A Dense Packing of Hard Spheres with Five-fold Symmetry

Bagley, B. G.

doi:10.1038/208674a0

Cited by 145 publications

(64 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…If we deal with rather a small pentagonal structure, it is more natural to imply perfect pentagonal bipyramid as an inherent elements than fcc units. Such an ideal structure with one fivefold symmetry axis covering the all space homogeneously, was described Bagley in 1965 [18]. It can be understood as a succession of pentagonal atomic shells or be presented as a packing of alternating planes in which atoms are arranged in concentric pentagons, where the number of spheres in the pentagon edges is even in one plane and odd in the other [18].…”

Section: Introductionmentioning

confidence: 99%

Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

Аникеенко¹,

Medvedev²,

Bezrukov³

et al. 2007

Journal of Non-Crystalline Solids

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

Аникеенко¹,

Medvedev²,

Bezrukov³

et al. 2007

Journal of Non-Crystalline Solids

View full text Add to dashboard Cite

“…In 1965 Bagley shown how to fill all the space by hard spheres which one axis of fivefold symmetry [3]. The central axis of this structure is the pile of pentagonal bipyramids, and in every of its five sectors is realized a crystalline structure close to FCC.…”

Section: Resultsmentioning

confidence: 99%

The coloring of the voronoi network: investigation of structural heterogeneity in the packings of spheres

Аникеенко

Gavrilova

Medvedev

2005

Japan J. Indust. Appl. Math.

View full text Add to dashboard Cite

The paper describes how the Voronoi-Delaunay approach can be used for investigation of the structural heterogeneity during the process of liquid crystallization. The basic geometric structure for the analysis is the Voronoi network (the Voronoi diagram in a 3-dimensional space). Every site of the Voronoi network is associated with a Delaunay simplex: four neighboring atoms representing the simplest element of the liquid structure. Having a quantitative measure for the shape of simplexes, we suggest to mark (color) Voronoi sites according to a given physical criterion. As a result, the structural investigation is reduced to a task of cluster analysis on a network. Evolution of aggregates of atoms comprised of tetrahedral configurations is studies on an example of Lennard-Jones liquid crystallization. The experiments show that pseudocrystalline aggregates of pentagonal bipyramids spring up along with the genuine crystalline nuclei. The pseudonuclei can stimulate crystallization at the first stage of the process, but slows it down in the final stage of fusion of crystal regions. The results obtained are important for in-depth understanding of the process of the homogeneous crystallization of simple liquids.

show abstract

“…Particles with five-fold symmetries are not described by the 32 crystallographic point groups although they are frequently observed as icosahedral and decahedral clusters [6,7]. Niggli [8] analyzed such non-crystallographic forms in icosahedral and general n-fold symmetries.…”

Section: Modeling Proceduresmentioning

confidence: 99%

GRcut: a modeling tool for nanoparticles including five-fold symmetries

Ogawa

2007

Molecular Simulation

View full text Add to dashboard Cite

A new modeling tool GRcut was developed to be used for atomistic simulation of isolated nanoparticles. It generates atomic coordinates in crystalline nanoparticles with equivalent crystallographic surfaces. In addition to 32 crystallographic point groups, nine non-crystallographic point groups with five-fold symmetries are implemented for modeling icosahedral and decahedral clusters in a systematic way. Curved surfaces with spherical, ellipsoidal and cylindrical shapes in arbitrary orientation are also available. This software is useful as a pre-processing tool for molecular simulation on metallic clusters, quantum dots, or fullerenes in high symmetries. The GRcut is distributed as a Java applet via the Internet to be used on web browsers.

show abstract

A Dense Packing of Hard Spheres with Five-fold Symmetry

Cited by 145 publications

References 9 publications

Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

The coloring of the voronoi network: investigation of structural heterogeneity in the packings of spheres

GRcut: a modeling tool for nanoparticles including five-fold symmetries

Contact Info

Product

Resources

About