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An analysis of the high-temperature entropy of transition metals

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Abstract

The high-temperature entropy at constant pressure, obtained from heat capacity data, is analyzed for Mo, Nb, Pd, Rh, Ru, Sc, Ti, V, W, Y, and Zr. The vibrational contribution to the entropy defines an entropy Debye temperature, θ S(T). Due to anharmonicity, θ S(T) decreases with the temperature T, typically by 10–20% between room temperature and the melting point. An unusual temperature dependence of θ S(T) may indicate inadequacies in the underlying data. On this ground, the C p data recommended by Hultgren et al. (1973) for W and Ru seem doubtful. A comparison is made between θ S and the elastic-limit Debye temperature θ D for the metals with a cubic lattice structure. θ S of Nb is found to be almost independent of T, a feature related to the fact that the elastic constant c 44 increases with T.

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References

  1. L. Kaufman and H. Bernstein, Computer Calculations of Phase Diagrams (Academic Press, New York, 1970).

    Google Scholar 

  2. J. Rosén and G. Grimvall, Phys. Rev. B27:7199 (1983).

    Google Scholar 

  3. G. Grimvall and J. Rosén, Int. J. Thermophys. 3:251 (1982).

    Google Scholar 

  4. D. A. Ditmars (in press).

  5. M. Thiessen, Int. J. Thermophys. 7:1183 (1986).

    Google Scholar 

  6. G. Grimvall and J. Rosén, Int. J. Thermophys. 4:139 (1983).

    Google Scholar 

  7. J. de Launay, in Solid State Physics, Vol. 2, F. Seitz and D. Turnbull, eds. (Academic Press, New York, 1956), pp. 263–269.

    Google Scholar 

  8. 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 (Am. Soc. Metals, Metals Park, Ohio, 1973).

    Google Scholar 

  9. V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic Properties of Metals (Pergamon, Oxford, 1978).

    Google Scholar 

  10. H. J. F. Jansen and A. J. Freeman, Phys. Rev. B30:561 (1984).

    Google Scholar 

  11. Landolt-Börnstein New Series, Group III, Vol. 18 (Springer-Verlag, Berlin, 1984), pp. 64–68.

  12. P. Gustafson, Int. J. Thermophys. 6:395 (1985).

    Google Scholar 

  13. G. K. White and S. J. Collocott, J. Phys. Chem. Ref. Data 13:1251 (1984).

    Google Scholar 

  14. G. Grimvall, M. Thiessen, and A. Fernández Guillermet (in press).

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Thiessen, M. An analysis of the high-temperature entropy of transition metals. Int J Thermophys 9, 159–164 (1988). https://doi.org/10.1007/BF00504008

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