Theory of the osmotic pressure of dilute mixtures of3He in liquid4He at low temperatures

The osmotic pressure of dilute mixtures of³He in liquid⁴He is calculated and compared with experiment. One parameter, which is a measure of the difference between the mean potential energy of³He atoms and⁴He atoms in the mixture is determined from the experiments, and good agreement is obtained with the measured values of as a function of concentration and temperature. It is shown that the osmotic pressure does not provide any accurate information about the effective interaction between³He atoms. A comparison with earlier calculations of the osmotic pressure and of the³He chemical potential is made.Work performed under the auspices of U.S. Atomic Energy Commission.     

NMR in superfluid3He at very low temperatures

Just a few years ago it was generally believed that the NMR properties of superfluid³He far below T_c would not be qualitatively different from those found at higher temperatures. Surprisingly, the strange enhancement of relaxation processes at around 0.4 T_c named catastrophic relaxation, was then found. Recently an extremely long lived induction signal with new dynamical properties was discovered in the region of 100 K. Some of the newly discovered properties can be partly explained, although there are still many unsolved problems. The main aim of this article is to raise new questions for future investigations at the lowest temperatures presently possible.     

Adiabatic expansion of3He in4He at very low temperatures

In this paper the results of the investigation of a one-shot cooling technique, called adiabatic expansion of³He in superfluid⁴He, are reported. The expansion cooler basically consists of an expansion cell and a⁴He reservoir connected by a superleak. In the expansion cell nearly pure³He is gradually diluted to a saturated mixture by the injection of superfluid⁴He from the⁴He reservoir. The expansion of the³He produces cooling, which, in the ideal (isentropic) case can lower the temperature by a factor 4.56. In practice, the performance of this cooling method is limited by irreversibilities and heat leaks. In this paper several irreversible processes such as heat conduction, viscous effects, and supercritical⁴He flow, have been analyzed. Furthermore the effect of³He in a sinter layer in the expansion cell is discussed. The experiments have shown that the fountain pressure in the⁴ He reservoir is very suitable for driving the⁴He in and out of the expansion cell. During an expansion/extraction the⁴He chemical potential difference across the superleak is zero. The realised cooling factor, defined as the ratio of the initial temperature and the final temperature, is about 3.5 for initial temperatures between 20 mK to 190 mK. This value is lower than the ideal factor of 4.56 that can be obtained for isentropic expansions. The discrepancy is mainly due to the relatively large heat leak. The lowest temperature obtained in this investigation was 5.7 mK. The analyses have revealed no fundamental limitations for obtaining lower temperatures.     

Thermal contact between cerium magnesium nitrate and liquid3He at very low temperatures

A new experimental arrangement has been used to measure the times for equilibrium between cerium magnesium nitrate (CMN) and liquid³He. Measurements have been made on a single crystal of CMN from temperatures of 5.5–15 mK and on a powdered specimen from temperatures of 2.5–35 mK. The thermal resistance deduced from the single-crystal data is proportional toT ^–2. The thermal resistance obtained from the powder data may be separated into three contributions: a resistance which is proportional toT ^–2in series with a parallel combination of a phonon resistance (with resistivity _P =3×10 ^–4 T ^–3sec·cm²·K ⁴ ·erg ^–1 ) and a magnetic resistance (with resistivity _M =9×10 ² T sec·cm ² ·erg ^–1 in zero applied magnetic field). A reduction in the magnetic resistance was observed when the powdered CMN was placed in a magnetic field, the magnitude of this reduction being comparable to that expected from a Redfield-like theory. TheT ^–2resistance is discussed in terms of two-dimensional energy transport within the CMN. The 17-Hz susceptibility of the powdered CMN was measured in magnetic fields of 0, 18.9, 30.2, and 37.8 G. The magnetic temperatureT* (H=37.8 G) was found to differ by +0.5 mK from the magnetic temperature in zero field whenT* (H=0)=3 mK.Work supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A.143.Supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under AFOSR Contract No. AFOSR/F-44620-72-C-0017.     

Measurements of the viscosity and the slip length on liquid3He at low temperatures

Measurements of the viscosity and the slip length are reported for both the normal liquid and superfluid³He within the slip approximation. We used the hollow torsional oscillator. For the normal liquid³He the slip length is shorter than the theoretical expectation and there is no anomaly near the superfluid transition, but the viscosity shows the anomalous deviation from the Fermi liquid behavior which is thought to be attributed to the superfluid fluctuation. For the superfluid³He, the temperature dependence of the slip length agrees with the theory qualitatively and the viscosity agrees well with the theory quantitatively as far as the slip approximation is valid.     

