New interest in zinc oxide has developed since it has been discovered to be piezoelectric. In line with this interest the zero field adiabatic elastic moduli have been measured. A high frequency, 60 to 500 Mc ultrasonic pulse technique was employed. Two crystals with sufficiently high conductivity to effectively short the electric field were available for the measurements. A density of 5.676 g/cm3 was used to calculate the zero-field adiabatic elastic moduli. This density was taken as exact with reference to the error limits. The moduli in units of 1012 dyn/cm2 at 25°C are: c11E = 2.097 ±0.1%, c12E = 1.211 ±0.15%, c13E = 1.051 ±0.15%, c33E = 2.109 ±0.1%, c44E = 0.4247 ±0.1%, c66E = 12(c11E−c12E) = 0.4429±0.1%.
Measurements have been made for all six third-order elastic moduli of germanium by measuring ultrasonic velocities in selected directions when directed static stresses are applied to the crystal. Three measurements are obtained by using hydrostatic pressures, three by using a static compression along the <001> axis, and six by stressing the <110> axis with measurements being made along the <001> direction and the <11̄0> direction. Using the finite strain formulas of Murnaghan, the measured velocities are related to the three second-order elastic moduli and the six third-order elastic moduli for a cubic crystal. The 12 sets of measurements provide considerable overlap, and the probable errors are shown to be moderate.
Ultrasonic attenuation and velocity measurements have been made in pure germanium and silicon (doping <1014 impurity atoms per cc) and in doped n-type germanium and p-type silicon. The attenuation in pure materials shows a continuous decrease as the temperature is decreased and a very low attenuation below 20°K. These results indicate that the energy losses are accounted for entirely by phonon-phonon interactions. A calculation has been made of these losses, using a model based on the Akheiser effect and incorporating the recently measured third-order elastic moduli of silicon and germanium. For both materials, the calculated values predict correctly the large difference between longitudinal and shear waves and agree quantitatively within 50% with the measured values over the whole temperature range.
Investigations on cylindrical rods of yttrium iron garnet (YIG) have shown that the magnetostrictive effect at microwave frequencies makes them effective microwave acoustic transducers, and that a lower bound of the acoustic Q is of the order of 2×105 at 1 kMc/sec. This paper describes measurements of acoustic Q's of nearly this same magnitude obtained with the nonmagnetic yttrium gallium garnet (YGaG) and yttrium aluminum garnet (YAlG). A table is given of the longitudinal and shear acoustic wave velocities, elastic stiffness constants, and elastic isotropy for yttrium gallium garnet and yttrium aluminum garnet. Similar data for yttrium iron garnet by Clark and Strakna are included for reference.
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