Thermal boundary resistance at interfaces between sapphire and indium

The Kapitza thermal boundary resistanceR _K has been measured above 1 K on several sapphire-indium boundaries prepared with different methods. By vapor-deposition of indium on sapphire and subsequent cold-welding with bulk indium, reproducible results were obtained. With the indium superconducting, we foundR _KT ^–3 within a certain temperature range, andR _K(1K)=42–44 and 30–36 cm² K/W for polished and rough sapphire surfaces, respectively. The calculation according to the acoustic mismatch theory yieldsR _K(1K)20 cm² K/W. Samples prepared by ultrasonic soldering also follow the relationR _KT ^–3 approximately, and giveR _K(1K)=14–17 cm² K/W. However, it is doubtful whether the calculation presuming a smooth boundary can be applied to the latter samples. Furthermore, we found that the method of vapor deposition and subsequent pouring on molten indium does not give good contacts. Moreover, the electronic contribution to the heat transfer across the boundary has been proved by ruling out other effects.     

Adsorption of nitrogen,argon, and neon on sintered copper and of neon on argon-coated sintered copper at low temperatures

The results of measurements of adsorption isotherms are given for nitrogen, argon, and neon on bare sintered copper and on sintered copper covered with a monolayer of argon. The temperatures employed where 77.3 K for the N₂ and argon, and 17.26, 20.22, 22.64, 25.71, and 27.00 K for the neon, and the pressure range was from 0.25 to 200 Torr. The sintered copper specimen was of mass 170 g, made with powder (Alcan Metal Powders, Inc., Druid Copper, grade MD60), which had an average particle size of 2 × 2 × 0.5 µ. The sintering was done at 650°C for 0.5 h. The bare surface area in m²/g, of the sintered copper specimen was found from the N₂ adsorption isotherms at 77.3 K. This gave =0.41 m²/g, based on a molecular area of N₂ of 13.8 Ų (solid N₂). The N₂ and argon isotherms on the bare sintered copper at 77.3 K yielded values of the monolayer coverage ofV _m =0.11 cm³(STP)/g for N₂ andV _m =0.11 cm³(STP)/g for argon. The neon results showed that at any given pressure and temperature the mass of neon adsorbed was less when the adsorption was on argon-coated copper than on bare copper. Calculations were made of the isosteric heat of adsorptionQ _st for neon, and the results are presented graphically as functions of the coverage. For neon adsorption on the bare copper,Q _st /R had a maximum value of about 390 K at a coverage of about 0.2 cm³(STP)/m², and it decreased to about 275 K at 0.5 cm³(STP)/m². For neon on the argon-coated copper,Q _st /R had a maximum value of about 320 K- at the lowest coverages and fell to about 245 K at 0.5 cm³(STP)/m². The shape of theQ _st /R curve vs. coverage for neon indicated that the argoncoated copper was more homogeneous from an adsorptive point of view than the bare copper. TheQ _st /R vs. coverage curves allowed an assessment to be made of the monolayer coveragesV _m , which were 0.38 cm³(STP)/m² for neon on the bare sintered copper and 0.34 cm ³ (STP)/m ² on the argon monolayer coated on the sintered copper. This indicated that the effective area for adsorption on the argon monolayer was 0.37 m ² /g, which was 10% less than that for the bare copper. In addition, theQ _st /R values at monolayer coverage were found to be 306 K on the bare copper and 275 K on the argon monolayer.Work supported by a contract with the Department of Defense (Themis Program) and with the Office of Naval Research and by a grant from the National Science Foundation.     