Thermal conductivity of normal liquid3He at finite temperatures

Greywall's experimental data for the thermal conductivity of normal liquid³He are reanalyzed. The temperature dependence at various pressures seems consistent with a law of corresponding states in the sense that it can be described by a universal function of a reduced temperature. It is suggested that the appreciable dynamical screening of the scattering amplitude for the quasiparticles in³He is responsible for this behavior. For illustration the thermal conductivity is calculated at finite temperature for a class of screened interaction models to leading order in the screening parameter. Good agreement is found with experiment by fitting the single Landau parameterA _a ⁰ .     

Surface tension of liquid3He at low temperature

The thermal contribution to the surface tension of liquid³He due to the single quasiparticle motion is estimated in the low-T regime using a local approximation for the entropy. The density and temperature dependence of the effective mass is shown to play a crucial role in determining the behavior of (T). The theoretical predictions explain the anomalous behavior of (T) recently observed at low temperature by Suzuki et al.³ Predictions for the temperature dependence of the interfacial tension of liquid³He-⁴He mixtures are also given.     

ESR line broadening in Cr3+/MgO at liquid helium temperatures

Line broadening has been observed at 9 GHz in the ESR absorption spectrum of Cr³⁺ in MgO in the liquid helium temperature range, for a range of Cr³⁺ concentrations from 800 7400 ppm. The broadened linewidths at 4.2 K are about two times larger than those at 77 K and depend on polar angle. The lineshapes are Gaussian, in contrast to the Lorentzian lineshape between 293 and 77 K. The broadening is interpreted by the combined effects of strain, due to the charge misfit of Cr³⁺ and the host cation, and temperature which causes both exchange striction and departure from the cubic symmetry to a lower symmetry. Analysis of the linewidth data gives D=(5.25±0.40)×10^–4 cm^–1 and confirms that the total linewidth, H _t, is given by H _t=H ₀+(2D/g) cos _H where H ₀ is the linewidth independent of concentration, temperature and polar angle, _H.     

The nuclear magnetic susceptibility of dilute solutions of3He in4He at low temperatures

A theory of the nuclear magnetic susceptibility of dilute solutions of ³ He in ⁴ He at low temperatures is presented. It is shown that ^–1 is a linear function of the corresponding inverse free fermion magnetic susceptibility. It is also shown that the experimental Curie constant differs from the theoretical one by an amount which is of the order of the ³ He concentration. It follows that the existing experimental results are not adequate for the calculation of the Fermi liquid magnetic susceptibility enhancement factor.     

Temperature-, concentration- and pressure-dependence of the viscosity of liquid3He-4He mixtures at low temperatures

We have investigated the viscosity of liquid³He-⁴He mixtures at various³He - concentrations (0.98%x9.5%) in the temperature range1 mK T 100 mK and at pressures 0 bar P 20 bar. At T10 mK the Fermi-liquid behaviour T² = const. as well as x^4/3 could be confirmed. However, there are significant deviations from theoretical predictions for the magnitude of the viscosity as well as for its pressure dependence.     

Method for measuring a vacuum in an environment at liquid helium temperatures

The experimental results of a new method to measure a vacuum in an environment at liquid helium temperatures are presented. The method uses a thin superconducting wire suspended in the vacuum vessel, the wire is heated by a current pulse > l_c. The cool down time, which depends on the heat transfer into the rest gas and on the axial heat conductance of the wire, is a measure of the vacuum and it is detected by the recovery of the wire to superconductivity. The results exhibit good resolution in the range of pressures from 5 × 10^?3 to 5 Pa (5 × 10^?5 to 5 × 10^?2 mbar).     

Attempts to increase the nuclear relaxation time of a3He gas at low temperatures

In an attempt to increase, at temperatures of a few kelvins, the relaxation time of a dilute³He gas enclosed in spherical Pyrex or pure silica bulbs 3 cm in diameter, we have studied the relaxing properties of various coatings, such as solid O₂ and solid N₂ and multiple coatings of H₂ on N₂, H₂ on O₂, and H₂ on H₂O. Contrary to naive expectations, thin films of solid oxygen proved to be very efficient coatings, although single molecules are paramagnetic. When multiple coatings are compared, they even provide the best undercoating to hydrogen films. The longest relaxation time we measured at 4.2 K was 8000 min, i.e., more than 5 days. We also found that Pyrex and pure silica, either bare or coated, give comparable results below 50 K. These experiments enabled us to measure the adsorption energy of³He on O₂, W(³He/O₂)=130±15 K, and of³He on N₂, W(³He/N₂)=200±50 K. In the absence of any theoretical calculation, these energies still need to be confirmed by other experimental techniques.Laboratory associated with the CNRS. U.A. 18.     

