Intrinsic thermal-resistive process of crystals: Umklapp processes at low and high temperatures

Han, Yong-Jin

doi:10.1103/physrevb.54.8977

Cited by 37 publications

(19 citation statements)

References 5 publications

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“…24 An estimation of the order of magnitude of B can be made as 14 B ∼ 2γ 2 k B µV 0 ω D ∼ 10 −19 , which agrees with our obtained value (γ = Gruneisen parameter, µ = shear modulus, V0 = volume per atom, and ωD = Debye frequency.) Constant C has the order of magnitude of the transverse phonons' frequency near the zone edge 16,18 . 25 For this, use ωα(kz) ≃ ci k 2 z + k 2 ⊥ , α ≡ {i, k ⊥ }, and…”

Section: ñmentioning

confidence: 99%

Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations

2003

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The lattice thermal conductivity of crystalline Si nanowires is calculated. The calculation uses complete phonon dispersions, and does not require any externally imposed frequency cutoffs. No adjustment to nanowire thermal conductivity measurements is required. Good agreement with experimental results for nanowires wider than 35 nm is obtained. A formulation in terms of the transmission function is given. Also, the use of a simpler, nondispersive "Callaway formula", is discussed from the complete dispersions perspective.

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Section: ñmentioning

confidence: 99%

Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations

2003

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“…Three-phonon interactions have been investigated for bulk materials at different levels of sophistication by several groups. [20][21][22][23][24] However, the most detailed description of such processes is presented by Srivastava. 25 A simplified method for calculating three-phonon interactions in carbon nanotubes was presented by Xiao et al 26 It is important to realize that in their approach, Xiao et al do not include several features which are important to three-phonon scattering, such as normal processes and low-lying nonacoustic branches in the phonon-dispersions for the tubes.…”

Section: Introductionmentioning

confidence: 99%

Phonon-phonon interactions in single-wall carbon nanotubes

Hepplestone

Srivastava

2006

Phys. Rev. B

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The lifetime of phonon modes undergoing three-phonon interactions in single-wall carbon nanotubes has been calculated. The calculations are based upon an approach using Fermi's golden rule and a quasielastic continuum model for the anharmonic potential. In deriving the relaxation-rate equation, the effects of both normal and umklapp processes have been included, and a clear distinction between class 1 and class 2 events is made. Dispersion relations for the phonon modes of a carbon nanotube were obtained from analytic expressions developed by Zhang et al. The lifetime of the lowest two optical modes is found to be comparable to the lifetime of the acoustic modes. The results show that the relaxation rate is dominated by normal processes at low temperatures and umklapp processes at room temperature and above. A linear relationship between the relaxation rate and temperature is obtained for temperatures greater than 200 K. The relaxation-rate contribution decreases ͑increases͒ with an increase in the tube radius for normal ͑umklapp͒ processes. These results are suggested to have interesting implications for mean-free-path and thermal-conductivity calculations.

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“…Such nonlinear phonon scattering can be described by integral equations (see, e.g., [44]) which take into account the Umklapp processes, or U-processes, that result from the periodicity of the lattice [58,59]. Three-phonon Uprocesses are known as the main intrinsic thermalresistive processes in crystals [60]. They are apparently important and unavoidable during MCI in a plasma crystal because this instability generates phonons dominantly in the very proximity of the fBz boundary [17].…”

Section: Asymmetric Umklapp Scatteringmentioning

confidence: 99%

Anisotropic confinement effects in a two-dimensional plasma crystal

et al. 2016

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The spectral asymmetry of the wave energy distribution of dust particles during mode-coupling induced melting, observed for the first time in plasma crystals by Couëdel et al. [Phys. Rev. E 89, 053108 (2014)], is studied theoretically and by molecular-dynamics simulations. It is shown that an anisotropy of the well confining the microparticles selects the directions of preferred particle motion. The observed differences in intensity of waves of opposed directions is explained by a nonvanishing phonon flux. Anisotropic phonon scattering by defects and Umklapp scattering are proposed as possible reasons for the mean phonon flux.

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Intrinsic thermal-resistive process of crystals: Umklapp processes at low and high temperatures

Cited by 37 publications

References 5 publications

Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations

Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations

Phonon-phonon interactions in single-wall carbon nanotubes

Anisotropic confinement effects in a two-dimensional plasma crystal

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