Adsorption of3He and4He on copper and on argon-coated copper below 20 K

Measurements have been made of adsorption isotherms of ³ He and of ⁴ He on copper and on a monolayer of argon deposited on copper in the temperature range 6.18–18.55 K and in the pressure range 0.25 to 75 Torr. From these many isotherms, calculations have been made of the isosteric heat of adsorptionQ _st/R. In the limit of zero coverage on the argon monolayerQ _st/R=76±2 K for ³ He and 76±2 K for ⁴ He. For adsorption on the bare copper,Q _st/R is difficult to extrapolate to zero coverage, but it probably lies (for both ³ He and ⁴ He) between 135 and 165 K. At theoretical monolayer helium coverage,Q _st/R=44±2 K for ³ He on the argon monolayer and 47±2 K for ⁴ He. At theoretical monolayer helium coverage on the bare copper,Q _st/R=61±4 K for ³ He and 77±5 K for ⁴ He. The results are compared with theoretical evaluations for helium adsorbed on an argon monolayer and with some previous experimental data, and the agreement is found to be fair. All the data are summarized in tables. Finally, a review is given of evaluations, including those from this work, of the monolayer capacity of ³ He and ⁴ He on the substrates studied.Work supported by a contract with the Department of Defense (Themis Program) and with the Office of Naval Research and by a Grant from the National Science Foundation.     

Adsorption of4He,Ar, and N2 on exfoliated graphite and of4He on Ar-coated exfoliated graphite at low temperatures

The results of measurements of adsorption isotherms are given for ⁴ He, Ar, and N ₂ on bare exfoliated graphite (Grafoil) and for ⁴ He on Grafoil covered with a monolayer of argon. The temperatures employed were 77.3 K for the argon and N ₂ , and the range 4.2–18.55 K for the⁴He. The pressure range was from 0.25 to 150 Torr. The Grafoil surface area was calculated from the argon isotherm at 77.3 K, yielding a value of 19.9 m ² /g or a total surface area of 672 m ² for the 33.81 g of adsorbent used in these experiments. From the ⁴ He isotherms the isosteric heats of adsorptionQ _st /R were calculated. In the limit of zero coverage,Q _st /R on the argon monolayer was 82 K, and on the bare GrafoilQ _st /R lies between 130 and 170 K. At theoretical monolayer coverage on the argon-coated GrafoilQ _st /T=68 K. These results are compared with theoretical evaluations and with previous calorimetric data on other graphites.Work supported in part by a grant from the National Science Foundation and by contracts with DOD (Themis Program) and ONR.     

A simple theory for the dependence of the electrical resistance of the magnetic superconductors TmRh4B4 and ErRh4B4 on temperature and field

The warmup rate of the¹⁶⁵Ho-enhanced nuclear spins in a HoVO₄ single crystal in contact with dilute³He is shown to be dominated by the Kapitza resistanceR _K at low bath temperature (T _b <100 mK). This result is obtained from an analysis of the NMR signal during the warmup, following a demagnetization which cools the sample to a temperature of about 5 mK. The temperature variation ofR _K (T _b< ^/–3 ) is consistent with the acoustic mismatch model, but the magnitude is 40 times smaller than the theoretical predictions for a solid-liquid interface. The spin-lattice relaxation is also estimated, and found to be in agreement with the results of other authors.     

3He diffusion in liquid isotopic mixtures

Spin echo techniques have been used to study the diffusion of³He in liquid isotopic mixtures with molar concentrations in the range fromX ₃=0.137toX ₃=0.850 over a temperature range from 3.0 to 0.4 K. AboveT the diffusive behavior is very similar to that of pure³He, although there is an increased scattering associated with⁴He. BelowT the diffusion coefficient increases with decreasing temperature and shows a dependence on the³He number density much like that of a classical gas. The excitations of⁴He have little influence on the³He diffusion coefficient, even at temperatures well above 1 K.The Rhodes Trust and the National Research Council of Canada supported one of us (R.B.H.) during the course of this research.     

Evaporation Probability of R− Rotons Relative to R+ Rotons in Superfluid 4He

The evaporation of superfluid ⁴ He by rotons is investigated using a recently developed pulsed source of both positive (R ⁺ ) and negative (R ^– ) group velocity rotons. The R ⁺ and R ^– rotons have very different momenta parallel to the free liquid surface and this causes angular dispersion of the two beams of evaporated atoms in the vacuum. On moving a bolometer horizontally through these beams, we find that the maximum flux of atoms from R ^– rotons occurs at an angle corresponding to an average R ^– roton energy of /k _B 10.5 K. The signal at this angle is compared with the evaporation signal at the maximum flux caused by R ⁺ rotons. These R ⁺ rotons have an average energy of 10.7K. The relative sizes of these two signals enables an estimate to be made of the probability of evaporation by R ^– rotons relative to that for R ⁺ rotons. We find that «P _–a »/«P _+a » 4 × 10^–3 where the brackets signify averages over the angles and energies allowed by the geometry of the experiment.     

