Mathematical model of coordination number of spherical packing
Keywords:
spherical packing, coordination number, dimension space, coordination index, inter-particle distanceAbstract
The article considers a mathematical model of the coordination number, which allows obtaining an equation for multi component spherical packing in the entire range of its change. The resulting model can be used in both 2-d and 3-d spaces. The concept of the coordination index is introduced as a function of the inter-particle distance related to a single particle located near the central particle. The model provides unambiguous compliance between the simulated and calculated data on the coordination numbers of the spherical packing.
References
. Mehta, A., 2011.Granular physics. Cambridge University Press, New York.
. Torquato, S.,2013. Random heterogeneous materials. Springer,London.
. Bondarev,V.G., Migal,L.V., Bondareva,Т.P.,2015. Structural characteristics of regular spherical packing.PMMS, Proceedings of the XIV International Seminar, Voronezh: 49 –54. (in Russian).
. Cambou, B., Jean, M., Radjai, F.,2009. Micromechanics of granular materials. Wiley, London.
. German, R.M.,1989. Particle packing characteristics. Metal Powder Industries Federation, Princeton.
. Arakawa, M., Nishino, M., 1973. Contact number and porosity in randomly packed sphere mixtures of various sizes.J. Soc. Mater. Sci.
Japan, 22: 658 – 662.
. Acharyya, M.,1993. Structural properties of planar random heap of hard discs. J. Phys. I France, 3: 905 – 908. DOI https://doi.org/10.1051/jp1:1993171.
. Bagi, K.,2007. On the concept of jammed configurations from a structural mechanics perspective. Granular Matter, 9: 109 – 134.
. Donev, A., Torquato, S., Stillinger, F.H., Conelly, R.,2004. Jamming in hard sphere and disk packings. J. Appl. Phys., 95(3): 989 – 999.
. Lubachevsky, B.D., Stillinger, F.H., Pinson, E.N.,1991. Disks vs. spheres: Contrasting properties of random packings. J. Stat. Phys., 64:
– 525.
. Williams, S.R., Philipse, A.P., 2003. Random packings of spheres and sphero cylinders simulated by mechanical contraction. Phys. Rev. E., 67:051301-1 – 051301-9.
. Frank, F.C., Kasper, J.S., 1958. Complex alloy structures regarded as spherical packings. I. Definitions and basic principles. ActaCryst., 11: 184 – 190.
. Hoppe, R.,1979. Effective coordination numbers and mean active fictive ionic radii. Zeitschrift fur Kristallographie. 150. 23-52. 10.1524/zkri.1979.150.1-4.23.
. Trömel, M.,1986. The crystal-chemistry of irregular coordinations. Z. Krist., 174: 196 – 197.
. Batsanov, S.S., 1977. Effective coordination number of atoms in crystals. Journal of Inorganic Chemistry, 22(5): 1155 – 1159. (in Russian).
. Brunner, G.O.,1977. A definition of coordination and its relevance in the structure types AlB2 and NiAs. ActaCryst., A33(1): 226 – 227.
. Bondarev, V.G., Migal, L.V., Bondareva,Т.P.,2008. Simulation of the structure of closely packed hard disk systems.Scientific bulletin of BelSU, 9(49), Issue 14: 248 – 261. (in Russian).
. Conway,J.H., Sloane,N.J.A.,1999. Spherical packings, lattices and groups. Springer, New York.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 COMPUSOFT: An International Journal of Advanced Computer Technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
©2023. COMPUSOFT: AN INTERNATIONAL OF ADVANCED COMPUTER TECHNOLOGY by COMPUSOFT PUBLICATION is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at COMPUSOFT: AN INTERNATIONAL OF ADVANCED COMPUTER TECHNOLOGY. Permissions beyond the scope of this license may be available at Creative Commons Attribution 4.0 International Public License.