Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

Specific heat of adsorbed films of3He,4He,and isotopic helium mixtures near monolayer coverages

Specific heat results are presented for near-monolayer films of³He,⁴He, and isotopic He mixtures adsorbed on Vycor porous glass in the temperature range between 1 and 4°K. In the case of the pure He monolayers and submonolayers, the specific heats depend only onT ² , like a two-dimensional Debye elastic medium. A film of slightly greater than monolayer coverage needs an additional temperature-independent term. Monolayer coverages of mixtures are difficult to define, but all coverages used, some of which are submonolayer, need bothT ² andT-independent terms. The constant term may arise from atoms in the second layer forming a classical noninteracting system, which in the mixture case would indicate selective adsorption of⁴He in preference to³He at the substrate wall, in agreement with previous adsorption experiments on the same substrate.Work supported in part by the U.S. Atomic Energy Commission.     

Measurement of the thermomechanical coefficient in confined normal liquid3He

The thermomechanical coefficient P/T has been measured for liquid³He from 2–20 mK. The temperature difference was established across³He in a porous plug with 90 nm pore diameter. The coefficient was 5 kPa K^–1 and only weakly temperature dependent; in terms of the heat capacity per unit volume, the coefficient varies from 4C at 2 mK to C at 20 mK.     

Specific heat of disordered and amorphous rare-gas solids: Quench-condensed pure and binary films

We report measurements of the low-temperature specific heatC of crystalline pure rare-gas films (Ne, Ar, Kr, Xe) and amorphous rare-gas mixtures (Ne-Xe, Ar-Xe) condensed at low temperatures (T6 K). For both the crystalline and the amorphous films a large contribution toC linear inT (0.5 mJ/mol K²) is found at very low temperatures (T<1 K), which is attributed to tunneling states. Annealing strongly decreases this contribution. At higher temperatures an enhancement ofC with respect to bulk samples is observed, which is explained by surface vibrations arising from the porous structure of the films. For the crystalline films, this contribution is reduced upon annealing, while only a slight annealing effect is found for the amorphous mixtures.     

Specific heat of monolayer films of3He-4He mixtures adsorbed on Grafoil between 0.04 and 4.2 K

The specific heat of mixtures of ³He and ⁴He adsorbed on Grafoil has been measured at four partial monolayer coverages corresponding to areal densities of 0.0279, 0.0419, 0.0485, and 0.066 »^–2 for 0.04 < T < 4.2 K. The ³He concentration in the mixtures was x ₃ = 0, 0.050, 0.091, 0.201, 0.485, 0.650, 0.908, and 0.999. A feature in the specific heat not seen in measurements with the pure isotopes is found for the two intermediate coverages at about 0.4 K. The measurements are analyzed at the higher temperatures using a theoretical virial expansion for two-dimensional gaseous mixtures. The entropy of mixing calculated by numerical integration of the specific heat curves shows that at 4 K the two isotopes are mixed. While mixing effects develop at temperatures below 1 K, the evidence for phase separation as in bulk mixtures is inconclusive.Work supported by the National Science Foundation, Grant DMR-72-03003A03.     

Specific heat of3He-4He mixtures in Vycor glass

The specific heat of a ³ He- ⁴ He mixture filling a narrow pore is calculated in the temperature range 0.5–1 K, including the effect of van der Waals forces due to the walls, and is found to be compatible with the enhancement over the bulk liquid value experimentally observed for mixtures in Vycor glass.     

On the possibility of surface ferromagnetism for liquid3He in confined geometries

Arguments are given to show that, near a surface, a high-density sheet of liquid³He between the first solid layer and the bulk paramagnetic liquid at zero pressure would behave as a two-dimensional itinerant ferromagnet. Such a picture could explain recent experiments on the magnetic properties of³He in confined geometries in the 1 mK temperature range.Laboratoire associé au CNRS.     

Properties of melting 3He: Specific heat,entropy, latent heat,and temperature

A sequence of experiments has been performed to measure thermal properties of liquid and solid ³ He between the temperatures 1 and 25 mK at melting curve densities. A two-phase mixture of ³ He sample was self-cooled by the Pomeranchuk method. A heat pulse technique was used, combined with measurements of pressure and volume, to yield separate determinations of liquid and solid properties: the specific heat of liquid ³ He in the normal Fermi liquid and superfluid phases; the entropy of solid ³ He above and through a nuclear magnetic transition at 1.10 mK; and an absolute thermodynamic temperature scale based on measurement of latent heat of conversion of liquid to solid.Support for this work was obtained from the Research Corporation, the NSF through Grant no. DMR 75-15933, and the Materials Science Center of Cornell University, Grant no. GH 33637. Also, the work was supported by travel grants from the NATO Science Fellowship Programme and the Danish Natural Science Research Council.Work performed while on leave from Phys. Lab. I, H. C. ørsted Institute, Universitetsparken, Copenhagen, Denmark.     

