3He Impurity Effects on the Growth Kinetics of 4He Crystals

We report the growth kinetics of the⁴He crystals with a small amount of³He impurities around 0.8 K. The growth resistance was measured using the response of the charged interface with respect to an externally applied voltage. In 5 ppm and 10 ppm³He mixtures, it is found that (1) the relaxation process can be expressed as an exponential behavior, (2) the growth resistance becomes larger compared to pure⁴He and does not have a strong³He concentration dependence, and (3) the temperature dependence of the growth resistance is much the same as pure⁴He. We discuss several possible explanations of the present experiment.     

NMR experiments on pure3He and3He-4He mixtures in silica aerogel

We have carried out a series of NMR experiments on³He systems filling the pores of silica aerogel with 95% porosity. The systems studied included³He-⁴He mixtures with a wide range of³He concentrations x₃ as well as pure³He. All experiments were conducted in an 8 T field and for temperatures T 6 mK. This resulted in strong spin polarization at the lowest temperatures (up to approximately 80%) for the localized layer observed for a pure³He sample. For pure³He, the magnetic behavior is dominated by the localized spins, which are found to constitute 6% of the sample. The coupled system of localized plus liquid spins displays rapid transverse magnetization relaxation with an anomalous temperature dependence. For intermediate x₃ magnetization measurements provide a preliminary indication of the phase diagram of mixtures filling this porous material. The magnetization is hysteretic over some ranges of x₃.     

Transition to Turbulence and Critical Velocity in Superfluid Solution of 3He in 4He

By the method of oscillating tuning fork, we carried out researches of the transition to turbulence in superfluid solution of 5% ³He in ⁴He at temperatures of 100 mK–300 mK. The critical velocity υ _c of the turbulence appearance is determined through measuring the volt-ampere characteristics. It is established that in the mixture the temperature dependence of the critical velocity is non-monotonous and differs strongly from that in pure ⁴He. Unlike ⁴He, the step-like anomalies on resonance curves were observed which, presumably, is connected with instability of the vortex system under the conditions where the core of the vortex is filled by the atoms of ³He. It is shown that such anomalies appear at the temperatures below 0.9 K, at the same time at temperatures below ～0.5 K they appear even at υ<υ _c .     

Self Diffusion in Solid 4He and 3He-4He Mixtures Near the bcc-hcp Phase Transition

We report experiments on the plastic flow of solid ⁴ He and ³ He- ⁴ He mixtures of 1.4% and 2.8% near the bcc-hcp transition. Plastic flow was generated by moving a wire through a macroscopic single crystal. We found that the plastic flow rate both in pure ⁴ He and in mixture helium crystals is enhanced in vicinity of the bcc-hcp phase transition. The results are interpreted in terms of self diffusion in the solid. Values of the self diffusion coefficient D_s at the respective transition temperatures of pure ⁴ He and of the mixtures are very close, and reach that found in normal liquids. The activation energy for self diffusion in the mixtures is lower by up to 3 K than in pure ⁴ He. We suggest that similar to what is observed in bcc metals, self-diffusion in solid He takes place through phonon assisted atom-vacancy exchange. The enhancement of the diffusion near the bcc-hcp transition is a result of the softening of a short wavelength transverse phonon. The temperature dependence of the energy of the phonon calculated using our data is in accord with the Landau theory of a phase transition driven by a soft mode. Work hardening was observed in mixture crystals, but not in pure ⁴ He. This implies that ³ He impurities pin dislocation lines.     

Temperature,pressure, and concentration dependence of the thermal conductivity of very dilute solutions of3He in superfluid4He

The thermal conductivity of³He–⁴He solutions at saturated vapor pressure has been measured for the concentration range 0.011–1.3 mole %³He and the temperature range 84–650 mK. Measurements were made at 10 and 24 atm for several of the concentrations. The thermal conductivity of solutions at 24 atm does not differ greatly from the thermal conductivity of pure⁴He at this pressure. Qualitative agreement with the Baym and Ebner theory is achieved only if the boundary scattering of phonons is treated in a different manner than suggested by them.     

Nuclear susceptibility of liquid3He-4He solutions along the demixing line

Pulsed NMR measurements of the nuclear magnetic susceptibility of liquid³He-⁴He solutions at saturated vapor pressure are presented. They extend over the whole temperature range between 50 mK and 825 mK, for both concentrations of the coexisting dilute and³He-rich phases. The results have been compared to those obtained with pure³He, and the temperature dependence of the ratio of molar susceptibilities of coexisting phases is derived. The consequences on the efficiency of fractional distillation as a method to enhance nuclear polarization are discussed.     