Thermal boundary conductance between the U2D2 solid and B superfluid phases of3He

We present the first measurement of the thermal boundary conductance, 1/R _B , between the U2D2 spin ordered solid and theB superfluid phases of³He. We find that 1/R _B is exceedingly high, roughly seven orders of magnitude greater than that between sintered silver powder and liquid³He. ForT<0.56 mK, 1/R _B appeared to be thermally activated, i.e. 1/R _B exp(–/k _B T), with =4.5(±0.5) mK, close to the superfluid gap energy. We also present a theory involving magnon-quasiparticle coupling as a model to explain the experimental observations.     

Nuclear magnetic relaxation of3He gas. II.3He-4He mixtures

Longitudinal relaxation timesT ₁ have been measured in³He-⁴He gas mixtures, using pulsed NMR, in the temperature range 0.6–15 K. Helium-3 number densities of the order of 10²⁴ atoms m^–3 were used. Relaxation takes place on or near the walls of the Pyrex sample cells and measurements ofT ₁ give information about the surface phases. A cryogenic precoating of solid molecular hydrogen was used to reduce the helium-substrate binding energy from 100 K on Pyrex to 13 K for³He and 15 K for⁴He. TheT ₁ data at high temperatures were similar to those observed previously in the pure³He-H₂ system. The presence of⁴He generally causedT ₁ to rise on cooling below 2 K due to the preferential adsorption of⁴He over³He at the surface. However,³He atoms that go into quasiparticle states in the superfluid helium film can be an extra source of relaxation. In uncleaned cells, relaxation probably takes place in quasiparticle states at the free surface of the superfluid film, which are bound with an energy of 5.1±0.3 K. Baking the Pyrex cells under vacuum and rf discharge cleaning the walls before sealing in the sample gas were found to increase the bulk gasT ₁ by two or three orders of magnitude. In a cleaned, sealed cell aT ₁ of 8 h was measured at 7.7 MHz and 0.8 K. In this case relaxation is probably occurring two or three helium layers away from the helium-hydrogen interface. It may be possible to observe a predicted minimum in the intrinsic dipolarT ₁ of the bulk gas by using a⁴He wall coating to suppress wall relaxation effects (which usually dominate the nuclear relaxation of the bulk gas).     

Heat exchange in liquid helium by phonon tunneling through very thin plates

Thin plates with a thicknessd smaller than the phonon mean-free path can be used to increase the heat exchange in ³ He- ⁴ He refrigerators at very low temperatures. The resistanceR for the heat current density of these plates is theoretically investigated. For plates withd still larger than the dominant thermal-phonon wavelength _T in the plate,R is given by twice the Kapitza resistance. Ford _T the resistanceR decreases due to phonon tunneling. Ford _T there exists a region whereR varies asT ^–1, in contrast to theT ^–3 dependence for thicker plates. Numerical calculations are carried out for copper plates immersed in pure ⁴ He. The results show that one obtains a large increase of the heat exchange due to phonon tunneling for plates with a thickness of a few microns at temperatures in the millidegree range.     

Multilayer adsorption of3He and4He on zeolite from 4 K to 80 K

The adsorption isotherms of⁴He, N₂, and argon have been measured on synthetic zeolite (Linde Molecular Sieve 13X) at 78 K, and of³He and⁴He, also on zeolite 13X, in the temperature range 4 K to 20 K. The results are presented in tabular and graphical form. The N₂ isotherms, which showed characteristic step-like behavior, served to assess the specific surface area, which was 527 m² g^–1 based on a standard N₂ molecular area of 16.2 Ų. It also provided a value ofE ₁ equal to 2530 cal mole^–1. The argon isotherm at 78 K yielded a specific surface area for the zeolite 13X in fair agreement with that from the N₂ data. Nine isotherms were taken for⁴He between 4 K and 20 K and four for³He in the same temperature range. These isotherms permitted good evaluations of the isosteric heats of adsorption to be made and plotted as a function of coverage, yielding, for⁴He,Q _st =1580 j mole^–1 at zero coverage,Q _st =1030 j mole^–1 at monolayer coverage andE ₂=480 j mole^–1 at two-layer coverage. For³He, which showed everywhere smaller Q _st values. Q _st =1420 at zero coverage. By use of the Steele equation applied to⁴He, we found that the monolayer coverageV _m1 0.29 cm³ (STP) m^–2, and the second-layer coverage,V _m2 0.10 cm³ (STP) m^–2.Supported in part by a grant from the National Science Foundation and by contracts with ONR and the Department of Defense (Themis).     

