Vibrational Frequencies and Entropies of Small Clusters of Atoms

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Abstract
The frequencies of the normal vibrations have been calculated in the harmonic approximation for small spherical clusters having 13 to 87 atoms in both the cubic and hexagonal‐close‐packed arrangements. The frequency distributions are rather complicated, but exhibit some regularities. The vibrational entropies were calculated from the frequency distributions, The entropy per atom is not a monotonic function of the cluster size but shows a maximum below 40 atoms per cluster and a minimum between 50 and 80 atoms. This behavior of the entropy function is explained by the competition of surface and edge vibrational modes which tend to increase the entropy and size effects which tend to lower it.