The Fermi Liquid theory of4He in3He

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in normal (non-superfluid) liquid³He is reviewed and slightly extended. The theory is expected to be valid only below 0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the⁴He concentration X₄ is so small that there is no macroscopic phase separation, only a gradual thickening of the⁴He-rich film on the walls. We confirm that the phase separation temperature T_ps(X₄) estimated from the thickening is close to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to T_ps(X₄) including the new data show that the⁴He effective mass m ₄ ^* is close to, and may be equal to, the bare mass m₄. The difference in binding at zero pressure between⁴He in liquid⁴He and in liquid³He is (E₄₄–EE₄₃)/k_B=(0.21+0.03/–0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E₄₃ indicates that the difference in binding has a minimum of (0.0±0.2) K near 11 atm. This implies that the solubility of⁴He in³He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of⁴He in liquid³He are also discussed.     

4He in Liquid 3He below 0.1 K: Measurements of the Solubility and Prewetting Transition

We have measured the solubility of ⁴He in liquid ³He down to 0.04 K at various pressures. The solubility was obtained indirectly, from the thickness of the superfluid film in contact with unsaturated solutions. We determined the film thickness from the ratio of two parallel plate capacitors with different gaps, immersed in the unsaturated liquid. The technique is described in detail, with its advantages and drawbacks, including the effects of the edge capacitance and capillary condensation. For use in interpreting the data, the adsorption area and the van der Waals potential of the cell walls were found by measuring the thickness of ³He and ⁴He–³He films under their vapor pressure. By fitting the temperature dependence of the solubility to the predictions of Fermi liquid theory, we determined the ⁴He effective mass m*₄, the binding energy E ₄ and the partial volume v*₄, as a function of pressure. At 24 atm, a prewetting transition was observed in the ⁴He-rich film in contact with the liquid ³He. The transition, which is related to a similar phenomenon discovered by Tholen and Parpia at very low temperature, is explained by a simple model. An Appendix describes a new derivation of the thermodynamic functions of ³He-rich mixtures in Fermi liquid theory.     

Wetting of3He-4He mixtures on alkali metal substrates

From available information concerning the wetting behavior of pure³He and pure⁴He on alkali metal substrates, as well as the known properties of bulk³He-⁴He mixtures, the complete wetting phase diagrams for such mixtures, showing prewetting, isotopic separation and lambda transitions for the film phases have been derived. We predict new phenomena such as a triple-point induced dewetting transition, and the absence of a superfluid film wetting Cs, Rb and K walls under concentrated³He solutions.     

Surface tension and mass density of dilute solutions of4He in3He

We report the first precise measurement on the surface tension of dilute solutions of⁴He in³He from 2.6 K to the phase separation temperature as well as the mass density of the solutions. Compared to liquid³He, the surface tension of dilute⁴He solutions increases by 3.5 ± 0.1 mdyne/cm for 2.5%⁴He and 7.4 ± 0.2 mdyne/cm for 5.2%⁴He at 1 K. The increase of the surface tension means a negative adsorption, i.e.,⁴He atoms are excluded from the free surface. The surface adsorption, which is calculated on the basis of the⁴He quasiparticle model, was compared with the data. Assuming that the effective potential near the surface for the⁴He quasiparticle is long-range, the temperature dependence of the surface adsorption is well explained.     

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.     

Pinning of Dislocation Motion in bcc Solid 3He

We have measured the dissipation of dislocation motion in bcc solid ³ He using the high-Q torsional oscillator technique at 1079 Hz. We observed a broad maximum in the temperature dependence of the dissipation. The maximum of the dissipation can be explained by the theory of Granato and Lucke in which the dislocation mobility depends upon the interactions of dislocations with point defects. ⁴ He impurities tend to bind to the dislocation lines at low temperatures and pin this dislocation motion. The maximum of the dissipation corresponds to the depinning of the dislocation motion. From the amplitude dependence of the depinning temperature we first obtained the activation energy of 1.03 K of the impurity ⁴ He atom trapped on the dislocations in bcc solid ³ He at a molar volume of 24.30 cm ³ /mol. The activation energy of the impurity atom in bcc ³ He was found to be larger than the value of 0.7 Kin hcp ⁴ He.     

The influence of3He on the wetting of4He to a cesiated substrate

We report preliminary measurements of the influence of ³ He in the adsorption of ⁴ He to a cesiated substrate by the use of quartz crystal resonance techniques. When compared with the case of pure ⁴ He, the presence of ³ He in the apparatus induces the wetting of the mixture film to Cesium at low temperatures. The wetting is hysteretic, beginning at a concentration-dependent T_c on cooling with continued wetting for T>T_c on warming. The temperatures T_c are given as a function of the total concentration of ³ He in the apparatus.     

Analysis of spin wave resonances in3He-4He mixtures

Spin waves have been reported previously in³He-⁴He mixtures using cw-NMR. The spin waves form standing waves in the rf coil used to detect the NMR signal. Only one resonance was observed, corresponding to ak vector of 1 mm^–1. This is in sharp contrast to similar experiments performed on pure³He, where several resonances were seen. An explanation is given of why this occurs and the resonant mode is identified. Furthermore, it is explained why there is an extra width to the resonance for temperatures below 2 mK. This is caused by radiation damping of the resonant mode. The theory is found to be in excellent agreement with the data. Further experiments are suggested, including details of an improved rf coil design, which should lead to information about the quasiparticle interaction.     

