The Kapitza resistance between copper and3He

The Kapitza resistanceR _K between copper and³He has been measured at low pressure in a guarded cell in the temperature range 0.05–0.5 K. An extreme sensitivity to surface damage was observed. For an annealed, electropolished surfaceR _K agreed within a factor of two with the acoustic mismatch theory below 0.1 K. It was also noted thatR _K between copper and liquid³He was identical toR _K between copper and an adsorbed³He film. The data are compared with several mechanisms proposed theoretically to account forR _K .This work was supported in part by the Advanced Research Projects Agency under Contract HC 15-67-C-0221.     

Roton growth resistance of helium-4 solid surfaces

Experimental data available on roton contribution to the growth resistance of helium-4 surfaces from the work of Amrit, Legros and Poitrenaud (ref. 4) are analysed using the quantum kind model of Edwards, Mukherjee and Pettersen (ref. 5). The results are in strong favour of dissipation being due to kink-roton interactions. Further, they also support the idea that the angular anisotropy of the roton growth resistance of rough crystral surfaces is related to the density of steps.     

The Kapitza resistance and phonon reflectivity between solids and liquid helium

Results of calculations of Kapitza resistance and phonon reflectivity are presented for clean and dirty solid surfaces in contact with liquid helium. We suppose the existence of a thin attenuating layer of absorbed solid helium at the interface. It is shown that even 5–15 » thick layers of contamination can very significantly improve the phonon transmission near 1–2 K, and could also explain results for hydrogen, deuterium, and neon.This work was partially supported by the France-Québec exchange program, the Groupe de recherches sur les semiconducteurs et les diélectriques, and the National Research Council of Canada.     

Tentative explanation of the anomalies in the Kapitza resistance between solids and liquid 4He II

More than 40 years after Kapitza's discovery of a discontinuity in the temperature between solids and liquid ⁴He II, called thermal boundary resistance or Kapitza resistance, the anomalies found in the measurements of this resistance, especially within the range 2-1 K, are still alive and no experimentally demonstrable explanation entirely satisfactory for those anomalies has been found. Based upon experiments with solid superleaks which showed that the pores, smaller than 10 nm, are empty above the onset temperature of the superleaks, it is suggested that filling with the superfluid of eventual pores or defects in the solid boundary, could provide the clue to explain those anomalies. A variation of the real contact area and, consequently, a variation of the phononic heat transfer, would take place until those pores or defects on the solid surface are totally filled with the liquid by the action of the thermomechanical effect. However, no prediction is possible due to the fact that the random geometry of the defects is unknown.     

Kapitza resistance between liquid and solid helium. II. Experiments

The Kapitza resistance between liquid and solid⁴He has been measured in the temperature range 0.1–0.43 K. The results are discussed in terms of the acoustic-mismatch theory of Khalatnikow and the theory of Marchenko and Parshin in which the phonon transmission is due to capillary effects at the interface. We have also found a novel effect in which high-frequency phonons generated in the liquid pass into the solid, decay into lower energy excitations, and become trapped in the solid. This phonon greenhouse effect is observed at temperatures below 0.15 K.This work was supported in part by the National Science Foundation through Grant No. DMR 80-12284, and through the Materials Research Laboratory of Brown University.     

Kapitza resistance between liquid and solid helium. I. Theory

Detailed calculations are presented of the phonon transmission between liquid and solid helium. The transmission coefficients are used to determine the Kapitza conductance. Calculations have been made based on the usual acoustic-mismatch theory, and also using a modified theory in which it is assumed that very rapid melting and freezing can occur at the interface.This work was supported in part by the National Science Foundation through Grant No. DMR 80-12284 and through the Materials Research Laboratory of Brown University.     

The Kapitza thermal boundary resistance

A theory of the Kapitza thermal boundary resistance has been developed which includes not only the scattering of phonons at the interface between two different materials, but also the scattering of phonons within either material near the interface. The theory is shown to be in good agreement with present measurements on solid-solid contacts as well as with previously published low-temperature data on the contact between liquid helium and copper.This work was supported in part by the Advanced Research Projects Agency under Contract HC 15-67-C-0221 and the National Science Foundation Grant GH 33634. Based on a Ph.D. dissertation submitted by R. E. Peterson to the University of Illinois.     

Kapitza resistance—A universal curve

It is shown that when all unquestionable data on Kapitza resistance are plotted as reduced thermal boundary resistivity versusT?_D, then a universal curve results. The curve shows that for smallT?_D they are close to the acoustic mismatch theory, and for largeT?_D they are close to the phonon radiation limit. The parameterT?_D extends over three orders of magnitude, which compares with the usual factor of two in most measurements. The universality has several implications: First, it shows that Kapitza resistance is to first approximation a bulk effect; next, the curve can be used to test theories of Kapitza resistance (an example is given); finally, the value for an unmeasured solid-liquid helium interface can be estimated with some reasonable confidence.     

