Heat capacities have been determined for unsupported aluminum clusters, Al49(+) - Al63(+), from 150 to 1050 K. Peaks in the heat capacities due to melting occur between 450 and 650 K (well below the bulk melting point of 933 K). The peaks for Al+51 and Al+52 are bimodal, suggesting the presence of a premelting transition where the surface of the clusters melts around 100 K before the core. For clusters with n > 55 the melting temperatures suddenly drop, and there is a dip in the heat capacities due to a transition between two solid forms before the clusters melt.

Calorimetry measurements (using a method based on multicollision induced dissociation) have been performed for unsupported gallium clusters, Gan+ (n = 30-50 and 55). Melting transitions have been identified from spikes in the heat capacities recorded as a function of temperature. There are enormous fluctuations in the melting temperatures and the heats of fusion with cluster size. Clusters with n = 31, 33, 37, and 45-47 are "magic melters" with particularly well-defined melting transitions. There is a strong correlation between the heats of fusion, entropies of fusion, and the stabilities of the clusters. However, these quantities are not strongly correlated with the melting temperatures.

Heat capacities have been measured as a function of temperature for aluminum cluster cations with 16-48 atoms. Some clusters show peaks in their heat capacities that are attributed to melting transitions. The smallest cluster to show a well-defined melting transition is Al 28 + . For clusters with significant peaks in their heat capacities, the results can be fitted by a two-state model incorporating only solidlike and liquidlike clusters. This indicates that these clusters melt directly, that is, without the involvement of partially melted intermediates. Our previously reported heat capacity measurements for clusters with 49-83 atoms have been reanalyzed using the two-state model and a three-state model that incorporates an intermediate state.Most of the melting transitions can be fitted using the two-state model. However, for a few clusters, the heat capacity peaks are either too broad or possess shoulders, and the three-state model is required to fit the experimental results. Both premelting and "postmelting" behaviors ͑where the second peak is smaller than the first͒ are observed. Using the models, we have determined melting temperatures and latent heats for clusters with 25-83 atoms. The melting temperatures and latent heats show large ͑and uncorrelated͒ size-dependent fluctuations. While most clusters have depressed melting temperatures, there are three regions of high melting temperatures ͑around 37, 47, and 66 atoms͒ where the melting temperatures approach or exceed the bulk melting point.

Dissociation energies have been determined for Al n + clusters ͑n =25-83͒ using a new experimental approach that takes into account the latent heat of melting. According to the arguments presented here, the cohesive energies of the solidlike clusters are made up of contributions from the dissociation energies of the liquidlike clusters and the latent heats for melting. The size-dependent variations in the measured dissociation energies of the liquidlike clusters are small and the variations in the cohesive energies of solidlike clusters result almost entirely from variations in the latent heats for melting. To compare with the measured cohesive energies, density-functional theory has been used to search for the global minimum energy structures. Four groups of low energy structures were found: Distorted decahedral fragments, fcc fragments, fcc fragments with stacking faults, and "disordered." For most cluster sizes, the measured and calculated cohesive energies are strongly correlated. The calculations show that the variations in the cohesive energies ͑and the latent heats͒ result from a combination of geometric and electronic shell effects. For some clusters an electronic shell closing is responsible for the enhanced cohesive energy and latent heat ͑e.g., n =37͒, while for others ͑e.g., n =44͒ a structural shell closing is the cause.

Heat capacities have been measured as a function of temperature for aluminum cluster anions with 35-70 atoms. Melting temperatures and latent heats are determined from peaks in the heat capacities; cohesive energies are obtained for solid clusters from the latent heats and dissociation energies determined for liquid clusters. The melting temperatures, latent heats, and cohesive energies for the aluminum cluster anions are compared to previous measurements for the corresponding cations. Density functional theory calculations have been performed to identify the global minimum energy geometries for the cluster anions. The lowest energy geometries fall into four main families: distorted decahedral fragments, fcc fragments, fcc fragments with stacking faults, and "disordered" roughly spherical structures. The comparison of the cohesive energies for the lowest energy geometries with the measured values allows us to interpret the size variation in the latent heats. Both geometric and electronic shell closings contribute to the variations in the cohesive energies ͑and latent heats͒, but structural changes appear to be mainly responsible for the large variations in the melting temperatures with cluster size. The significant charge dependence of the latent heats found for some cluster sizes indicates that the electronic structure can change substantially when the cluster melts.