The Metal-Nonmetal Transition in Mercury Clusters

Modem supersonic molecular beam techniques provide a direct way to study the stability and valence electron structure of noninteracting, isolated atomic clusters. One of the most widely studied properties is the threshold for photo-ionization and its dependence on cluster size. In Fig. 4.20 we reproduce some experimental results for argon-, krypton-, xenon- (Gantefor et al., 1989), and mercury-clusters (Rademann et al.. 

The ionization energies determined by photoelectron-photoion coincidence spectroscopy are plotted as a function of the cube root of the reciprocal number of atoms x in the cluster. The latter is determined by in situ mass spectroscopy of the ionized clusters. 

Data such as those in Fig. 4.20 can be compared directly with Born s theory of solvation (Makov et al., 1988). The ionization energy is taken to be the difference in solvation energies of a charge e in an infinite dielectric and in a sphere of the same dielectric constant  

Here represents the radius of a sphere containing x atoms, each having the atomic volume calculated from the molar volume of the solid and W is the work function of the corresponding bulk material in the condensed (solid or liquid) phase. This theory works well for the rare gases and the data extrapolate to the limit Ip = W oi the bulk materials. 

In the case of mercury we have to account for the fact that very large clusters are conducting. In the limit — oo appropriate for an ideal conducting sphere, Eq. (4.23) reduces to 

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U. Even Prof. Gerber, could you follow the metal-nonmetal transition in mercury clusters ... 

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