On the representation of random packings of spheres for sintering simulations

In this work, we have developed an algorithm which generates a random packing of irregular sized spheres using the ballistic deposition method. Our aim is to provide useful tools to represent a three-dimensional array of spheres of different sizes that can be used to study the sintering of fine spherical particles. Apart from the well known devices that have been introduced such as relative density, coordination number and radial distribution function, we show how the Voronoi polyhedra can give useful information that can be followed during a sintering simulation. We extend the definition of Voronoi polyhedra such that it will be useful for describing an array of particles of different sizes during sintering.

[1]  J. M. Chaix,et al.  A computer method for random packing of spheres of unequal size , 1986 .

[2]  T. Sanderson,et al.  Physical Sciences: Galactic Gamma-radiation between 200 MeV and 10 GeV , 1972, Nature.

[3]  Exact solution of a generalized ballistic-deposition model. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[5]  G. Bierwagen,et al.  Studies of the Effects of Particle Size Distribution on the Packing Efficiency of Particles , 1974 .

[6]  R. McMeeking,et al.  A diffusional creep law for powder compacts , 1992 .

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

[8]  José L. F. Abascal,et al.  The Voronoi polyhedra as tools for structure determination in simple disordered systems , 1993 .

[9]  Randall M. German,et al.  Particle packing characteristics , 1989 .

[10]  Tamás Vicsek,et al.  Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model , 1985 .

[11]  G. Herdan,et al.  Small particle statistics , 1954 .

[12]  Richard J. Wakeman,et al.  Packing densities of particles with log-normal size distributions , 1975 .

[13]  Hong Yong Sohn,et al.  The effect of particle size distribution on packing density , 1968 .

[14]  R. Jullien,et al.  Particle Size Segregation by Shaking in Two-Dimensional Disc Packings , 1993 .

[15]  E. M. Tory,et al.  Anisotropy in Simulated Random Packing of Equal Spheres , 1968, Nature.

[16]  M. Ashby,et al.  Practical applications of hotisostatic Pressing diagrams: Four case studies , 1983 .

[17]  K. Z. Y. Yen,et al.  A dynamic simulation of particle rearrangement in powder packings with realistic interactions , 1992 .

[18]  Tohru Ogawa,et al.  A new algorithm for three-dimensional voronoi tessellation , 1983 .

[19]  Meakin,et al.  Three-dimensional model for particle-size segregation by shaking. , 1992, Physical review letters.

[20]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[21]  P. Chaudhari,et al.  Computer simulation of amorphous thin films of hard spheres , 1977 .

[22]  G. Cargill.  Dense Random Packing of Hard Spheres as a Structural Model for Noncrystalline Metallic Solids , 1970 .

[23]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[24]  Michitaka Suzuki,et al.  Co-ordination number of a multi-component randomly packed bed of spheres with size distribution , 1985 .

[25]  G. D. Scott,et al.  Radial Distribution of the Random Close Packing of Equal Spheres , 1962, Nature.

[26]  J. D. BERNAL,et al.  Packing of Spheres: Co-ordination of Randomly Packed Spheres , 1960, Nature.

[27]  Paul Meakin,et al.  Random packings of spheres built with sequential models , 1992 .

[28]  M. J. Vold,et al.  Sediment Volume and Structure in Dispersions of Anisometric Particles , 1959 .

[29]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[30]  Charles H. Bennett,et al.  Serially Deposited Amorphous Aggregates of Hard Spheres , 1972 .

[31]  H. Leamy,et al.  Columnar microstructure in vapor-deposited thin films , 1977 .

[32]  E. Arzt.  The influence of an increasing particle coordination on the densification of spherical powders , 1982 .

[33]  Norman A. Fleck,et al.  Yielding of metal powder bonded by isolated contacts , 1992 .

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

[35]  Paul Meakin,et al.  Restructuring effects in the rain model for random deposition , 1987 .

[36]  J. Tien,et al.  Obtaining the radial distribution of random dense packed hard spheres , 1986 .

[37]  J. Wejchert,et al.  On the distribution of cell areas in a Voronoi network , 1986 .

[38]  Robert M. McMeeking,et al.  Power-law creep of powder bonded by isolated contacts , 1992 .

[39]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[40]  Paul Meakin,et al.  Simple Three-Dimensional Models for Ballistic Deposition with Restructuring , 1987 .

[41]  M. J. Powell.  Computer-simulated random packing of spheres , 1980 .

[42]  A. J. Matheson.  Computation of a random packing of hard spheres , 1974 .

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

[44]  M. J. Vold,et al.  THE SEDIMENT VOLUME IN DILUTE DISPERSIONS OF SPHERICAL PARTICLES , 1960 .

[45]  H. Leamy,et al.  Microstructure and magnetism in amorphous rare‐earth–transition‐metal thin films. I. Microstructure , 1978 .

[46]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[47]  N. N. Medvedev,et al.  The algorithm for three-dimensional Voronoi polyhedra , 1986 .

[48]  B. Fox,et al.  Construction of Voronoi Polyhedra , 1978 .

[49]  D. J. Adams,et al.  Computation of Dense Random Packings of Hard Spheres , 1972 .

[50]  D. W. Henderson,et al.  Simulation of structural anisotropy and void formation in amorphous thin films , 1974 .

[51]  W. Visscher,et al.  Random Packing of Equal and Unequal Spheres in Two and Three Dimensions , 1972, Nature.

[52]  A. Cocks.  Overview no. 117 The structure of constitutive laws for the sintering of fine grained materials , 1994 .

[53]  E. Kaldis.  Current Topics in Materials Science , 1980 .

[54]  E. M. Tory,et al.  Simulated random packing of equal spheres , 1973 .

[55]  E. M. Tory,et al.  Computer simulation of isotropic, homogeneous, dense random packing of equal spheres , 1981 .

[56]  J. D. Bernal,et al.  Geometry of the Structure of Monatomic Liquids , 1960, Nature.

[57]  Mihai Popescu,et al.  Defect formation in amorphous structures as revealed by computer simulation , 1984 .