Longitudinal and transverse parts of the correction term in the Callaway model for phonon conductivity

Sood, K. C.; Roy, Mrinmoy

doi:10.1088/0953-8984/5/18/001

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…For germanium, the high-temperature predictions are in better agreement with the experimental data than those from the Callaway model. The Holland model has since been used to investigate many other materials, and refined to account for more realistic phonon dispersion, 18 the effect of the Callaway correction term, 19 and additional phonon scattering mechanisms 15 ͑e.g., fourphonon processes and dislocations͒. The added complexity leads to more fitting parameters.…”

Section: Callaway-holland Approachmentioning

confidence: 99%

Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

2004

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The phonon thermal conductivity of the Lennard-Jones argon face-centered cubic crystal is predicted between temperatures of 20 K and 80 K using the Boltzmann transport equation under the single-mode relaxation time approximation. The temperature and frequency dependencies of the phonon dispersion and phonon relaxation times are obtained from lattice-dynamics calculations based on the results of molecular-dynamics simulations. No fitting parameters are required. The predicted thermal conductivities are in reasonable agreement with independent predictions made from the simulations using the Green-Kubo method. The assumption of an isotropic medium, as used in the Boltzmann transport equation formulation, leads to an overprediction of the Green-Kubo results at low temperatures. At higher temperatures, where anharmonic effects become increasingly important, the harmonic nature of the relaxation time calculation method leads to an underprediction of the Green-Kubo results. Assuming that the low-frequency behavior of the relaxation times can be extended over the entire frequency range, that there is no dispersion, or that the dispersion is independent of temperature, leads to significant errors in the predictions. This finding indicates that in analytical calculations, where such assumptions are often made, these errors are offset by the use of fitting parameters.

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Section: Callaway-holland Approachmentioning

confidence: 99%

Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

2004

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“…In order to model the phononic thermal conductivity perpendicular to the chain, a phenomenological model, devised by Callaway 35 , can be used. Although this model has undergone several revisions and extensions [53][54][55][56][57][58] , the main approach is to model κ ph within the Debye approximation as 59…”

Section: Appendixmentioning

confidence: 99%

Spinon heat transport and spin-phonon interaction in the antiferromagnetic spin-1/2 Heisenberg chain cuprates Sr2CuO3 and SrCuO2

Hlubek,

Zotos,

Singh

et al. 2011

Preprint

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We have investigated the thermal conductivity κmag of high-purity single crystals of the spin chain compound Sr2CuO3 which is considered an excellent realization of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model. We find that the spinon heat conductivity κmag is strongly enhanced as compared to previous results obtained on samples with lower chemical purity. The analysis of κmag allows to compute the spinon mean free path lmag as a function of temperature. At low-temperature we find lmag ∼ 0.5 µm, corresponding to more than 1200 chain unit cells. Upon increasing the temperature, the mean free path decreases strongly and approaches an exponential decay ∼ 1 T exp T * u /T which is characteristic for umklapp processes with the energy scale kBT * u . Based on Matthiesen's rule we decompose l mag into a temperature-independent spinon-defect scattering length l0 and a temperature dependent spinon-phonon scattering length lsp(T ). By comparing l mag (T ) of Sr2CuO3 with that of SrCuO2, we show that the spin-phonon interaction, as expressed by l sp is practically the same in both systems. The comparison of the empirically derived l sp with model calculations for the spin-phonon interaction of the one-dimensional spin-1/2 XY model yields reasonable agreement with the experimental data.

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“…The relationship between τ, τ c , τ N and τ U was first established by Callaway [13]. The τ N and τ U terms are generally modeled with expressions of the form [13][14][15][16][17][18][19][20] 1…”

Section: Callaway-holland Approachmentioning

confidence: 99%

“…The Callaway correction term was ignored. The Holland model has since been used to investigate many other materials, and refined to account for more realistic phonon dispersion [18], the effect of the Callaway correction term [19], and additional scattering mechanisms [20] (e.g., four phonon processes and dislocations). The added complexity leads to more fitted parameters.…”

Section: Callaway-holland Approachmentioning

confidence: 99%

Integration of Molecular Dynamics Simulations and Boltzmann Transport Equation in Phonon Thermal Conductivity Analysis

McGaughey¹,

Kaviany²,

Chung³

2003

Heat Transfer, Volume 4

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The thermal conductivity of the Lennard-Jones argon crystal is predicted using the Boltzmann transport equation under the single mode relaxation time approximation. The temperature and frequency dependence of the phonon dispersion and phonon relaxation times are obtained from lattice dynamics calculations based on the results of molecular dynamics simulations. No fitting parameters are required. The thermal conductivity results are in agreement with predictions from the simulations using the Green-Kubo method. Assuming that the dispersion is linear or temperature independent, as is often done in analytical calculations, leads to large errors in the predictions. This result suggests that the fitting parameters required in such calculations offset significant errors introduced by these simplifying assumptions.

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Longitudinal and transverse parts of the correction term in the Callaway model for phonon conductivity

Cited by 4 publications

References 6 publications

Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

Spinon heat transport and spin-phonon interaction in the antiferromagnetic spin-1/2 Heisenberg chain cuprates Sr2CuO3 and SrCuO2

Integration of Molecular Dynamics Simulations and Boltzmann Transport Equation in Phonon Thermal Conductivity Analysis

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