Abstract
Kapitza1 in 1941 discovered that heat flowing across a solid in contact with superfluid helium (<2 K) encounters a strong thermal resistance at the interface. Khalatnikov2 demonstrated theoretically that this constitutes a general phenomenon related to all interfaces at all temperatures, given the dependence of heat transmission on the acoustic impedance (sound velocity × density) of each medium. For the solid/superfluid interface, the measured transmission of heat is almost one hundred times stronger than the Khalatnikov prediction. This discrepancy could be intuitively attributed to diffuse scattering of phonons3 at the interface but, despite several attempts4,5,6,7, a detailed quantitative comparison between theoretical and experimental findings to explain the occurrence of scattering and its contribution to heat transmission had been lacking. Here we show that when the thermal wavelength λ of phonons of the less dense medium (liquid 4He) becomes comparable to the r.m.s. surface roughness σ, the heat flux crossing the interface is amplified; in particular when σ ≈ 0.33λ, a spatial resonant mechanism occurs, as proposed by Adamenko and Fuks8. We used a silicon single crystal whose surface roughness was controlled and characterized. The thermal boundary resistance measurements were performed from 0.4 to 2 K at different superfluid pressures ranging from saturated vapour pressure (SVP) to above 4He solidification, to eliminate all hypothetical artefact mechanisms. Our results demonstrate the physical conditions necessary for resonant phonon scattering to occur at all interfaces, and therefore constitute a benchmark in the design of nanoscale devices9,10 for heat monitoring.
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Acknowledgements
This work received partial financial aid from the LabEx LaSIPS of the Paris-Saclay University. We express our deep gratitude to the Institute of Nuclear Physics in Orsay for technical support. A.R. benefited from a grant from the Ministry of Education via ED 543 MIPEGE. We acknowledge discussions with I. N. Adamenko.
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A.R. and J.A. ran the experiments. A.R., S.V. and J.A. analysed the data, performed the calculations and wrote the manuscript.
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Ramiere, A., Volz, S. & Amrit, J. Thermal resistance at a solid/superfluid helium interface. Nature Mater 15, 512–516 (2016). https://doi.org/10.1038/nmat4574
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DOI: https://doi.org/10.1038/nmat4574
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