Magnetic heat conductance between CMN single crystals and liquid3He

Measurements of the magnetic Kapitza resistance between single crystals of CMN and lanthanum-diluted CMN in contact with ultrapure liquid³He are presented. The investigations were performed in the temperature range 2–100 mK and in magnetic fields up to 600 Oe. For the first time, a magnetic thermal coupling between bulk crystals with dimensions of up to 3 mm and liquid³He was observed. In the case of pure CMN and liquid³He below 7 mK, the relationR T ⁿ withn=4±1 is seen. A strong dependence ofR with magnetic field and Ce³⁺ content is found.     

Simultaneous measurements of heat capacity and pressure coefficient of liquid He4 and He3 - He4 mixtures

An apparatus for simultaneous measurements of heat capacities and pressure coefficients was designed and constructed for experimental studies of critical phenomena near the lambda points of liquid He⁴ and He³ - He⁴ mixtures.The pressure was measured with a capacitance pressure sensor involving a copper-beryllium thin plate (0.4 mm thickness). An oscillator circuit, including the capacitance pressure sensor, and driven by a tunnel diode was attached to the bottom of the calorimeter. The resolutions of temperature and pressure in this apparatus are ～ 2 × 10^?7 K and ～2 × 10^?6 bar (～2 × 10^?1 N m^?2) respectively.     

Heat transfer between liquid3He and sintered metal heat exchangers

A new model to explain the unexpectedly large heat transfer between liquid³He and sintered metal heat exchangers is described and evaluated. The heat transfer results from a direct coupling of³He quasiparticles in the pores to vibrational modes of the sintered metal powder. It is proposed that for a range of temperatures below 20 mK the dominant vibrational modes of the sinter are localized oscillations involving a few powder particles with frequencies distributed over a constant density of states. The³He is then treated as a Fermi gas in a set of boxes corresponding to the pores in the sinter. The vibrating or shaking boxes transfer energy to the³He quasiparticles inside the box. The calculated heat transfer between liquid³He and the vibrational modes of sintered metal heat exchangers isQ/(VT)4×10 ^–15 T/d ³ W m^–3 K^–1, where Q is the heat flow for a temperature differenceT, V is the volume of the sinter (metal and helium), andd is the powder particle diameter in meters; this has the observed linear temperature dependence, and in magnitude is larger than or comparable to published results from several laboratories. The heat transfer between the vibrational modes and the electron gas in the metal sinter that is needed to complete the heat path can also be described by the same model with the result that the electron-phonon coupling is significantly larger than the³He-phonon coupling. When the model is applied to heat transfer between liquid³He-⁴He mixtures and sinter the calculated results are again comparable to or larger than those measured. The postulated localized oscillator modes give a specific heat, linear in temperature, that is in reasonable agreement with measurements for pressed powder by Pohl and Tait.     

Specific heat of 5% and 3% 3He-4He solutions under pressure

Specific heat measurements have been made under pressure on a 5% ³He-⁴He solution between 10 and 93 mK, yielding values for the specific heat mass, m ^*, of 2.45 m ₃, 2.74 m ₃, and 3.07 m ₃ at pressures of 0, 10, and 20 atm, respectively; corresponding values of the zero-concentration effective mass m ₀ are 2.38 m ₃, 2.64 m ₃, and 2.90 m ₃ for the above pressures. Measurements were also made on a 3% solution. Above 35 mK, all the measurements show deviations from a free-Fermi-gas behavior.This work was partially supported by the U.S.-Israel Binational Science Foundation (BSF), Jerusalem.     

