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Contributions to the heat capacity of alpha (HCP) titanium from 200–1000 K

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Abstract

The heat capacity at constant pressure C p of alpha (HCP) titanium from 200 to 1000 K has been analyzed for contributions from lattice vibrations and electron excitations. Experimental data in the literature have been used to obtain the heat capacity at constant volume C V by the dilation correction. From C V has been subtracted an harmonic lattice contribution C VH given by the Debye heat capacity using a single Debye temperature and an electronic contribution C VE . The difference C V −(C VH +C VE ) is positive, and from about 600 to 1000 K it is real in the sense that it is larger than the experimental uncertainty in C V . This difference is attributed to an anharmonic lattice vibration contribution C VA . Two models for C VE have been used. One, which includes electron-phonon enhancement, leads to a C VA of about 15% of C V at 1000 K. The other takes into account the shift in the density of states with temperature and leads to a C VA of about 5% of C V

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References

  1. M. Zemansky, Heat and Thermodynamics, 3rd ed. (McGraw-Hill, New York, 1951).

    Google Scholar 

  2. W. M. Cash and C. R. Brooks, J. Chem. Thermo. (in press).

  3. V. O. Shestopal, Sov. Phys.—Solid State 7:2798 (1966).

    Google Scholar 

  4. K. Clusius and P. Franzosini, Z. Phys. Chem. (Frankfurt) 16:194 (1958).

    Google Scholar 

  5. B. Stalinski and Z. Bieganski, Roczniki Chem. 35:273 (1961).

    Google Scholar 

  6. C. W. Kothen and H. L. Johnston, J. Am. Chem. Soc. 75:3101 (1953).

    Google Scholar 

  7. R. H. Willens, Air Force Office of Sci. Res. Rep. No. 1839 (1961).

  8. R. L. P. Berry and G. V. Raynor, Research 6:21S (1953).

  9. J. Spreadborough and J. W. Christian, Proc. Phys. Soc. (London) 74:609 (1959).

    Google Scholar 

  10. F. L. Yaggee, E. R. Gilbert, and J. W. Styles, J. Less-Common Metals 19:39 (1969).

    Google Scholar 

  11. P. Hidnert, J. Res. Natl. Bur. Stds. 30:101 (1943).

    Google Scholar 

  12. E. S. Greiner and W. C. Ellis, Trans. AIME 180:657 (1949).

    Google Scholar 

  13. H. E. McCoy, Trans. ASM 57:743 (1964).

    Google Scholar 

  14. E. S. Fisher and C. J. Renken. Phys. Rev. 135:A482 (1964).

    Google Scholar 

  15. V. A. Korshunov, Phys. Met. Metallog. 42(2):54 (1976).

    Google Scholar 

  16. K. A. Gschneidner, In Solid State Physics, Vol. 16, F. Seitz and D. Turnbull, ed., (Academic Press, New York, 1964).

    Google Scholar 

  17. E. W. Collins and J. C. Ho, Phys. Rev. B 2:235 (1970).

    Google Scholar 

  18. M. Shimizu, T. Takahashi, and A. Katsuki, J. Phys. Soc. Japan 18:1192 (1963).

    Google Scholar 

  19. G. Grimvall, J. Phys. Chem. Solids 29:1221 (1968).

    Google Scholar 

  20. F. Y. Fradin, Solid State Commun. 16:1193 (1975).

    Google Scholar 

  21. S. L. Altmann and C. J. Bradley, Proc. Phys. Soc. 92:764 (1967).

    Google Scholar 

  22. G. Cordoba and C. R. Brooks, Phys. Stat. Sol. (a) 6:581 (1971).

    Google Scholar 

  23. C. R. Brooks and R. E. Bingham, J. Phys. Chem. Solids 29:1553 (1968).

    Google Scholar 

  24. C. R. Brooks, J. Phys. Chem. Solids 29:1377 (1968).

    Google Scholar 

  25. G. Cordoba and C. R. Brooks, Phys. Stat. Sol. (a) 13:K111 (1972).

    Google Scholar 

  26. C.-C. Yeh and C. R. Brooks, High Temp. Sci. 19:545 (1973).

    Google Scholar 

  27. C. R. Brooks, Phys. Stat. Sol. (b) 89:K123 (1978).

    Google Scholar 

  28. A. A. Maradudin and P. A. Flinn, Ann. Phys. 15:337 (1961).

    Google Scholar 

  29. R. C. Shukla, Int. J. Thermophys. 1:73 (1980).

    Google Scholar 

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Brooks, C.R. Contributions to the heat capacity of alpha (HCP) titanium from 200–1000 K. Int J Thermophys 2, 371–380 (1981). https://doi.org/10.1007/BF00498767

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