Critical densities in hard sphere packings. Delaunay simplex analysis.

Аникеенко, А. В.; Medvedev, N. N.; Elsner, Antje; Lochmann, K.; Stoyan, Dietrich

doi:10.1109/isvd.2006.17

Cited by 2 publications

(4 citation statements)

References 22 publications

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“…We can say that the increase of the density before the Bernal's limit occurs via growth of the number of tetrahedral configurations and their coalescence into polytetrahedral aggregates. A similar behavior of the curves as in Fig.5 (quick rise and sharp fall) was recently obtained in [2] for ratio of fraction of tetrahedral (nT) and quartoctahedral (nQ) Delaunay simplexes. It was shown that the value nT/nQ grows rapidly with densification in disordered packings of hard spheres and reaches about 2/3 at the limiting density, then it quickly decreases to value 1/2 related for crystals.…”

Section: Resultssupporting

confidence: 85%

“…4 shows portion of space occupied by the tetrahedral Delaunay simplexes in packings via the packing density. The behavior of the curve is very similar to obtained in [2] for fraction of the tetrahedral Delaunay simplexes selected by using measure T with boundary value T b = 0.018. It means that both measures select practically the same Delaunay simplexes.…”

Section: Resultssupporting

confidence: 71%

“…Packing with higher densities contains crystalline regions necessarily. Following experiments confirmed this estimation [5,10,30], computer simulations provide the same value [12,22,29], or a bit larger 0.645-0.646 [2,3]. What is important, this density is substantially lower than the maximum packing fraction attainable in the densest crystalline structures 0.74.…”

Section: Introductionmentioning

confidence: 52%

“…It was shown that the value nT/nQ grows rapidly with densification in disordered packings of hard spheres and reaches about 2/3 at the limiting density, then it quickly decreases to value 1/2 related for crystals. Position of the peak was estimated as 0.6455 on interval from 0.644 to 0.647 [2]. Note the position of peak in Fig.5 lies also on this interval.…”

Section: Resultsmentioning

confidence: 92%

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The Role of Quasi-Regular Tetrahedra in Dense Disordered Packings of Hard Spheres

Аникеенко

Medvedev

2007

4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)

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Delaunay simplexes were used for structure analysis of hard sphere packings of different density. A special attention was paid to the simplexes of tetrahedral shape. Clusters of the tetrahedra adjacent by faces represent relatively dense aggregates of spheres atypical for crystalline structures. Such "polytetrahedral" aggregates reveal a characteristic feature of the dense disordered packings. The tetrahedra in point are not completely perfect. They coincide with the class of "quasi-regular tetrahedra" introduced by Hales in his proof of the Kepler conjecture. In this work we discuss a meaning of these tetrahedra and their role in formation of the dense disordered packings. Polytetrahedral principle of a spatial organization seems to be preferable from the statistical viewpoint, as in this case a variety of dense local configurations can be realized. However it has its limit and further increase in density can be provided by formation of crystalline nuclei.

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Section: Resultssupporting

confidence: 85%

Section: Resultssupporting

confidence: 71%