Decahedral clusters

**Figure 2.13:** Global minima based upon a decahedron with three atoms along the fivefold axis.
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**Figure 2.14:** Global minima based upon a decahedron with four atoms along the fivefold axis.
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The growth sequence for the decahedral clusters is quite simple; they grow by capping exposed $\{100\}$ faces and by 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 50). For the clusters based upon a pentagonal bipyramid with 5 atoms along the fivefold axis ( $N\ge 50$ ), 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.

Deviations from this basic growth scheme occur for N=21-30 (Figure 2.13) and 51C. These structures are formed by addition of atoms to the $\{111\}$ faces surrounding the fivefold axis in the hcp sites with respect to the five fcc tetrahedra that make up the decahedral structures. These structures are more favourable even though they are more strained than the usual decahedral structures, because they have a larger n_nn. For N=21-30 these structures are actually fragments of the 55-atom Mackay icosahedron. The difference from the icosahedral structures is that the growth occurs from the five tetrahedra at the bottom of the Mackay icosahedron, rather than the centre.

**Figure 2.15:** Global minima based upon a decahedron with five atoms along the fivefold axis.
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As we mentioned in §2.2.1 the complete Marks' decahehedron, 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 decahedral structures. It is also the global minimum[71] for 75. This stability is also indicated by the large peak in $\Delta_2 E$ for $\rho_0$ =10 and 14. Other particular stable structures occur at N=64 and 71; these are fragments of 75C with 3 and 4 $\{100\}$ faces of the Marks' decahedron complete.