Plots of the heat capacities determined for clusters as a function of temperature. The heat capacities are plotted in terms of the classical value , where , is the total number of atoms in the cluster, and is the Boltzmann constant. The spacing between the tick marks on the vertical axes is . The filled red squares show the measured values for clusters. The open black squares are heat capacities recorded for clusters (from Refs. 46 and 52). The solid lines are spline fits. The plots are labeled with the total number of atoms in the cluster . The dashed lines show heat capacities derived from a modified Debye model (Ref. 53).
Examples of fits of the two and three-state models (see text) to the experimental results. Fits of the two-state model to the experimental results are shown for (top left), (top right), and (bottom left). Note that the vertical scale for is more extended than for the other clusters. The filled black squares are the experimental results, the open blue circles are the fits with in Eq. (2) set to (as in the experiments). The solid blue line shows the result of the simulation with . The dashed-dotted lines show the components of the heat capacity due to the latent heat. The solid lines at the bottom of each plot shows the relative abundances of the solidlike (light green) and liquidlike (dark green) clusters as a function of temperature. The fit of the three-state model to the experimental results for is shown in the bottom right panel. The solid lines at the bottom of this plot show the relative abundances of the solid (light green), intermediate (red), and liquid (dark green).
The top panel shows melting temperatures determined from the two-state fits to the experimental results. The filled red circles are the measured values for clusters. The open black circles are for clusters (from Refs. 46 and 52). The middle panel shows the latent heats determined from the area of the peak in the heat capacities for (filled red circles) and (open black circles). The bottom panel shows the entropy changes for melting (see text) for (filled red circles) and (open black circles).
A representative selection of the structures adopted by cluster anions. The yellow (light) sphere represents the Cu impurity. The total number of atoms is given above each structure. For we show three nearly degenerate isomers. All the clusters with share the same structural motif, so we show only two structures explicitly. The same happens within the size ranges and .
Energy released after substitutional doping with copper, as a function of the cluster size (total number of atoms). The doping process, as described in the text, does not change the total number of valence electrons in the cluster (the 10 d-electrons of the copper atom are not considered as valence electrons in this discussion).
Left panel: the difference between the aluminum Mulliken charges in doped and pure clusters is plotted as a function of the distance to the Cu impurity. The dashed line is a simple polynomial fit intended as a guide to the eye. Right panel: vertical ionization potential (VIP) of , plotted as a function of the total number of atoms . The VIP is the energy difference between the cluster anion and the neutral cluster, with both in the optimum geometry of the anion.
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