Home Derivation and consistency of the partial functions of a ternary system involving interaction coefficients
Article
Licensed
Unlicensed Requires Authentication

Derivation and consistency of the partial functions of a ternary system involving interaction coefficients

  • Ramana G. Reddy EMAIL logo and Singareddy R. Reddy
Published/Copyright: February 8, 2022
Become an author with De Gruyter Brill
Author Information
International Journal of Materials Research
From the journal International Journal of Materials Research Volume 95 Issue 9

Abstract

Margules equations are used to express the thermodynamics of a ternary system containing one solvent and two solutes in the vicinity of solvent, in terms of first order interaction coefficients of binary and ternary systems. Considering just the first order Margules coefficients, the resultant excess Gibbs energy function was convergent and the derived logarithmic activity coefficients of solvent and solutes were thermodynamically consistent. In the present study Margules equations are modified to get consistent equations. Partial functions of a ternary system are deduced using these modified equations via the excess Gibbs energy function. Derived partial functions are thermodynamically consistent and also deduced results are the same as those obtained using Maclaurin infinite series. Using the activity coefficient expressions of solvent and solutes, the activity coefficients of solvent and solute are calculated in Ni– Cr–Fe and Fe–Ti –C ternary systems, which are in excellent agreement with the experimental data.

R. G. Reddy Department of Metallurgical and Materials Engineering The University of Alabama, Tuscaloosa, Alabama 35487-0202, USA Tel.: +1 205 348 4246 Fax: +1 205348 2164

References

[1] M. Margules: Sitz.-Ber. Math. – Naturw. Kl. Bayer. Akad. Wiss. München IIa, 104 (1895) 1243.Search in Google Scholar

[2] E. Hala, J. Pick, V. Fried, O. Vilim: Vapour – Liquid Equilibrium, 2nd Ed., Pergamon Press, London (1967).Search in Google Scholar

[3] N.A. Gokcen: Statistical Thermodynamics of Alloys, Plenum Publ., New York (1986).10.1007/978-1-4684-5053-8Search in Google Scholar

[4] N.A. Gokcen, R.G. Reddy: Thermodynamics, Plenum Publ., New York (1996).10.1007/978-1-4899-1373-9Search in Google Scholar

[5] J.P. Hajra, S. Ravindra Reddy, M.G. Frohberg: Metall. Mater. Trans. B 26 (1995) 495.10.1007/BF02653865Search in Google Scholar

[6] C.W. Bale, A.D. Pelton: Metall. Trans. A 21 (1990) 1997.10.1007/BF02647247Search in Google Scholar

[7] C. Wagner: Thermodynamics of Alloys, MA, Addision Wesley Press, Cambridge, (1952).Search in Google Scholar

[8] C.H.P. Lupis, J.F. Elliott: Acta Metall. 14 (1966) 529; C.H.P. Lupis: Chemical Thermodynamics of Materials, North Holland (1983).10.1016/0001-6160(66)90320-8Search in Google Scholar

[9] R. Schuhmann Jr.: Metall. Trans. B 16 (1985) 807.10.1007/BF02667517Search in Google Scholar

[10] L.S. Darken: Trans. T.M.S – AIME 239 (1967) 80.Search in Google Scholar

[11] L.S. Darken: Trans. T.M.S – AIME 239 (1967) 90.10.1093/brain/90.1.239-cSearch in Google Scholar

[12] A.D. Pelton, C.W. Bale: Metall. Trans. A 17 (1986) 1211.10.1007/BF02665320Search in Google Scholar

[13] S. Srikanth, K.T. Jacob: Metall. Trans. B 19 (1988) 269.10.1007/BF02654212Search in Google Scholar

[14] J.P. Hajra, M.G. Frohberg: Steel Research 11 (1989) 479.10.1002/srin.198901690Search in Google Scholar

[15] J.P. Hajra, M.G. Frohberg: Metall. Trans. 22B (1992) 23.10.1007/BF02654032Search in Google Scholar

[16] N.A. Gokcen, T. Tanaka, Z. Morita: J. Chim. Phys. 90 (1993) 233.10.1051/jcp/1993900233Search in Google Scholar

[17] F. Kongoli, Y. Dessureault, A.D. Pelton: Metall. Mater. Trans. 29B (1998) 591.10.1007/s11663-998-0094-ySearch in Google Scholar

