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Magnetic contributions to the thermodynamic functions of pure Ni, Co, and Fe

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Abstract

An empirical mathematical equation is proposed for the magnetic contribution to the specific heat of pure metals. The corresponding functions for enthalpy, entropy, and Gibbs energy are of simple form. Two parameters used for each element are the critical temperature,T c, and the total magnetic entropy. The parameters have been determined from a careful separation of magnetic and nonmagnetic contributions to the specific heat. Debye temperatures for Ni, Co, and Fe have been determined considering data to much higher temperatures than other studies. The magnetic specific heats extracted from experimental data agree very well with the proposed equation over the entire temperature range and for all three elements. Comparisons with different mathematical functions found in the literature give agreement only for the case of iron. The total magnetic entropy given by a classical relation is found to be high, and a quantitative correction is given. Various magnetic standard states are discussed. The lattice stabilities of bcc- and fcc-iron are calculated assuming that the difference of the nonmagnetic specific heats is linear from 500 K to 1810 K. A simple equation is obtained in which the anomalous temperature dependence is explained by the independently determined magnetic contribution. The calculated values agree very well with Orr and Chipman’s assessment. The stability of bcc iron at low temperatures is quantitatively rationalized.

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References

  1. C. Zener:Trans. AIME, 1955, vol. 203, pp. 619–30.

    Google Scholar 

  2. J. L. Meijering:Philips Res. Repts., 1963, vol. 18, pp. 318–30.

    CAS  Google Scholar 

  3. M. Hillert, T. Wada, and H. Wada:J. Iron Steel Inst., 1967, vol. 205, pp. 539–46.

    Google Scholar 

  4. L. Kaufman and H. Bernstein:Computer Calculation of Phase Diagrams, Academic Press, New York, NY, 1970.

    Google Scholar 

  5. G. Inden: Project Meeting CALPHAD V, 21–25 June 1976, Max- Planck-Inst. Eisenforschung, Düsseldorf, W. Germany, 1976, pp. III.4/1-IH.4/13.

    Google Scholar 

  6. A. P. Miodownik:CALPHAD, 1977, vol. 1, pp. 133–58.

    Article  CAS  Google Scholar 

  7. M. Hillert and M. Jarl:CALPHAD, 1978, vol. 2, pp. 227–38.

    Article  CAS  Google Scholar 

  8. T. Nishizawa, M. Hasebe, and M. Ko:Acta Metall., 1979, vol. 27, pp. 817–28.

    Article  CAS  Google Scholar 

  9. G. Inden:Physica, 1981, vol. 103B, pp. 82–100.

    Google Scholar 

  10. G. Inden:Bull. Alloy Phase Diagr., 1982, vol. 2, pp. 412–22.

    CAS  Google Scholar 

  11. A. P. Miodownik:Bull. Alloy Phase Diagr., 1982, vol. 2,pp. 406–12.

    CAS  Google Scholar 

  12. S. Hertzman and B. Sundman:CALPHAD, 1982, vol. 6, pp. 67–80.

    Article  CAS  Google Scholar 

  13. R. J. Weiss and K. J. Tauer:Phys. Rev., 1956, vol. 102, pp. 1490–95.

    Article  CAS  Google Scholar 

  14. J.A. Hofmann, A. Paskin, K.J. Tauer, and R.J. Weiss:J. Phys. Chem. Solids, 1956, vol. 1, pp. 45–60.

    Article  CAS  Google Scholar 

  15. C. Kittel:Introduction to Solid State Physics, 5th ed., John Wiley, New York, NY, 1976, pp. 16, 136, 466, and 470.

    Google Scholar 

  16. Y.A. Chang and R. Hultgren:J. Phys. Chem., 1965, vol. 69, pp. 4162–65.

    Article  CAS  Google Scholar 

  17. K. A. Gschneider , Jr.: J. Solid State Physics, 1964, pp. 275–426 , esp. p. 363.

  18. L. Kaufman, E. V. Clougherty, and R. J. Weiss:Acta Metall., 1963, vol. 11, pp. 323–35.

    Article  CAS  Google Scholar 

  19. R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, K. K. Kelley, and D.D. Wagman:Selected Values of the Thermodynamic Properties of the Elements, ASM, Metals Park, OH, 1973, pp. 126–33, 180–91, and 350–57.