Effect of anharmonicity on Kapitza resistance

To understand the effect of anharmonicity on the Kapitza resistance, a one-dimensional model is used to simulate the system of heavy element-light element solids. The system is coupled to high- and low-temperature sources, respectively, at its end points. The Lennard-Jones potential is used as the interaction potential in the light solid. For various parameters in the potential, the Kapitza resistance is calculated. It is found that the stronger the anharmonicity in the light side, the smaller is the Kapitza resistance. Also, the cases that only one to four pairs of light atoms with anharmonic interaction across the boundary is considered. With the number of anharmonic pairs across the interface increasing, the Kapitza resistance is found to be decreasing.     

The Kapitza resistance and thin surface films

Experimentally observed values for the Kapitza resistance across a solid-liquid He II boundary show that for specimens of gold, copper, and sapphire an enhanced heat flow is achieved between the two media if a surface film of barium stearate is deposited on the solid. The magnitude of the improved heat flow is less than that predicted from a simple model for phonon transmission across a solid-film-liquid arrangement, but is greater than that expected from the Khalatnikov theory.One of us (M.F.W.) is grateful to the Fredk. D. Edwards Scholarship Trust for a grant, and to S.R.C. for a studentship which enabled this work to be carried out.     

Kapitza resistance measurement using glass capacitors

Glass capacitors provide an inexpensive but precise method for measuring Kapitza resistance. A small piece of glass is coated with metal on two sides to form a capacitor which is then immersed in liquid helium. Once calibrated, the capacitor serves as a sensitive thermometer which can be heated ohmically and used to measure the Kapitza resistance between the helium and the metal or any coating placed over the metal. We discuss techniques for both preparing samples and measuring Kapitza resistance, including suggestions for future development.     

Dynamic measurement of the Kapitza resistance

To measure the Kapitza resistance between a solid and liquid helium, a thin sample is immersed in the liquid and subjected to pulsed heating. The Kapitza resistance is determined from the time variation of the sample temperature, measured by a built-in nuclear orientation thermometer. The system Au/dilute ³He-⁴He is used as an example. Potentials and limitations of the method are discussed.This work was supported by the Deutsche Forschungsgemeinschaft (SonderforschungsbereichThis work was supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich     

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.     

Measurements of the Kapitza resistance and Onsager cross-coefficient for the4He crystal-superfluid interface

The effect of a heat current across the atomically rough crystal-superfluid interface in⁴He has been studied below 1 K. The chemical potential difference Δμ and temperature difference ΔT were measured simultaneously, the ΔT by means of a “superfluid melting-curve thermometer.” The results give the mean phonon transmission coefficient across the interface \(\bar \tau \) and a dimensionless quantity β that determines the Onsager coefficient linking Δμ with the heat current. The transmission probability \(\bar \tau \) is proportional toT ² below 0.2 K, in agreement with other experiments and with various theories, and it depends slightly on the crystal orientation, increasing near thec axis. The coefficient β, which is roughly independent of temperature and orientation, agrees with a recent theory of Bowley and Edwards.     

Kapitza resistance between the transition metals Fe,Co, and Ni and superfluid helium

Measurements of the Kapitza resistanceR _K between Fe, Co, and Ni and superfluid helium in the range 1–2 K are presented. The results are in strong numerical disagreement with the Khalatnikov model. We also find thatR _K depends hardly at all upon the state of mechanical deformation of the surface, in sharp disagreement with the previous work of Wey-Yen on nickel. The results are internally consistent and fit into the general pattern of available published work on other materials.     

Kapitza resistance and thermal conductivity of Kapton in superfluid helium

We have determined simultaneously the Kapitza resistance, R_K, and the thermal conductivity, κ, of Kapton HN sheets at superfluid helium temperature in the range of 1.4–2.0 K. Five sheets of Kapton with varying thickness from 14 to 130 μm, have been tested. Steady-state measurement of the temperature difference across each sheet as a function of heat flux is achieved. For small temperature difference (10–30 mK) and heat flux density smaller than 30 W m⁻², the total thermal resistance of the sheet is determined as a function of sheet thickness and bath temperature. Our method determines with good accuracy the Kapitza resistance, R_K=(10540±444)T⁻³×10⁻⁶ K m² W⁻¹, and the thermal conductivity, κ=[(2.28±0.54)+(2.40±0.32)×T]×10⁻³ W m⁻¹ K⁻¹. Result obtained for the thermal conductivity is in good agreement with data found in literature and the Kapitza resistance’s evolution with temperature follows the theoretical cubic law.     

Comparison of steady-state and second-sound measurements of the Kapitza resistance

The Kapitza thermal boundary resistance R _k has been measured using both the steady-state (dc) and the second-sound (ac) techniques on the same copper sample during the same low-temperature run. The two techniques give the same values for R _k; R _k is therefore a constant for measuring frequencies ranging from dc to 600 Hz. We could not reproduce the strong temperature dependence of R _k observed in earlier ac measurements unless both second-sound resonators were thermally coupled to the superfluid helium bath.This work was supported in part by the U.S. Department of Energy under Contract DE-AC02-76ER01198.