The molecular dynamics calculations in this work were carried out using the penicillin code (Dornford-Smith and Grimes 1995), which uses a fifth-order Gear predictor-corrector integration scheme (Allen and Tildesley 1987). Changes in temperature were imposed by a simple rescaling of velocities every 5 ps, leading to the approximately linear variation of temperature with time shown in Figure 1. It should be noted that the temperature was held constant at 10 K during the time interval marked A in the figure. The time step may be adjusted automatically in the course of a calculation between such rescalings to ensure energy conservation, although time step adjustment did not in fact occur in the course of the calculations reported here. For the finite isolated clusters of ions treated here, interactions (including the Coulomb terms) are computed directly.
In order to study the correspondence between the small clusters studied here and the classical continuum, we have characterised the clusters by their overall dimensions. To be precise, we have computed the principal squared radii of gyration (moments of inertia divided by total mass) of the clusters as the clusters were heated from 10 K to above their vaporization temperature. These quantities show the changes of shape of the clusters, and an example is plotted in Figure 1. The uppermost graph shows the principal squared radii of gyration as a function of time for the 552-particle cluster: note the change to the right-hand axis to cover the expansion of the cluster after evaporation. The vibrations in the solid regime (region A) are enlarged in the central graph, where, to show all three squared radii of gyration on the same scale, the averages over the period from 2 to 12 ps have been subtractd. The bottom graph in Figure 1 shows the oscillations of the liquid drop (region B): the low-frequency oscillations, corresponding to the lowest vibration mode of the drop, have been accentuated by a 31-point moving average, but it is clear from comparing this graph with the uppermost that this has not introduced any spurious features.