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Heat pulses in Al203 single crystals at low temperatures. Chung, David Yih

Abstract

Heat pulse experiments have been made on Al₂O₃ single crystals in the temperature range 3.8° K to 35°K with the aim of gaining further insight into the nature of heat transport in solids at low temperatures. Short heat pulses were produced by heating a thin metal film evaporated on to one end of the crystal. The thermal pulse arriving at the other end of the crystal was detected by an indium film thermometer placed in a coil connected to a sensitive radio-frequency bridge, so that the variation of resistance was finally displayed on an oscilloscope. The pulses received at low temperatures (3.8°K to 8°K) show two quite separate parts, an initial sharp rise followed by a slow rise, starting at a definite delay time corresponding to the phonon velocity in the medium. The results up to 18°K do not show appreciable variation in delay time, showing that the heat pulse propagation has not entered a second sound region. As the temperature increases, the amplitude of the initial phonon pulse decreases very much compared with the amplitude of the slow rise. Above 18°K, the small sharp rise can no longer be seen clearly so that the delay time is no longer well defined, and at 30°K only the slow rise is observed. It is found that the conventional theory of heat conduction is inadequate to interpret our results at low temperatures, as it fails to predict the finite delay of the initial rise of the received pulse. A phenomenological approach is taken, using a modified heat equation which has an electrical transmission line analogy. Using Laplace transforms, a solution is obtained and the results calculated with a computer are compared with the experimental curves. It is found that the pulse shape can be interpreted quite satisfactorily, especially at the lowest temperatures. The thermal diffusivity, D, for different temperatures is found, and the apparent thermal conductivity, K, is calculated and compared with Herman's (1955) results. The solution of the modified heat equation is also calculated for liquid He II at 0.25°K and compared with the heat pulses observed by Kramers et al (1954); very good agreement is obtained.

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