Journal of the Iranian Chemical Society

, Volume 7, Issue 4, pp 986–994 | Cite as

The combinatorial factor method for investigation of order-disorder in two-dimensional binary alloy



The aim of this study was to investigate order-disorder in the two-dimensional AB alloy to find out whether the number of components, N A and N B, was equal or not. To this end, using the nearest neighbor interactions, first, we applied a two-dimensional lattice which consisted of infinite rows, R and columns, L, so that, RL = N A + N B. For such a model, using the combinatorial factor method, we derived an exact equation for the partition function. Because, the derived partition function was very complicated, the thermodynamic properties of the lattice could not be calculated; however, but these properties could be estimated for the models with a limited number of rows. Our results show that, for models with finite number of rows, for each mole fraction of A in the specific temperature, a phase transition, like Onsager transition, takes place.


Isin model Spin glasses Binary alloy Combinatorial factor Phase transition 


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  1. [1]
    G.W. Ardley, Acta Met. v3, 6 (1955) 525.Google Scholar
  2. [2]
    J.H. Westbrook (Ed.), Mechanical Properties of Intermetallic Compounds, John Wiley & Sons, Inc., 1960.Google Scholar
  3. [3]
    I. Bena, M. Droz, A. Lipowski, cond-mat/0510278 v1 (2005) 11.Google Scholar
  4. [4]
    D.F. Styer, M.K. Phani, J.L. Lebowitz, Phys. Rev. B34 (1986) 3361.Google Scholar
  5. [5]
    H.L. Scott, Phys. Rev. A37 (1988) 263.Google Scholar
  6. [6]
    J. Kogut, L. Susskind, Phys. Rev. D11 395 (1975).Google Scholar
  7. [7]
    W. Lenz, Phys. Zeitschr. 21 (1920) 613.Google Scholar
  8. [8]
    E. Ising, Zeitschr. F. Phys. 31 (1925) 253.Google Scholar
  9. [9]
    H.A. Kramers, G.H. Wannier, Phys. Rev. 60 (1941) 252.Google Scholar
  10. [10]
    L. Onsager, Phys. Rev. 65 (1944) 117.Google Scholar
  11. [11]
    S. Ranjbar, G.A. Parsafar, J. Phys. Chem. B 103 (1999) 7514.Google Scholar
  12. [12]
    S. Ranjbar, Chinese J. Phys. 41 (2003) 383.Google Scholar
  13. [13]
    S. Ranjbar, Chem. Phys. 326 (2006) 483.Google Scholar
  14. [14]
    S. Ranjbar, J. Iran. Chem. Soc. 7 (2010) 84.Google Scholar
  15. [15]
    D.A. McQuarrrie, Statistical Mechanics, Harper Collins Publishers Inc., New York, 1976.Google Scholar
  16. [16]
    A. Münster, Statistical Thermodynamics, Vol. 1, Springer-Verlag: Berlin, 1969, p. 265.Google Scholar

Copyright information

© Iranian Chemical Society 2010

Authors and Affiliations

  1. 1.Chemistry CollegeRazi UniversityKermanshahIran
  2. 2.Chemistry Department Azad UniversityGachsaranIran

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