Geometrical frustration: a study of four-dimensional hard spheres.
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.
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https://hdl.handle.net/10161/12592Published Version (Please cite this version)
10.1103/PhysRevE.79.030201Publication Info
van Meel, JA; Frenkel, D; & Charbonneau, P (2009). Geometrical frustration: a study of four-dimensional hard spheres. Phys Rev E Stat Nonlin Soft Matter Phys, 79(3 Pt 1). pp. 030201. 10.1103/PhysRevE.79.030201. Retrieved from https://hdl.handle.net/10161/12592.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Patrick Charbonneau
Professor of Chemistry
Professor Charbonneau studies soft matter. His work combines theory and simulation
to understand the glass problem, protein crystallization, microphase formation, and colloidal
assembly in external fields.

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