The ultrasonic attenuation of longitudinal acoustic waves in slightly disordered crystalline quartz has been measured over a temperature range from 1.3 to 300 K, using the pulse-echo technique. Neutron irradiation is demonstrated to increase the ultrasonic attenuation at low temperatures indicating the presence of two-level tunneling systems similar to those of glasses. Our low-temperature acoustic results agree with a frequency independence and a T 3 behaviour for the relaxation process predicted by the two-level tunneling TLS-model where the regime ωT 1 ≫ 1 holds.
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Laermans et al. (1986) studied this question.
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