Title

Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials

Author(s)/Creator(s)

Mark Bowick, Department of Physics, Syracuse University, Syracuse, NYFollow
Angelo Cacciuto, Syracuse University and University of Illinois at Urbana-ChampaignFollow
David R. Nelson, Harvard University
Alex Travesset, Iowa State University and Ames Lab

Document Type

Article

Date

9-29-2005

Language

English

Disciplines

Physics

Description/Abstract

The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other potentials. We focus here on long range power law interactions of the form 1/r^gamma (0 < \gamma < 2), with the classic Thomson problem given by gamma=1. At large R/a, where R is the sphere radius and a is the particle spacing, the problem can be reformulated as a continuum elastic model that depends on the Young's modulus of particles packed in the plane and the universal (independent of the pair potential) geometrical interactions between disclination defects. The energy of the continuum model can be expressed as an expansion in powers of the total number of particles, M sim (R/a)^2, with coefficients explicitly related to both geometric and potential-dependent terms. For icosahedral configurations of twelve 5-fold disclinations, the first non-trivial coefficient of the expansion agrees with explicit numerical evaluation for discrete particle arrangements to 4 significant digits; the discrepancy in the 5th digit arises from a contribution to the energy that is sensitive to the particular icosadeltahedral configuration and that is neglected in the continuum calculation. In the limit of a very large number of particles, an instability toward grain boundaries can be understood in terms of a "Debye{--}Huckel" solution, where dislocations have continuous Burgers' vector "charges". Discrete dislocations in grain boundaries for intermediate particle numbers are discussed as well.

Additional Information

17 pages, revtex style More information at http://arxiv.org/abs/cond-mat/0509777

Recommended Citation

Bowick, Mark; Cacciuto, Angelo; Nelson, David R.; and Travesset, Alex, "Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials" (2005). Physics - All Scholarship. 149.
https://surface.syr.edu/phy/149

Source

Harvested from Arxiv.org

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.