Statistical verification of crystallization in hard sphere packings under densification

Abstract. The performance of various structure characteristics in the task of indicating structural peculiarities in packings of hard spheres is investigated. Various characteristics based on Voronoi polyhedra, spherical harmonics, and Delaunay simplices are considered together with the pair correlation function and the mean number of r-close triples. They are applied to a set of hard sphere packings of density φ from 0.62 to 0.72. It turns out that all used structure characteristics are able to indicate changes of order from non-crystalline to crystalline packings. However, not all of them are sensitive enough to indicate different stages of structure transformation under densification. The characteristics based on Delaunay simplices turn out to be the most sensitive for this purpose. For the models considered three principal structure classes are found: packings of densities lower than the known critical value 0.64 showing a non-crystalline behavior; packings with considerable crystalline regions for φ up to 0.66–0.67; rather complete crystals although with numerous defects for φ above 0.67.

[1]  J. D. Bernal,et al.  The Bakerian Lecture, 1962 The structure of liquids , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  Clarke,et al.  Structural changes accompanying densification of random hard-sphere packings. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  V. Luchnikov,et al.  Crystallization of dense hard sphere packings , 2002 .

[4]  P. Debenedetti,et al.  Computational investigation of order, structure, and dynamics in modified water models. , 2005, The journal of physical chemistry. B.

[5]  L. Oger,et al.  Geometrical characterization of hard-sphere systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  J. Mościński,et al.  C-language program for the irregular close packing of hard spheres , 1991 .

[7]  M. J. Ruiz-Montero,et al.  Numerical evidence for bcc ordering at the surface of a critical fcc nucleus. , 1995, Physical review letters.

[8]  Tomaso Aste,et al.  Variations around disordered close packing , 2005 .

[9]  Alfons van Blaaderen,et al.  Real-Space Structure of Colloidal Hard-Sphere Glasses , 1995, Science.

[10]  G. Mason.  Radial Distribution Functions from Small Packings of Spheres , 1968, Nature.

[11]  S. Torquato,et al.  Hard-sphere statistics along the metastable amorphous branch , 1998 .

[12]  D. Kilgour,et al.  The density of random close packing of spheres , 1969 .

[13]  William G. Hoover,et al.  Melting Transition and Communal Entropy for Hard Spheres , 1968 .

[14]  Thomas M Truskett,et al.  Structural precursor to freezing in the hard-disk and hard-sphere systems , 1998 .

[15]  D Frenkel,et al.  Numerical prediction of absolute crystallization rates in hard-sphere colloids. , 2004, The Journal of chemical physics.

[16]  E. M. Tory,et al.  Simulation of random packing of spheres , 1979 .

[17]  W. Brostow,et al.  Distinguishing liquids from amorphous solids: Percolation analysis on the Voronoi network , 1990 .

[18]  J. L Finney,et al.  A procedure for the construction of Voronoi polyhedra , 1979 .

[19]  Thomas M Truskett,et al.  Is random close packing of spheres well defined? , 2000, Physical review letters.

[20]  Pieter Rein ten Wolde,et al.  Numerical calculation of the rate of crystal nucleation in a Lennard‐Jones system at moderate undercooling , 1996 .

[21]  H. Reiss,et al.  Hard spheres: scaled particle theory and exact relations on the existence and structure of the fluid/solid phase transition , 1986 .

[22]  Tomaso Aste,et al.  Volume fluctuations and geometrical constraints in granular packs. , 2006, Physical review letters.

[23]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[24]  Jodrey,et al.  Computer simulation of close random packing of equal spheres. , 1985, Physical review. A, General physics.

[25]  Jayanth R Banavar,et al.  Molecular dynamics simulations of crystallization of hard spheres. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Random close packing revisited: ways to pack frictionless disks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  D. Stoyan,et al.  Statistical Analysis of Simulated Random Packings of Spheres , 2002 .

[28]  N. N. Medvedev,et al.  Shape of the Delaunay simplices in dense random packings of hard and soft spheres , 1987 .

[29]  J. L. Finney,et al.  Random packings and the structure of simple liquids. I. The geometry of random close packing , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[30]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[31]  Salvatore Torquato,et al.  Diversity of order and densities in jammed hard-particle packings. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Luc Oger,et al.  Voronoi and Radical Tessellations of Packings of Spheres , 2002, International Conference on Computational Science.

[33]  Thomas M Truskett,et al.  Towards a quantification of disorder in materials: distinguishing equilibrium and glassy sphere packings , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[34]  Nikolai N. Medvedev,et al.  Geometrical analysis of the structure of simple liquids : percolation approach , 1991 .

[35]  J. D. Bernal,et al.  A Geometrical Approach to the Structure Of Liquids , 1959, Nature.

[36]  M. Gavrilova,et al.  The coloring of the voronoi network: investigation of structural heterogeneity in the packings of spheres , 2005 .

[37]  T Aste,et al.  Geometrical structure of disordered sphere packings. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  P. Steinhardt,et al.  Bond-orientational order in liquids and glasses , 1983 .

[39]  S. B. Yuste,et al.  Is there a glass transition for dense hard-sphere systems? , 1998 .

[40]  Srikanth Sastry,et al.  What do we learn from the local geometry of glass-forming liquids? , 2002, Physical review letters.

[41]  Adrian Baddeley,et al.  A Third Order Point Process Characteristic , 1998, Advances in Applied Probability.

[42]  A. C. Mitus,et al.  Local structure analysis of the hard-disk fluid near melting , 1997 .