3He低温热力学性质实验数据综述

全面收集整理了3He在相变曲线、液体区、气体区和临界区低温热力学性质的实验数据和关联式,为建立3He覆盖不同区间的状态方程以及开发3He低温物性数据程序奠定了基础,同时也可供3He低温物性的研究人员参考.     

Spin relaxation of 3He to paramagnetic centers in surfaces at very low temperatures

The memory function formalism is used to derive a generalized golden rule expression for the spin-lattice relaxation rate 1/T ₁ for ³He to paramagnetic centers embedded in or residing on surfaces in contact with the ³He. This expression is applied to several simple models of relaxation to paramagnetic spins which do not interact among themselves, both for ³He in the Fermi-liquid phase and for a solid surface layer of ³He on the substrate. The magnitude of 1/T ₁ is calculated for each case as well as the temperature and magnetic field dependence. Finally, the relationship between the spin-lattice relaxation rate and the Kapitza conductance across surfaces via magnetic interactions is determined.Supported by National Science Foundation grant number DMR77-18329.Research performed under the auspices of ERDA.     

The molar polarizability of3He at low temperatures and its density dependence

Simultaneous capacitance and PVT measurements on liquid and gaseous³He under a variety of temperature and pressure conditions indicate that the molar polarizability of the classical Clausius-Mossotti equation can best be expressed as:(mole/cm³)=0.123413–0.002376 (g/cm³). Some significant, but often neglected, experimental corrections are discussed.Work performed under the auspices of the U.S. Atomic Energy Commission.     

An equilibrium theory of the dilute solutions of3He in superfluid4He at very low temperatures

An equilibrium theory of the dilute solutions of ³ He in superfluid ⁴ He is derived systematically. The theory is based on a model which (a) goes beyond the parabolic Landau-Pomeranchuk approximation for the ³ He quasiparticle energy by taking into account the fourth-order term in the momentum expansion of this quantity, (b) disregards contributions to the ³ He quasiparticle effective interaction whose order in the momentum is higher than two, and (c) allows the effective interaction to be nonlocal. The simplicity of the model enables the development of a unified parametrization of the various equilibrium properties of the solutions. The expressions obtained for these properties are both easy to apply and highly accurate over a wide temperature range spanning from T=0 to temperatures of the order of the ³ He quasiparticle degeneracy temperature. It is shown that the parameters appearing in the expression for the ³ He quasiparticle effective interaction at fixed ⁴ He number density are replaced in the fixed-pressure, low-temperature expansions of the equilibrium properties by other parameters whose appearance in the theory seems to be due to the renormalization of this interaction by the interactions between the ³ He quasiparticles and the virtual fluctuations of the ⁴ He number density Finally, a comparison is made between theory and experiment. Three quantities are considered in detail : the ³ He osmotic pressure and the ³ He quasiparticle inertial and specific heat effective masses. The analysis of the experimental data makes it possible to determine the parameters associated with the effective interaction at several pressures. It is found that the theory is, in general, in a very good accord with the experimental situation and that, within its framework, the experimental values of the osmotic pressure and the two effective masses are indeed consistent with one another.     

Magnetic properties of Ag sinters and their possible impact on the coupling to liquid3He at very low temperatures

We report on measurements of the magnetization of metal sinters made of different Ag powders with average (nominal) grain sizes of 40nm and 70nm at1.6K≤T≤250K and0≤B≤6T. Besides the dominating diamagnetism of Ag, the sinters show unexpected magnetic properties; e.g. once exposed to a magnetic field B, the sinters keep a permanent magnetic moment (in zero external field) which strongly depends on the magnitude of B. The possible impact of the unexpected magnetic properties of the Ag sinters on various experimental observations at very low temperatures, e.g. the magnetic field dependence of the thermal boundary resistance between an Ag sinter and³He at millikelvin temperatures is discussed.     

Measurement of the magnetic susceptibility of normal fluid3He at very low temperatures

We present pulsed NMR measurements of the low temperature (0.003 K) magnetic susceptibility of normal liquid ³ He as a function of pressure. Our results agree well with the extrapolation from 0.035 K of the data of Ramm et al. We calculate new values for the Fermi liquid parameter F ₀ ^a using the heat capacity data of Greywall.     

Field dependence of the magnetization of adsorbed3He films at ultra low temperatures

We present measurements of the magnetization of pure³He films adsorbed on graphite at a density of p = 0.235 atoms/Ų, which corresponds to the 2D Heisenberg ferromagnetic regime. Different NMR frequencies (461.3kHz and 1.004 MHz) were used to study the magnetic field dependence of the nuclear magnetization. Measurements were performed on a Papyex sample to investigate the influence of the platelet size. The results are discussed in the context of theoretical models presented recently to describe these systems.