Anomalous Size Dependence in the Melting Temperatures of Free Sodium Clusters: An Explanation for the Calorimetry Experiments

The meltinglike transition in unsupported ${\mathrm{Na}}_N$ clusters ($N=55$, 92, 147, 181, 189, 215, 249, 271, 281 and 299) is studied by first-principles isokinetic molecular dynamics simulations. The irregular size dependence of the melting temperatures $T_m$ observed in the calorimetry experiments of Schmidt et al. [Nature (London) 393, 238 (1998)] is quantitatively reproduced. We demonstrate that structural effects alone can explain all broad features of experimental observations. Specifically, maxima in $T_m(N)$ correlate with high surface stability and with structural features such as a high compactness degree.

Figure 1

Comparison between siesta (full symbols) and OF-DFT (continuous line) interatomic forces, for a ${\mathrm{Na}}_{55}$ atomic configuration extracted from a run at 150 K, which was not directly employed in the pseudopotential fitting.

Figure 2

OF-DFT ground state isomers of ${\mathrm{Na}}_{181}$ and ${\mathrm{Na}}_{215}$ found by simulated annealing. Atoms at the surface are represented by light (golden) spheres and interior atoms by dark (blue) spheres.

Figure 3

Caloric curve (left) and specific heat per particle in units of $k_B$ (right) of ${\mathrm{Na}}_{299}$. The latent heat $l_m$ is obtained from the caloric curve as shown. $T^{*}$ signals the beginning of melting.

Figure 4

Size variation of the volume per atom (top) and melting temperature (bottom) in sodium clusters. The dashed line in the upper panel is the best linear fit to the data.