Kapitza resistance

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Kapitza resistance

A resistance to the flow of heat across the interface between liquid helium and a solid. A temperature difference is required to drive heat from a solid into liquid helium, or vice versa; the temperature discontinuity occurs right at the interface. The Kapitza resistance, discovered by P. L. Kapitza, is defined in the equation below,

where TS and TH are the solid and helium temperatures and is the heat flow per unit area across the interface. See Conduction (heat)

In principle, the measured Kapitza resistance should be easily understood. In liquid helium and solids (such as copper), heat is carried by phonons, which are thermal-equilibrium sound waves with frequencies in the gigahertz to terahertz region. The acoustic impedance of helium and solids can differ by up to 1000 times, which means that the phonons mostly reflect at the boundary, like an echo from a cliff face. This property together with the fact that the number of phonons dies away very rapidly at low temperatures means that at about 1 K there are few phonons to carry heat and even fewer get across the interface. The prediction is that the Kapitza resistance at the interface is comparable to the thermal resistance of a 10-m (30-ft) length of copper with the same cross section. See Acoustic impedance, Phonon, Quantum acoustics

The reality is that above 0.1 K and below 0.01 K (10 mK) more heat is driven by a temperature difference than is predicted. Above 0.1 K this is now understood to be a result of imperfections such as defects and impurities at the interface, which scatter the phonons and allow greater transmission. See Crystal defects

The enormous interest in ultralow-temperature (below 10 mK) research generated by the invention of the dilution refrigerator and the discovery of superfluidity in liquid helium-3 (3He) below 0.9 mK also regenerated interest in Kapitza resistance, because heat exchange between liquid helium and solids was important for both the dilution refrigerator and superfluidity research. An ingenious technique was invented to overcome the enormous Kapitza resistance at 1 mK: The solid is powdered, and the powder is packed and sintered to a spongelike structure to enhance the surface area. In this way a 1-cm3 (0.06-in.3) chamber can contain up to 1 m2 (10 ft2) of interface area between the solid and the liquid helium.

It was found that at 1 mK the Kapitza resistance is 100 times smaller than predicted by the phonon model. There have been two explanations for the anomaly, and probably both are relevant. One is that energy is transferred by magnetic coupling between the magnetic 3He atoms and magnetic impurities in the solid or at the surface of the solid; the other is that the spongelike structure has quite different, and many more, phonons than a bulk solid and that these can transfer heat directly to the 3He atoms. Whatever its cause, this anomaly has had a major impact on ultralow-temperature physics. See Adiabatic demagnetization, Liquid helium, Low-temperature physics, Superfluidity

Kapitza resistance

[′kä·pit·sə ri¦zis·təns]
(cryogenics)
A thermal resistance to the flow of heat across the interface between liquid helium and a solid.