Dilute 3He Research Articles

Anisotropic reduced diffusion in dilute liquid 3He–4He mixture in ordered aerogel

We report on the first observation of 3He diffusion anisotropy in 3He–4He liquid mixture confined in ordered aerogels at 1.5–4.2 K temperatures. The used aerogels are arrays of long Al2O3 parallel 8 nm strands. The possible origins of diffusion anisotropy are considered and the changes of roton properties introduced by parallel aerogel strands are discussed. Among the responsible mechanisms we account for Knudsen diffusion, potential anisotropy of layer mode excitations or of bulklike excitations, and helium vortices. The observed reduced 3He diffusion in aerogels is discussed and suggested to appear due to helium excitations at strong confinement conditions. These observations pave the way for future experiments to gain insight into the crossover regime expected at lower temperatures (below 1 K) for which roton density is lower and 3He collisions with strands play significant role.

Thermodynamics of dilute 3He–4He solid solutions with hcp structure

To interpret the anomalies in heat capacity CV(T) and temperature-dependent pressure P(T) of solid hexagonal close-packed (hcp) 4He we exploit the model of hcp crystalline polytype with specific lattice degrees of freedom and describe the thermodynamics of impurity-free 4He solid as superposition of phononic and polytypic contributions. The hcp-based polytype is a stack of 2D basal atomic monolayers on triangular lattice packed with arbitrary long (up to infinity) spatial period along the hexagonal c axis perpendicular to the basal planes. It is a crystal with perfect ordering along the layers, but without microscopic translational symmetry in perpendicular direction (which remains, nevertheless, the rotational crystallographic axis of third order, so that the polytype can be considered as semidisordered system). Each atom of the hcp polytype has twelve crystallographic neighbors in both first and second coordination spheres at any arbitrary packing order. It is shown that the crystal of such structure behaves as anisotropic elastic medium with specific dispersion law of phonon excitations along c axis. The free energy and the heat capacity consist of two terms: one of them is a normal contribution [with CV(T) ∼ T3] from phonon excitations in an anisotropic lattice of hexagonal symmetry, and another term (an “excessive” heat) is a contribution resulted by packing entropy from quasi-one-dimensional system of 2D basal planes on triangular lattice stacked randomly along c axis without braking the closest pack between neighboring atomic layers. The excessive part of the free energy has been treated within 1D quasi-Ising (lattice gas) model using the transfer matrix approach. This model makes us possible to interpret successfully the thermodynamic anomaly (heat capacity peak in hcp 4He) observed experimentally.

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.

Lattice Relaxation of 4He with 3He Impurities: NMR Studies

Measurements of the 3He nuclear spin relaxation times of dilute 3He impurities in solid 4He have been used to explore the unusual dynamics of solid 4He at low temperatures. The 3He impurities move through the lattice by quantum mechanical exchange with neighboring 4He atoms. Because of the larger zero point motion of the 3He atoms, there is an appreciable lattice distortion that accompanies the tunneling 3 He atom and the tunneling motion depends on the elastic properties of the 4He lattice. This motion modulates the 3He-3He nuclear dipole- dipole interactions and thus determines the NMR relaxation rates. We compare the observed temperature dependence of the NMR relaxation rates with that expected from the measurements of the shear modulus by Syshchenko et al. [Phys. Rev. Lett. 104, 195301 (2009)].

Design and analysis of concentric helical heat exchanger for dilution fridge

The lowest temperature which can be reached in a continuously operating dilution fridge is determined by the performance of heat exchanger. Operation of dilution system requires a continuous tubular heat exchanger (Hex) for heat exchange primarily between the concentrated 3He and dilute 3He solution. The helical Hex is made of two thin walled cupro-nickel capillary tubing with stainless steel ends. The inner tube is spirally wound and inserted inside the outer tube. Based on the proposed flow rate of 15 ymoles/s, lengths and diameters have been optimized as to minimize the viscous and axial conduction heating. Flow impedances of the concentrated and diluted phase flow channels are maintained 10−7cm−3and 10−6 cm−3 respectively. Analytical results show that a base temperature of around 100mK can be achieved with this Hex. Effectiveness of condenser for condensation of helium isotopic gas mixture and temperature dependent quality factor has also been determined. This paper presents the detailed analytical results based on enthalpy and energy balance consideration relevant to the Hex.

