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Which cluster sizes form complete icosahedral shells?
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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 the study of atomic clusters, certain sizes exhibit unusual stability because they possess the exact number of atoms required to form complete, regular icosahedral shells.
The first three cluster sizes in this series are:
- 13 atoms: This forms the base icosahedral structure where all but one atom occupy equivalent sites.1
- 55 atoms: This structure consists of the 13-atom core with an additional 12 atoms placed at the vertices and 30 atoms positioned at the centers of the icosahedron's edges.1
- 147 atoms: This cluster is built upon the 55-atom core, with 12 atoms at the outermost vertices, one atom at the center of each of the 20 faces, and two atoms along each of the 30 edges.1
These specific values are examples of magic numbers, which correspond to geometric configurations that yield significantly higher binding energies compared to clusters of other sizes.2