Heat Pulses in Quartz and Sapphire at Low Temperatures

Abstract

Experiments have been performed on the propagation of heat pulses in single-crystal dielectric materials at temperatures sufficiently low that only boundary and "defect" scattering should be effective in deflecting the phonons from direct rectilinear flow. Such heat-pulse experiments can give more direct and unambiguous information then the usual thermal conductivity measurements on how the thermal phonons travel across the crystal since their trajectories can be resolved both in time and in space. The technique is somewhat similar to pulse measurements of the attenuation of microwave phonons except that the phonons have a much higher frequency, are incoherent, and are not monochromatic. Also, the thermal detector is sensitive to the arrival of scattered phonons arriving at various times. Heat-pulse techniques do not appear to have been previously applied to solid materials, although somewhat similar methods have been used extensively on liquid helium (at very much slower speeds).The major findings to be reported here for the temperature range 3.8-8. 5°K are that (1) approximately 1/15 of the heat flux for quartz and -f for sapphire reaches the detector in essentially uninterrupted direct rectilinear line-of-sight propagation; (2) the remainder of the heat flux is scattered, the angular and temperature dependences being those characteristic of a smallangle scattering process; (3) the velocities of the unscattered heat pulses are not given by the conventional longitudinal and transverse sound velocities, but by suitably defined "wave" (energy) velocities; (4) related to this, more than two unscattered transverse heat pulses are observed in quartz.Both X-cut and Z-cut samples of natural quartz and synthetic sapphire obtained from the Valpey Crystal Co. were investigated. They were cylindrical in shape (Z)= f in.) with polished end faces on which were evaporated thin metallic films to generate and detect the heat pulses. The generator was of constantan, -500 A thick, and 0.020 in. square. The resistance was about 15 Q, and current pulses of up to 1 A and of duration as short as 0.1 /isec were used. The detector was a thin alloyed superconducting film FIG. 1. Schematic diagram of the sample (length L) showing the circular detector (diameter d), the square heat pulse generator, and the peripheral cut made to control the scattered phonons. The annular detector width is 0.004 in. The shaded areas are evaporated silver "lands." The phonon trajectories lie along and near the cone of angle 0.of thickness -1500 A, whose resistance was sensitive to temperature changes. A 6% Sn-94% In alloy was used at 3.8°K and a 35% Bi-65% Pb alloy at 8. 5°K. Because of the circular shape of the detector (Fig. 1), the important phonons were those whose net motion lay near a cone centered on the axis of the sample, the cone angle (0) being determined by the length (L) and diameter (d), where sinO =d/2L.The thermal time constant of the 3.8°K detector was measured to be less than 0.04 iisec by the use of an attenuated giant pulse ruby laser to...

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