Behavior of Coherent Microwave Phonons at Low Temperatures inAl2O3Using Vapor-Deposited Thin-Film Piezoelectric Transducers

The intrinsic attenuation and velocity of compressional and shear waves have been measured in a single crystal of ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ at 1 Gc/sec for $a$-axis propagation. While the slow-shear-mode attenuation shows a $T^4$ temperature dependence as predicted by the Landau-Rumer theory, the fast shear mode has a $T^7$ dependence below 50°K and a $T^4$ dependence at higher temperatures. The compressional mode has a $T^9$ dependence below 50°K and a $T^4$ dependence above this temperature. A theory for this behavior is proposed. The measured 300°K velocities are $v_L=11.03\mathrm{}\times {10}^5$, $v_{T_1}=6.78\mathrm{}\times {10}^5$, and $v_{T_2}=5.72\mathrm{}\times {10}^5$ cm/sec. The three planewave modes were generated and detected by a single pair of ZnS vapor-deposited thin-film piezoelectric transducers. The crystallographic orientation of the ZnS films relative to the ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ was determined by means of reflection electron diffraction and x-ray diffraction. The piezoelectric matrix for ZnS is used to show how independent generation of the three modes was achieved.