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Why do clusters usually have lower melting points than the same material in bulk form?

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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.

Clusters typically exhibit lower melting points than their corresponding bulk materials primarily because a large fraction of the particles in a cluster are located on its surface.12

Atoms or molecules on the surface of a cluster are bonded to fewer neighbors than those in the interior, resulting in lower average binding energies. This high surface-to-volume ratio enhances particle mobility, as the cluster can more easily expand by increasing the spacing between particles or by transferring atoms from the interior to the surface, which creates vacancies that further facilitate movement. Additionally, the curved shape of a cluster's surface makes it easier for particles to detach compared to the flat surface of bulk matter.12

These factors collectively lower the energy barrier required for the transition from a solidlike to a liquidlike state, often resulting in melting temperatures for small clusters that are roughly half those of the corresponding bulk solids.2