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Thermodynamic properties of4He. II. The bcc phase and theP-T and V-T phase diagrams below 2 K

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The constant-volume heat capacity of 4He has been measured at molar volumes from 20.45 to 29.71 cm3/mole in the temperature range from 0.3 to 4 K. The entropy has been obtained as a function of volume and temperature by extrapolation of the data to 0 K. The P-T equilibrium curves below 2 K were obtained from the volume dependence of the entropy in the two-phase regions. The V-T curves were obtained above 1.25 K by observation of heat capacity discontinuities at the phase boundaries and below 1.25 K from the equilibrium pressure-temperature data and the properties of the pure phases. The minimum in the melting pressure occurs at 0.774 K and is 8.04 × 10−3 atm below the 0 K value. The corresponding maxima in the molar volumes of the solid and liquid were also determined. In the bcc phase (∂S/∂V) T and (∂C v /∂V) T are everywhere positive. Both the temperature and volume dependence of the heat capacity are similar to those of bcc 3He, in the very limited ranges of volume and temperature in which the phase could be studied. An unexpected rise in heat capacity in the 20 mK interval below the melting temperature was observed.

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References

  1. W. R. Gardner, J. K. Hoffer, and N. E. Phillips, Phys. Rev. A 7, 1029 (1973).

    Google Scholar 

  2. J. K. Hoffer, W. R. Gardner, C. G. Waterfield, B. Krusor, and N. E. Phillips, to be published.

  3. W. H. Keesom and A. P. Keesom, Commun. Leiden No. 235 d; Physica 2, 557 (1935).

    Google Scholar 

  4. K. R. Atkins and M. H. Edwards, Phys. Rev. 97, 1429 (1955).

    Google Scholar 

  5. L. Goldstein, Phys. Rev. Lett. 5, 104 (1960); Phys. Rev. 122, 726 (1961).

    Google Scholar 

  6. F. E. Simon and C. A. Swenson, Nature 165, 829 (1950).

    Google Scholar 

  7. C. A. Swenson, Phys. Rev. 79, 626 (1950).

    Google Scholar 

  8. C. A. Swenson, Phys. Rev. 86, 870 (1952).

    Google Scholar 

  9. C. A. Swenson, Phys. Rev. 89, 538 (1953).

    Google Scholar 

  10. J. H. Vignos and H. A. Fairbank, Phys. Rev. Lett. 6, 265 (1961); Phys. Rev. 147, 185 (1966).

    Google Scholar 

  11. A. F. Shuch and R. L. Mills, Phys. Rev. Lett. 8, 469 (1962).

    Google Scholar 

  12. E. R. Grilly and R. L. Mills, Ann. Phys. (N.Y.) 8, 1 (1959).

    Google Scholar 

  13. E. R. Grilly and R. L. Mills, Ann. Phys. (N.Y.) 18, 250 (1962).

    Google Scholar 

  14. G. Ahlers, Phys. Rev. Lett. 10, 439 (1963); Phys. Rev. 135, A10 (1964).

    Google Scholar 

  15. D. O. Edwards and R. C. Pandorf, Phys. Rev. 144, 143 (1966).

    Google Scholar 

  16. J. F. Jarvis, D. Ramm, and H. Meyer, Phys. Rev. 170, 320 (1968).

    Google Scholar 

  17. W. R. Gardner, Ph.D. thesis, University of California, Berkeley, 1966, unpublished.

    Google Scholar 

  18. J. K. Hoffer, Ph.D. thesis, University of California, Berkeley, 1968, unpublished.

    Google Scholar 

  19. J. K. Hoffer, W. R. Gardner, C. G. Waterfield, and N. E. Phillips, in Proc. 11th Int. Conf. Low Temp. Phys, St. Andrews, 1968, J. F. Allen, D. M. Finlayson, and D. M. McCall, eds. (University of St. Andrews), p. 453.

  20. E. R. Grilly, in Proc. Xth Int. Conf. on Low Temp. Phys., Moscow 1966 (Viniti, Moscow, 1967), Vol. 1, p. 253.

  21. E. R. Grilly, J. Low. Temp. Phys. 11, 33 (1973).

    Google Scholar 

  22. J. Wiebes and H. C. Kramers, Phys. Lett. 4, 298 (1963).

    Google Scholar 

  23. George O. Zimmerman, in Proc. IXth Int. Conf. Low Temp. Phys, Columbus, 1964, J. G. Daunt, D. O. Edwards, F. J. Milford, and M. Yaqub, eds. (Plenum Press, New York, 1965),p. 240.

