Solutions Of 3He In 4He Research Articles

The critical velocity of transition to turbulence in 3He–4He liquid solutions

The transition between laminar and turbulent flows around a quartz tuning fork vibrating with frequency ω in superfluid 4He and concentrated solutions (5 and 15% 3He in 4He) in the temperature range 0.3–2.3 K has been studied. The temperature dependences of the amplitude of the critical transition velocity vcr are obtained. The relationship vcr ∼ √(ηω/ρ) is shown to be applicable for the description of these dependences in concentrated solutions of 3He in 4He with density ρ and viscosity η, but this formula does not hold for the temperature dependence of vcr in pure 4He over the entire temperature range explored. It is also shown that in contrast to pure 4He temperature has virtually no effect in concentrated 3He–4He solutions on the drag coefficient in both laminar and turbulent regimes. The concentration dependences of the drag coefficient in the laminar regime normalized to the effective cross section of the vibrating body are plotted in the temperature range 0.5–1 K. The calculated dependences show that for low concentrations of a solution with x3 < 1% 3He the normalized drag coefficient weakly depends on the concentration of 3He and can be qualitatively described by the formula λ/S∼ρηω. In the x3 > 1% 3He concentration range, this coefficient increases sharply, and the reason for such a growth is currently not clear. Overall, the results of the study show that an increase in the 3He concentration in the solution enhances its stability with respect to the development of turbulence as the exciting force of a quartz tuning fork increases.

Dissipation mechanisms of tuning fork vibrations in superfluid 3He–4He solutions

The amplitude–frequency characteristics of tuning forks immersed in superfluid 3He–4He solutions were measured in the temperature range of 0.1–2.5 K. The tuning fork resonance frequency and the resonance width were measured as functions of temperature for 5% and 15% concentrations of 3He and, for comparison, for pure 4He. The experimental results for the key dissipation mechanisms, that is, viscous friction and first and second-sound emission of a tuning fork, were analyzed. For separation and evaluation of the contributions of viscous damping and first and second-sound waves, “closed” (in a factory capsule) and “open” (without a capsule) tuning forks were used. The resonance width, which is a measure of dissipation of tuning fork vibrations, was found to be higher in solutions than in pure 4He, and to increase with increasing 3He concentration. It was shown that the existing analytical expression for the contribution of viscous friction provides a good description of the experimental data for 4He only in the hydrodynamic region. For the solutions, the viscosity contribution is consistent with the experiment only at high temperatures (above 1.4 K). For the “open” tuning fork, the contribution of the first-sound is consistent with the calculation results only for 4He, whereas for the solutions, the calculated values are underestimated compared to the experiment. The possible contribution of the second-sound to the dissipation of the tuning fork vibrations in solutions was estimated using experiments with the “closed” tuning fork. This contribution was found to vary non-monotonically with a maximum at temperatures of ≈ 0.6–0.8 K. The ratio of the tuning fork energy loss due to the thermal diffusion wave versus the loss due to the radiation flux of the second-sound wave in superfluid solutions was calculated using literature data with an accuracy of 10–3–10–4.

Excitation of concentration and temperature fluctuations by vibrating bodies in superfluid 3Не–4Не solution

The excitation of concentration and temperature fluctuations in waves of the first and second sounds, as well as in the thermal wave, by a vibrating tuning fork, in a superfluid 3He–4He solution with a concentration of 3Не exceeding 10% was studied. In particular, the possibility of emission of second sound and dissipative thermal wave by an oscillating tuning fork, the efficiency of such emission as a function of the solution concentration, and the possible effect of this emission on the damping of the tuning fork vibrations, which have been observed in experiments but not explained theoretically to date, are considered in this paper.

Effect of phase separation kinetics on the homogenization kinetics of solid solution of 4He in 3He

New features of the kinetics of phase separation and the subsequent homogenization of solid solutions of 4He in 3He are observed at temperatures of 0.1–0.5 K. Separation was initiated by rapid cooling of a uniform solution, as well as by cooling it in small temperature steps. Information on the kinetics of the phase transitions was obtained using precision measurements of the pressure of the solid helium at constant volume. The homogenization kinetics are found to depend substantially on the kinetics of the preceding separation. The time constants for homogenization in the separation region are smaller by more than a factor of 5 with rapid cooling, than with slow cooling. These results are consistent with a model of homogeneous nucleation.

