Central European Journal of Physics

, Volume 9, Issue 1, pp 222–229 | Cite as

A thermodynamic lattice theory on melting curve and eutectic point of binary alloys. Application to fcc and bcc structure

  • Nguyen V. HungEmail author
  • Dung T. Tran
  • Nguyen C. Toan
  • Barbara Kirchnner
Research Article


A thermodynamic lattice theory has been developed for determination of the melting curves and eutectic points of binary alloys. Analytical expressions for the melting curves of binary alloys composed of constituent elements with the same structure have been derived from expressions for the ratio of root mean square fluctuation in atomic positions on the equilibrium lattice positions and the nearest neighbor distance. This melting curve provides information on Lindemann’s melting temperatures of binary alloys with respect to any proportion of constituent elements, as well as on their eutectic points. The theory has been applied to fcc and bcc structure. Numerical results for some binary alloys provide a good correspondence between the calculated and experimental phase diagrams, where the calculated results for Cu1−x Ni x agree well with the measured ones, and those for the other alloys are found to be in a reasonable agreement with experiment.


thermodynamic lattice theory Lindemann’s melting temperature eutectic point binary alloys 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F.A. Lindemann, Z. Phys. 11, 609 (1910)Google Scholar
  2. [2]
    J. J. Gillvarry, Phys. Rev. 102, 308 (1956)CrossRefADSGoogle Scholar
  3. [3]
    N. Snapipiro, Phys. Rev. B 1, 3982 (1970)CrossRefADSGoogle Scholar
  4. [4]
    H. H. Wolf, R. Jeanloz, J. Geophys. Res. 89, 7821 (1984)CrossRefADSGoogle Scholar
  5. [5]
    C. J. Martin, D. A. O’Connor, J. Phys. C Solid State 10, 3521 (1977)CrossRefADSGoogle Scholar
  6. [6]
    C. Kittel, Introductionto Solid State Physics, 7 th edition (Wiley & Son, New York, 1996)Google Scholar
  7. [7]
    T. B. Massalski, Binary Alloy Phase Diagrams, 2nd edition (ASM International Materials Parks, OH, 1990)Google Scholar
  8. [8]
    D. Machon, P. Toledano, G. Krexner, Phys. Rev. B71, 024110 (2005)ADSGoogle Scholar
  9. [9]
    E. A. Stern, P. Livins, Z. Zhang, Phys. Rev. B43, 8850 (1991)ADSGoogle Scholar
  10. [10]
    D. Alfè, L. Vočadlo, G. D. Price, M. J. Gillan, J. Phys. — Condens. Mat. 16, 937 (2004)Google Scholar
  11. [11]
    H. Löwen, T. Palberg, R. Simon, Phys. Rev. Lett. 70, 1557 (1993)CrossRefADSGoogle Scholar
  12. [12]
    H. Löwen, Phys. Rep. 237, 249 (1994)CrossRefADSGoogle Scholar
  13. [13]
    F. H. Stillinger, Science 267, 1935 (1995)CrossRefADSGoogle Scholar
  14. [14]
    Y. Zhou, M. Karplus, K. D. Ball, R. S. Berry, J. Chem. Phys. 116, 2323 (2002)CrossRefADSGoogle Scholar
  15. [15]
    C. Chakravaty, P. G. Debenedetti, F. H. Stillinger, J. Chem. Phys. 126, 204508 (2007)CrossRefADSGoogle Scholar
  16. [16]
    P. K. Skiff, N. S. Stoloff, Scripta Metall. 11, 7 (1997)Google Scholar
  17. [17]
    J. Ancsin, Metrologia 41, 198 (2004)CrossRefADSGoogle Scholar
  18. [18]
    J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, London, 1972)Google Scholar
  19. [19]
    Z. H. Jin, P. Gumbsch, K. Lu, E. Ma, Phys. Rev. Lett. 87, 055703 (2001)CrossRefADSGoogle Scholar
  20. [20]
    N. V. Hung, J. J. Rehr, Phys. Rev. B56, 43 (1997)ADSGoogle Scholar
  21. [21]
    M. Daniel, D. M. Pease, N. V. Hung, J. I. Budnick, Phys. Rev. B69, 134414 (2004)ADSGoogle Scholar
  22. [22]
    N. V. Hung, P. Fornasini, J. Phys. Soc. Jpn. 76, 084601 (2007)CrossRefADSGoogle Scholar
  23. [23]
    N. V. Hung, T. S. Tien, L. H. Hung, R. R. Frahm, Int. J. Mod. Phys. B22, 5155 (2008)ADSGoogle Scholar
  24. [24]
    Y. S. Touloukian, R. K. Kirby, R. E. Taylor, P. D. Desai, Thermal expansion, Metallic, Elements and Alloys. Thermophys. properties of matter, Vol. 12 (IFI/Plenum, New York-Washington, 1975)Google Scholar

Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nguyen V. Hung
    • 1
    Email author
  • Dung T. Tran
    • 1
  • Nguyen C. Toan
    • 1
  • Barbara Kirchnner
    • 2
  1. 1.Department of PhysicsUniversity of ScienceThanh Xuan, HanoiVietnam
  2. 2.Wilhelm-Ostwald-Institute for Physical and Theoretical ChemistryUniversity of LeipzigLeipzigGermany

Personalised recommendations