Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2008-09-10
Physics
Condensed Matter
Soft Condensed Matter
4 pages, 3 figures; revised interpretation
Scientific paper
10.1103/PhysRevE.79.030201
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. 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 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 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.
Charbonneau Patrick
Frenkel Daan
van Meel Jacobus A.
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