Structure and dynamics of spherical crystals characterized for the Thomson problem

Candidates for global minima of the Thomson problem for $N$ charges on a sphere are located for $N\le 400$ and selected sizes up to $N=972$. These results supersede many of the lowest minima located in previous work, with particularly large improvements for $N>400$. Our analysis reveals interesting topological defects, which are likely to play an important role in determining the mechanical and electrical properties of systems confined to a spherical geometry. We also find low-energy rearrangements for the Thomson model, an observation which suggests that suitable mesoscopic systems with analogous coarse-grained structure may exhibit fluxional dynamics.

Figure 1

(Color online) Voronoi representations of global minima for selected sizes that exhibit pentagon patches. $N=47$ also has a pentagon pair defect.

Figure 2

(Color online) Global minima for selected sizes that exhibit the $3\times 3$ defect. Both the Voronoi construction and a real-space view are shown for $N=172$.

Figure 3

(Color online) Global minima for selected sizes that exhibit extended dislocations consisting of a heptagon and two pentagons.

Figure 4

(Color online) Global minima for selected sizes that exhibit grain boundaries and twinned grain boundaries.

Figure 5

(Color online) Defect migrations linking the global minimum to a low-lying local minimum for $N=732$ (top) and two low-lying minima for $N=972$ (bottom). The forward and reverse barriers in atomic units are $6.60\times {10}^{-4}$ and $4.22\times {10}^{-4}$ for $N=732$ and $4.24\times {10}^{-3}$ and $1.04\times {10}^{-3}$ for $N=972$.