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


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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    • "For example, the value T=0.05 indicates that the simplex is close to regular quartoctahedron, but there are obviously many other distorted simplexes with the same value of T. Thus, a special measure needs to be introduced in order to recognize simplexes of other specific shapes. For distinguishing simplexes of quartoctahedral shape, where one edge is in 2 times larger than others, it was suggested to calculate the following characteristic [6] "
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    ABSTRACT: The concept of Procrustes distance is applied to the shape analysis of the Delaunay simplexes. Procrustes distance provides a measure of coincidence of two point sets {x<sub>i</sub>} and {y<sub>i</sub>}, i=1..N. For this purpose the variance of point deviations is calculated at the optimal superposition of the sets. It allows to characterize the shape proximity of a given simplex to shape of a reference one, e.g. to the shape of the regular tetrahedron. This approach differs from the method used in physics, where the variations of edge lengths are calculated in order to characterize the simplex shape. We compare both methods on an example of structure analysis of dense packings of hard spheres. The method of Procrustes distance reproduces known structural results; however, it allows to distinguish more details because it deals with simplex vertices, which define the simplex uniquely, in contrast to simplex edges.
    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: We investigate the origin of the Bernal's limiting density of 64% in vol-ume fraction associated with the densest non-crystalline phase (random close packing limit) in equal sphere packings. To this end, we analize equal sphere packings obtained both from experiments and numerical simulationsuse by using a Delaunay simplexes decomposition. We show that the fraction of 'quasi-perfect tetrahedra' grows with the density up to a saturation fraction of ∼ 1/3 reached at the Bernal's limit. Aggre-gate 'polytetrahedral' structures, made of quasi-perfect tetrahedra which share a common triangular face, reveal a clear sharp transition occurring at the density 0.646. These results are consistent with previous findings 1 concerning numerical investigations.
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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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