Solid 3He 4He Mixtures Research Articles

Kinetic properties of solid 3He–4He mixtures in the model of freely moving impuritons

Within the framework of the gas-kinetic model of a mixture of weakly interacting gas of quasiparticles—phonons and impurities—the dissipative properties of 3He–4He solid solutions are considered: diffusion, self-diffusion, and thermal conductivity in the range of concentrations and temperatures, where impurities of 3He can be considered as quasiparticles freely moving through the crystal. Explicit expressions are obtained for the dissipative coefficients of spin and mass diffusion and the coefficient of thermal conductivity. The observed in experiments on spin relaxation, heat transfer, and separation of solutions dependencies and parameters of quasiparticles are discussed.

Fast Diffusion Process in Quenched hcp Dilute Solid 3He–4He Mixture

The study of phase structure of dilute 3He–4He solid mixtures of differing quality is performed by the spin echo NMR technique. The diffusion coefficient is determined for each coexistent phase. Two diffusion processes are observed in rapidly quenched (non-equilibrium) hcp samples: the first process has a diffusion coefficient corresponding to hcp phase and the second one has huge diffusion coefficient corresponding to liquid phase, which is evidence of liquid-like inclusions formation during fast crystal growing. It is established that these inclusions disappear in equilibrium crystals after careful annealing.

Fluctuation Effects at Pre-Separation Region in Solid 3He-4He Mixtures

An anomalous temperature dependence of pressure in concentrated solid 3He-4He mixtures near the phase separation temperature T s is first found experimentally. Beginning with temperatures 50–70 mK above T s , as the temperature decreases and T s is approached, the pressure increases and continues to increase below T s in the metastable region. The theory is proposed that gives good quantitative description of the experimental data. The observed temperature dependence of the pressure is completely determined by correlation effects in the impurity subsystem. Due to fluctuations in the local concentration the nuclei of a new phase grow as compact clusters. This effect implies an increase in pressure far from the phase transition onset.

Description of Phase Separation in Solid 3He–4He Mixtures Based on the Diffusion Mechanism

We present the solution of the one-dimensional diffusion problem that describes the decay kinetics of solid 3He–4He mixtures taking into account the diffusion processes in both phases of the stratified solution and the surface resistance of the interphase boundary. The time-dependent pressure change is estimated. The results may be compared with experimental data.

Features of Phase Separation Kinetics of Solid 3He-4He Mixtures. Role of Boundary Resistance

Precise pressure measurements were carried out at phase separating the solid 3He - 4He mixtures in the temperature range of 100∓200 mK for pressures between 30∓36 bar. The relaxation time τ was found to be temperature independent at large supersaturations and/or low temperatures. This fact was explained with existence of large resistance under impurity atom transfer through the inclusion-matrix boundary. The results were compared with the τ calculate in the framework of diffusion problem which takes into account the finiteness of atom stay time on the boundary. The comparison of the calculated and experimental data allowed us to find the value of the new phase inclusion concentration. The measured temperature dependence of τ is in agreement with theoretical predictions that the diffusion coefficient must be proportional to x−4/3 (x is a impurity concentration) when there is strong impurity interaction.

Giant asymmetry of the processes of separation and homogenization of 3He–4He solid mixtures

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.

Spin Diffusion Processes in Solid 3He-4He Mixtures Near the BCC-HCP Phase Transition at the Melting Curve

The spin diffusion coefficient of 1% 3He in solid of 4He has been measured in the vicinity of the BCC-HCP phase transition at the melting curve by pulsed NMR. The applied spin echo technique does allow to distinguish the contributions from all of coexisting phases. In addition to well-known diffusion in BCC, HCP, and bulk liquid phases the new fast diffusion process is observed and the diffusion coefficient of this process is shown to be close to that in liquid mixture being dependent on the time between the NMR pulses (bounded diffusion). The possible reason for the effect may be connected with formation of liquid droplets during the BCC-HCP transition.

Correlation effects in the heat capacity of separating 3He-4He solid solutions

We propose to describe the impurity heat capacity of solid 3He-4He mixtures both below and above the phase separation temperature Ts by an extension of the Bethe-Guggenheim approximation for the lattice gas model. It is shown that at T > Ts, the temperature behavior of the heat capacity is completely defined by correlation effects in the impurity subsystem. The developed theory enables us to explain from the common stand-point the experimental data by Edwards, McWilliams, and Daunt for all concentrations of 4He and make some conclusions about the structure of second phase nuclei.

Kinetics of Liquid 3He Droplets in Solid 4He Matrix

Precise measurements of pressure in the crystal at constant volume were used to obtain the data on growth and dissolution kinetics of liquid 3 He droplets formed as a result of isotopic phase separation of solid 3 He- 4 He Mixtures. We studied several crystals with an initial 3 He concentration of 2.05% in the pressure range of 26–27 bar. It is shown that the growth of the liquid droplets during the stepwise cooling of the two-phase crystal is correctly described by the superposition of two exponential processes: diffusion decomposition with a small time constant and strain relaxation with a big time constant. The strain layer near the droplet boundaries is due to a great difference in molar volume between the droplets and the matrix, and leads to a plastic deformation of the matrix and to a non-equilibrium 3 He concentration in the matrix. Under such conditions quantum diffusion is significantly suppressed and 3 He atom transport occurs only as the strain is relaxed.

