Thermodynamic properties of liquid $sup 3$He--$sup 4$He mixtures near the tricritical point. II. Data analysis by the scaling-field method

Journal Article · Sun Feb 01 04:00:00 EST 1976 · J. Low Temp. Phys., v. 22, no. 3/4, pp. 369-402

DOI:https://doi.org/10.1007/BF00654713· OSTI ID:4110211

Riedel, E K; Meyer, H; Behringer, R P

The scaling theory for tricritical phenomena by Riedel is applied to the analysis of thermodynamic properties of liquid $sup 3$He--$sup 4$He mixtures near the tricritical point. Within this theory experimental data for the phase diagram, the $sup 3$He molar concentration X, and the concentration susceptibility S are discussed in terms of two scaling fields that are functions of the temperature T and the difference $delta$ of the chemical potentials of the two helium isotopes. The quantities X and S in terms of the fields T and $delta$ as independent variables are obtained for the intervals -0.1 less than T - T/sub t/ < 0.53K and -9 < $delta$ - $delta$/sub t/ less than 0.8 J/mole, from vapor pressure and calorimetric data. The transformed data are analyzed to yield the tricritical exponents, amplitudes, scaling fields, and scaling functions. The values of the tricitical exponents are found to agree with those predicted by the renormalization-group theory of Riedel and Wegner. (Logarithmic corrections are beyond the precision of the present experiment.) Relations between amplitudes are derived and tested experimentally. The (linear) scaling fields are determined by using their relationship to geometrical features of the phase diagram. The data for X and S are found to scale in terms of these generalized scaling variables. The sizes of the tricritical scaling regions in the normal and superfluid phases are estimated; the range of apparent tricritical scaling is found to be appreciably larger in the normal-fluid phase than in the superfluid phase. Finally, when the critical line near the tricritical point is approached along a path of constant $delta$ less than $delta$/sub t/, the experimental data are found to exhibit the onset of the crossover from tricritical to critical behavior. in qualitative agreement with crossover scaling. (auth)

• Research Organization: Duke Univ., Durham, NC
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-018433
• OSTI ID: 4110211
• Journal Information: J. Low Temp. Phys., v. 22, no. 3/4, pp. 369-402, Journal Name: J. Low Temp. Phys., v. 22, no. 3/4, pp. 369-402; ISSN JLTPA
• Country of Publication: United States
• Language: English

Related Subjects

*HELIUM 3-- THERMODYNAMIC PROPERTIES
*HELIUM 4-- THERMODYNAMIC PROPERTIES
640700*
LIQUIDS
N62100* --Physics (Fluid)--Electrofluid Mechanics
SCALING LAWS
SUPERFLUIDITY