Clusters are bonded groups of atoms which are not finite, though for large clusters, their bulk may resemble a periodic crystal. The difference between a cluster and a molecule is somewhat ambiguous though elementally pure entities (such as fullerenes) are generally considered clusters, as are entities where the principal bonding forces are intermolecular.

Surface energies

The key difference between clusters and crystals is the presence of surfaces in clusters. A surface is the interface between the bulk of a material and a void and atoms on the surface are typically higher in energy as there are fewer stabilising forces. A stable geometry for a cluster is therefore one which balances favourable interactions in the bulk and at the surface. As the number of atoms in a cluster increases, the ratio of surface atoms to bulk atoms decreases, and interactions in the bulk begin to dominate. For this reason, the shape of small clusters of different numbers of atoms are more varied, while the shape of large clusters of different numbers of atoms may appear similar. At what point does a cluster become a finite quantity of a crystal? That is somewhat philosophical.

Magic Numbers

Some numbers of atoms or molecules within a cluster may lead to disproportionately low energy crystals. These numbers are termed “magic numbers” and usually arise due to the vertices facilitating a high symmetry crystal.