Mathematical model of coordination number of spherical packing

Authors

  • Migal LV Candidate of Ph.-M. Sci., Senior Researcher FRC of Monitoring, Belgorod State University, Pobeda str. 85, Belgorod, 308015, Russia
  • Bondarev VG Candidate of Ph.-M. Sci., Senior Researcher FRC of Monitoring, Belgorod State University, Pobeda str. 85, Belgorod, 308015, Russia
  • Bondareva TP Candidate of Ph.-M. Sci., Senior Researcher FRC of Monitoring, Belgorod State University, Pobeda str. 85, Belgorod, 308015, Russia
  • Belyaeva IN Candidate of Ph.-M. Sci., Senior Researcher FRC of Monitoring, Belgorod State University, Pobeda str. 85, Belgorod, 308015, Russia

Keywords:

spherical packing, coordination number, dimension space, coordination index, inter-particle distance

Abstract

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.

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Published

2024-02-26

How to Cite

Migal, L. V., Bondarev, V. G., Bondareva, T. P., & Belyaeva, I. N. (2024). Mathematical model of coordination number of spherical packing. COMPUSOFT: An International Journal of Advanced Computer Technology, 8(06), 3187–3191. Retrieved from https://ijact.in/index.php/j/article/view/501

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Section

Original Research Article