Geometric acoustic attenuation at gigacycle frequencies in single crystals of quartz

Successive acoustic echo amplitudes have been calculated from a model for microwave frequency acoustic propagation based on ray optics that ignores any intrinsic attenuation. The computed echoes resemble experimental acoustic decay patterns generated by microwave pulses in single crystals of piezoelectric materials. The attenuation has been found to be due to off-axis propagation of the acoustic energy in the crystal and to acoustic phase averaging by the microwave transducers used to couple energy in and out of the crystal. Calculated acoustic echo patterns show the changes caused by various crystal orientations and different crystal endface parallelisms at several frequencies. It is found that the number of echoes and the amplitude of the last few echoes are frequency independent and are determined by the crystal geometry alone. On the other hand, the character of all but the last few echoes is dominated by phase averaging effects over the crystal end wall and is strongly frequency-dependent. Experimental data is presented showing the changes in the nulls and maximums of the echo patterns with frequency and the changes in acoustic patterns produced by altering the endface parallelism by flexing the crystal. Measured acoustic echo patterns of flexed and unflexed crystals are discussed. It is shown that flexing has increased the number of observable echoes by factors from 4 to 10 for various samples, has improved the average intensity of comparable echoes by amounts varying from 4 to 14 db, and has reduced the apparent acoustic attenuation from an unflexed value of 1.86×10^-1db/cm to 1.63×10^-2db/cm for a particular sample.