Theoretical study of gas-phase NanPb clusters and implications for liquid Na–Pb alloys

Abstract

The production of an exceptionally abundant and stable intermetallic cluster Na6Pb has recently been reported. In an attempt to understand why this particular cluster appears so prominently in the experiments, we have performed ab initio total energy calculations on the clusters NanPb with n=3–8. The lowest energy structures and the evaporation energies for these clusters were determined. The energy to evaporate a Na atom from the octahedral cluster Na6Pb was found to be 1.58 eV, larger than that for bigger clusters. We propose that the high abundance of the Na6Pb cluster results from a cascade of evaporations from larger clusters which becomes blocked at Na6Pb because of the large evaporation energy. We also found that the cluster Na4Pb was particularly stable, and suggest how the relative stability of this cluster and Na6Pb might be related to the possible formation of complexes in Na–Pb liquid alloys.

Study of clusters of interest for liquid ionic alloys

“…Our results can be compared to ab initio density functional calculations [13,201 for Na,Pb, performed with the Car-Parrinello method [21] (see Fig. l), which give evaporation energies 2.04, 1.19, 1.58, 0.76 and 1.33 eV for n = 4 -8 respectively [13]. Local maxima appear again for NaPb and Na6Pb and there is good overall agreement between the results of the two methods.…”

“…The l p shell becomes filled with 6 electrons in PbNa, and separated from the empty 2s shell by an energy gap of 1.26 eV; then the 2s shell becomes filled in PbNa6, and separated from the empty Id shell by a gap of 1.20 eV. This physical picture of shell closing for NaPb and Na6Pb is supported by the ab initio calculations [13,20,221 despite the more complex geometries for the latter: up to NasPb, the Pb atom is on the cluster surface, but starting from Na6Pb the ab initio geometries also place the Pb atom in the inner region of the cluster.…”

“…The picture for Li, K, Rb and Cs clusters is very similar, with the fluctuations in the evaporation energy becoming progressively smaller from Li to Cs clusters. Our results can be compared to ab initio density functional calculations [13,201 for Na,Pb, performed with the Car-Parrinello method [21] (see Fig. l), which give evaporation energies 2.04, 1.19, 1.58, 0.76 and 1.33 eV for n = 4 -8 respectively [13].…”

“…Na#b is a very abundant cluster in gas phase experiments [14], and this abundance has been proposed to arise from an evaporation cascade that becomes blocked at this cluster [13] due to its relatively large evaporation energy. The same picture is derived from the present SAPS calculations.…”

“…Our proposed explanation for the large abundance of NasPb in gas-phase experiments was that an evaporation cascade from clusters slightly larger than NasPb is blocked at Na6Pb due to its large evaporation energy, building a large population of this cluster in the molecular beam. On the other hand, in the liquid alloy all the different clusters can compete, and Na4Pb becomes favoured over Na6Pb because the energy required to remove a Na atom from NaPb is larger and because of packing considerations [13].…”