8.2 Background

Carbon clusters have been the subject of research for decades. [137] However, the discovery of the fullerene structure of $\mathrm {C}_{60}$,[138] (figure  8.1) led to a renewal and subsequent explosion of interest in the properties of the clusters. An understanding of the physical and chemical properties of these clusters is important for a large variety of systems; they have a role in the chemistry of comets, carbon stars and molecular clouds (References 2-9 in  [139]), and their properties are important in chemical vapour deposition processes such as the growth of diamond, silicon carbide and carbon nitride thin films.

Figure 8.1: The $\mathrm {C}_{60}$ ``buckyball'' fullerene.

The discovery of the fullerenes, defined as a closed cage structures containing only pentagonal and hexagonal faces, [140] has subsequently generated a substantial body of research dedicated to their structure and molecular properties. Fullerene clusters may now be produced in macroscopic quantities, although structure and mass selection still remains something of an art. A rich variety of physical and chemical properties has been demonstrated, but despite many experimental and theoretical advances the detailed energetics of these systems are not yet fully understood. The question ``which is the smallest stable fullerene?'' remains both interesting and contentious due to the sensitivity of cluster formation to experimental conditions and the challenges posed to accurate theoretical methods by system size.

A 20 atom cluster is the smallest geometrically able to form a fullerene. [140] However, the smallest stable fullerenes most commonly identified in experiments are the $\mathrm{C}_{30}$ and $\mathrm {C}_{32}$ clusters. [141,142,143] The sizes and types of cluster are usually identified experimentally by mass spectrometry and time of flight measurements. Under typical experimental conditions, rings are found to dominate up to approximately 28 carbon atoms (see for example, Ref. [142]), while for clusters of more than 28 atoms, fullerenes are mostly observed, although rings continue to be present. Figure 8.2 illustrates the influence of experimental conditions on relative cluster abundance.

Figure 8.2: Time of flight mass spectra of carbon clusters from two experiments. (a) from H. Handschuh et al. [141] and (b) from H. Kietzmann et al., [143] where a higher abundance of $\mathrm {C}_{32}$ than $\mathrm {C}_{60}$ was observed. The difference in abundance between the two experiments is mostly due to an optimised annealing of the clusters in (b).