Measurement of the 4He Chemical Potential in Phase-Separated 3He-4He Liquid Mixtures

As a first step towards thermodynamic measurements in highly polarised dense ³ He fluids, an accurate determination of the ⁴ He chemical potential ₄ was performed in unpolarised phase-separated ³ He- ⁴ He liquid mixtures at low pressures (0-1 bar) over a temperature range 0.12 - 0.65 K. A method introduced by H. London and relying on heat flush effects was used. Two volumes containing : a) a cold, phase-separated helium mixture and b) a warmed, pure ⁴ He liquid are connected by a narrow tube, and their temperatures are recorded under various conditions. The results agree with existing data obtained by the same technique for T >0.2K, but cannot be analysed with the simple regular solution model fitting vapour pressure data at T >0.6K. The sensitivity of the technique is shown to be sufficient to observe expected effects of nuclear polarisation on ₄.     

Electron-Phonon Coupling in Bolometers Used for Cryogenic Particle Detection

Superconducting transition-edge sensors have been used extensively in cryogenic particle detectors, either as thermometers for microcalorimetry or as bolometers for the detection of the prompt phonons resulting from a particle decay in a single crystal absorber. Bolometer action depends upon the energy coupling of the prompt phonons to the bolometer electrons. A study has been made of the electron-phonon coupling for a series of Au-Ti bolometers on a Si substrate and of the use of these bolometers for prompt phonon detection below 1 K. The electron-phonon coupling was found to be proportional to the normalized resistance (R/R _n) of the bolometer; R is the bolometer resistance and R _n is the normal resistance. When extrapolated to R/R _n = 1, this coupling was consistent with /VT ³ = 3 × 10⁹ Wm^–3K^–4 where is the thermal conductance from the bolometer electrons to the Si phonons and V and T are the volume and transition temperature of the bolometer. The response of the bolometers to heat pulses generated by a thin film heater on the opposite face of a Si single crystal were similar to that generally seen above 1 K, apart from a delay time constant that varied from 0.5 to 1.3 µs as the transition temperature decreased from 600 to 200 mK. This delay time constant is attributed to the thermal equilibrium time of normal regions of the bolometer.     

Coherent diffusion of isotopic impurities in solid helium

A theory of coherent diffusion (impuriton propagation) of dilute isotopic impurities in solid He is described. An expression for the mean square distance R ² (t) traveled by the impurity is derived. For short times pure band propagation occurs and so R ² (t) grows as t ². For times longer than a characteristic impurity-phonon scattering time this time dependence becomes linear, and a diffusion constant can be defined. This characteristic scattering time is estimated to be ~7 × 10^–5 T ^–9 sec (T in K) for a ³He impurity in ⁴He at V _m = 21 cm³/mole. The corresponding diffusion constant is consistent with that measured in the NMR experiment of Allen and Richards if the ³He-⁴He tunneling frequency J ₃₄ is taken as 7 × 10⁵ sec^–1.     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