Kinetic processes in solid helium involving impurities and vacancies (Review)

A brief review is given of the kinetic behavior of impurities and vacancies in solid helium, which Andreev and Lifshitz predicted should be delocalized and converted into unique quasiparticles. Primary attention is devoted to the unusual diffusion processes in solid 3He-4He solutions as they undergo phase separation. Because mechanical stresses develop in the crystal during separation, the diffusive flow is substantially reduced and the effective diffusion coefficient becomes smaller than the coherent quantum diffusion coefficient. During the inverse transition from a separated mixture into the homogeneous state, anomalously rapid mass transfer is observed which can be explained qualitatively in terms of a model in which 3He inclusions are dissolved in three stages. Experimental data on the kinetics of phase separation are compared with a diffusive description of the process that takes into account the difference between diffusion processes outside and inside a nucleus of the new phase. Good agreement is obtained between a theoretical calculation and the experimental data. A homogeneous nucleation model is used to estimate the concentration of nuclei. For the first time, the coefficient of mass diffusion is estimated over the entire range of the concentration of the solutions. The behavior of delocalized vacancies in 4He and 3He solid solutions is studied near the separation temperature. The observed features of the pressure in this kind of system during repeated temperature cycling are explained by the formation of pure 4He vacancy clusters. Although the crystal itself has no strict periodicity owing to the random separation of 3He and 4He atoms at the lattice sites, a periodic structure is realized within a cluster and vacancies become delocalized.

Effect of an intermediate bcc phase on the evolution of superfluid inclusions in an hcp3He–4He matrix

Pulsed NMR is used to study the evolution of liquid inclusions formed in an hcp matrix during rapid cooling of a 3He-4He solution containing 1.05% 3He. The diffusion coefficient of 3He in the liquid inclusions as they evolve is measured by a spin echo technique with two probe pulses. The measurements were made at 1.67 K, which corresponds to the region of the bcc phase in the phase diagram, and at 1.38 K, where the bcc phase is absent. It is found that during the evolution in both cases, the liquid inclusions are smaller than the diffusion length and diffusion is restricted. The measured coefficient of restricted diffusion made it possible to determine the characteristic size of the inclusions. In the first case, during the evolution of the liquid inclusions an intermediate bcc phase in the form of dendrites develops and separates the liquid inclusions into a mass of fine droplets. Because of the rapid growth of the bcc phase, the size of the droplets decreases rapidly and the process ends with the disappearance of the bcc phase and the formation of an amorphous state. The results derived from the measured diffusion coefficient correlate with the behavior of the spin-lattice relaxation time in this kind of system. In the second case, at a lower temperature, the bcc phase does not develop and the evolution of the liquid inclusions is accompanied by a very slow reduction in their size until their complete solidification.

Dynamical Superfluid Response of 3He–4He Solutions Confined in a Nanometer-Size Channel

We measured the superfluid response of dilute 3He–4He solutions confined in a one-dimensional channel of 2.8 nm in diameter using a twofold torsional oscillator. We prepared three 3He concentrations of 0.0, 2.0, and 4.0 at. %, and found that the response of 4.0 at. % decreases by 70 mK at 0.13 MPa from that of liquid 4He. The decrease does not depend strongly on the pressure and is proportional to the 3He concentration. Furthermore, we found the measurement frequency dependence in the same manner as for liquid 4He. The response of 4.0 at. % at a measurement frequency of 0.5 kHz at 0.13 MPa is suppressed by about 40 mK from 2 kHz, and the magnitude of the suppression does not depend strongly on both the 3He concentration and the pressure.

Studies of kinetic processes in a concentrated 3He-4He solution using an oscillating tuning fork

The dissipative processes causing the damping of quartz tuning fork vibrations in a solution of 15% 3He in 4He, are studied in a temperature range of 0.5–2.3 K. The resonance curves of the tuning forks are measured in the laminar flow region of the liquid, and their width is determined by the width of the dissipative processes. We examined tuning forks with a resonance frequency of 32 kHz, located inside a flask (“enclosed”) and tuning forks without a flask (“unenclosed”). The results of the experiment are compared to existing theories. It was found that a significant contribution to the damping of tuning fork oscillations for a solution, as opposed to pure 4He, is from the second sound radiation, the contribution of which exceeds the input of viscous dissipation at low temperatures. The radiation of the first sound does not contribute to the damping of the oscillations of the “enclosed” fork due to the small size of the cell versus the wavelength. In the case of the “unenclosed” fork, the damping is determined by three processes: viscous dissipation and radiation of the first and second sounds.

Mobility of 2D Electrons on Pure 4He and on 3He–4He Dilute Solution

The mobility of 2D electrons on pure 4He and on 0.5 % solution of 3He in 4He was investigated for different electron densities in the temperature range 0.12 to 1.3 K. The electrons in the same electron density show the same transition temperature from liquid state to Wigner crystal state in both pure 4He and in the solution. In the high temperature range where the gas-scattering is dominant, the electrons show a smaller mobility in the solution than in the pure 4He due to the electron collision with 3He gas atoms which have a higher vapor pressure. In the middle temperature range where the ripplon-scattering is dominant, the mobility in the solution is smaller than in 4He. This is explained by a smaller surface tension caused by 3He atoms collected at the surface. In the low temperature range where electrons are in the Wigner crystal state, the mobility gradually increases with decreasing temperature in the solution, while it stays almost constant in the pure 4He. The mobility increase is more pronounced in the low electron density. The results are qualitatively in agreement with the existing theory which includes the bulk 3He quasiparticle reflection from surface dimples and the effect of the surface layer of 3He atoms.

Kinetics of nucleation during the bcc-hcp structural transition in solid helium

The nucleation kinetics of the hcp phase in the supercooled bcc phase of solid 4He and a 3He-4He solution containing 1% 3He is studied experimentally. Precision measurements of the pressure in the crystal are made as it is cooled along an isochore near the bcc-hcp phase equilibrium curve. The lifetime of the metastable bcc phase in 4He is found to have a complicated dependence on the level of supercooling which can be described in terms of two nucleation mechanisms—homogeneous and heterogeneous. The homogeneous mechanism occurs for the highly supercooled bcc phase in carefully annealed crystals, while the heterogeneous mechanism, for which the activation coefficients are several orders of magnitude lower than for the homogeneous mechanism, occurs with low supercooling. The influence of defects and impurities on the nucleation process is also studied. In unannealed (defective) 4He crystals the nucleation rate is found to have an enormous scatter, which is indicative of poor reproducibility from one crystal to another. For annealed samples of 3He-4He solution the nucleation kinetics data can be described only by the heterogeneous nucleation mechanism.

Cryogenic electrolytes

Experimental evidence of metastable ion dipoles in solid helium is examined. Similar quasiparticles with positive scattering lengths for injected electrons are assumed to exist in the liquid phases of cryogenic liquids. Phenomena that can be used for detecting and monitoring a dipole gas in superfluid helium (referred to as cryogenic electrolyte) are discussed. The most interesting of these phenomena are: special features of the dielectric behavior of ion dipole gases, the temperature dependence of the ion dipole gas osmotic pressure at the boundary of liquid 3He-4He solution stratification, relaxation phenomena of collective origin in cryogenic electrolytes, and the transformation of the phonon spectrum of liquid helium owing to strong interactions between phonons and heavy dipole quasiparticles.

Use of a quartz resonator of the tuning fork type as a thermometer in a dilution refrigerator

The temperature dependences of the resonance frequency and resonance width of a tuning-fork-type quartz resonator, which is placed directly in the dilution chamber of a refrigerator, were measured in order to test the possibility of using it as a secondary thermometer under such conditions. Measurements were performed both in the upper and lower phases of a stratified solution of 3He in 4He in the temperature range 15–350 mK. The dependences obtained indicate that the parameters of resonators depend on not only the temperature, thus making it problematic to use them for thermometry in a cryostat’s dilution chamber.

Neutron reflection from the surfaces of liquid 4He and a Dilute 3He—4He solution

We report and discuss the first neutron reflection measurements from the free surfaces of normal and superfluid 4He and of a liquid 3He-4He mixture. In case of liquid 4He the surface roughness is different above and below the lambda transition, being smoother in the superfluid state. For the superfluid, we also observe the formation of a surface layer ∼ 200 Å thick which has a subtly different neutron scattering cross-section. The results can be interpreted as an enhancement of the Bose-Einstein condensate fraction close to the helium surface. We find that the addition of 3He isotopic impurities leads to the formation of Andreev levels at low temperatures.

Osmotic Pressure of 3He-4He Solutions at 25.3 Bar and Low Temperatures

The osmotic pressures of dilute 3He-4He solutions were determined at 25.3 bar from measurements of crystallization curves at temperatures from 5 mK to 60 mK, when the 3He component of the solution obeying the Fermi-Dirac statistics was deep in the degenerate state. We determine the shift of the crystallization pressure of the solution of interest relative to pure 4He when both these substances are present in the cell in two separate volumes at the same temperature. We used our novel ultra-sensitive capacitive gauge for measurements of small pressure differences between the two substances. We used a quartz resonator for determination of solution’s concentration in situ. The difference between the crystallization pressure of the saturated solution and pure 4He, both extrapolated to zero temperature, is (339±2) mbar.

