e. graphite and diamond) contain various types of imperfections. These so-called lattice defects are classified by their dimensions into 0D (point), 1D (line), 2D (planar) and 3D (volume) defects. Lattice defects control the physical properties of crystals and are often a fingerprint of the geological environment in which they formed and were modified. Direct observations of lattice defects are commonly accomplished by transmission electron microscopy. We present and discuss the ideal and real structures of carbon allotropes, the energetics of lattice defects and their significance in understanding geological processes and conditions.