Conference Paper
A Novel Delaunay Simplex Technique for Detection of Crystalline Nuclei in Dense Packings of Spheres.
DOI: 10.1007/11424758_84 Conference: Computational Science and Its Applications  ICCSA 2005, International Conference, Singapore, May 912, 2005, Proceedings, Part I
Source: DBLP

Conference Paper: Critical densities in hard sphere packings. Delaunay simplex analysis.
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ABSTRACT: A large set of computer models (more then 200 models) of hard sphere packings with packing fraction eta between 0.52  0.72 is examined. Every packing consist of 10.000 identical spheres in the model box with periodic boundary conditions. Delaunay simplexes (quadruples of mutually closest spheres) with shape resembling to perfect tetrahedron or quartoctahedron are studied. Fraction of such simplexes is studied as a function of packing density. Structure changes at the transition from disordered to crystalline phase are discussed. A limited packing fraction of the noncrystalline packing is estimated as 0.6455plusmn0.0015. The ratio of tetrahedral to quartoctahedral simplexes (T/Q) in the packing at this density provided to be close to 2/3. We pay attention to one more critical interval of density at around eta=0.665 plusmn0.005. At this density the crystalline nuclei which were in the packing run into unified crystal and the ratio T/Q reaches a crystalline value 1/2.3rd International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2006, Banff, Alberta, Canada, July 25, 2006; 01/2006  [Show abstract] [Hide abstract]
ABSTRACT: In this chapter we apply a computational geometry technique to investigate the structure of packings of hard spheres. The hard sphere model is the base for understanding the structure of many physical matters: liquids, solids, colloids and granular materials. The structure analysis is based on the concept of the Voronoi Diagram (VoronoiDelaunay tessellation), which is well known in mathematics and physics. The Delaunay simplexes are used as the main instrument for this work. They define the simplest structural elements in the threedimensional space. A challenging problem is to relate geometrical characteristics of the simplexes (e.g. their shape) with structural properties of the packing. In this chapter we review our recent results related to this problem. The presented outcome may be of interest to both mathematicians and physicists. The idea of structural analysis of atomic systems, which was first proposed in computational physics, is a subject for further mathematical development. On the other hand, physicists, chemists and material scientists, who are still using traditional methods for structure characterization, have an opportunity to learn more about this new technique and its implementation. We present the analysis of hard sphere packings with different densities. Our method permits to tackle a renowned physical problem: to reveal a geometrical principle of disordered packings. The proposed analysis of Delaunay simplexes can also be applied to structural investigation of other molecular systems.10/2008: pages 1345;  [Show abstract] [Hide abstract]
ABSTRACT: The crystallization process of a simple liquid upon slow cooling has been modeled by the MonteCarlo method. The model contains 10,000 LennardJones atoms in the model box with periodic boundary conditions. The model structure is investigated at different stages of crystallization using Delaunay simplices. The simplex belonging to one or another particular crystal structure was determined by the shape of the given simplex taking into account the shape of its neighboring simplices. Simplices typical of the fcc and hcp crystal structures, as well as of polytetrahedral aggregates, not typical of crystals, were studied. The analysis has shown that the “precursors” of a hcp structure are strongly dominating over the “precursors” of a fcc structure in liquid phase before the beginning of crystallization. When crystallization starts, small embryos of the fcc structure are observed; the simplices peculiar to hcp are present at that in great amount, but they are distributed over the sample more uniformly. As crystallization proceeds, the portion of the fcc phase grows faster than hcp. However, no unified crystal appears in our case of slow cooling of the model. A complex polycrystalline structure containing crystalline regions with multiple twinning, pentagonal prisms and elements of icosahedral structures arises instead.Journal of Structural Chemistry 01/2006; 47(2):267276. · 0.58 Impact Factor
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Marina L. Gavrilova 