Skip to main content
Log in

Reliability of the thermodynamic data obtained using the Gibbs-Duhem equation for ternary systems

  • Published:
Russian Metallurgy (Metally) Aims and scope

Abstract

The reliability of the thermodynamic data obtained by the Gibbs-Duhem equation for binary systems is analyzed, and the testing of this reliability is shown to be highly efficient. A similar testing technique is developed for a ternary system, and the application of this technique to a model system supports its validity and efficiency. The use of the developed technique for testing the data for the ternary Cd-Bi-Pb system of metallic melts confirms its validity and efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. Vagner, Thermodynamics of Alloys (Metallurgiya, Moscow, 1957) [in Russian].

    Google Scholar 

  2. L. S. Darken and R. W. Gurry, Physical Chemistry of Metals (McGraw-Hill, New York, 1953; Metallurgizdat, Moscow, 1960).

    Google Scholar 

  3. O. Redlich and A. T. Kister, “Algebraic Representation of Thermodynamic Properties and the Classification of Solutions,” Ind. Eng. Chem. 4(2), 345 (1948).

    Article  Google Scholar 

  4. R. Hultgren et al., Selected Values of the Thermodynamic Properties of Binary Alloys (ASM, Ohio, 1973).

    Google Scholar 

  5. S. Walas, Phase Equilibria in Chemical Engineering (Butterworth, Boston, 1985; Mir, Moscow, 1989).

    Google Scholar 

  6. A. G. Morachevskii, Thermodynamics of Molten Metallic and Salt Systems (Metallurgiya, Moscow, 1987) [in Russian].

    Google Scholar 

  7. L. S. Darken, “Application of Gibbs-Duhem Equation to Ternary and Multicomponent Systems,” J. Am. Chem. Soc., No. 7, 2909 (1950).

  8. A. G. Morachevskii and I. B. Sladkov, Thermodynamic Calculations in Metallurgy (Metallurgiya, Moscow, 1993) [in Russian].

    Google Scholar 

  9. B. P. Burylev, I. T. Sryvalin, and V. G. Korpachev, Application of Approximate Methods for the Calculation of the Thermodynamic Properties of Halide, Oxide, and Metallic Systems (ONIITEKhIM, Krasnodar, 1986) [in Russian].

    Google Scholar 

  10. N. V. Kopchenova and I. A. Maron, Computing Mathematics in Examples and Problems (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  11. I. I. Gul’tyai and M. M. Lemenev, “Types of Deviations from Ideality in Binary Metallic Melts and Their Description Using Ideal Chemical Theory,” Izv. Ross. Akad. Nauk, Ser. Met., No. 1, 17 (2005) [Russian Metallurgy (Metally), No. 1, 12–19 (2005)].

  12. C. A. Eckert and J. S. Smith, “A Chemical Theory for the Thermodynamics of Highly-Solvated Liquid Metal Mixtures,” AIChE J. 2(2), 325 (1982).

    Article  Google Scholar 

  13. I. I. Gul’tyai and M. M. Lemenev, “Description of Positive Deviations from Ideality in Binary Metallic Melts Using the Ideal Chemical Theory,” Izv. Ross. Akad. Nauk, Ser. Met., No. 6, 45 (2005) [Russian Metallurgy (Metally), No. 6, 540-550 (2005)].

  14. Z. Moser and L. Zabdyr, “Thermodynamic Studies of Liquid Cd-Bi and Cd-Bi-Pb Solutions,” High Temp.- High Pres. 7, 425 (1975).

    CAS  Google Scholar 

  15. A. Krupkowski, “General Solution of the Gibbs-Duhem Equation for Multicomponent System,” Bull. Acad. Polon. Sci. Lett. A 1, 15 (1950).

    Google Scholar 

  16. W. Ptak, Z. Moser, and W. Zakulski, “Thermodynamic Studies of Liquid Zn-Sn-Cd-Bi-Pb Alloys,” Arch. Metal. 33, 333 (1988).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. I. Gul’tyai.

Additional information

Original Russian Text © I.I. Gul’tyai, 2009, published in Metally, 2009, No. 2, pp. 41–53.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gul’tyai, I.I. Reliability of the thermodynamic data obtained using the Gibbs-Duhem equation for ternary systems. Russ. Metall. 2009, 129–139 (2009). https://doi.org/10.1134/S0036029509020062

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036029509020062

PACS number

Navigation