Thermal expansion coefficient, scaling, and universality near the superfluid transition of He4 under pressure

K. H. Mueller, Guenter Ahlers, and F. Pobell
Phys. Rev. B 14, 2096 – Published 1 September 1976
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Abstract

Experimental results for the isobaric-thermal-expansion coefficient βP of pressurized He4 near the superfluid transition temperature Tλ are reported. Near Tλ, βP is an asymptotically linear function of the specific heat at constant pressure CP. Therefore these measurements yield some of the same critical-point parameters as those derivable from CP. The measurements were made with high-temperature resolution over the range 2×105|t||TTλ1|<7×102, along nine isobars. They span the pressure interval 5P30 bar. A new experimental technique was employed which yielded a temperature resolution of two parts in 107 and a pressure stability of 1 × 107 bar. The results for each isobar were fitted with the equation βP=(Aα)tα(1+Dtx)+B above Tλ, and with the same expression with primed coefficients below Tλ. When the amplitudes D and D of the confluent singularity are assumed to be equal to zero (i.e., the data are fitted with a pure power law), the leading exponents are pressure dependent and vary from 0.00 at low P to 0.06 at high P. This analysis also yields B>B. The inequality between B and B, and the pressure dependence of α and α, are contrary to the predictions of the phenomenological and renormalization-group theories of critical phenomena. When D and D are permitted to assume nonzero values, it is statistically allowed by the data to impose the theoretically predicted relations α=α, x=x, and B=B as constraints in the analysis. With these constraints, and the value of x chosen to be equal to 0.5, we obtain pressureindependent (universal) amplitude ratios and leading exponents, as expected from theory. Their values are α=α=0.026±0.004, AA=1.11±0.02, and DD=1.29±0.25. Similar results are obtained when x is chosen to be equal to 0.4 or 0.6. The result for α is consistent with that derived previously from specificheat measurements. The universal AA is contrary to the previous report of a pressure-dependent specificheat amplitude ratio. Using thermodynamic relations, we compare our βP results directly with the CP measurements. For P15 bar the agreement is excellent; but at the higher pressures there are small but significant differences of unknown origin.

  • Received 26 April 1976

DOI:https://doi.org/10.1103/PhysRevB.14.2096

©1976 American Physical Society

Authors & Affiliations

K. H. Mueller*

  • Institut für Festkörperforschung, Kernforschungsanlage, 517 Jülich, West Germany

Guenter Ahlers

  • Bell Laboratories, Murray Hill, New Jersey 07974

F. Pobell

  • Institut für Festkörperforschung, Kernforschungsanlage, 517 Jülich, West Germany

  • *Present address: Los Alamos Scientific Laboratory, University of California, Los Alamos, N. M. 87544.
  • Part of the work by Guenter Ahlers done while this author was on temporary leave from Bell Laboratories at the Kernforschungsanlage Jülich.

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Vol. 14, Iss. 5 — 1 September 1976

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