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How can a cluster change gradually from solidlike to liquidlike as temperature rises?

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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 can undergo a gradual transition from solidlike to liquidlike states as temperature rises because, unlike bulk matter, they do not have a single, fixed melting point at a given pressure. Instead, solid and liquid clusters of the same composition can coexist within a specific temperature range.1

As temperature increases, the proportion of liquid clusters within a collection grows. At lower temperatures, clusters are predominantly solid, with atoms vibrating around fixed equilibrium positions. As the temperature rises, some clusters transform into a liquidlike state, where particles gain the mobility to diffuse and wander from their equilibrium positions. This transition often appears "slushy" as the mixture shifts from solid to predominantly liquid.1

This gradual change is further influenced by the high surface-to-volume ratio of clusters. A large fraction of particles resides on the surface, which enhances particle mobility and allows the cluster to expand or transfer particles from the interior to the surface, creating vacancies that facilitate liquidlike behavior. Additionally, clusters exhibit an ergodic property, where individual clusters spontaneously and periodically transform between solidlike and liquidlike states over time.1