Abstract
The structure of models of close packings of hard spheres is examined, with density of the packings exceeding the maximum value for uniform disordered packings (η = 0.64). High densities are achieved due to regions of the closest packing (η = 0.74) emerging in the models. Spatial geometry of good tetrahedral atomic configurations and of simplest elements of the crystal structure identified by Delaunay simplices was studied using the Voronoi— Delaunay method. Models with a packing coefficient η varying from 0.639 to 0.706 were considered. At smaller densities, a well-known disordered close “Bernal packing” is realized. At η = 0.706 (the greatest density achieved), a unified crystal structure with numerous defects is formed. At intermediate densities, stochastically oriented crystalline nuclei are observed. Specific atomic aggregates — stacks of five-membered rings in good tetrahedral configurations of spheres — are revealed in models having a substantial fraction of crystalline phase (η = 0.664). Such non-trivial structures can occur only in packings that are intermediate between amorphous and crystalline phases.
Similar content being viewed by others
References
R. A. Andrievskii, Usp. Khim., 71, No. 18, 967–981 (2002).
A. Bezrukov, M. Bargiel, and D. Stoyan, Part. Part. Syst. Char., No. 19, 111–118 (2002).
C. S. Hsu and A. J. Rahman, J. Chem. Phys., 70, 5234–5240 (1979).
V. Luchnikov, A. Gervois, P. Richard, et al., J. Mol. Liq., 96/97, 185–194 (2002).
N. N. Medvedev, Yu. I. Naberukhin, and V. A. Luchnikov, Zh. Str. Khim., 35, No. 1, 53–63 (1994).
V. A. Luchnikov, N. N. Medvedev, Yu. I. Naberukhin, and V. N. Novikov, Phys. Rev. B, 51, No. 21, 15569–15572 (1995).
I. I. Gainutdinov and Yu. T. Pavlyukhin, Dokl. Ross. Akad. Nauk, 364, No. 2, 203–207 (1999).
M. G. Alinchenko and N. N. Medvedev, Proc. X Russian Conf. “Structure and properties of metal and slag melts,” Vol. 1, Ekaterinburg, YuUrGU (2001), pp. 19–23.
N. N. Medvedev, Physica A, 314, 678–685 (2002).
W. S. Jodrey and E. M. Tory, Phys. Rev. A, 32, No. 4, 2347–2351 (1985).
J. D. Bernal, Proc. Royal. Soc. London, A280, 299–320 (1964); J. Bernal and S. King, in: Physics of Simple Liquids [Russian translation], Mir, Moscow (1971), pp. 116–135.
J. L. Finney, Proc. Royal Soc. London, 319, 479–494 (1970); ibid, 319, 495–507 (1970).
N. N. Medvedev and Yu. I. Naberukhin, J. Non-Cryst. Sol., 94, 402–406 (1987).
Y. G. Wu, Z. G. Fan, and Y. Z. Lu, J. Mat. Sc., 19, 2019–2025 (2003).
G. F. Voronoi, Studies of Primitive Parallelohedra [in Russian], Vol. 2, AN USSR, Kiev (1952).
B. N. Delaunay, St. Petersburg School of Number Theory [in Russian], AN SSSR, Moscow (1947).
N. N. Medvedev, Voronoi—Delaunay Approach in Studies of Structures of Non-Crystalline Systems [in Russian], SO RAN, Novosibirsk (2000).
A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Wiley, Chichester (2000).
Y. C. Liao, D. J. Lee, and P. J. He, Powder Techn., 123, No. 1, 1–8 (2002).
N. N. Medvedev and Yu. I. Naberukhin, J. Phys. A: Math. Gen., 21, L247–L252 (1988); N. N. Medvedev, Yu. I. Naberukhin, and V. P. Voloshin, Zh. Str. Khim., 30, No. 2, 98–105 (1989).
N. N. Medvedev and Yu. I. Naberukhin, Dokl. AN SSSR, 288, No. 5, 1104–1107 (1986).
V. P. Voloshin, Yu. I. Naberukhin, and N. N. Medvedev, Mol. Simulation, 4, 209–227 (1989).
N. N. Medvedev, V. P. Voloshin, A. Bezrukov, and D. Stoyan, From Imperfect Amorphous Structures to a Defective Crystals, Proc. X APAM Top. Sem. and III Conf. “Materials and Technology,” Novosibirsk, Russia (2003), pp. 62–63.
Author information
Authors and Affiliations
Additional information
Original Russian Text Copyright © 2004 by N. N. Medvedev, A. Bezrukov, and D. Shtoyan
__________
Translated from Zhurnal Strukturnoi Khimii, Vol. 45, Supplement, pp. 24–31, 2004.
Rights and permissions
About this article
Cite this article
Medvedev, N.N., Bezrukov, A. & Shtoyan, D. From amorphous solid to defective crystal. A study of structural peculiarities in close packings of hard spheres. J Struct Chem 45 (Suppl 1), S23–S30 (2004). https://doi.org/10.1007/s10947-006-0092-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10947-006-0092-3