[18] A.D. Pelton: Metall. Mater. Trans. 28B (1997) 869.10.1007/s11663-997-0015-5Search in Google Scholar

[19] D.P. Tao: Metall. Mater. Trans. 33B (2002) 502.10.1007/s11663-002-0061-ySearch in Google Scholar

[20] S.W. Gilby, G.R.St. Pierre: Trans. TMS-AIME 245 (1969) 1749.Search in Google Scholar

[21] Y.C. Guo, C.Z. Wang, H.L. Yu: Metall. Trans. B 21 (1990) 537.10.1007/BF02667866Search in Google Scholar
Received: 2003-10-13
Accepted: 2004-06-25
Published Online: 2022-02-08

© 2004 Carl Hanser Verlag, München

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Editorial
  4. 85 Years DGM
  5. Fachausschuss ,,Materialographie“
  6. Fachausschuss ,,Mechanische Oberflächenbehandlungen“
  7. Fachausschuss „Titan“
  8. Fachausschuss ,,Gefüge und Eigenschaften von Polymerwerkstoffen“
  9. Characterization of the fcc/bcc orientation relationship by EBSD using pole figures and variants
  10. Microstructural and thermodynamic study of γ-Ga2O3
  11. Spray forming of 2014-Al alloy based composites with injection of SiC particulates
  12. Size effects in the plastic deformation of NiAl thin films
  13. Fracture parameters of chevron-notched Al2O3/Nb sandwich specimens
  14. HVEM in situ study of fracture of Al2O3/Nb sandwich specimens
  15. Articles Basic
  16. Assessment of thermodynamic functions in the MgO–Al2O3–SiO2 system
  17. Derivation and consistency of the partial functions of a ternary system involving interaction coefficients
  18. Contribution to the zinc-rich side of the Ti–Zn system
  19. Measurement of the surface tension of liquid Ga, Bi, Sn, In and Pb by the constrained drop method
  20. Articles Applied
  21. Model of growth kinetics of nitrided layer in the binary Fe–N system
  22. Einfluss von Molybdän auf die Beständigkeit von Stahlanoden zum Verchromen in „Chromispel-C“-Elektrolyten
  23. The mechanism of columnar-to-equiaxed transition during electromagnetic centrifugal solidification
  24. Notifications/Mitteilungen
  25. Personal/Personelles
  26. News/Aktuelles
  27. Books/Bücher
  28. Conferences/Konferenzen
https://doi.org/10.1515/ijmr-2004-0149

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Editorial
  4. 85 Years DGM
  5. Fachausschuss ,,Materialographie“
  6. Fachausschuss ,,Mechanische Oberflächenbehandlungen“
  7. Fachausschuss „Titan“
  8. Fachausschuss ,,Gefüge und Eigenschaften von Polymerwerkstoffen“
  9. Characterization of the fcc/bcc orientation relationship by EBSD using pole figures and variants
  10. Microstructural and thermodynamic study of γ-Ga2O3
  11. Spray forming of 2014-Al alloy based composites with injection of SiC particulates
  12. Size effects in the plastic deformation of NiAl thin films
  13. Fracture parameters of chevron-notched Al2O3/Nb sandwich specimens
  14. HVEM in situ study of fracture of Al2O3/Nb sandwich specimens
  15. Articles Basic
  16. Assessment of thermodynamic functions in the MgO–Al2O3–SiO2 system
  17. Derivation and consistency of the partial functions of a ternary system involving interaction coefficients
  18. Contribution to the zinc-rich side of the Ti–Zn system
  19. Measurement of the surface tension of liquid Ga, Bi, Sn, In and Pb by the constrained drop method
  20. Articles Applied
  21. Model of growth kinetics of nitrided layer in the binary Fe–N system
  22. Einfluss von Molybdän auf die Beständigkeit von Stahlanoden zum Verchromen in „Chromispel-C“-Elektrolyten
  23. The mechanism of columnar-to-equiaxed transition during electromagnetic centrifugal solidification
  24. Notifications/Mitteilungen
  25. Personal/Personelles
  26. News/Aktuelles
  27. Books/Bücher
  28. Conferences/Konferenzen
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 29.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ijmr-2004-0149/html
Scroll to top button