Interrelation of Short- and Long-Range Orders

  • Alexandr I. Gusev
  • Andrej A. Rempel
  • Andreas J. Magerl
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 47)


Short- and long-range orders characterize various types of mutual arrangements of atoms in crystalline solids. Long-range order emerges from the interference of perturbation waves induced by interchangeable elements and covers the whole volume of the crystal. Short-range order characterizes the mutual distribution of atoms of different species depending on the atom at the lattice site chosen. Short-range order vanishes with distance from a chosen atom and normally it covers no more than a few lattice constants.


Solid Solution Coordination Sphere Cluster Variation Method Nonstoichiometric Compound Range Order Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. A. Rempel, A. I. Gusev: Short-range order in ordered alloys and interstitial phases, Fiz. Tverd. Tela 32, 16–24 (1990) (in Russian). (Engl. transl.: Sov. Physics — Solid State 32, 8–13 (1990)Google Scholar
  2. 2.
    A. A. Rempel, A. I. Gusev: Short-range order in superstructures, Phys. Stat. Sol. (b) 160, 389–402 (1990).Google Scholar
  3. 3.
    E. Ising: Beitrag zur Theorie des Ferromagnetismus, Z. Phys. 31, 253–258 (1925)CrossRefGoogle Scholar
  4. 4.
    H. A. Bethe: Statistical theory of superlattices, Proc. Roy. Soc. London A 150, 552–575 (1935)CrossRefGoogle Scholar
  5. 5.
    F. C. Nix, W. Shockley: Order-disorder transformations in alloys, Rev. Modern Phys. 10, 1–71 (1938)CrossRefGoogle Scholar
  6. 6.
    R. Kikuchi: Theory of cooperative phenomena, Phys. Rev. 81, 988–1003 (1951)CrossRefGoogle Scholar
  7. 7.
    M. Kurata, R. Kikuchi, T. Watari: Theory of cooperative phenomena. Detailed discussions of the cluster variation method, J. Chem. Phys. 21, 434–448 (1953)CrossRefGoogle Scholar
  8. 8.
    J. Hijmans, J. de Boer: Approximation method for order—disorder problem, Physica 21, 471–516 (1955)CrossRefGoogle Scholar
  9. 9.
    R. Kikuchi, S. G. Brush: Improvement of the cluster-variation method, J. Chem. Phys. 47, 195–203 (1967)CrossRefGoogle Scholar
  10. 10.
    R. Kikuchi: The cluster variation method, J. Physique Colloq. 38, C7–307—C7–313 (1977)Google Scholar
  11. 11.
    E. A. Guggenheim: Statistical mechanics of regular solutions, Proc. Roy. Soc. London A 148, 304–312 (1935)CrossRefGoogle Scholar
  12. 12.
    R. Kikuchi, H. Sato: Characteristics of superlattice formation in alloys of face centred cubic structure, Acta Met. 22, 1099–1112 (1974)CrossRefGoogle Scholar
  13. 13.
    W. Gorsky: Röntgenographische Untersuchung von Umwandlungen in der Legierung CuAu, Z. Phys. 50, 64–81 (1928)CrossRefGoogle Scholar
  14. 14.
    W. L. Bragg, E. J. Williams: The effect of thermal agitation on atomic arrangement in alloys, Proc. Roy. Soc. London A 145, 699–730 (1934)CrossRefGoogle Scholar
  15. 15.
    A. G. Khachaturian: Theory of Structural Transformations in Solids ( John Wiley and Sons, New York 1983 ) 574 pp.Google Scholar
  16. 16.
    A. A. Rempel, A. I. Gusev: Relation between short-range and long-range order in solid solutions with b.c.c. and f.c.c. structures, Phys. Stat. Sol. (b) 130, 413–420 (1985)CrossRefGoogle Scholar
  17. 17.
    A. A. Rempel, A. I. Gusev: The relationship between short-range and long-range order in ordered alloys, Fiz. Metall. Metalloved. 60, 847–854 (1985) (in Russian). (Engl. transl.: Phys. Met. Metallogr. 60, 11–17 (1985))Google Scholar
  18. 18.
    A. A. Rempel, A. I. Gusev: Cluster-variation method of analysis of short-order and long-range order in ordered crystals, in Solid State Chemistry 9 P. V. Geld (Ed.) ( Urals Polytechnical Institute, Sverdlovsk 1986 ) pp. 117–124 (in Russian)Google Scholar
  19. 19.
    A. I. Gusev, A. A. Rempel: Structural Phase Transitions in Nonstoichiometric Compounds ( Nauka, Moscow 1988 ) 308 pp. (in Russian)Google Scholar
  20. 20.
    N. G. Parsonage, L. A. K. Staveley: Disorder in Crystals ( Clarendon Press, Oxford 1978 ) 926 pp.Google Scholar
  21. 21.
    L. D. Landau, E. M. Lifschitz: Statistical Physics. Course of Theoretical Physics 5 (Pergamon, Oxford 1980 ) 544 pp.Google Scholar
  22. 22.
    J. M. Cowley: An approximation theory of order in alloys, Phys. Rev. 77, 669–675 (1950)CrossRefGoogle Scholar
  23. 23.
    D. Ya. Khvatinskaya, I. Karimov, V. S. Presman: Short-range order of carbon atom positions in niobium carbide, Dokl_ Akad. Nauk Uzb. SSR No 1, 23–25 (1988) (in Russian)Google Scholar
  24. 24.
    A. I. Gusev, A. A. Rempel: Order parameter functional method in the theory of atomic ordering, Phys. Stat. Sol. (b) 131, 43–51 (1985)CrossRefGoogle Scholar
  25. 25.
    A. I. Gusev, A. A. Rempel: Calculating the energy parameters for CV and OPF methods, Phys. Stat. Sol. (b) 140, 335–346 (1987)CrossRefGoogle Scholar
  26. 26.
    A. I. Gusev: Atomic ordering and the order parameter functional method, Philosoph. Mag. B 60, 307–324 (1989)CrossRefGoogle Scholar
  27. 27.
    A. I. Gusev: Physical Chemistry of Nonstoichiometric Refractory Compounds ( Nauka, Moscow 1991 ) 286 pp. (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexandr I. Gusev
    • 1
  • Andrej A. Rempel
    • 1
  • Andreas J. Magerl
    • 2
  1. 1.Ural Division of the Russian Academy of SciencesInstitute of Solid State ChemistryEkaterinburgRussia
  2. 2.Lehrstuhl für Kristallographie und StrukturphysikUniversität Erlangen-NürnbergErlangenGermany

Personalised recommendations