The Transport of Heat Between Dissimilar Solids at Low Temperatures

Abstract

The resistance offered to the flow of heat by the mismatch of the elastic constants at the interface between two materials has been calculated. It is shown that for a perfectly joined interface the heat flow is proportional to the difference of the fourth powers of the temperature on each side of the interface. Deviations from this temperature dependence are to be expected for rough surfaces and for surfaces pressed into contact with one another. The calculated contact resistance between some common solids is given, and graphs are presented from which the heat flow between any two materials may be computed. It is shown too that the spin–phonon, phonon–electron, and phonon–phonon relaxation processes give rise to additional resistive processes in some solids, some of which restrict the heat flow at the surface. The theoretical results compare well with the available experimental data. However, the problem of the contact resistance between helium and metals is still unresolved. A tentative explanation of this is presented which predicts that there should be an appreciable difference between the contact resistance of a metal in the normal and in the superconducting state.

Sources of loss processes in phonon generation and detection experiments with superconducting tunneling junctions

“…The enhanced transmission is in accord with the reduced Kapitza resistance found in heat conduction experiments [28]. So far no satisfactory explanation is known for the physical mechanism of the Kapitza resistance [16,17,[28][29][30][31][32][33] reduction.…”

“…The signal current (5IQ is now replaced by the ballistic signal IB, and from (8), (12), (13), (16) and VD= Fod we obtain the calculated ratio of the ballistic signal current and the generator current with:…”

“…The models contain assumptions for phonon generation, emission, propagation and detection. By variation of the experimental parameters as: orientation of the crystal, perpendicular or oblique emission, measurement with helium contact or under vacuum conditions, and taking account of phonon focusing in the crystal [, 16-20], we have been able to check the intensity distribution for the emitted phonons and the strength of the phonon emission into the helium bath and into the substrate crystal. In Section 2 we discuss the three different experimental situations and the corresponding models used to derive the phonon yield.…”

A review of thermal rectification observations and models in solid materials

“…In 1959 Little developed the first model for predicting the thermal transport at a solidsolid interface at low temperatures called the Acoustic Mismatch Model (AMM) [71]. The AMM is only valid for perfect interfaces at temperatures below 7 K and the transmission is based on the acoustic impedance of the two materials.…”

Thermal boundary resistance at an epitaxially perfect interface of thin films

“…However, the mechanism of the TBR occurring at an interface between thin films has not been clarified up to now even though the various models had been suggested such as an acoustic mismatch model (AMM) [18], a diffuse mismatch model (DMM) [19] and an acoustic impedance mismatch model (AIMM) with a reference system [20]. The AMM and the DMM were proposed by Little and Swartz et al, respectively and those models were based on the phonon transmission phenomena at an interface.…”