    Google Scholar 

  20. R. S. Tebble and D. J. Craik:Magnetic Materials, Wiley-Interscience, London, 1969, pp. 1–80, esp. pp. 50-51.

    Google Scholar 

  21. E. S.R. Gopal:Specific Heat at Low Temperatures, Plenum Press, New York, NY, 1966, pp. 84–111.

    Google Scholar 

  22. J. H. Van Vleck: inMagnetic Properties of Metals and Alloys, ASM, Metals Park, OH, 1959, pp. 1–17.

    Google Scholar 

  23. D. J. Wallace: inPhase Transitions and Critical Phenomena, C. Domb and M.S. Green, eds., Academic Press, New York, NY, 1976, vol. 6, pp. 293–356.

    Google Scholar 

  24. U. Gahn:J. Phys. Chem. Solids, 1982, vol. 43, pp. 977–89.

    Article  CAS  Google Scholar 

  25. K.P. Belov:Magnetic Transitions, Consultants Bureau, New York, NY, 1961, pp. 1–15.

    Google Scholar 

  26. W. Bendick and W. Pepperhoff:Acta Metall., 1982, vol. 30, pp. 679–84.

    Article  CAS  Google Scholar 

  27. M. Braun and R. Kohlhaas:Phys. Status Solidi, 1965, vol. 12, pp. 429–44.

    Article  CAS  Google Scholar 

  28. B. Bergman and J. ågren: Technical Report TRITA-MAC-0232, Materials Center, Royal Inst. Technology, Stockholm, Sweden, March 1984.

    Google Scholar 

  29. Y.-Y. Chuang, R. Schmid, and Y. A. Chang:Metall. Trans. A, 1984, vol. 15A, pp. 1921–30.

    CAS  Google Scholar 

  30. R.L. Orr and J. Chipman:Trans. TMS-A1ME, 1967, vol. 239, pp. 630–33.

    CAS  Google Scholar 

  31. J. ågren:Metall. Trans. A, 1979, vol. 10A, pp. 1847–52.

    Google Scholar 

  32. L. Kaufman and H. Nesor:Z. Metallkde., 1973, vol. 64, pp. 249–57.

    CAS  Google Scholar 

  33. L.S. Darken and R.P. Smith:Ind. Eng. Chem., 1951, vol. 43, pp. 1815–20.

    Article  CAS  Google Scholar 

  34. E. Schürmann and V. Neubert:Arch. Eisenhüttenwes., 1979, vol. 50, pp. 415–22.

    Google Scholar 

  35. W. A. Dench and O. Kubaschewski:J. Iron Steel Inst., 1963, vol. 201, pp. 140–43.

    CAS  Google Scholar 

  36. P. D. Anderson and R. Hultgren:Trans. TMS-AIME, 1962, vol. 224, pp. 842–45.

    CAS  Google Scholar 

  37. D.C. Wallace, P.H. Sidles, and G.C. Danielson:J. Appl. Phys., 1960, vol. 31, pp. 168–76.

    Article  CAS  Google Scholar 

  38. M. Olette and A. Ferrier: “The Physical Chemistry of Metallic Solu- tions and Intermetallic Compounds,” N.P.L., Sympos. No. 9, paper 4H, H.M. Stationary Off., London, 1959.

    Google Scholar 

  39. J.P. Morris, E.F. Foerster, C.W. Schultz, and G.R. Zellars: U.S. Bur. Mines, Rept. Invest. No. 6723, 1966.

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Authors and Affiliations

  1. Department of Metallurgical and Mineral Engineering, University of Wisconsin, 53706, Madison, WI

    Ying-Yu Chuang (Research Associate), Rainer Schmid (Visiting Associate Professor) & Y. Austin Chang (Professor and Chairman)

  2. Technical University Clausthal, West Germany

    Y. Austin Chang (Professor and Chairman)

Authors
  1. Ying-Yu Chuang
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  2. Rainer Schmid
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  3. Y. Austin Chang
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Chuang, YY., Schmid, R. & Chang, Y.A. Magnetic contributions to the thermodynamic functions of pure Ni, Co, and Fe. Metall Trans A 16, 153–165 (1985). https://doi.org/10.1007/BF02816041

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