Abstract
We have utilized the enhancement of thermal conductivity by Poiseuille flow of the phonon gas to obtain highly sensitive measurements of phonon scattering by isotopic impurities in single crystals of helium. Crystal orientation, size, and quality may be inferred from the thermal conductivity data themselves. Our hcp4He crystals were grown at a constant pressure of 85.1 atm using apparatus and techniques that made possible some control over crystal orientation. An isotopic impurity concentration of 1.0×10−5 decreases the peak conductivity in these crystals by a factor of 1.9 along a direction perpendicular to thec axis. In the Poiseuille region a relaxation time limit has been achieved experimentally that allows our data to be fitted as a function of temperature and concentration with only one parameter. The observed scattering strength is a factor of 2.7 greater than can be explained in terms of mass-defect scattering alone. A number of current theories are examined in the light of this result. Our pure4He data strongly support aT −3 dependence for the normal-process relaxation time. Measurements of the thermal conductivity parallel to thec axis reveal no anisotropy in either the normal-process relaxation time or the isotopic scattering strength.
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This work was supported in part by the National Science Foundation and the Office of Naval Research.
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Lawson, D.T., Fairbank, H.A. Thermal conductivity and isotopic impurities in single crystals of helium. J Low Temp Phys 11, 363–394 (1973). https://doi.org/10.1007/BF00656559
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DOI: https://doi.org/10.1007/BF00656559