Crystalline Order on a Sphere and the Generalized Thomson Problem
Abstract
We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E_{core} of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r^{γ} (0<γ<2) to four significant figures. The generality of our approach is illustrated by a study of grain boundary proliferation for tilted crystalline order and square lattices on the sphere.
 Publication:

Physical Review Letters
 Pub Date:
 October 2002
 DOI:
 10.1103/PhysRevLett.89.185502
 arXiv:
 arXiv:condmat/0206144
 Bibcode:
 2002PhRvL..89r5502B
 Keywords:

 61.72.Mm;
 61.72.Bb;
 64.60.Cn;
 82.70.Dd;
 Grain and twin boundaries;
 Theories and models of crystal defects;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Colloids;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixed