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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.

A review of experimental and theoretical studies of the plastic flow of solid helium in the temperature range of 0.1–1.0 K is presented. The most reliable and interesting results were obtained in the two scientific groups where a plastic flow was observed between interconnected chambers containing solid helium that occurred after an overpressure in one of the chambers, and in which the direct contact of solid helium with the superfluid phase was excluded in the measuring cell. A significantly different nature of plastic flow was found in solid 4He and 3He: if in solid 4He the plastic flow rate decreases with decreasing temperature, which corresponds to a thermally activated process, then in solid 3He at temperatures below ≈0.2 K, quantum creep was first recorded when the flow rate ceased to depend on temperature. Only in one group in the experiments conducted near the melting curve, an increase in the flow rate of 4He was observed with decreasing temperature, which allowed the authors to conclude that some form of superfluidity manifested itself. In the thermally activated region of the plastic flow of 4He and 3He, the values of the activation energy and the activation volume, where the activation volume exceeds the atomic volume by a factor from 30 to 70. The analysis of the possible physical mechanisms of plastic flow of solid helium was carried out.A review of experimental and theoretical studies of the plastic flow of solid helium in the temperature range of 0.1–1.0 K is presented. The most reliable and interesting results were obtained in the two scientific groups where a plastic flow was observed between interconnected chambers containing solid helium that occurred after an overpressure in one of the chambers, and in which the direct contact of solid helium with the superfluid phase was excluded in the measuring cell. A significantly different nature of plastic flow was found in solid 4He and 3He: if in solid 4He the plastic flow rate decreases with decreasing temperature, which corresponds to a thermally activated process, then in solid 3He at temperatures below ≈0.2 K, quantum creep was first recorded when the flow rate ceased to depend on temperature. Only in one group in the experiments conducted near the melting curve, an increase in the flow rate of 4He was observed with decreasing temperature, which allowed the authors to conclude that som...

The method of precision barometry has been used to study the structural relaxation processes in nonequilibrium helium crystals obtained by liquid crystallization during rapid cooling in the temperature range of 1.3–1.7 K. The pressure at the ends of a cylindrical measuring cell with solid helium and their variation with time during stepwise heating of the sample were measured. The experimental results for the relaxation kinetics, when the pressure values recorded by both sensors increased with time, were analyzed. Analysis of the experimental results provides estimates of the average atomic concentration of vacancies in the crystal, the vacancy diffusion coefficient values, and the activation energy of vacancy motion. The present work continues the study of structural pressure relaxation initiated in a previous work (LTP 44, 402 (2018)), where a model describing the relaxation of internal stresses in nonequilibrium helium crystals associated with the diffusion of vacancies was proposed for interpretation of the experimental data.

The pulsed nuclear magnetic resonance method was used for the first time to study diffusion processes in 3He, adsorbed nanostructured material MCM-41. The material contained bundles of nanotubes with internal cylindrical channels whose diameter was 2.5 nm. The measurements were made using the Hahn–Carr–Purcell spin echo method with a sequence of 90°–τ–180° probing pulses, where τ is the time interval between pulses. Two different diffusion processes were detected in the system, with diffusion coefficients differing by an order of magnitude. This result was confirmed by an independent multi-echo method with a pair of 90°–τ–120° probing pulses, and with a noticeable increase in the duration of the pulses themselves. It was also found that both diffusion coefficients depend on the value of τ, which is a characteristic feature of restricted diffusion. The results obtained set new directions for the further study of this system.

The nuclear magnetization of 3He adsorbed by the nanostructured material MCM-41 with a channel size of 2.5 nm was investigated using the pulse nuclear magnetic resonance method. The amplitude of the spin-echo signal was measured in the experiment after the application of two probe pulses to the system. The resulting temperature dependence of the signal magnitude, for various 3He coatings, is described by common dependence corresponding to the Curie law. It is demonstrated that the values of the echo signal amplitude determined in the experiment coincide with the calculated value of the corresponding amplitude due to nuclear magnetization that arises in the system of 3He nuclear spins in an external magnetic field.The nuclear magnetization of 3He adsorbed by the nanostructured material MCM-41 with a channel size of 2.5 nm was investigated using the pulse nuclear magnetic resonance method. The amplitude of the spin-echo signal was measured in the experiment after the application of two probe pulses to the system. The resulting temperature dependence of the signal magnitude, for various 3He coatings, is described by common dependence corresponding to the Curie law. It is demonstrated that the values of the echo signal amplitude determined in the experiment coincide with the calculated value of the corresponding amplitude due to nuclear magnetization that arises in the system of 3He nuclear spins in an external magnetic field.

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 disapp...

Diffusion processes are investigated with NMR technique in the two-phase system of solid helium matrix with superfluid inclusions. The system is formed by rapid cooling, and liquid inclusions are nonequilibrium. The diffusion coefficients of $$^{3}$$ He are measured in each of the coexisting phases in a sample of a solid $$^{3}$$ He– $$^{4}$$ He mixture with 1.0 % $$^{3}$$ He using the spin-echo technique in the presence of a magnetic field gradient. It was found that the diffusion coefficient in superfluid inclusions decreases with the increasing diffusion length, which is a feature of restricted diffusion. The data obtained allowed us to estimate the typical size of the inclusions. It is shown that inclusion size decreases with time. A similar study on the equilibrium in liquid–crystal two-phase system, formed by rapid cooling of the sample near the melting curve, is performed for comparison. In this case, the restricted diffusion in the liquid phase also was observed; however, the system was stable, and the diffusion coefficient is sensitive to changes in temperature only.

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 dete...

Creep in solid 4He at temperatures of ∼100–1000 mK is studied experimentally by detecting the flow of helium through a frozen porous membrane under a constant external force. Creep curves are measured for different temperatures and mechanical stresses. This method has made it possible to detect low creep rates in helium down to the lowest temperatures in these experiments. It is found that throughout this temperature range, creep is thermally activated and the activation energy decreases with falling temperature and increasing mechanical stress. An analysis shows that for temperatures above ≈500 mK, Nabarro-Herring diffusive creep takes place in solid helium with mass transfer by self diffusion of atoms and a counterflow of vacancies. The experimental data have been used to obtain the self-diffusion coefficient as a function of temperature for different stresses. At temperatures below ≈500 mK creep takes place at a very low flow rate (∼10−13 cm/s) and a very low activation energy (∼0.5–0.7 K), while the creep mechanism remains unclear.

Processes of spin-lattice relaxation in superfluid inclusions, formed during growth and rapid cooling of helium crystals, are studied by the pulse nuclear magnetic resonance method. Measurements of spin-lattice relaxation times were carried out using the two spin-echoes method. This allows to obtain reliable data for each of the coexisting phases of a two-phase system HCP matrix—superfluid inclusions. The samples of the solid solution 1% 3He in 4He with molar volume 20.2 cm3/mol are investigated in the temperature range 1.4–1.9 K. It is found that the time of spin-lattice relaxation in superfluid drops differs significantly from that in bulk superfluid. It is shown that in both cases the dominant relaxation mechanism is the wall relaxation, which is a few orders of magnitude faster than the bulk relaxation. However, in the bulk fluid, the velocity of wall relaxation is determined by the time of diffusion of atoms to the walls, while the spin relaxation processes directly on the wall play a major role in the superfluid inclusions. In the case of superfluid droplets, 3He atoms are the only magnetic impurities on the walls of the inclusions. They are much less efficient magnetic centers than the strong magnetic particles on the walls of the cell. Moreover, a spontaneous dramatic change is observed in the amplitude of one of the echo-signals, which is associated with the solidification of superfluid droplets and the formation of long-lived metastable disordered (glass) state.

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.

Temperature dependences of the pressure P(T) in homogeneous solid 3He–4He mixtures have been studied experimentally in the wide range of concentrations (35.0%, 62.0%, 68.3%, 74.1%, 75.0%, and 89.3% 3He) above and below the equilibrium phase separation temperature Ts. An anomalous behaviour of the pressure in the vicinity of Ts is found for all investigated samples. With decreasing temperature, as Ts is approached, the pressure increases instead of expected reduction due to decrease in the phonon contribution ( P ph ∼ T 4 ). Such an increase in pressure continues in the metastable region below Ts until the mixture separates. Theoretical interpretation of the observed effects based on a rigorous thermodynamic approach is proposed. The found experimentally pressure behaviour can be described only with the consistent account for fluctuations in the impurity subsystem which near Ts dominates over phonon contribution into the pressure. The obtained theoretical results are in good quantitative agreement with the experimental data. Density fluctuations in the concentrated mixtures give rise to a spontaneous formation of impuriton nano-clusters containing several hundreds of atoms. The fluctuation can be rigorously interpreted as a nucleus of the second phase in the pre-separated homogeneous solid mixture. The estimated size of the fluctuation nano-clusters agrees with the corresponding value for second phase nuclei obtained from the Lifshits–Slesov phenomenological theory of homogeneous nucleation.

A method has been proposed to create disorder in helium crystals by their deformation immediately during the experiment. Precise measurements of the pressure have been performed at a constant volume in samples of various qualities. It has been revealed that excess pressure, which is characterized by the quadratic temperature dependence typical of the disordered glassy phase and of the dislocation contribution to the pressure, is observed in the deformed crystals along with the phonon contribution to the pressure. The effect is observed in the supersolid-state region and disappears after the careful annealing of the crystals. The ultraslow relaxation of the pressure also characteristic of the glassy phase has been observed in the process of annealing of the crystals. The obtained experimental results have been analyzed in the framework of the dislocation model and the model of two-level tunneling states.

The amplitude-frequency characteristic of the spectral line of electromagnetic absorption in liquid helium is measured in the frequency range 40–200GHz at temperatures in the interval 1.4–2.75K. It is found that in the roton frequency region a narrow resonance absorption line on a broad pedestal is observed. The results are compared with data on the roton spectrum found in neutron scattering experiments in liquid helium. The narrow line is due to the creation of a single roton. It is shown that the momentum conservation law is satisfied on account of the transfer of momentum to the superfluid component. The analogy of this effect with the Mossbauer effect is pointed out.

The kinetics of phase separation in quantum crystals of concentrated He3–He4 mixtures containing 34.0, 61.3, and 89.9% He3 are investigated experimentally by the method of precision barometry. The variation of the pressure P(T) of the system upon stepwise cooling and heating is registered. The P(T) curves observed in the experiment are compared with a theory based on a diffusion description of the kinetics of isotropic phase separation. This yields the first information about the mass diffusion coefficient in the whole concentration range. It is shown that in concentrated mixtures the mass diffusion coefficient is several orders of magnitude lower than in dilute mixtures, owing to the interaction of impurities and the presence of elastic strains in the crystal. At the same time, because of the high concentration of new-phase nuclei and the small diffusion length, the phase transition process takes place over a comparatively short time.

The velocity of fast and slow collective modes of 90, 94 and 98% porosity aerogels filled with superfluid helium were measured by means of low-frequency resonant technique at temperatures 0.5–2.5 K. The temperature dependences of velocities of both modes are compared with the hydrodynamic theory which was modified taking into account the mobility of the aerogel matrix, porosity of media and tortuosity of an acoustic way. It has been found that the fast and slow modes in an aerogel are coupled much stronger than the first and second sounds in bulk He II.

Precision measurements of the temperature dependence of the pressure are made on high-quality crystals of He4 and He3–He4 solutions grown at a constant volume. The phonon and vacancion contributions to the pressure are separated on the basis of the Debye model for the phonons and the model of wide-band vacancion excitations. This approach is also used to analyze all the other available thermodynamic data for the solid pure isotopes of helium and their solutions. This yields information about the Debye temperature and vacancy activation energy, and a universal dependence of these parameters on the molar volume is found for He3, He4, and He3–He4 solutions. The values found for the corresponding Gruneisen parameters turn out to be independent of the molar volume.

The kinetics of the bcc–hcp structural phase transition in He4 is investigated by the method of precision barometry in the pressure range 25–31 bar and temperature range 1.25–1.90K. Under constant-volume conditions the kinetics of the pressure and temperature variations is recorded in the range of molar volumes Vm=20.85–21.10cm3∕mole. It is found that the process of cooling is accompanied by an unusual two-stage relaxation of the pressure: initially an exponential decrease of the pressure occurs due to thermal contraction of the supercooled bcc phase, and then the structural transition itself occurs very rapidly. The latter is accompanied by a pronounced thermal effect due to the release of the heat of the phase transition. It is shown that the inverse, hcp–bcc phase transition occurs in one stage (without a delay) and is accompanied by absorption of the heat of transition. Experimental data on the variation of the pressure are obtained in the bcc and hcp single-phase regions and along the bcc–hcp phase e...

A precision barometric study has revealed unusual behavior of the pressure of 3He−4He solid solutions with a concentration of around 30% 3He: in the pre-separation region the pressure increases with decreasing temperature long before the start of the phase transition. It is established that such an anomaly is due to correlation effects in the impurity subsystem which give rise to large-scale fluctuations of the impurity concentration, and the fluctuation contribution to the pressure is much greater than the phonon contribution. Quantitative agreement between the experimental data and the proposed theory is obtained, and it is shown that the observed temperature dependence of the pressure in the pre-separation and metastable regions can be explained only when the long-range character of the interaction between impurities is taken into account.

The influence of phase separation on the thermal stability of superfluid 3He-4He mixtures heated from below by a heat flux with a power density Q up to 20 μW/cm2 is investigated in the temperature region 100–500 mK. It is found that instability is observed only in the presence of phase separation (in the high-temperature region) even at manifestly high heat flux densities. With increasing power of the heat flux at low temperatures the system undergoes phase separation and then, on further increase of Q, suffers thermal instability, which is manifested in a sharp increase in the effective thermal conductivity. These effects are apparently due to the destabilizing influence of the interface between the separated phases owing to capillary effects. The values of the Rayleigh and Marangoni numbers, which characterize the influence of the buoyancy and capillary forces, respectively, in relation to each other are analyzed, and it is noted that the concentrated phase is more sensitive to the action of capillary...

A comparison of the kinetics of the separation processes and homogenization of 3He–4He solid mixtures is made with the use of precision barometry for samples of three types—dilute mixtures of 3He in 4He and of 4He in 3He and concentrated 3He–4He mixtures. It is found that in all types of mixtures studied the rate of the initial stage of homogenization can exceed the rate of separation by more than 500 times. An appreciable rate of phase separation in the concentrated mixtures, where, according to existing ideas, the impurity atoms in quantum crystals should be localized, attests to a new, unknown mechanism of mass transfer under those conditions, while the fast homogenization indicates that this process is nondiffusional in nature.

The effective thermal conductivity of superfluid mixtures of 3He in 4He with an initial concentration of 9.8% 3He is investigated in the temperature interval 70–500 mK. The results, together with previously available experimental data on the thermal conductivity, viscosity, and mass and spin diffusion, are analyzed in the framework of the kinetic theory of the phonon–impuriton system of superfluid mixtures. It is shown that the experimental results for all the kinetic coefficients can be described from a unified viewpoint if the corresponding impuriton–impuriton scattering times are used as adjustable parameters. The role of each relaxation process in the complex hierarchy of relaxation times is determined as a function of temperature and concentration. It is found that even in concentrated mixtures a substantial contribution to the establishment of equilibrium is made by three-phonon processes. The phonon–impuriton relaxation times are calculated by integrating over the phonon energy in the entire region...

Precision measurements of the pressure during phase separation in samples of solid solutions of 4He in 3He have been used to obtain data on the characteristic times of the phase transition. A processing of the results gives additional evidence supporting the view that homogeneous nucleation is realized in 3He–4He solid solutions at significant supercoolings and heterogeneous nucleation at the smallest supercoolings. Two different ways are proposed for comparing the results with a theoretical calculation taking into account the processes at the boundary of a nucleus of the new phase. Both give roughly similar values of the coefficient of surface tension at the nucleus–matrix boundary, and those values agree with those obtained in other studies. It is conjectured that the bcc–hcp transition has a substantial influence on the kinetics of separation at the lowest supersaturations.

The relaxation of temperature and concentration of a superfluid 3He–4He mixture with an initial molar concentration of 9.8% 3He is investigated in the temperature interval 100–500 mK for different values of the heat flux. It is shown that the kinetics of the change in temperature of the liquid can be approximated by an exponential function, and the time constants obtained depend weakly on temperature. The concentration relaxation processes are analogous to the temperature relaxation processes only in the region of the single-phase mixture, while below the phase separation temperature the change in concentration with time is of a nonmonotonic character and can be described by a superposition of two exponential functions. This kind of kinetic behavior of the mixture is explained in the framework of a simple model which illustrates the distribution of the concentration over the height of the cell at various times after a heat flux is turned on. In this case the concentration relaxation of the dilute phase co...

A generalized relation for the characteristic time constants of mixture separation was found in the framework of the homogeneous nucleation theory. It allows us to describe the data on the separation kinetics at various concentrations c, molar volumes, and supercooling levels. Using precise pressure measurements, the separation time constants were obtained for 5 samples with the 4 He concentration of 2.2 - 3.34% in the pressure range 31.5-38.6 bar. The data obtained for all the samples are in good agreement with the generalized relation if the impurity diffusion coefficient is proportional to c -4/3 . The value of surface tension on the inclusion boundary was estimated from comparison between experiment and theory. It is in adequate agreement with the data obtained in other experiments. The obtained results are considered as evidence of homogeneous nucleation at phase separation of solid 3 He - 4 He mixtures.

The thermal instability of 3He-4He mixtures caused by heating the liquid from below has been studied experimentally. The temperature gradients were measured which appeared in the mixture with initial concentration 9.8% of 3He below 0.5 K in the presence of different heat flows from the heater at the cell bottom. At a certain critical heat flow the effective thermal conductivity of the liquid was observed to increase sharply which was naturally attributed to the convective heat transfer. It is shown that the thermal convection develops at high temperature gradients. In this case the Rayleigh numbers exceed many orders of magnitude those for heating from above. Thus the convective instability develops in a system in which the light liquid is at the top and where no prerequisite for instability is seemingly available. The resugts obtained are analyzed in terms of the theory of convective instability in binary mixtures. It is suggested that the phase separation, of superfluid mixtures caused by a heat flow could be a destabilizing factor initiating convection. The vortex formation in superfluid helium and the related turbulent flows appearing at high temperature gradients can be another factor favourable for instability of the liquid.

The kinetics of the separation of dilute solid mixtures of 4He in 3He is investigated in the ranges of temperature 100–200 mK, 4He concentration x=2.2–3.3%, and pressure 32–35 bar. It is found that the characteristic time τ required for the separating mixture to come to equilibrium depends substantially on the degree of supercooling. When the mixture is supercooled by more than 40–50 mK relative to the separation temperature of the initial mixture, the characteristic time τ

Precise measurements of the pressure in solid solutions of 4He in 3He are performed with temperature cycling in the phase-separation range. It is found that as a result of such cycling the difference ΔP of the pressures between the minimum (≈100 mK) and maximum (≈200 mK) temperatures decreases by a factor of approximately 3 and then remains unchanged for a long time. The initial values of ΔP and the pressure P0 in a uniform solid solution 4He–3He are restored only after the sample is heated to a temperature substantially above the phase-separation point. The data obtained are explained on the basis of the hypothesis that under these conditions clusters of pure 4He form around quasiequilibrium vacancies. A thermodynamic calculation of such clusters is performed. The computational results made it possible to give a quantitative explanation of the distinctive features observed. Comparing the calculations with experiment made it possible to determine the cluster concentration, 8×10−5, and the cluster radius, ...

The temperature and concentration gradients ∇T and ∇x created by a heat flow in a superfluid 3He–4He mixture with a concentration of 9.8% 3He are measured in the steady state in the temperature range T=70–500 mK. It is found that the ratio ∇x/∇T obtained in the experiment can be described on the basis of a dependence of the osmotic pressure on the temperature and concentration. The data are used to find the thermodiffusion ratio and, hence, the thermodiffusion coefficient of this mixture.

The concentration dependence of the attenuation coefficient of first sound in superfluid 3He–4He solutions in the saturation and supersaturation regions is investigated experimentally at pressures of 0–10 atm. An original technique of continuous variation of the concentration in situ by variation of the osmotic and thermomechanical pressures is used, permitting measurements to be made in the long-lived metastable phase of the superfluid solutions. It is shown that the data obtained are described well in terms of the theory of sound propagation in a gas of Fermi excitations without taking the Fermi-liquid corrections into account. The corresponding values of the effective mass and relaxation time of 3He quasiparticles are taken from an analysis of the existing experimental data. Within the experimental error, no excess sound attenuation was found in the region of supersaturated solutions.

A cryogenic unit designed for physical research on quantum crystals at ultralow temperatures is described. The unit includes a dilution refrigerator with a hybrid 3He circulation system, an antivibration protection system, and a system of automated control and data acquisition and processing. The construction of the basic units, the thermometry system, the algorithms for measurements, and the software for conducting research on quantum crystals by the method of precision pressure measurements are described. The unit may be used for performing a wide range of tasks in research on various condensed systems at millikelvin temperatures.

The pulsed NMR technique was used to investigate diffusion on the BCC-HCP phase-equilibrium and melting curves of a dilute solution of 3He in 4He. The contributions from all coexisting phases were identified using the spin-echo method. It is established that, along with the contributions from the equilibrium BCC and HCP phases or from bulk liquid (in the melting curve measurements), there is an additional diffusional process that is characterized by an anomalously high diffusion coefficient. It is found that the latter is close to the diffusion coefficient in liquid helium, while the diffusion itself is spatially restricted. The observed effect may be caused by the formation of liquid droplets in the course of the BCC-HCP transition.

New features are observed for the pressure in a phase-separated dilute solid solution of 4He in 3He subjected to multiple temperature cycling within the phase-separation region. The results are explained within the framework of the hypothesis of A.F. Andreev and D.I. Pushkarov that the vacancies in a crystal without ideal periodicity are surrounded by clusters with a periodic structure. The equation for determining the radius of a cluster of pure 4He in a solution of 4He in 3He is refined. This hypothesis is shown to provide quantitative agreement between the calculated and experimental data under the assumption that the homogenization of the phase-separated solution is accompanied by the formation of metastable vacancies with a concentration of ∼(4–5)×10−5.

A method is proposed for constructing the separation phase diagram of 3He–4He solid solutions on the basis of precision measurement of the pressure jump due to phase separation at constant volume. The technique is implemented on high-quantity samples of the solid solutions, making it possible to obtain reliable and reproducible experimental data with no appreciable manifestation of hysteresis effects. The line of phase separation constructed from the experimental data is compared with the results of various theoretical approaches describing phase separation in solid solutions of helium isotopic mixtures. It is found that good agreement with experiment is observed only for the Edwards–Balibar model, which is an extension of the theory of regular solutions to take into account the differences of the crystal structures (hcp and bcc) of the phases existing in the system.

The spin–spin relaxation time in a 3He–4He solid solution is measured before and after phase separation in the temperature range 1–250 mK. The spin echo technique is used, which permits separating the contributions of the two separated phases to the magnetic relaxation. It is found that in the concentrated phase the spin–spin relaxation time is practically independent of temperature above 50 mK and is described by the same exchange mechanisms as in pure 3He. In the dilute phase the relaxation time is inversely proportional to the concentration and agrees with the corresponding values for homogeneous solutions. The dominant contribution to the spin–spin relaxation process is from 3He–4He tunneling exchange. At the lowest temperatures the spin echo exhibits anomalous behavior, which may be a manifestation of quasi-one-dimensional diffusion.

Pressure measurements are used to study the kinetics of phase separation of 3He–4He solid solutions under conditions such that after the transition a two-phase system is formed, consisting of liquid drops of the concentrated phase (nearly pure 3He) in a crystalline matrix of the dilute phase (nearly pure 4He). It is shown that under stepped cooling of the two-phase sample the growth of the liquid drops can be described by a superposition of two exponential functions representing processes with long and short time constants. This is due to the strong influence of the stresses arising in the crystal at the phase transition owing to the large difference in the molar volumes of the two phases and which probably cause plastic deformation of the matrix and the giving rise to nonequilibrium concentrations of 3He in it. The transport of 3He atoms occurs only in connection with stress relaxation. It is established that cyclic processes of growth and dissolution of the liquid drops strongly degrade the quality of t...

Comprehensive experimental results on growth, dissolution, and melting kinetics of solid inclusions of 3He formed as a result of phase separation of solid mixtures of 3He in 4He are described. A new method developed for obtaining high- quality crystals by cycling the temperature of a solid mixture within the separation region makes it possible to obtain reproducible values of time constants for growth and dissolution of inclusions. Precise measurements of pressure in the crystal at constant volume are used for obtaining data on effective mass diffusion of 3He atoms in the crystal. It is shown that quantum diffusion is strongly suppressed at low temperatures due to elastic fields induced near the boundaries of inclusions. Abnormally rapid transport of matter of the threshold type is observed during dissolution of inclusions. The observed effects can be explained qualitatively in the proposed model of multistage dissolution of 3He inclusions. The data on the variation of pressure as a result of melting and ...

It is discovered that the characteristic phase separation time constant of solid 3He–4He mixtures at low temperatures exhibits a nonmonotonic temperature dependence with a minimum. It means that the rate of mass transport slows down at very low temperatures, and the corresponding values of the effective diffusion coefficient also depend nonmonotonically on temperature and concentration and differ significantly from the spin diffusion coefficient measured earlier in NMR experiments on quantum diffusion. The discovered nonmonotonicity may be associated with the influence of the nonuniform field of elastic stresses in the crystal because of the difference in the molar volumes of the phases.

NMR investigations of restoration of longitudinal equilibrium magnetization in phase-separated solid 3He–4He mixtures are carried out in the temperature range 1–200 mK. It is found that below 100 mK, the results depend on the energy of tipping NMR pulses, while at the lowest temperatures the restoration of magnetization becomes nonmonotonic. The obtained results are explained on the basis of a proposed model in which both magnetic (spin-lattice) and thermal relaxation are assumed to take place between the Zeeman system and the lattice.

The kinetics of isotopic phase separation of 3He–4He solid mixtures for various molar volumes has been studied by precision pressure measurements at a constant volume. It is found that the attainment of equilibrium between coexisting phases formed as a result of stratification is described correctly by an exponential dependence for various modes of crystal cooling and heating. The characteristic phase separation time decreases with temperature, thus confirming the athermal quantum nature of the growth of a new phase during the phase transition. The phase separation time is found to increase considerably with crystal pressure. It is shown that the prevailing theory can provide only a qualitative description of the established regularities. A quantitative description of experimentally observed decay times requires an analysis of diffusion processes in a gas of impurity excitations in the presence of a concentration gradient.

Experimental and theoretical investigations of the growth kinetics of BCC3He precipitates in isotopic phase separation of HCP3He–4He are carried out. Low frequency pulsed NMR is used to study the mixture with an initial3He concentration of 3.18% at a pressure 3.7 MPa on stepped cooling down into the separation region. The separation time constant is shown to decrease monotonically with cooling. The evolution of heterophase structure resulted from separation is investigated by solving an equation for spatially non-homogeneous order parameter of decomposing mixture. The obtained temperature dependence of separation time constant is found to be in good agreement with the experiment.

The earlier systematic measurements of attainable supersaturations of superfliud3He-4He solutions depending on temperature and pressure have been continued. The experiments were carried out at continuously varied solution concentration and at constant temperature and pressure. The results obtained are analysed using various models of nucleation in supersaturated liquid solutions. The fast nucleation line which is constructed from experimental results is in strong contrast with the kinetic theory of homogeneous nucleation for supersaturated3He-4He solutions. It is shown that reasonable agreement with experimental results can be obtained assuming that completed centres of nucleation generated on quantized vortices in superfluid liquid are available.

The spin–lattice relaxation time in a 3He–4He solid solution with the initial concentration 3.18%3He is measured during phase separation by using the pulsed NMR technique. The relaxation time in a concentrated bbc phase formed as a result of phase separation is found to be independent of temperature over the entire range of its existence and is determined by the Zeeman-exchange interaction mechanism. In the dilute hcp daughter phase, the spin–lattice relaxation time increases on cooling according to the law T1∼x−n, where n=0.88±0.12, and x is the 3He concentration. The values of T1 in this phase coincide with the values corresponding to a homogeneous (nonseparated) solution of the same concentration.

Phase separation kinetics and growth of the new phase in supersaturated superfluid3He-4He solutions was studied using the method of continuous change of3He concentration in situ and developed theory. Simultaneous measurements of the first sound velocity and the dielectric constant were carried out during the change of concentration. The velocity and attenuation of the first sound and the dielectric constant in supersaturated metastable solutions were calculated on the assumption that the excess3He in the solution is in the form of both atoms and droplets of the new phase. It was shown that the sound velocity, unlike the dielectric constant, is very sensitive to the formation of droplets. Comparison of the theory and the experimental data allowed us to elucidate the growth dynamics of the nuclei of the new phase from the metastable supersaturated mixture.

A disordered (glassy) state has been searched for in solid $^{3}\mathrm{He}$ deformed in the course of the experiment through precise measurements of pressure. The analysis of the temperature dependence of the crystal pressure measured at a constant volume shows that the main contribution to the pressure is made by the phonon subsystem, with the influence of the disordered phase being very weak. Annealing of the deformed crystal does not affect this state. The results obtained differ greatly from the corresponding data for solid $^{4}\mathrm{He}$ measured in the region of supersolid effects, where a pressure excessive in comparison with the phonon one was registered. The excess pressure had a quadratic dependence on temperature, which is typical of a disordered system. Absence of the distinct excess pressure in solid $^{3}\mathrm{He}$ is yet unclear; some speculative interpretations are suggested.

Low temperature experiments [1–4] on the interaction of electromagnetic field with liquid helium have produced a number of interesting and unexpected results that have yet to be explained in a conventional manner. One of such effects is the resonance absorption and radiation of electromagnetic waves in superfluid helium at a frequency f corresponding to the roton gap of the energy spectrum, e = Δ/ħ. For Δ =8.65 K, which corresponds to a temperature of the order of 1.4 K, f = 2πω ≈ 180.3 GHz. The temperature dependence of this absorption near the temperature of transition to superfluid state coincides precisely with temperature dependence of the roton gap obtained in neutron scattering experiments [5, 6]. Since at this frequency the photon momentum p pt = 3.8 × 103 cm−1 is many orders of magnitude smaller than the roton momentum p r = 1.9 × 108 cm−1, the question of how the momentum conservation law can be obeyed in a such process must be addressed.

The kinetics of growth and dissolution of a new phase during phase separation and homogenization of solid 3He–4He mixtures is studied experimentally. It is found that both these processes have different kinetics, while homogenization is ensured by an anomalously rapid transport of matter in the crystal. It is shown that the prevailing theories about diffusion processes in a quantum crystal cannot explain the obtained results.

High-precision pressure measurements in solid {sup 4}He, grown by the capillary blocking technique, have been made in temperatures range from 50 to 500 mK. The temperature dependence of pressure indicates that aside from the usual phonon contribution {approx}T {sup 4}, there is an additional contribution {approx}T {sup 2}, the latter becoming dominant at temperatures T