    Google Scholar 

  24. S. G. Sydoriak and R. L. Mills, in Proc. IXth Int. Conf. Low Temp. Phys., Columbus, 1964, J. G. Daunt, D. O. Edwards, F. J. Milford, and M. Yaqub, eds. (Plenum Press, New York, 1965), p. 273.

    Google Scholar 

  25. C. LePair, K. W. Taconis, R. DeBruyn Ouboter, and P. Das, Physica, 29, 755 (1963).

    Google Scholar 

  26. G. C. Straty and E. D. Adams, Phys. Rev. Lett. 17, 290 (1966); 17, 505 (1966).

    Google Scholar 

  27. J. K. Hoffer, C. G. Waterfield, W. R. Gardner, and N. E. Phillips, Phys. Lett. 27A, 29 (1968).

    Google Scholar 

  28. J. Wiebes, Thesis, University of Leiden, 1969.

  29. L. Goldstein and R. L. Mills, Phys. Rev. 159, 136 (1967).

    Google Scholar 

  30. Henry A. Kierstead, Phys. Rev. 138, A1594 (1965).

    Google Scholar 

  31. Henry A. Kierstead, Phys. Rev. 144, 166 (1966).

    Google Scholar 

  32. Henry A. Kierstead, Phys. Rev. 162, 153 (1967).

    Google Scholar 

  33. O. V. Lounasmaa and Leila Kaunisto, Ann. Acad. Sci. Fenn. AVI, 59 (1960).

    Google Scholar 

  34. R. L. Mills and S. G. Sydoriak, Ann. Phys. (N.Y.) 34, 2761 (1965).

    Google Scholar 

  35. R. C. Pandorf and D. O. Edwards, Phys. Rev. 169, 222 (1968).

    Google Scholar 

  36. G.Ahlers, private communication; also quoted in Ref. 39.

  37. G. C. Straty and E. D. Adams, Phys. Rev. 169, 232 (1968).

    Google Scholar 

  38. H. H. Sample and C. A. Swenson, Phys. Rev. 158, 188 (1967).

    Google Scholar 

  39. S. B. Trickey, W. P. Kirk, and E. D. Adams, Rev. Mod. Phys. 44, 668 (1972).

    Google Scholar 

  40. B. J. Alder, W. R. Gardner, J. K. Hoffer, N. E. Phillips, and D. A. Young, Phys. Rev. Lett. 21, 732 (1968).

    Google Scholar 

  41. R. W. Hill and O. V. Lounasmaa, Phil. Trans. Roy. Soc. (London) 252, 357 (1960).

    Google Scholar 

  42. G. Ahlers, Phys. Rev. A 2, 1505 (1970).

    Google Scholar 

  43. E. C. Heltemes and C. A. Swenson, Phys. Rev. 128, 1512 (1962).

    Google Scholar 

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Author information

Author notes

  1. J. K. Hoffer

    Present address: Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico

  2. W. R. Gardner

    Present address: Xerox Corporation, Dallas, Texas

  3. C. G. Waterfield

    Present address: Central Laboratories, British Titan Products Company Ltd., Stockton-on-Tees, Teeside, England

Authors and Affiliations

  1. Department of Chemistry and Inorganic Materials Research Division of the Lawrence Berkeley Laboratory, University of California, Berkeley, California

    J. K. Hoffer, W. R. Gardner, C. G. Waterfield & N. E. Phillips

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  1. J. K. Hoffer
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  2. W. R. Gardner
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  3. C. G. Waterfield
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  4. N. E. Phillips
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Additional information

Work supported by the U.S. Energy Research and Development Administration.

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Hoffer, J.K., Gardner, W.R., Waterfield, C.G. et al. Thermodynamic properties of4He. II. The bcc phase and theP-T and V-T phase diagrams below 2 K. J Low Temp Phys 23, 63–102 (1976). https://doi.org/10.1007/BF00117245

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