Nuclear magnetic relaxation of3He gas. I. Pure3He

Longitudinal relaxation timesT ₁ have been measured in³He gas, using pulsed NMR, for number densities between 3 × 10²³ and 6 × 10²⁵ spins m^–3 and temperatures between 0.6 and 15 K. Relaxation takes place on or near the walls of the Pyrex sample cells and measurements ofT ₁ give information about the surface phases. A cryogenic wall coating of solid molecular hydrogen was found to delay the formation of a³He monolayer on cooling, andT ₁ measurements were consistent with a binding energy of 13 K for a³He atom to a hydrogen surface. At temperatures below 2 K a completed³He monolayer forms on the H₂ coating. No variation of the areal density of monolayer completion with bulk number density at fixed temperature could be observed and the completed³He monolayer is thought to be a dense fluid. Baking the Pyrex sample cells under vacuum and using an rf discharge in³He gas to clean the walls before sealing in the sample gas were found to increase the observed T₁'s by up to three orders of magnitude. Once a³He monolayer has formed on the H₂ surface in these cleaned, sealed cells, the dipolar interaction between adsorbed spins is thought to be the dominant source of longitudinal relaxation. The data are consistent with a dipolar relaxation model with a correlation time of 2 × 10^–9 sec. This time is long compared to the value of 10^–11 or 10^–12 sec in the 3D fluid. This suggests that if the surface phase is a 2D fluid and the dipolar mechanism is indeed the dominant one, then the atoms in the 2D fluid are less mobile than in three dimensions. This is consistent with recent susceptibility measurements.     

NMR Relaxation times of 3He adsorbed on graphite below 4.2 K

Pulsed NMR measurements were performed at 10 and 20 MHz on thin ³He films on graphitic surfaces in the temperature range between 0.35 and 4.2 K. Most of the measurements reported here have been obtained with basal-plane oriented graphite (Grafoil) outgassed at 130 C, but in some experiments graphitized carbon black powder (Sterling FT), vacuum-baked at 1100 C, was used for comparison. The ³He coverages examined range from 0.1 to 80 monolayers on Grafoil and from 0.3 to 1.0 monolayers on Sterling FT. Measurements have also been made on ³He-⁴He films on Grafoil with one-monolayer quantity of ³He mixed with various amounts of ⁴He. The measured free-induction decay time T ₂ , the spin-echo decay time T ₂ , and the spin-lattice relaxation time T ₁suggest that the observed relaxation phenomena in ³He are largely governed by the ³He-substrate interaction. In the case of ³He on Grafoil, T ₂ is much longer than T ₂ , evidently as a result of large local magnetic field gradients and significant lateral mobility of ³He on this substrate. These results, in conjunction with a simple model of spin diffusion in restricted geometries, lead to values of the diffusion coefficient D _sof about 2.1 × 10^–5 cm²/sec at 4.2 K and 7.0 × 10^–6 cm²/sec at 1.2 K for one-monolayer coverages ; these values of D _sare indicative of a nonlocalized ³He system. To verify the model used, the restricted diffusion analysis was applied to room-temperature measurements on C₆F₆ in Grafoil ; the values of the diffusion coefficient obtained in this way are in good agreement with diffusion rates measured directly in bulk liquid C₆F₆ at room temperature. In the case of ³He on Sterling FT, the restricted diffusion analysis of the T ₂ data gives D _s\t`t2 × 10^–8 cm²/sec for 0.6 monolayer of ³He; this value of D _ssuggests a relatively localized system. The measured T ₂ is found to decrease monotonically with coverage and there is no evidence of any phase transition in ³He films for coverages up to one monolayer.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

Thermal conductivity of Grafoil from 0.2 to 3 K

The thermal conductivity of compressed exfoliated graphite was measured in the directions parallel (K ) and normal (K ) to the rolling plane, in the temperature range of 0.2–3 K. The temperature dependence was determined in both cases. ForK=aT ^b in the temperature range of 0.2–0.7 K we get values forb of 0.95 forK and 1.6 forK ; in the range 0.7–2 K we get 1.6 forK and 2.1 forK ; and in the range 2–3 K we get 1.9 forK . TheK temperature dependence forT<0.7 K is smaller than what would be expected. ForK , evaluations of lattice and electronic contributions show that below 0.7 K the thermal conductivity is basically electronic. Above 2 K, where results are found in the literature, our data are in good agreement with them.     

The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD _s and the longitudinal relaxation timeT ₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT . The spin-echo method measures the diffusion coefficient for magnetizationD _s, which differs from the usual diffusion coefficient for particlesD belowT .D _s depends on the³He-³He scattering cross section _FF and the³He-roton/phonon cross section _FB, whileD depends only on _FB. The distinction betweenD _s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD _s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.