Spherical Clusters of Simple Metals: Madelung Energies and Structure.
CORNELL UNIV ITHACA NY LAB OF ATOMIC AND SOLID STATE PHYSICS
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Recent experiments on the magic numbers of small sodium clusters suggest that variation of the binding energy of clusters as a function of their size is dominated by the filling of energy levels of electrons moving in a spherical potential. For large clusters it is expected that the electron density distribution starts to be more and more spherical as the cluster increases. The purpose of this communication is to show that if the electron density distribution is assumed to be spherically symmetric, the resulting ionic configuration is determined mainly due a classical Madelung energy. Furthermore it is shown that the ground state structures of the clusters are generally not small pieces of simple lattices bcc, fcc, or hcp, but take always a more spherical shape e.g. icosahedral in the case of a 13 atom cluster. The variation of the structural energy as a function of the cluster size is found to be somewhat smaller than the variation arising from the filling of single electron energy shells giving support to the idea that the dominant magic numbers are determined by the electronic shell structure of a square well potential.
- Solid State Physics