^{1}, Anne K. Starace

^{1}, Colleen M. Neal

^{1}, Martin F. Jarrold

^{1,a)}, Sara Núñez

^{2}, José M. López

^{2}and Andrés Aguado

^{2,b)}

### Abstract

Heat capacities have been measured for clusters and compared with results for pure clusters. and have the same number of atoms and the same number of valence electrons (excluding the copper d electrons). Both clusters show peaks in their heat capacities that can be attributed to melting transitions; however, substitution of an aluminum atom by a copper atom causes significant changes in the melting behavior. The sharp drop in the melting temperature that occurs between and 56 for pure aluminumclusters does not occur for the analogs. First-principles density-functional theory has been used to locate the global minimum energy structures of the dopedclusters. The results show that the copper atom substitutes for an interior aluminum atom, preferably one with a local face-centered-cubic environment. Substitution does not substantially change the electronic or geometric structures of the host cluster unless there are several isomers close to the ground state. The main structural effect is a contraction of the bond lengths around the copper impurity, which induces both a contraction of the whole cluster and a stress redistribution between the Al–Al bonds. The size dependence of the substitution energy is correlated with the change in the latent heat of melting on substitution.

We gratefully acknowledge the support of the National Science Foundation, the Spanish MEC, and the European Regional Development Fund (Project Nos. MAT2005-03415 and VA068A06).

INTRODUCTION

EXPERIMENTAL METHODS

EXPERIMENTAL RESULTS

PRELIMINARY DISCUSSION OF EXPERIMENTAL RESULTS

COMPUTATIONAL METHODS

THEORETICAL RESULTS

DISCUSSION

CONCLUSIONS

## Figures

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).

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).

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).

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 .

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).

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.

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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