Thermal resistance between powdered cerium magnesium nitrate and liquid helium at very low temperatures

Experiments have been performed from magnetic temperatures of 2–20 mK on the effect of minute⁴He impurities and a magnetic field on the thermal resistance between powdered cerium magnesium nitrate (CMN) and liquid³He. The thermal resistance decreases with decreasingT and increasing small field but is increased dramatically at a givenT by the addition of roughly a monolayer of⁴He. The resistance is interpreted as resulting from a surface magnetic coupling between CMN and liquid³He.This work has been supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A. 143, and by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant No. AF-AFOSR-631-67A.     

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 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 .     

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.     

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.     

Thermal boundary resistance between liquid helium and silver sinter at low temperatures

We present measurements of the thermal coupling between Ag sinter (nominal grain size 700 Å) and superfluid³He-B atp = 0.3, 10, and 20 bar as well as a phase-separated³He⁴-He mixture atp = 0.5 bar in the submillikelvin regime. In order to analyze the data of the pure³He-B sample with respect to different contributions to the thermal resistance, a one-dimensional model for the heat flow in the sinter is presented. As a result it is shown that the thermal conductivity of the liquid in the sinter has to be taken into account to extract the temperature and pressure dependence of the boundary resistance in the confining geometry of the sinter. Depending on the value of this thermal conductivity, a boundary resistance proportional toT ^–2 orT ^–3 is found. Moreover, it is shown that a pressure dependence of the boundary resistance might be explained by a pressure dependence of the thermal conductivity of the liquid in the sinter. The data on the phase-separated mixture are equally well described by aT ^–2- and aT ^–3-dependence of the boundary resistance. We point out that a common problem in most measurements of the Kapitza resistance performed so far is the small temperature interval investigated, which usually does not allow a definite conclusion concerning the temperature dependence.     

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.     

Thermal contact conductance of pressed contacts at low temperatures

The influence of variations of interface temperature in the range 50-300 K on the thermal contact conductance between aluminium and stainless steel joints was determined. Predictions were done by modeling the deformation at the interface for different values of surface finish and contact pressure over the range of interface temperatures. Both elastic and plastic deformation was considered. Experiments were carried out in a closed loop cryostat and the results were shown to compare well with the predictions. A reduction of the interface temperature resulted in a smaller value of thermal contact conductance. Interfacial pressure variation had much lower influence at the smaller value of temperatures. The role of surface roughness at the contact was also seen to be less significant at lower interface temperatures and the zone of hysteresis was smaller. A correlation was developed for estimating thermal contact conductance at joints over this temperature range. An explicit dependence of contact conductance on temperature was not seen to be necessary as long as the changes in the hardness and thermal conductivity of the material with temperature are incorporated in the correlation.     

Heat release,refrigeration and thermometry in3He-4He solutions at very low temperatures

We report on our measurements performed in liquid³He-⁴He solutions in the microkelvin temperature range at the Bayreuth nuclear demagnetization cryostat. One aspect of our work is the application of the vibrating wire technique for thermometry in the ballistic regime of phase-separated solutions. The establishment of reliable thermometry along with the particular design of our experimental cells enables us to study two main limitations on the minimum temperature of about 100K achieved in³He-⁴He solutions so far: the thermal resistance between the liquid and the cell, and the origins of the heat leaks.     

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.     

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.     

The velocities of first and second sound in dilute solutions of3He in superfluid4He at very low temperatures

