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Why does a 13-atom copper or argon cluster have most of its atoms on the surface?

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cluster Figure 1: The four stable geometric structures of the seven-atom cluster of argon, in order of increasing energy: (A) A pentagonal bipyramid. (B) A regular octahedron with one face capped by the seventh atom. (C) A regular tetrahedron with three of its faces capped by other atoms. (D) A trigonal bipyramid with two of its faces capped by other atoms; although this has the highest energy of the four structures, it is very close in energy to the tricapped tetrahedron.

In a 13-atom cluster of copper or argon, the high proportion of surface atoms is a direct consequence of the cluster's small size and its geometric arrangement. Specifically, 12 of the 13 atoms are positioned on the surface, while only one atom occupies the interior.1

This occurs because, unlike bulk matter where the vast majority of particles are located in the interior, a small cluster consists of a limited number of atoms where the surface-to-volume ratio is extremely high. In the case of a 13-atom cluster, the atoms typically form a regular icosahedron, a highly stable structure where 12 atoms surround a single central atom.123

Because surface atoms are bonded only to atoms within their own layer and those directly beneath them, they have fewer neighbors holding them to the main body compared to atoms in the interior. This structural reality is a primary reason why the average binding energies of atoms in small clusters are generally lower than those found in bulk matter.1