Figure 1

Upper panel: Clusters of icosahedral growth pattern. The 2nd, 3rd, and 4th layers are given in yellow, green, and red, respectively. One of the 20 triangular faces is colored in a deeper shade. Only the structure of the closed shell icosahedra at $N=55$ and 147 has been confirmed so far, and for the other sizes different outer layers are possible [22, 25]. Lower panel: Size dependence of the melting temperature ($T_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}$, black), the latent heat of fusion per atom ($q$, red), and the entropy change upon melting per atom ($\Delta s$, blue). The data, given by the open circles, are joined (for $N>92$) by splines. Error bars are given only for $N$ above 200, in order to avoid cluttering the figure. The error bars for $T_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}$ have about the size of the symbol used. The data for $\Delta s$ and $q$ have their maxima at the same $N$, while those for $T_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}$ can be shifted. The cluster sizes are indicated for some peaks. The $N$ values are given above the data if the cluster geometry is known or can be guessed. The black solid lines, overlapping partially with the blue line, give the calculated entropy change upon melting. The simple hard sphere model gives a surprisingly good fit of the peak shapes.Reuse & Permissions

Figure 2

Photoelectron spectra for cold, negatively charged sodium clusters. The $N=147$ and 309 atom clusters are of icosahedral symmetry; the spectra agree well with theoretical results [22]. The geometry for $N=298$ is unknown. These three spectra are well modulated giving a large modulation (see text). The $N=164$ cluster has such a low symmetry that the electronic bands overlap, giving a low modulation.Reuse & Permissions

Figure 3

Comparison of the latent heat (red) with the modulation of the photoelectron spectra (black). There are six peaks (at $N=147$, 178, 192, 216, 271, and 298) where the maxima occur at the same $N$ in both curves. The code for placing $N$ values is the same as in Fig. 1. The $N$ values are in black if the cluster has icosahedral symmetry. Blue $N$ values indicate possible Marks decahedra [4]. The modulation spectrum also shows electronic shell closings (138, 268) marked in green. Note that the PES have been measured for negatively charged clusters while the melting experiment used positively charged ones. Nevertheless, maxima occur at the same $N$, indicating that geometrical and not electronic shell closings are important in most cases.Reuse & Permissions