A unified theory of first and second sound in dilute solutions of ³ He in superfluid ⁴ He at very low temperatures is presented. The theory is based on the detailed semimicroscopic model for the ³ He quasiparticle excitations described by Disatnik and Brucker a few years ago. In contrast with Khalatnikov's macroscopic theory, the application of this model enables the derivation of relatively simple expressions for the sound velocities in which no omissions of terms representing contributions due to the thermal expansion are made. The sound velocities are given in the final expressions in terms of various parameters of the ³ He quasiparticle spectrum and effective interaction. These expressions are both highly accurate and easy to use over a wide temperature regime spanning from the quantum limit to temperatures of the order of the ³ He quasiparticle degeneracy temperature. The actual application of the theory to measurements of the sound velocities is described in detail. Numerical values or estimates for various characteristic parameters of the ³ He quasiparticle system, including in particular the ³ He quasiparticle effective mass, are obtained from the comparison between the theory and the experiment. The example of the second sound velocity is used to illustrate a procedure for analyzing data from very low-temperature measurements of the equilibrium properties of the solutions, which is expected to produce meaningful information regarding the parameters of the basic model. In practice, the theory is found to be in a very good accord with the measurements of the sound velocities. The result obtained for the zero concentration limit of the ³ He quasiparticle effective mass (m ₀ =2.19m ₃ ) is somewhat lower than the empirical estimates reported in the past. On the other hand, this result is in very good agreement with variational calculations based on the detailed microscopic theory of the solutions. A discussion of this and other results obtained from the comparison between theory and experiment is included.Work supported in part by the United States-Israel Binational Science Foundation.Killed in action, 16 October 1973.     

Thermoelectric refrigeration at very low temperatures

It is shown that thermoelectric refrigeration might become an effective technique at or below a temperature of several mK. This is because the heat conduction due to the lattice vibrations becomes very small at these low temperatures. The thermoelectric material should have a high Debye temperature and a low carrier concentration, controlled so as to correspond to a Seebeck coefficient of a few hundred μV K^?1. One of the major difficulties in the achievement of low temperature thermoelectric refrigeration would, in fact, be the establishment of this optimum carrier concentration; it is suggested that it might be established through either an injection process or the application of a high magnetic field.     

The melting pressure of helium-3 at very low temperatures

The melting pressure of³ He at very low temperatures was shown earlier to be determined overwhelmingly by the solid phase. Using an extended solid³He model based on isotropic effective first-neighbor-pair antiferromagnetic and second-neighbor-pair ferromagnetic exchange interactions, the melting process is reinvestigated here. One of its motivating aspects may be said to be tied to its possible use, suggested by us earlier, for the establishment of a thermodynamic temperature scale at very low temperatures. As a consequence of the assumed multineighbor interactions, spin ordering is accelerated and, at the same temperature, the extended-model solid entropy falls below that of the simpler nearest-neighbor-pair interaction model. Equivalently, the spinordering critical transition temperature is raised over that associated with the simpler interaction scheme. The overall result is a decrease in the melting pressure variations at very low temperatures below those arising from the simple solid model. In the absence of a reliable experimental temperature scale at very low temperatures, only a qualified and cursory comparison is justified with recent experimentally estimated melting pressures. Discrepancies arise between theory and preliminary data on the temperature derivatives of the melting pressure or the entropy of the solid at melting. They might be due in part to the tentative experimental temperatures, which appear shifted toward too low temperatures when compared with the theoretical temperature scale implicit in the treatment of the generalized solid model. However, from the viewpoint which accepts the rather preliminary, scarce, very low temperature melting pressure data at face value, failure of the extended exchange model of solid³He at those temperatures must be kept in mind.Work performed under the auspices of the U.S. Atomic Energy Commission.     

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.     

Thermal conductivity of superconducting UPt3 at low temperatures

We study the thermal conductivity within the E_1g and E_2u models for superconductivity in UPt₃ and compare the theoretical results for electronic heat transport with recently measured results reported by Lussier, Ellman and Taillefer. The existing data down to T/T_c 0.1 provides convincing evidence for the presence of both line and point nodes in the gap, but the data can be accounted for either by an E_1g or E_2u order parameter. We discuss the features of the pairing symmetry, Fermi surface, and excitation spectrum that are reflected in the thermal conductivity at very low temperatures. Significant differences between the E_1g and E_2u models are predicted to develop at excitation energies below the bandwidth of the impurity-induced Andreev bound states. The zero-temperature limit of the axis thermal conductivity, lim_T0 k_c/T, isuniversal for the E_2u model, but non-universal for the E_1g model. Thus, impurity concentration studies at very low temperatures should differentiate between the nodal structures of the E_2u and E_1g models.