The melting pressure of helium-3 at very low temperatures

The melting pressure of³ He at very low temperatures was shown earlier to be determined overwhelmingly by the solid phase. Using an extended solid³He model based on isotropic effective first-neighbor-pair antiferromagnetic and second-neighbor-pair ferromagnetic exchange interactions, the melting process is reinvestigated here. One of its motivating aspects may be said to be tied to its possible use, suggested by us earlier, for the establishment of a thermodynamic temperature scale at very low temperatures. As a consequence of the assumed multineighbor interactions, spin ordering is accelerated and, at the same temperature, the extended-model solid entropy falls below that of the simpler nearest-neighbor-pair interaction model. Equivalently, the spinordering critical transition temperature is raised over that associated with the simpler interaction scheme. The overall result is a decrease in the melting pressure variations at very low temperatures below those arising from the simple solid model. In the absence of a reliable experimental temperature scale at very low temperatures, only a qualified and cursory comparison is justified with recent experimentally estimated melting pressures. Discrepancies arise between theory and preliminary data on the temperature derivatives of the melting pressure or the entropy of the solid at melting. They might be due in part to the tentative experimental temperatures, which appear shifted toward too low temperatures when compared with the theoretical temperature scale implicit in the treatment of the generalized solid model. However, from the viewpoint which accepts the rather preliminary, scarce, very low temperature melting pressure data at face value, failure of the extended exchange model of solid³He at those temperatures must be kept in mind.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Entropy and magnetization measurements relating to the nature of the adsorbed phases of helium-3 under pressure

NMR and compressional cooling experiments have been carried out in Vycor porous glass immersed in liquid ³He in a Pomeranchuk cell at various temperatures and pressures. The expected nucleation of a solid phase near the substrate at a few bar does not take place, but compressional cooling occurs at about 2/3 bar below the melting curve. Modification of a simple statistical layer model to take into account the two-dimensional nature of the second layer gives better agreement with the observations, but other considerations show that the phase is probably fluid. These experiments therefore show the existence of a previously undiscovered high-density (>solid) disordered phase which is probably mobile. The NMR measurements show that the ferromagnetic interactions in the adsorbed ³He are larger than in bulk liquid, and increase with increasing pressure and decreasing temperature.This work was supported in part by the Science Research Council under Grant No. B/RG/1795, and in part by the U.S. Government through its European Research Office (Contract No. DAJA 37-C-2416 and Grant No. DA-ERO-128-74-C1G0046).     

Phase separation in solid mixtures of helium-3 and helium-4

Phase separation temperatures have been determined in bcc³He-⁴He mixtures as a function of³He concentration and melting pressure from measurements of changes in the X-ray lattice parameter and Bragg peak shape. A new rigid tail dilution refrigerator cryostat was used to study³He-⁴He crystals with³He concentrations of 0.10, 0.20, 0.30, 0.45, 0.60, and 0.70 and melting pressures between 3.0 and 4.3 MPa. The phase separation temperatures determined are in good agreement with regular solution theory and give little support for an asymmetry in the coexistence curve expected from a Nosanow-type model and reported from previous experiments using other signatures of phase separation. At a given concentration, differences in phase separation temperatures determined from slow cooling and warming data, respectively, are as much as 25 mdeg, but this is less than half the differences reported from previous experiments. A bcc-hcp transformation was seen in a crystal with 10%³He at aboutT=0.3 K for a melting pressure of3.7 MPa.     

A small helium-3 pulse-tube refrigerator

A new three-stage pulse-tube refrigerator (PTR) is developed by scaling down a previous PTR by 50%. The new system is small in size and weight, capable of operating using little input power, and uses a small amount of working gas and regenerator material. In addition to that the system is flexible and convenient for modifications. The volume of the low-temperature part of the new PTR (pulse tubes + regenerator) is as small as 0.28 l. With ³He as a working fluid a no-load temperature of 1.73 K is reached and a cooling power of 124 mW at 4.2 K is realized.     