Nuclear Spin Relaxation of Very Dilute 3He impurities in Solid 4He

We report measurements of the nuclear spin-lattice and spin-spin relaxation times of very dilute 3He in solid 4He in the temperature range 0.01 ≤ T ≤ 0.5 K for densities where anomalies have been observed in torsional oscillator and shear modulus measurements. We compare the results with the values of the relaxation times reported by other observers for higher concentrations and the theory of Landesman that takes into account the elastic properties of the 4He lattice. A sharp increase in the magnitude of the nuclear spin-lattice relaxation times compared to the the classical Landesman theory is observed close to the temperatures where the torsional and shear modulus anomalies are observed. The NMR results suggest that the tunneling of 3He impurities in the atomic-scale elastic distortion is affected by the same processes that give rise to the macroscopic elastic dissipation anomalies.

Heat Capacity of Dilute 3He–4He Films on Graphite

The heat capacity of dilute 3He–4He films is measured to clarify whether the second adsorbed layer of 4He films on graphite solidify into the so-called “4/7 phase.” The 3He areal density is fixed at 0.2 nm−2, whereas the 4He areal density is gradually increased. The measured heat capacities suddenly decrease with an increasing areal density approaching that of the 4/7 phase. Above the areal density of the 4/7 phase, the heat capacities do not reduce completely to zero and have finite values. The behavior of the heat capacity does not change over a rather wide areal density regime, although it suddenly increases or recovers at around the areal density of the third-layer promotion. These behaviors can be interpreted as the separation of 3He–4He mixture films into a 3He-rich phase and a 4He-rich phase, with the 3He-rich phase solidifying into the 4/7 phase and the 4He-rich phase remaining fluid below the areal density of the third-layer promotion. These observations strongly suggest that a 4He film adsorbed on a graphite surface does not solidify into the 4/7 phase.

Simulations of Non-linear Spin Dynamics in Spin Polarized Dilute 3He–4He Mixtures

Studies of spin dynamics of highly polarized dilute mixtures of 3He in superfluid 4He have been performed by various researchers over the past three decades. One series of experiments performed at Cornell University in the early 1990’s revealed a novel long timescale excitation. We present the numerical solution of the non-linear Leggett spin dynamics equation in one spatial dimension subject to boundary conditions consistent with the Cornell experiments. Experimentally observed phenomena are composed of trains of bursts in the transverse magnetization lasting several seconds. The simulations capture the time evolution of the individual bursts localized in time. Preliminary results of two dimensional simulations are also presented.

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.

NMR Studies of 3He Impurities in 4He in the Proposed Supersolid Phase

Preliminary results are reported for measurements of the NMR relaxation times of very dilute 3He in samples of solid 4He at low temperature, 0.25 K <T< 1.3 K. The results were obtained for carefully prepared samples with different 3He concentrations. The measurements of the spin-spin relaxation time, T2, show several interesting features. A temperature independent plateau attributed to the exchange motional narrowing is observed down to the lowest temperature studied, and the observed variation of T2 with 3He concentration favors the nonlinear theory suggested by Landesman. The best fit to the data is given by T2∝x3−1.89±0.1 rather than x3−1. No evidence of an exchange-phonon bottleneck for the spin-lattice relaxation is seen down to 25 mK. The vacancy activation energy is determined to be 13.5±0.3 K for a sample with x3=5×10−4 and molar volume 20.9 cm3.

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.

Long-range diffusion of hyperpolarized 3He in explanted normal and emphysematous human lungs via magnetization tagging

Long-range diffusivity of hyperpolarized 3He gas was measured from the decay rate of sinusoidally modulated longitudinal nuclear magnetization in three normal donor and nine severely emphysematous explanted human lungs. This (long-range) diffusivity, which we call Dsec, is measured over seconds and centimeters and is approximately 10 times smaller in healthy lungs (0.022 cm2/s) than the more traditionally measured Dmsec, which is measured over milliseconds and submillimeters. The increased restriction of Dsec reflects the complex, tortuous paths required to navigate long distances through the maze of branching peripheral airways. In emphysematous lungs, Dsec is substantially increased, with some regions showing nearly the unrestricted value of the self-diffusion coefficient (0.88 cm2/s for dilute 3He in air, a 40-fold increase). This suggests the presence of large collateral pathways opened by alveolar destruction that bypass the airways proper. This destruction was confirmed by comparison with histology in seven lungs and by removal of trapped gas via holes in the pleural surface in five lungs.

