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 9-12, 2005, Proceedings, Part I
Source: DBLP

ABSTRACT The paper presents a new approach for revealing regions (nuclei) of crystalline structures in computer models of dense packings
of spherical atoms using the Voronoi-Delaunay method. A simplex Delaunay, comprised of four atoms, is a simplest element of
the structure. All atomic aggregates in an atomic structure consist of them. A shape of the simplex and the shape of its neighbors
are used to determine whether the Delaunay simplex belongs to a given crystalline structure. Characteristics of simplexes
defining their belonging to FCC and HCP structures are studied. Possibility to use this approach for investigation of other
structures is demonstrated. In particular, polytetrahedral aggregates of atoms untypical for crystals are discussed. Occurrence
and growth of regions in FCC and HCP structures is studied on an example of homogeneous nucleation of the Lennard-Jones liquid.
Volume fraction of these structures in the model during the process of crystallization is calculated.

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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 non-crystalline 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 2-5, 2006; 01/2006
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    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 (Voronoi-Delaunay 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 three-dimensional 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 13-45;
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    ABSTRACT: The crystallization process of a simple liquid upon slow cooling has been modeled by the Monte-Carlo method. The model contains 10,000 Lennard-Jones 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):267-276. · 0.50 Impact Factor

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Jun 1, 2014

Marina L. Gavrilova