STATISTICAL MECHANICS OF He$sup 3$-He$sup 4$ LIQUID MIXTURES

Journal Article · Thu Aug 01 04:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.131.907· OSTI ID:4680269

Hecht, C E; Kikuchi, R; Stein, P R

The partition function method proposed by Feynman for pure liquid He/sup 4/ and previously extended to treat pure liquid He/sup 3/ by Kikuchi is applied to liquid mixtures of He/sup 3/-He/sup 4/. The variation of the a point with mole fraction He/sup 3/, the isotopic phase separation curve, and the excess functions of mixing are discussed. The theoretical lambda line is interpreted as a cooperative boson transition and follows the experimental results closely up to X/sub 3/ = 0.5 irrespective of the effective mass of the Hea atoms, whole above X/sub 3/ = 0.5 the lambda temperatures are too high. An asymmetric isotopic phase separation is found in the mixtures at temperatures below a critical temperature that depends slightly on further assumptions in the model but which is of the correct order of magnitude (1 deg K. The phase separation is due to the quantum dynamical effects as opposed to the purely statistical effects arising out of the different inherent symmetries of the wave functions for He/sup 3/ and He/sup 4/. The calculated excess Gibbs free energies of mixing become positive in time'' to effect the phase separation but are less positive than the experimental values and are in fact of the wrong sign above 1 deg K. The calculated excess entropies of mixing are much too positive. The model used assumes zero excess volumes of mixing. (auth)

• Research Organization: Univ. of Chicago
• NSA Number: NSA-17-031172
• OSTI ID: 4680269
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 131; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ATOMS
BOSONS
ENERGY
ENERGY LEVELS
ENTROPY
EQUATIONS
FREE ENERGY
HELIUM 3
HELIUM 4
LIQUIDS
LOW TEMPERATURE
MASS
MECHANICS
MIXING
PARTITION FUNCTION
PHYSICS
QUANTUM MECHANICS
STATISTICS
TEMPERATURE
THERMODYNAMICS
VOLUME