1964
DOI: 10.1103/physrev.134.a581
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Hypersonic Absorption in Quartz at Temperatures Below 30°K

Abstract: We have extended earlier absorption measurements between 500 and 10 000 Mc/sec to temperatures below 30°K where the mean free path of thermal phonons is likely to be larger than the ultrasonic wavelength. The absorption of transverse waves follows in magnitude, as well as in the dependence on temperature and frequency, as expected for a three-phonon process. However, the measured absorption per cm for longitudinal waves depends only slightly on frequency in contrast to the expectations for a four-phonon proces… Show more

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Cited by 62 publications
(5 citation statements)
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“…The three-phonon interactions can be separated into those of the type ω L + ω L → ω L and ω L + ω T → ω L , where L and T represent longitudinal and transverse polarizations, respectively. Collinear processes of the type ω L +ω L → ω L are sometimes neglected due to the dispersion of the branches, however, previous works have shown that these processes may occur as the finite lifetime of the branches compensates for the dispersion [39,40] and that they can play a large role especially at short wavevectors where the dispersion relation is quasi-linear. In fact, we find that ω L → ω L + ω L processes contribute most to the total intrinsic phonon lifetime.…”
mentioning
confidence: 99%
“…The three-phonon interactions can be separated into those of the type ω L + ω L → ω L and ω L + ω T → ω L , where L and T represent longitudinal and transverse polarizations, respectively. Collinear processes of the type ω L +ω L → ω L are sometimes neglected due to the dispersion of the branches, however, previous works have shown that these processes may occur as the finite lifetime of the branches compensates for the dispersion [39,40] and that they can play a large role especially at short wavevectors where the dispersion relation is quasi-linear. In fact, we find that ω L → ω L + ω L processes contribute most to the total intrinsic phonon lifetime.…”
mentioning
confidence: 99%
“…2 'h2). (6) The simple (unweighted) average of the roomtemperature attenuation coefficients listed in Table I is a~25 dB/em. Using this value in Eq.…”
Section: Experimental Procedures and Resultsmentioning
confidence: 99%
“…Using estimations of the relaxation time of thermal phonons t p h , deduced from thermal conductivity data [7], we see that the condition w Zph > 1 is met. I n this case, acoustic losses are proportional t o the frequency w of the acoustic wave, t o the absolute temperature T , and t o the specific heat C,, [S] or to the number of interacting thermal phonons [9]. This would lead, at temperatures much lower than the Debye one, t o a T4 and, a t higher temperature, to a somewhat lower temperature dependence.…”
Section: Antplification and Attenuation Of Thermal Vibrationsmentioning
confidence: 99%