Thermal properties of paramagnetic solid helium-3

It was shown in recent work that over a limited molar volume range and at asymptotically high temperatures the thermal modulations of the pressure along isochores of paramagnetic solid³He could be accounted for through the formalism of the Heisenberg model of an antiferromagnetically interacting localized spin-1/2 system. The internal consistency of this formalism requires the characteristic exchange-interaction parameter of the model derived from pressure modulation data to be identical with that appearing in the other thermal properties of this quantum solid. In a restricted temperature region where the spin excitations are the dominant thermal excitations of the solid, heat capacity data yield exchange-interaction parameters in fair agreement with those derived from pressures along isochores of larger molar volume. At higher temperatures, within well-defined limitations, thermal excitations involve both spin and phonon excitations. Here, because of the opposite temperature variations of the spin and phonon heat capacity components, the ensuing heat capacity minimum determines exactly the exchange-energy parameter and the relevant limiting Debye temperature as a function of the measured temperature location and value of the heat capacity extremum along the experimentally explored isochore. The exchange-energy parameters so derived display larger deviations from their predicted pressure-based values than those resulting from the lower temperature but still asymptotic spin-only heat capacities. At the present time, ambiguities in the experimental determinations of the characteristic Weiss temperatures of the asymptotic paramagnetic susceptibilities prevent one from deriving exchange-energy parameters with them. The present work leads to the prediction, within the limitations of the model formalism, of thermal properties of magnetized solid³He. Experimental investigations of these properties offer new approaches for probing the validity of the model formalism applied to paramagnetic solid³He.     

Model formalism of paramagnetic solid helium-3

The statistical-thermodynamic formalism of a collection of localized spin-1/2 atoms whose spin Hamiltonian refers to the isotropic antiferromagnetic Heisenberg exchange-interaction scheme is applied here to account for a set of important equilibrium-thermodynamic measurements on paramagnetic solid³He performed some time ago by University of Florida investigators. The measured properties were the temperature-dependent modulations of the pressure, which were proved earlier to arise overwhelmingly from the nuclear spin system. The present formalism of the pressure modulations or of the spin pressures, along specified isochores of the solid, includes the density- or molar-volume-dependent microscopic exchange energy parameter and its derivative. In this paper we have derived directly hitherto unavailable exact values of these parameters from spin pressure data on magnetized solid³He, as well as indirectly through the intermediary of spin pressures in the absence of a magnetic field. The directly derived exact parameters result from a single characteristic equilibrium-thermodynamic state of the solid in the presence of a constant and uniform magnetic field of adequate strength. The indirectly derived but exact parameters, of possibly somewhat lower accuracy, require the knowledge of a single directly derived exchange-energy parameter together with a set of spin pressures of asymptotic high-temperature equilibrium states in the absence of a magnetic field. The indirectly derived microscopic parameters along two of the three experimentally explored magnetized solid isochores yielded calculated spin pressures in fair and acceptable agreement, respectively, with their measured values. The directly derived exact parameters used in calculating the spin pressures along the third experimentally investigated isochore, in the absence of a magnetic field and at three different field strengths, led to complete agreement with the data. These results lend support to the tentative proposition advanced in early work that over a range of temperatures and molar volumes of paramagnetic solid³He, the statistical-thermodynamic formalism based on the antiferromagnetic exchange-interaction scheme may give an acceptable account of the spin pressures as well as of other thermal properties of this quantum solid.     

Very low temperature properties of liquid helium-3

Heat capacity and phase-boundary-line data on liquid³He in the few millikelvin temperature range obtained by Wheatley and his co-workers are analyzed within the framework of thermodynamics. The data favor the thermally anomalous disordered high temperature liquid phase to become of normal thermal behavior in its ordered B phase. The latter exhibits entropy decrease on isothermal compression, or its isobaric volume expansion coefficient is positive. At temperatures substantially below the phase-boundary temperatures, the ordered liquid might revert smoothly into a modification of anomalous thermal behavior, i.e., with entropy increase on isothermal compression. This alternation in the thermal behavior of the B phase, on experimental confirmation, could become helpful for a determination of the nature of its dominant thermal excitations in the indicated two temperature ranges, a situation reminiscent of the one existing in liquid⁴He II. Currently available magnetic susceptibility data raise the possibility, at very low temperatures, of further cooling liquid³He-B on adiabatic magnetization.     

