# Thermal expansion coefficient, scaling, and universality near the superfluid transition of /sup 4/He under pressure

## Abstract

Experimental results for the isobaric-thermal-expansion coefficient ..beta../sub P/ of pressurized /sup 4/He near the superfluid transition temperature T/sub lambda/ are reported. Near T/sub lambda/, ..beta../sub P/ is an asymptotically linear function of the specific heat at constant pressure C/sub P/. Therefore these measurements yield some of the same critical-point parameters as those derivable from C/sub P/. The measurements were made with high-temperature resolution over the range 2 x 10/sup -5/ approximately-less-than vertical-bar t vertical-bar equivalent vertical-bar T/T/sub lambda/ - 1 vertical-bar < 7 x 10/sup -2/, along nine isobars. They span the pressure interval 5 approximately-less-than P approximately-less-than 30 bar. A new experimental technique was employed which yielded a temperature resolution of two parts in 10/sup 7/ and a pressure stability of 1 x 10/sup -7/ bar. The results for each isobar were fitted with the equation ..beta../sub P/ = (A/..cap alpha..) t/sup -alpha/(1 + Dt/sub x/) + B above T/sub lambda/, and with the same expression with primed coefficients below T/sub lambda/. 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 0.00more »

- Authors:

- Publication Date:

- Research Org.:
- Institut fur Festkorperforschung, Kernforschungsanlage, 517 Julich, West Germany

- OSTI Identifier:
- 7178674

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., B; (United States)

- Additional Journal Information:
- Journal Volume: 14:5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HELIUM 4; THERMAL EXPANSION; HELIUM II; LAMBDA POINT; MEDIUM PRESSURE; SPECIFIC HEAT; EVEN-EVEN NUCLEI; EXPANSION; HELIUM ISOTOPES; ISOTOPES; LIGHT NUCLEI; NUCLEI; PHYSICAL PROPERTIES; STABLE ISOTOPES; THERMODYNAMIC PROPERTIES; TRANSITION TEMPERATURE; 640450* - Fluid Physics- Superfluidity

### Citation Formats

```
Mueller, K H, Ahlers, G, and Pobell, F.
```*Thermal expansion coefficient, scaling, and universality near the superfluid transition of /sup 4/He under pressure*. United States: N. p., 1976.
Web. doi:10.1103/PhysRevB.14.2096.

```
Mueller, K H, Ahlers, G, & Pobell, F.
```*Thermal expansion coefficient, scaling, and universality near the superfluid transition of /sup 4/He under pressure*. United States. doi:10.1103/PhysRevB.14.2096.

```
Mueller, K H, Ahlers, G, and Pobell, F. Wed .
"Thermal expansion coefficient, scaling, and universality near the superfluid transition of /sup 4/He under pressure". United States. doi:10.1103/PhysRevB.14.2096.
```

```
@article{osti_7178674,
```

title = {Thermal expansion coefficient, scaling, and universality near the superfluid transition of /sup 4/He under pressure},

author = {Mueller, K H and Ahlers, G and Pobell, F},

abstractNote = {Experimental results for the isobaric-thermal-expansion coefficient ..beta../sub P/ of pressurized /sup 4/He near the superfluid transition temperature T/sub lambda/ are reported. Near T/sub lambda/, ..beta../sub P/ is an asymptotically linear function of the specific heat at constant pressure C/sub P/. Therefore these measurements yield some of the same critical-point parameters as those derivable from C/sub P/. The measurements were made with high-temperature resolution over the range 2 x 10/sup -5/ approximately-less-than vertical-bar t vertical-bar equivalent vertical-bar T/T/sub lambda/ - 1 vertical-bar < 7 x 10/sup -2/, along nine isobars. They span the pressure interval 5 approximately-less-than P approximately-less-than 30 bar. A new experimental technique was employed which yielded a temperature resolution of two parts in 10/sup 7/ and a pressure stability of 1 x 10/sup -7/ bar. The results for each isobar were fitted with the equation ..beta../sub P/ = (A/..cap alpha..) t/sup -alpha/(1 + Dt/sub x/) + B above T/sub lambda/, and with the same expression with primed coefficients below T/sub lambda/. 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 ..cap alpha.. and ..cap alpha..', 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 ..cap alpha.. = ..cap alpha..', 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 pressure-independent (universal) amplitude ratios and leading exponents, as expected from theory. Their values are (AIP)},

doi = {10.1103/PhysRevB.14.2096},

journal = {Phys. Rev., B; (United States)},

number = ,

volume = 14:5,

place = {United States},

year = {1976},

month = {9}

}