Superfluidity of4He films adsorbed on hydrogen plated graphite

The superfluidity of⁴He on graphite with various preplatings of HD is under investigation using a torsional oscillator. Results for a bilayer of HD follow a similar pattern to those obtained earlier on pure⁴He films and are consistent with third sound measurements on graphite plated with a bilayer of hydrogen. In our case the first⁴He layer solidifies, consistent with behaviour observed in NMR studies of³He on a similarly prepared substrate. At a coverage of 11nm^–2 there is the onset of a region in which the transition temperature increases rapidly with coverage and the transition itself becomes sharper. At certain coverages pronounced signatures have been observed in the period shift and dissipation, which may indicate a further phase transition in the film at lower temperatures.     

Ion trapping on vortex lines in rotating 3He-4He mixtures

The trapping lifetime and mobility of positive and negative ions on vortex lines in ³He-⁴He mixtures have been measured in the temperature range between 0.1 and 1.3 K. The binding energy of the positive ion is found to be reduced by the ³He, and the mobility of both ion species is lowered, providing evidence that the ³He condenses at the vortex core. The negative ion trapping lifetime is smaller than that of the positive ion in the region 0.3–0.5 K, indicating that the bubble structure may be modified by the presence of the condensed ³He. At 0.3 K the negative ion lifetime increases sharply, in qualitative agreement with theoretical models predicting an increase in the bubble radius at that temperature.Work supported by the National Science Foundation.     

NMR Studies of 3He Droplets in Dilute 3He-4He Solid Solutions

We have performed measurements of the temperature dependence of the nuclear spin-lattice relaxation times (T ₁) for a wide range of ³He concentrations for dilute mixtures of ³He in solid ⁴He. The temperatures for phase separation are determined for ³He concentrations 500<x ₃<2000 ppm for a molar volume V _M =20.7 cm³. We report the temperature dependence of the nuclear spin-lattice relaxation times for ³He in the droplets formed after phase separation at low temperatures. The temperature dependence suggests that the interface ³He atoms responsible for the relaxation are degenerate, not solid-like.     

Nuclear magnetic susceptibility of3He adsorbed on graphite below 4.2 K

The nuclear magnetic susceptibility of³He films adsorbed on graphite substrates was measured by means of pulsed NMR techniques at 10 and 20 MHz. Submonolayer, monolayer, and multilayer coverages were examined, as well as one monolayer of³He mixed with various amounts of⁴He. The temperature range of measurements extended from 0.35 to 4.2 K. For pure³He and for³He mixed with⁴He the nuclear magnetic susceptibility displays departures from Curie's law. The observed behavior in pure³He layers can be fitted to an ideal-Fermi-gas curve with an effective degeneracy temperature of 0.15 K. The nuclear magnetic susceptibility of³He–⁴He films is also found to fall below the values predicted by Curie's law as the temperature is lowered, but the results suggest that in this case the film is not uniform, possibly as a result of a phase separation in the film at low temperatures.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

Viscosity of saturated3He-4He mixture below 200 mK

The shear viscosity of saturated³He-⁴He mixture has been measured at temperatures between 7 mK and 200 mK using a vibrating-wire viscometer and a calibrated pressure cell. The reliability of the vibrating-wire technique was tested by measuring the viscosity of pure⁴He. The results are internally consistent. A phenomenological expression is given for the viscosity of saturated³He-⁴He mixture between 7 mK and 80 mK.     

Positive-ion mobility in dilute solutions of 4He in 3He

The mobility of positive ions in essentially pure ³He and in solutions with 100, 300, 1000, 3000, and 10,000 ppm of ⁴He has been studied at pressures of 60 Torr, 10, 20, and 25.6 bar. For temperatures below about 100 mK the pureliquid mobility data are consistent with a ln (T ₀/T) behavior except at the very lowest temperatures, where field-dependent effects may cause departures; both phenomena are in agreement with recent calculations of Bowley based on the Josephson-Lekner formalism. In the more concentrated solutions an increase in the ion radius (corresponding to a decrease in the mobility) is observed starting below ~200mK; this is interpreted as a polarization-potentialinduced phase separation resulting in a liquid ⁴He-rich halo about the solid ion core. At still lower temperatures a vanishing ⁴He content causes the solution data to rather abruptly rejoin the pure-liquid data. At still higher ⁴He concentrations additional very low-mobility species are observed which are likely ions with large metastable halos produced by a large ⁴He concentration at the field-emission tip where the ions are created.Work supported by the U.S. Energy Research and Development Administration and the National Science Foundation under Grants DMR-74-12186 and DMR-76-21370.