Anomalous nuclear spin relaxation of adsorbed helium-3

Within the framework of a general theory of two-dimensional NMR we are able to elucidate certain anomalous features of spin relaxation in adsorbed and porous systems. We explain the linear dependence of relaxation time on applied magnetic field, and this is demonstrated to be related to the relative insensitivity ofT ₁to temperature. We also show thatT ₁remains field dependent on the “fast” side of theT ₁minimum.     

氦-3的汽化热和熔解热

基于Clausius-Clapeyron方程、维里方程和最新开发的氦-3相平衡曲线方程计算了氦-3在平衡曲线上的两个重要性质:汽化热(0 K～3.315 7 K)和熔解热(0.001 K～35 K).计算结果覆盖的温度范围广,精度也满足工程应用的需求.     

A practical vapor pressure equation for helium-3 from 0.01 K to the critical point

A saturation vapor pressure equation, p(T), is an essential component in the ³He state equation currently under development. The state equation is valid over the range 0.01-20 K with pressures from 0 to the melting pressure or 15 MPa. The vapor pressure equation consequently must be valid from 0.01 K to the critical temperature. This paper surveys available ³He critical temperature and pressure measurements, leading to new recommended critical values of 3.3157 K and 114603.91 Pa. The ITS-90 temperature scale is defined by the ³He vapor pressure from 0.65 to 3.2 K. A new vapor pressure equation is developed for the interval from the upper end of the T₉₀ scale to this newly defined critical point, employing a mathematical form in which the second derivative d²p/dT² diverges in agreement with scaling laws at the critical point. Below 0.65 K, an empirical vapor pressure expression is adopted, consistent with a theoretical expression valid in the limit T → 0. These two new components are fitted to be piecewise continuous with the EPT-76 p(T) scale rather than the ITS-90 T(p) scale between 0.65 and 3.2 K. Probable deviations between this vapor pressure scale and PLTS-2000 melting pressure-temperature scale are recognized, but not reconciled.     

The effective exchange energy of paramagnetic solid helium-3

An analysis is made of recent extensive National Bureau of Standards spin-pressure-modulation data, of increased accuracy and precision, along isochores of paramagnetic solid ³ He in the absence and presence of an externally applied constant and uniform magnetic field of strength up to 8 T. This leads to values of the exchange-energy parameterJ(V) and its derivativedJ(V)/dV along a set of isochores of molar volumeV within the formalism of the Heisenberg antiferromagnetic exchange-interaction model. To the order of the asymptotic product termJ(V)dJ(V)/dV and up to terms quartic in the magnetic field strength the validity of the model has been verified in the relevant temperature range along isochores of molar volumes between 22.5 and 24.4 cm ³ /mole. The termperature and field-strength independence of the elementary interaction parameter is further supported by control calculations of the temperature-dependent part of the isochoric pressures of the free and magnetized solid, ensuring the internal consistency of the formal approach to the stated order of approximation. These results strengthen the conclusion reached in previous work based on earlier initial isochoric solid ³ He pressure data of University of Florida investigators, namely, that over a range of temperatures and molar volumes the thermal and magnetic equation-of-state properties of paramagnetic solid ³ He can be quantitatively accounted for through the asymptotic formalism involving the Heisenberg exchange-energy function and its volume derivative.     

Nucleation of negatively charged vortex rings in superfluid helium-4 near its solidification pressure

The rate at which negative ions nucleate vortex rings in He II has been measured at 25 bar for electric fields E up to 12 kV/cm and temperatures T down to 0.4 K. A strong temperature dependence of v observed for T 0.6K and E<5kV/cm is attributed to the influence of isotopic impurities. Although the temperature-independent behavior found for T 0.6K and 5<E< 12 kV/cm is consistent with a theoretical prediction by Bowley, the relatively very much larger values of measured near 1 K indicate a serious deficiency in the model on which the theory is based.Supported by the Science Research Council under grants GR/A/0388.3 and GR/A/4874.7.     

