The temperature dependence of the absorption of 1.13 Gc/sec longitudinal sound waves in calcium fluoride

Abstract

The temperature dependent attenuation of 1.13 Gc/sec ultrasonic lattice waves has been measured in calcium fluoride. The attenuation was measured for longitudinal ultrasonic waves propagating in each of the three major crystallographic directions ([100], [110], [111]). It was found that the attenuation is relatively temperature-independent below 30°K and increases rapidly above this temperature until about 70°K where it is again temperature independent. The relative change in attenuation and the temperature at which the maximum attenuation was reached were different for the three crystallographic directions. These results are qualitatively the same as the results obtained by Bommel and Dransfeld in quartz. The theory of Woodruff and Ehrenreich has quantitatively explained the results in quartz. Their theory fits our data well using the approximate attenuation formula ... where Y is the GrUneisen constant, K is the thermal conductivity, is the sound wave frequency, pis the density, C is an average velocity of the thermal phonons, and ' is a mean thermal phonon relaxation time. In order to obtain the fit to our data for the three directions of propagation, it was necessary to assume 2 to 5 times greater than the values which would be obtained using the method used by Woodruff and Ehrenreich.