Decahedral clusters

The decahedral global minima are shown in Figs. 11-13. The structures have been grouped according to the number of atoms along the fivefold axis of the pentagonal bipyramid upon which they are based, and the decahedral region of the structural phase diagram (Fig. 4) has also been subdivided on this basis.

  

Figure 11: Global minima based upon a decahedron with three atoms along the fivefold axis.

Decahedral clusters grow by capping exposed $\{100\}$ faces and filling in the grooves produced by the re-entrant $\{111\}$ faces. As this process progresses the structure changes from prolate to approximately spherical to oblate. This cycle begins again when a prolate cluster with a longer decahedral axis becomes lower in energy than the oblate cluster (e.g. at $N\approx 30$ and 54). For the clusters based upon a pentagonal bipyramid with 5 atoms along the fivefold axis ($N\ge 54$), the growth proceeds asymmetrically--the decahedral axis does not always pass through the center of the cluster. For example, for 54C the surface structure of the 75-atom Marks decahedron is completed on one side of the cluster before atoms are added to the other.

  

Figure 12: Global minima based upon a decahedron with four atoms along the fivefold axis.

Deviations from this basic growth scheme occur for N=21-30 (Fig. 11) and N=48-52, 58, 60 and 62 (Fig. 12). These structures are formed by addition of atoms to the $\{111\}$ faces surrounding the fivefold axis in sites which are hcp with respect to the five fcc tetrahedra that make up the decahedra. These structures are more favourable even though they are more strained than the usual decahedra because they have a larger n_nn. For N=21-30 these structures are actually fragments of the 55-atom Mackay icosahedron.

The complete Marks decahedron, 75C, is particularly stable. The value of $\rho_0$ at which it becomes the global minimum (5.81) is the lowest of any of the decahedra. As this value of $\rho_{min}$ suggests, it is also the global minimum for $\rm LJ_{75}$.[38] This stability is also indicated by the large peak in $\Delta_2 E$ for $\rho_0$=10 and 14. Other particularly stable structures occur at N=64 and 71; these are fragments of 75C with 3 and 4 $\{100\}$ faces of the Marks decahedron complete.

  

Figure 13: Global minima based upon a decahedron with five atoms along the fivefold axis.

Decahedral structures have been regularly seen in supported metal clusters.[30] However, it is only recently that further experimental evidence for the existence of Marks decahedra has been found in studies of gold clusters passivated by alkylthiolates.[33,34,35] Whetten and coworkers were able to isolate fractions with narrow size distributions which corresponded to the 75-, 101- and 146-atom Marks decahedra. It is significant to note that our previous paper on Morse clusters[38] foreshadowed this discovery by recognizing the especial stability of the 75-atom Marks decahedron, thus again showing the utility of Morse clusters as a model system.