Defect motifs for spherical topologies
Abstract
Putative global minima for the Thomson problem of N charges on a sphere are located for selected sizes in the range N≤4352 . For small sizes most global minima simply exhibit 12 disclinations. However, around N=400 extended dislocations are common, where a heptagon lies between two pentagons in the Voronoi representation. At larger sizes around N=1000 twinned grain boundaries are favorable and then between about N=1000 and 2000 “rosette” defects appear, containing a central pentagon surrounded by five heptagons alternating with five additional pentagons in the Voronoi representation. Structures with 12 rosettes and I point group symmetry are particularly low in energy for N=1632 and 1902. Above N=2000 the lowest minima located generally contain irregular grain boundaries, sometimes with a few rosette defects. Face dual carbon clusters corresponding to Ih local minima at N=432 and 582 are characterized as local minima for C860 and C1160 .
- Publication:
-
Physical Review B
- Pub Date:
- June 2009
- DOI:
- 10.1103/PhysRevB.79.224115
- Bibcode:
- 2009PhRvB..79v4115W
- Keywords:
-
- 61.72.Mm;
- 02.60.Pn;
- 41.20.Cv;
- 61.72.Bb;
- Grain and twin boundaries;
- Numerical optimization;
- Electrostatics;
- Poisson and Laplace equations boundary-value problems;
- Theories and models of crystal defects