Thermal boundary resistance at very low temperatures-a size effect

Abstract

It has been commonly observed that the Kapitza resistance between solids and liquid ³He at temperatures of 1 to 10 mK is one or two orders of magnitude lower than that expected theoretically. This has generally been explained by means of magnetic coupling between magnetic spins in the solid and the nuclear spins in the liquid ³He. It is proposed that the results can be explained alternatively by a size effect; when the temperature is sufficiently low for the dominant phonon wavelength to be comparable with the size of the solid, then the acoustic mismatch theory is modified and a lower boundary resistance is predicted. Qualitative, but not quantitative, agreement is found from this preliminary analysis.