The specific heat capacity and thermal conductivity of normal liquid3He

By observing the diffusion of a heat pulse along a 10-cm column of normal liquid³He with the aid of two vibrating wire thermometers, it has been possible to measure the heat capacityC and thermal conductivityK of the liquid in the temperature range fromT _C to 10 mK and at pressures of 0.21, 4.39, 9.97, 20.01, and 29.32 bar. By using a Pt NMR thermometer, an LCMN thermometer, and a³He melting curve thermometer calibrated using the melting curve given by Greywall in 1983, a temperature scale has been established and (1) it has been shown that this melting curve is consistent in the temperature range 5–22 mK with the Korringa law for the Pt thermometer with a Korringa constant of 29.8±0.2 sec mK, (2) departures have been observed from the Curie-Weiss law for LCMN at low temperatures, and (3) values of the superfluid transition temperature have been obtained that are about 4% lower than the Helsinki values. The measured heat capacities agree well with those of Greywall, but values ofKT are higher than those of Greywall and show more temperature dependence below 10 mK. The implications for the present results of the very different melting curve given by Greywall in 1985 are discussed in an Appendix.     

Specific heat of quench-condensed hydrogen films

The specific heatC(X, T) of quench-condensed films of H₂ has been measured as a function of ortho concentration X with 0.28–2 at temperatures between 0.4 and 3.0 K. The films were condensed on evaporated gold substrates held at several temperaturesT. _cond between 1.0 and 3.5 K. The observed specific heat is attributed to orientational ordering of the ortho-H₂ molecules. For the films withX = 0.74 condensed atT _cond>2.5 K, there is a peak which indicates a bulk-like ordering transition. At temperatures below the peak, there is a large contribution toC, which is not present in bulk H₂, and which we attribute to short-range ordering size effects. AsT _cond is decreased below 2.5 K, the shape of the specific heat curve changes, and the peak at 1.5 K is replaced by a gradual rise with a sharp drop above 2.6 K. Despite this strong dependence ofC onT _cond, the entropy per molecule at 3 K is only weakly dependent onT _cond and comparable to that for bulk H₂. Film annealing at 3.4 K produces a change in the specific heat curve, and a study of this effect is presented. The ortho-para conversion rate of the films condensed at the various temperatures is found to be same as in bulk, well-annealed H₂. As in bulk H₂, the transition temperature inferred from the location of the specific heat peak or anomaly decreases withX. Unlike in bulk H₂, there is no temperature hysteresis inC for any of the quench-condensed films. This implies that the ordering transitions are not accompanied by a martensitic transformation.     

Anomalous specific heat of liquid 3He above the superfluid transition temperature

The contribution to the specific heat due to order parameter fluctuations in liquid ³He just above the superfluid transition temperature T _c is calculated exactly within a Landau theory approach. The effect turns out to be unobservably small and thus cannot explain the large (9%) rise in specific heat above the normal state value at the saturated vapor pressure in a recently reported experiment. We do not find the divergence of the specific heat at T cobtained earlier by Thouless from a microscopic calculation and indicate how the difference can be reconciled.     

3He impurity states on liquid4He: From thin films to the bulk surface

The structure of the states accessible to³He impurities in films of liquid⁴He on Nuclepore is investigated using a density functional approach with a finite-range effective interaction. In thick films, one finds that the two lowest states are localized in the surface region. For thinner films, the variation with film thickness of the first three states results from a delicate balance between the attractive tail of the substrate potential and the quantum finite-size effect. The existence of states localized in the second layer of the films is discussed. The energy difference between the ground state and the first excited state agrees with the recent determination of Higley, Sprague, and Hallock from magnetization measurements. The effective mass of the ground state has a structure similar to that obtained by Krotscheck and coworkers and exhibits a maximum for a⁴He coverage of 0.15 Å^–2, in agreement with the data of Gasparini and coworkers. A similar behavior is predicted for the effective mass of the first, second, and third excited states. The structure of the energy spectrum may also explain former results on third-sound measurements in thin mixture films by Laheurte et al. and by Hallock.Unité de Recherche des Universités Paris 11 et Paris 6 associée au CNRS.     

Continuing Specific Heat Measurements of 3He in 3He - 4He Mixture Films

Additional data from our on-going experiments for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.4 bulk-density atomic lagers, on a ⁴ He film of thickness 4.33 bulk-density atomic lagers. This is a two-dimensional Fermi liquid system, in which we can change the ³ He coverage and thus tune the Fermi temperature.     

Microscopic calculation of the heat transfer between a granular structure and liquid3He

A recent formula for the heat transfer coefficient between ³He quasiparticles and phonons of a sintered metallic powder is evaluated using the phonon density of states of a microscopic model of a granular structure. The microscopic model describes a simple crystalline granular structure and contains extended modes only. When the dominant phonon wavelength is less than a typical grain size, possesses a low-temperature enhancement typical of a sintered metallic powder and over a limited range exhibits a linear variation with temperature.