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Dissipation induced by phonon elastic scattering in crystals

View Article: PubMed Central - PubMed

ABSTRACT

We demonstrate that the phonon elastic scattering leads to a dominant dissipation in crystals at low temperature. The two-level systems (TLSs) should be responsible for the elastic scattering, whereas the dissipation induced by static-point defects (SPDs) can not be neglected. One purpose of this work is to show how the energy splitting distribution of the TLS ensemble affects the dissipation. Besides, this article displays the proportion of phonon-TLS elastic scattering to total phonon dissipation. The coupling coefficient of phonon-SPD scattering and the constant P0 of the TLS distribution are important that we estimate their magnitudes in this paper. Our results is useful to understand the phonon dissipation mechanism, and give some clues to improve the performance of mechanical resonators, apply the desired defects, or reveal the atom configuration in lattice structure of disordered crystals.

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The dependence of the constant for the product Q · f 3  on temperature, influenced by the range of frequency splitting.The upper panels (a–c) indicate the situations for the lower bound νi = 2 GHz, 10 GHz and 20 GHz, respectively. The lower panels (i)–(iii) respectively correspond to the upper panels (a–c), and each of them contains two lines for displaying the temperature dependences at two kinds of upper bound νf indicated via two lines in each of upper panels (a–c). Besides, the circle points in the lower panels are fixed due to the experiment8, i.e., const = 4.2 × 1015 at 15 mK and 2.2 × 1016 at 3.8 K in Fig. 2.
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f3: The dependence of the constant for the product Q · f 3  on temperature, influenced by the range of frequency splitting.The upper panels (a–c) indicate the situations for the lower bound νi = 2 GHz, 10 GHz and 20 GHz, respectively. The lower panels (i)–(iii) respectively correspond to the upper panels (a–c), and each of them contains two lines for displaying the temperature dependences at two kinds of upper bound νf indicated via two lines in each of upper panels (a–c). Besides, the circle points in the lower panels are fixed due to the experiment8, i.e., const = 4.2 × 1015 at 15 mK and 2.2 × 1016 at 3.8 K in Fig. 2.

Mentions: It is necessary to take the parameters for formula (14), including both longitudinal and transverse coupling parameters γl = 0.6 eV and γt = 0.4 eV, both longitudinal and transverse sound speeds cl ≈ 7 × 103 m/s and ct ≈ 4 × 103 m/s7, and the mass density of quartz ρ = 2.6 × 103 kg/m337. In addition, the undetermined constant of the u-distribution P0 is discussed below. In Fig. 3, we display the product constant of Q ⋅ f 3  as a function of temperature from 0.01 to 10 K with different ranges of transition frequency of the TLS ensemble. We take νi = 3 GHz, 10 GHz and 20 GHz corresponding respectively to the upper panels (a–c). The lower panels (i–iii) are chosen by the lines in panels (a–c), respectively. Besides, the curves in three lower panels are fixed partly by two measured points exhibited in Fig. 2. All panels in this figure show that the constant and thus the quality factor turn higher with temperature rising, in the situation where thermal-induced dissipation is still restricted at such low temperature.


Dissipation induced by phonon elastic scattering in crystals
The dependence of the constant for the product Q · f 3  on temperature, influenced by the range of frequency splitting.The upper panels (a–c) indicate the situations for the lower bound νi = 2 GHz, 10 GHz and 20 GHz, respectively. The lower panels (i)–(iii) respectively correspond to the upper panels (a–c), and each of them contains two lines for displaying the temperature dependences at two kinds of upper bound νf indicated via two lines in each of upper panels (a–c). Besides, the circle points in the lower panels are fixed due to the experiment8, i.e., const = 4.2 × 1015 at 15 mK and 2.2 × 1016 at 3.8 K in Fig. 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036349&req=5

f3: The dependence of the constant for the product Q · f 3  on temperature, influenced by the range of frequency splitting.The upper panels (a–c) indicate the situations for the lower bound νi = 2 GHz, 10 GHz and 20 GHz, respectively. The lower panels (i)–(iii) respectively correspond to the upper panels (a–c), and each of them contains two lines for displaying the temperature dependences at two kinds of upper bound νf indicated via two lines in each of upper panels (a–c). Besides, the circle points in the lower panels are fixed due to the experiment8, i.e., const = 4.2 × 1015 at 15 mK and 2.2 × 1016 at 3.8 K in Fig. 2.
Mentions: It is necessary to take the parameters for formula (14), including both longitudinal and transverse coupling parameters γl = 0.6 eV and γt = 0.4 eV, both longitudinal and transverse sound speeds cl ≈ 7 × 103 m/s and ct ≈ 4 × 103 m/s7, and the mass density of quartz ρ = 2.6 × 103 kg/m337. In addition, the undetermined constant of the u-distribution P0 is discussed below. In Fig. 3, we display the product constant of Q ⋅ f 3  as a function of temperature from 0.01 to 10 K with different ranges of transition frequency of the TLS ensemble. We take νi = 3 GHz, 10 GHz and 20 GHz corresponding respectively to the upper panels (a–c). The lower panels (i–iii) are chosen by the lines in panels (a–c), respectively. Besides, the curves in three lower panels are fixed partly by two measured points exhibited in Fig. 2. All panels in this figure show that the constant and thus the quality factor turn higher with temperature rising, in the situation where thermal-induced dissipation is still restricted at such low temperature.

View Article: PubMed Central - PubMed

ABSTRACT

We demonstrate that the phonon elastic scattering leads to a dominant dissipation in crystals at low temperature. The two-level systems (TLSs) should be responsible for the elastic scattering, whereas the dissipation induced by static-point defects (SPDs) can not be neglected. One purpose of this work is to show how the energy splitting distribution of the TLS ensemble affects the dissipation. Besides, this article displays the proportion of phonon-TLS elastic scattering to total phonon dissipation. The coupling coefficient of phonon-SPD scattering and the constant P0 of the TLS distribution are important that we estimate their magnitudes in this paper. Our results is useful to understand the phonon dissipation mechanism, and give some clues to improve the performance of mechanical resonators, apply the desired defects, or reveal the atom configuration in lattice structure of disordered crystals.

No MeSH data available.


Related in: MedlinePlus