Influence of Adsorption Potential on 3He Fluid States Formed on 4He-Preplated Substrates

From heat capacity measurements for 3He adsorbed on 4He-preplated mesopore in substrates, FSM-16, HMM-2, and Hectorite, we found fluid states of the 3He adatoms. At very dilute 3He densities, however, it strongly depends on the substrate whether the adatoms are in a localized or a fluid state. The molar heat capacity of a two-dimensional gas or a degenerate Fermi fluid appears above densities nc = 0, 0, and 2 μmol/m2 for FSM-16, HMM-2, and Hectorite, respectively. The critical coverages nc are extremely small or zero for the former two SiO2-based substrates. On the other hand, nc for Hectorite is large. Since Hectorite has strong adsorption sites due to the electric-dipole field gradients around ions located on the substrate surface, these potentials are likely to affect the localization of the dilute 3He adsorbed even on the 4He film.

Dimensional-Crossover of 3He Gas Formed in One-Dimensional Nanometer Tunnel

We have measured the heat capacity of 3He adsorbed on one-dimensional (1D) nanopores of FSM-16 with different pore-diameters. Dilute 3He atoms on more than one layers of 4 He preplated nanotunnels with 22 A in diameter show a Schottky type peak around 0.25 K, which is similar to our recent report for 28 A nanotunnels. This behavior of heat capacity is explained as the crossover from 1D to 2D motion of Fermi gas in a confined geometry. The pore-size effect on the temperature and magnitude of the peak is quantitatively reproduced by a simple calculation for non-interacting Fermi gas in the adsorption potential from the substrate.

Towards Superfluidity of 3He Diluted by 4He

Search for the superfluid state of dilute 3He dissolved to 4He is one of the major remaining problems of low temperature physics. We describe our two experiments designed to pursue the lowest achieved temperature in such mixtures essentially below the values reported before.

A simple method for the analysis of sub-Kelvin refrigerators that use a dilute superfluid 3He– 4He mixture as a working fluid

The recent development of new types of sub-Kelvin refrigerators that use dilute superfluid 3He– 4He mixtures has made it apparent that a simple method of cycle analysis is needed. General control volume forms of the first and second laws of thermodynamics appropriate to this working fluid are presented. Simple analytic constitutive relations for the internal energy, entropy, enthalpy, osmotic enthalpy and 4He chemical potential are presented. Several examples are worked out using these relations.

Zero temperature spin wave damping in spin polarized 3He: does it exist?

Previous spin echo experiments at equilibrium polarizations in 3He- 4He mixtures have confirmed the prediction of zero temperature polarization-induced spin wave damping in Fermi liquids. We have measured the damping of spin waves in dilute 3He, spin polarized by a 4He circulating dilution refrigerator. The maximum polarization is almost a factor of 5 higher than the equilibrium polarization in a magnetic field of 10.54 T at temperatures between 10 and 25 mK. The spin wave damping is much smaller than expected on the basis of the spin echo experiments and shows that the existence of polarization-induced spin wave damping is an open question.

Transport in 3He–4He Mixtures in Restricted Geometry

The effect of wall scattering on transport in dilute degenerate 3He–4He mixtures in quasi-2D flow channels or films is discussed. The calculation of the quasiparticle mean free path combines particle–wall and particle–particle collisions including the interference between them. The spin polarization affects the wall-driven contribution by changing bulk mean free path and particle wavelength. The expressions for the wall contribution to transport coefficients are especially transparent in the limiting cases of large and small bulk mean free paths. The calculated temperature, concentration, and polarization dependences of the transport coefficients allow one to extract parameters of surface roughness from experimental data on transport.

Mesoscopic behaviour of 3He quasiparticles in a dilute 3He– 4He solution in Vycor glass

We have been investigating the properties of the 3He component in dilute 3He– 4He solutions in Vycor glass using cw NMR techniques. According to the simple model of a Fermi gas in a restricted geometry, the porous medium significantly changes the density of states and thereby increases the zero-point energy of the quasiparticles. As a result, the 3He quasiparticles should be progressively excluded from the Vycor glass as the temperature is lowered. We observe this effect using the strength of the cw NMR response from the confined 3He.

Nonlinear spin dynamics of dilute 3He– 4He at very high B/ T

We are conducting an experimental search for spin-diffusion anisotropy in dilute 3He– 4He mixtures at very high B/ T (17 T, 2 mK). Previous experiments have not reached sufficiently high B/ T ratios to observe the effect in very dilute mixtures, for which quantitative theoretical predictions exist. The planned experiments will require NMR experiments at very high values of the dimensionless spin rotation parameter μM. We have performed numerical simulations of the nonlinear spin dynamics to assess the feasibility of spin-wave and spin-echo experiments.