Thermomagnetic relaxation in two-phase solid 3He–4He mixtures at ultralow temperatures

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.

Quantum Diffusion of Impuritons in the Gas of Phonons in Quantum Mixtures of Helium Isotopes

The system of kinetic equations for distribution functions of impurity excitations in solid 3He–4He mixtures in the presence of phonons is solved. The results obtained allows us to calculate the spin diffusion coefficient of3He–4He quantum crystals. The found expression differs from the results of the previous theoretical studies. A comparison of the obtained diffusion coefficient with experimental data makes it possible to determine the numerical values of the energy band width of impurity excitations.

Diffusion of Impurity Excitations in Superfluid and Solid 3He–4He Mixtures

Starting from the system of linearized kinetic equations, the exact expressions for the spin and mass diffusion coefficients and thermal diffusion ratio in quantum mixtures of helium isotopes with any degree of degeneration is obtained. From the general expression the various limiting expressions have been obtained, which are determined by various relations between collision rates of quasiparticles. The results of the calculations are compared with available experimental data. It is shown that in the low-temperature region, where an impuriton gas is one-component, the relaxation of concentration of 3 He in superfluid 3 He– 4 He mixtures is determined by the acoustic and dissipative collective modes with an effective diffusion coefficient. From the general relation, the expression for a spin diffusion coefficient in solid 3 He– 4 He quantum mixtures is derived. The comparison of the results obtained with the experimental data makes it possible to find a numerical value for the width of the impuriton energy zone.

Evolution of the concentrated phase in separated solid 3He-4He mixtures

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.

FLUCTUATION EFFECTS IN THE HEAT CAPACITY OF 3HE-4HE SOLID SOLUTIONS

The impurity heat capacity of solid3He–4He mixtures is theoretically investigated both below and above phase separation temperature Ts. It is shown that at T > Tsthe temperature behavior of the heat capacity is completely defined by correlation effects in the impuriton subsystem. The proposed theory is in good agreement with experimental data.

Lectures on the properties of liquid and Solid 3He-4He mixtures at low temperatures

We give a concise review of the empirical properties of liquid and solid 3He-4He mixtures and their phenomenological interpretation. The bulk of the paper is about dilute solutions of 3He in liquid 4He at temperatures well below the tricritical point, where the roton and phonon excitations are comparatively unimportant. We describe the thermodynamic properties in terms of the Landau-Pomeranchuk 3He quasiparticles and the effective interaction between them, introduced by Emery and Bardeen, Baym and Pines. The scattering amplitude, needed to fit the low temperature transport properties, and the effective interaction are related, provided the multiple virtual scattering calculated by Fu and Pethick is included. The multiple scattering should always be included, even for very small concentrations. We present the evidence for the velocity dependence of the effective interaction, and urge that this also be taken into account in the interpretation of experiments. We give a short description of spin-polarized liquid mixtures and of the possibility of pairing superfluidity in solutions of 3He in liquid 4He. The existence of supersaturated solutions may be a way to attain p-wave pairing at accessible temperatures. Beacause of phase separation, the concentration of 4He in dilute mixtures of 4He in liquid 3He becomes very small as the temperature is lowered, making it unlikely that a degenerate Bose gas of 4He quasiparticles can be produced. In addition, the superfluid 4He film on the walls of the vessel makes the achievement of a supersaturated solution very difficult. We briefly review the measurements of the phase separation, the density and specific heat, and show that the spectrum of the 4He quasiparticles and the role of their effective interactions are still in doubt. In solid 3He-4He mixtures the thermodynamic properties and the phase diagram, including the crystallographic transformation, fit the regular solution model very well. On the other hand, dilute solid solutions of either 3He or 4He in the other isotope have NMR relaxation times and spin diffusion which agree with the theory of impuritons (mass fluctuation waves) which tunnel more or less freely through the crystal. The reconciliation of these two theories and an explanation of the accuracy of the regular solution model remain mysteries. A deviation from the regular solution model, the fluctuation specific heat above the phase separation temperature, is discussed in detail. The review includes two tables which list most of the experiments on liquid and solid 3He-4He mixtures published between 1975 and 1990.

Fluctuation effects in the phase separation of solid3He-4He mixtures

We analyze the excess specific heat above the phase-separation temperature in solid mixtures of3He and4He as due to the fluctuations that represent the symmetry of the condensing state. In a3He-rich solid, the fluctuations of the4He-rich phase are two-dimensional, while in an even mixture they are three-dimensional. The density fluctuations are characterized by a length scale that is essentially the interparticle spacing.

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T 1, T 2, and T 1ϱhave been measured for 3He-4He solid mixtures at the exchange plateau region (~0.5K). The 3He concentrations X 3of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm3/mole in hcp phase. The spectral density function J(Ω) for dipolar field fluctuations was determined in the low-frequency branch from T 1ϱmeasurements and in the high-frequency branch from conventional T 1measurements. It was found that J(Ω) is given by J(ω) = cJ(ω)|3−4 + (1−c)J(ω)|3−3, where J(Ω)|3−4 is the spectral density function due to the 3He-4He tunneling motions, and J(Ω)|3−3 is that due to the 3He-3He tunneling motions. Using the Torrey theory, the correlation frequency of the 3He-4He tunneling motions was evaluated from T 1ϱdata, and was found to be in good agreement with Landesman 's theory.