Kapitza Resistance

Abstract

Kapitza resistance (${R}_{K}$) is the thermal boundary resistance which occurs at the interface when heat flows from a solid into liquid helium. This review attempts a comprehensive presentation of experimental and theoretical knowledge since the discovery of Kapitza resistance in 1941. The experiments discussed and data presented include measurements of ${R}_{K}$ at interfaces between liquid $^{4}\mathrm{He}$ and: copper, lead, mercury, tin, indium, nickel, constantan, gold, silver, platinum, tungsten, silicon, quartz, lithium fluoride, and sapphire. The experiments between solids and liquid $^{3}\mathrm{He}$ are also discussed. The treatments include discussion of the dependence of ${R}_{K}$ on these variables: temperature, pressure, surface structure and preparation, and elastic properties of the solid. The principal experimental problems are associated with the surface properties, so these are discussed in detail. The principal theoretical discussion is of the acoustic impedance theory, following Khalatnikov and Mazo and Onsager, and the results are compared with the experiments. Modifications of the theory connected with improved matching at the interface, due, for example, to condensed He are also considered. When the theory is applied to interfaces between metals and liquid He, then it must be modified to take into account phonon electron interactions. The theory gives a temperature dependence ${R}_{K}\ensuremath{\propto}{T}^{\ensuremath{-}3}$, which is approximately what is experimentally, observed. However, the observed ${R}_{K}'\mathrm{s}$ are usually an order of magnitude or more smaller than theoretical values. The source of the disagreement lies either in a lack of knowledge of the surface physics or in another, dominant, mechanism for thermal energy exchange across the interface. Evidence for each possibility and some suggestions aimed at resolving the discrepancies are offered.