Low-temperature melting properties of strongly magnetized solid helium-3

Various equilibrium thermal properties of strongly magnetized solid³He at melting are discussed in terms of the asymptotic, isotropic, nearest-neighbor pair-exchange interaction model at temperatures above 3 mK. Experimental verification of the predictions of the model to a limited degree of approximation suggests the possibility of using solid³He, at or near melting, for the production of fractional or small fractional millikelvin temperatures. This requires its adiabatic demagnetization from currently accessible several millikelvin initial temperatures and large magnetic field strengths to final field strengths above but close to its critical magnetic field strength where its paramagnetism still prevails.Work performed under the auspices of U.S. ERDA.     

Dynamics of superfluid helium-3 in flow channels with restricted geometries

The dynamics of superfluid helium-3 in flow channels with transverse sizes smaller than the mean free path of quasiparticles with respect to collisions with each other is considered, taking into account the diffusive reflection of quasiparticles from the walls. For quasiclassical Green functions the boundary conditions obtained by Ovchinnikov for the similar problem in superconductors have been used. Equations are derived defining the behavior of the difference between chemical potentials of normal and superfluid components of helium-3. These equations describe a phenomenon similar to the branch imbalance (or charge imbalance) in superconductors, and determine the relaxation depth of the pressure gradient in superfluid helium-3. The time-dependent Ginzburg-Landau equations are also obtained for the order parameter in the case when the transverse size of the channel is close to the critical value when the superfluid transition temperature goes to zero. The approach makes it possible to study theoretically effects related to the overcritical flows of superfluid helium-3 through narrow channels under pressure.     

Action of quantum effects on thermal conductivity of light gases (helium-3, helium-4, and hydrogen)

Expressions are found for quantum corrections considering symmetry effects expressed in terms of collision integrals, and their contribution to the thermal-conductivity coefficient of gases is calculated. It is shown that quantum effects for light gases are insignificant at temperatures above 20°K.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 843–847, November, 1977.     

Nuclear magnetic relaxation of helium-3 adsorbed on Mylar film

Pulsed NMR measurements on helium-3 adsorbed on Mylar film have been made at a Larmor frequency of 5 MHz for fractional monolayer coverages between 0.3 and 1. Relaxation times were measured at temperatures between 1.2 and 4 K for different orientations of the substrate plane with respect to the static magnetic field. Our results are consistent with a patchy solid model where approximately 0.1 of a monolayer remains relatively immobile, providing the relaxation mechanism, while the rest of the adsorbate remains fluid. We have no evidence for an abrupt transition of this fluid to a solid phase.     

Formal treatment of some low-temperature properties of melting solid helium-3

Recent observations of the low-field-strength paramagnetic susceptibility of melting solid ³He indicate its Curie-Weiss-type behavior at temperatures T > 5 mK. These require an identical temperature behavior of the magnetic melting-pressure shift over the same temperature range. Melting-pressure-shift measurements should thus independently confirm the observed temperature behavior of the susceptibility and yield, in addition, the Curie constant of melting solid ³He. Using the theoretical value of this constant in the low- or moderate-field-strength melting-pressure-shift formula, the calculated shifts appear to be currently accessible to measurements with acceptable accuracy at T > 5 mK. The inverse problem of determination of the paramagnetic moment or magnetization of melting solid ³He from melting-pressure shifts may be solved on the basis of a differential magnetothermodynamic relation without significant limitations on the applied external magnetic field strength or on the temperature range. Helium-3 melting-pressure and temperature measurements in the presence of a constant and uniform magnetic field of known strength should enable, within the above formalism, the determination of the magnetic phase diagram of solid ³He at melting down to the lowest experimentally accessible temperatures. This approach may supplement other independent methods of magnetic phase-boundary-line determinations of solid ³He.Work done under the auspices of the U.S. Department of Energy.