Convective Turbulence in Superfluid Solutions 3He–4He

In present work, we continue our experimental investigations of heat instability in superfluid 3He–4He solutions heated from below. We research two solutions with 3He concentrations 5.0% and 9.5% for temperature of 270 mK. It is found that for 5% solution the dependence \(\nabla T(\dot{Q})\) is linear in temperature range studied whereas for the solution of 9.5% we observed the deviation from linear dependence above some critical value \(\dot{Q}_{c}\) . This effect manifests the thermal instability which appears under start of phase separation in 9.5% solution if heat flow is switched on. For 5.0% solution where one does not observe the phase separation at the values of \(\dot{Q}\) applied, the instability was not observed. To identify the possible mechanism of a thermal instability in stratified solution, we estimated the dependence of the Nusselt number on relative Raileigh number Ra/Ra c . One observes that the dependence can be fitted as Nu=(Ra/Ra c ) b where b=0.31±0.04. Note that the dependence obtained agrees rather good with the empiric expression of (Busse in Rep. Prog. Phys. 41:1929, 1978) and connecting the numbers Nu and Ra for turbulent convection. This gives grounds to conclude the heat transfer in a stratified solution is realized by transition to the regime of turbulent convection.

Nonlinear excitation of temperature waves in He3–He4 superfluid solutions due to absorption of light waves

The nonlinear excitation of temperature waves in superfluid solutions of He3 in He4 through the absorption of optical waves is considered. A nonlinear equation which describes such an interaction is derived, an expression for the nonlinear interaction length is obtained, and the necessary value of the interaction length for which second sound excited by two light waves can be amplified from fluctuations to observable values is estimated in order of magnitude.

Adiabatic Melting of 4He Crystal in Superfluid 3He at Sub-millikelvin Temperatures

Adiabatic melting of 4He crystal to phase separated 3He–4He solution (at T< 2 mK) is probably the most promising method to cool the dilute phase down to temperatures substantially below 0.1 mK. When started well below the superfluid transition temperature Tc of pure 3He, this process allows, in principle, to get the final temperature (Tf) several orders of magnitude less than the initial one (Ti). This work is the first practical implementation of the method below the Tc of 3He. The observed cooling factor was Ti/Tf=1.4 at 0.9 mK, being mainly limited by the bad performance of the superleak filling line, by incomplete solidification of 4He in the cell, and by the improper thermal contact between the cell wall and the liquid.

Thermal Instability of Superfluid Phase-Separated 3He-4He Solution Heated From Below

The phase separation influence on thermal instability of 3He-4He superfluid mixtures heated from below is studied in the temperature range of 70 – 550 mK. The experiments are carried out in a cylindrical cell of 2.38 cm in diameter and 4.7 cm in height with the initial concentration of 9.8 %3He. The thermal instability is registered by observing the anomaly in the dependences of temperature and concentration gradients in the cell as a function of heat flux. The instability is shown to occur only in the phase-separated solutions. We explain this behavior by the influence of capillary effects on the interface of the two-phase liquid. The experimental results are analyzed in terms of the critical Rayleigh and Marangoni numbers.

The role of a surface flow in experiments with atomic hydrogen adsorbed on liquid helium

We apply a quantum hydrodynamics of the surface of 3He-4He solutions to account for the in-plane transport of the two-dimensional (2D) spin-aligned atomic hydrogen (H↓) adsorbed on superfluid helium film. We discuss how the surface flow of 2D H↓ may be traced in experiment thus allowing to study the interaction of the 2D hydrogen with ripplons and surface-bound 3He as well as to observe the superfluidity of the 2D Bose gas of H↓. As an example we consider the formation of the ESR spectrum of the 2D H↓ and find that in spatially non-uniform case the surface flow contributes significantly to the conditions of the ESR spectrum instability observable at high microwave power. We also analyze the conditions at which the surface flow of the 2D hydrogen plays an important role in thermal compression experiments.

Vacancy-impurity nanoclusters in solid solutions ofHe3−He4

The existence of vacancy--impurity clusters due to quantum properties of vacancies in phase separated solid solutions of 4He in 3He is analyzed and discussed. Additional mechanism called vacancy assisted nucleation is proposed. According to this assumption the vacancy-impurity clusters should have b.c.c. structure.