1971
DOI: 10.1016/b978-0-12-395668-2.50011-9
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Interaction of Sound Waves with Thermal Phonons in Dielectric Crystals

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Cited by 84 publications
(83 citation statements)
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“…It should be noticed that below a few kilohertz, internal friction (of a longitudinal or transverse wave) in an homogeneous medium is dominated by thermoelastic dissipation [26]. This is no longer the case when frequencies are greater than 5 MHz at low temperatures, like in the experiments discussed in this paper: phonon-phonon dissipation dominates inside the substrate [6,18,19,[27][28][29].…”
Section: Discussionmentioning
confidence: 66%
See 1 more Smart Citation
“…It should be noticed that below a few kilohertz, internal friction (of a longitudinal or transverse wave) in an homogeneous medium is dominated by thermoelastic dissipation [26]. This is no longer the case when frequencies are greater than 5 MHz at low temperatures, like in the experiments discussed in this paper: phonon-phonon dissipation dominates inside the substrate [6,18,19,[27][28][29].…”
Section: Discussionmentioning
confidence: 66%
“…These electrodes were separated from the resonator surface by 5 shows the typical behavior of mechanical losses as a function of temperature for the A and B modes in the case of a bare and Ta 2 O 5 /SiO 2 coated quartz substrate. A 1/T n , where 4 < n < 7, dependence for 6 K < T < 12 K is the signature of three-phonon processes in the Landau-Ruomer regime [18,19]. This power low demonstrates that the intrinsic dissipation in the bare quartz substrate are dominant and no suspension related losses are important.…”
Section: Results With Dielectric Coatingsmentioning
confidence: 85%
“…5). According to the theory18, the acoustic wave attenuation α is proportional to the resonance angular frequency ω as long as , and where τ denotes the average lifetime of thermal phonons, ℏ the Planck constant, and k B the Boltzmann constant. As a consequence, the Q phonon–phonon -factor of an acoustic wave propagating with velocity V would no longer depend on frequency ω .…”
Section: Discussionmentioning
confidence: 99%
“…Indeed, attenuation in crystals, especially at low temperature is not a trivial thing, as well explained in Ref. [49].…”
Section: Dispersionmentioning
confidence: 96%