The low temperature thermodynamic properties of superfluid solutions of 3He in 4He

Abstract

The low temperature thermodynamic properties of dilute solutions of 3He in 4He are reviewed. The main emphasis is on experiments and theoretical work performed since the discovery that some 3He remains in solution even at T = 0. The experiments include measurements of the heat capacity, phase-separation, equation of state, osmotic pressure, heat of mixing, nuclear magnetic susceptibility and first- and second-sound velocities. The discussion is limited to 3He concentrations below about 15% and temperatures small enough ( T ⪅0.6 K) that the contributions from thermal phonons and rotons are neglible. The dependence of the various properties on temperature, concentration and, where data exist, pressure is described and analyzed in terms of various simple theories of helium solutions. The original theory is that of Landau and Pomeranchuk in which the 3He impurities are supposed to behave as free Fermi excitations of effective mass m where m depends only on the pressure. The “Fermi entropy model”, which is useful in the analysis of thermodynamic data at finite temperature, is an empirical generalization of the Landau-Pomeranchuk theory in which the entropy is still given by the ideal Fermi gas formula, but the effective mass is allowed to depend on concentration as well as pressure. The most accurate theory (“dilute solution theory”) includes the effects of interactions between 3He excitations, and it is developed here as an expansion of the ‘osmotic energy’, U − N 4 μ 4, in terms of the 3He quasi-particle distribution function. Various theories of the effective interaction potential and its relation to the transport properties are reviewed. The results of the experiments are compared with the predictions of the theory, based on the most recent conjectures for the interaction potential, only in the limit of T → 0 at zero pressure. The one exception is the normal mass density of the 3He component ϱ n for which the theory is compared with the results of second sound experiments at all temperatures such that the effects of thermal phonons and rotons are neglible. Finally, application of the solution thermodynamics is made to the theory of dilution refrigerators.