Skip to main content
Article thumbnail
Location of Repository

Geometrical frustration: a study of four-dimensional hard spheres.

By JA van Meel, D Frenkel and P Charbonneau

Abstract

The smallest maximum-kissing-number Voronoi polyhedron of three-dimensional (3D) Euclidean spheres is the icosahedron, and the tetrahedron is the smallest volume that can show up in Delaunay tessellation. No periodic lattice is consistent with either, and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms "icosahedral" and "polytetrahedral" packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4D Euclidean hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in four dimensions is less facile than in three dimensions, which is consistent with earlier observations [M. Skoge, Phys. Rev. E 74, 041127 (2006)]. We conclude that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization

Year: 2009
DOI identifier: 10.1103/PhysRevE.79.030201
OAI identifier: oai:dukespace.lib.duke.edu:10161/12592
Provided by: DukeSpace
Journal:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://hdl.handle.net/10161/12... (external link)
  • http://www.ncbi.nlm.nih.gov/pu... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.