Mapping the Magic Numbers in Binary Lennard-Jones Clusters

Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of Lennard-Jones parameters. In particular, we have shown that just having atoms of different sizes leads to a remarkable stabilization of polytetrahedral structures, including both polyicosahedral clusters and at larger sizes structures with disclination lines.

Figure 1

The energy of the BLJ global minimum for the six values of ${\sigma }_{BB}/{\sigma }_{AA}$ studied, relative to $E_{\mathrm{MI}}^{\mathrm{LJ}}$, a fit to the energies of the Mackay icosahedra for LJ clusters. A line corresponding to the LJ global minima is also included.

Figure 2

The six panels correspond to the energy of the global minimum for the six values of ${\sigma }_{BB}/{\sigma }_{AA}$ studied, relative to $E_{\mathrm{ave}}({\sigma }_{BB}/{\sigma }_{AA})$, a fit to the energies of the global minima at that size ratio using the form $a+b{N}^{1/3}+c{N}^{2/3}+dN$.

Figure 3

The dependence of the energies of the four ${\mathrm{BLJ}}_{13}$ global minima on ${\sigma }_{BB}/{\sigma }_{AA}$.

Figure 4

A selection of the particularly stable BLJ global minima grouped according to their structural type: (a) polyicosahedral, (b) polytetrahedral with disclinations, and (c) the 55-atom Mackay icosahedron with an anti-Mackay overlayer. For the larger clusters, to the right of the cluster, the $A$-atom core is also depicted, and in (b) to the left is the disclination network.

Figure 5

Structural phase diagram showing how the structure of the global minimum depends on $N$ and ${\sigma }_{BB}/{\sigma }_{AA}$. Each point corresponds to the value of ${\sigma }_{BB}/{\sigma }_{AA}$ at which the global minimum for a given $N$ changes. The lines divide the diagram into regions where the global minima have the same structural type. The labels $I_{13}$ and $I_{55}$ stand for the 13- and 55-atom Mackay icosahedra.