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Published in Zbigniew Galazka, Transparent Semiconducting Oxides, 2020
Low temperature measurements of Czochralski-grown crystals by Handwerg et al. [293] revealed that the thermal conductivity between 150 and 300 K follows phonon–phonon Umklapp scattering (∝T−1), while at lower temperatures, there is an increasing deviation from the phonon–phonon scattering, as shown in Fig. 4.38b. This deviation is assigned to point defect scattering, which might play an important role in thermal conductivity. On the other hand, Jiang et al. [297] claimed that the thermal conductivity of EFG-grown crystals between 80 and 400 K follows the ∝T−1.3 relation.
New Thermoelectric Materials with Precisely Determined Electronic Structure and Phonon Dispersion
Published in D. M. Rowe, Materials, Preparation, and Characterization in Thermoelectrics, 2017
The materials consisting of heavy elements generally possess a small lattice thermal conductivity because the heavy mean atomic weight leads to the reduction of the energy of phonons and consequently to the reduction of sound velocity and increase of umklapp scattering provability at a given temperature. In the same manner as the materials of heavy constituent elements, the materials characterized by rather weak bonds between the atoms in the unit cell should possess a small lattice thermal conductivity.
Thermal Transport Properties of Skutterudites
Published in Ctirad Uher, Thermoelectric Skutterudites, 2021
The thermal conductivity of single crystals of CoSb3 at low temperatures measured by Morelli et al. (1995) is shown in Figure 5.29a. Also included are two curves that represent fits to the data assuming the Debye model with umklapp and boundary scattering of phonons (curve A) and the fit that includes scattering by vacancies with the density 1 × 1018 cm−3 (curve B). The charge carrier contribution to the total thermal conductivity is less than 10% for all samples and temperatures. The very steep rise with decreasing temperature is characteristic of the dominance of phonon-phonon umklapp scattering. The different peak heights near 12 K are most likely due to the presence of vacancies on the pnicogen sites. For comparison, Figure 5.29a also includes thermal conductivity of a well-compacted polycrystalline CoSb3, Uher et al. (1997), where the effect of boundary scattering is obvious from a strong reduction of the peak height (and a shift of the peak to higher temperatures), while there is little difference in room temperature values of the thermal conductivity. The temperature dependence of the thermal conductivity of a single crystal of CoSb3 at temperatures above the ambient measured by Caillat et al. (1996a) and of a polycrystal of CoSb3 measured by Katsuyama et al. (1998b) is displayed in Figure 5.29b. The conductivity decreases from its room temperature value of about 10.5 Wm−1 K−1 and reaches a minimum near 700 K in the case of the single crystal and between 600 and 650 K in the case of the polycrystal. At still higher temperatures, intrinsic excitations start to set in and the bipolar thermal conductivity contribution gives rise to an increasing thermal conductivity. This general trend has also been confirmed in measurements with arsenide skutterudites, Caillat et al. (1995c), and the decreasing thermal conductivity with the increasing temperature up to about 750 K was reported for IrSb3 by Slack and Tsoukala (1994).
Thermal Resistance by Transition Between Collective and Non-Collective Phonon Flows in Graphitic Materials
Published in Nanoscale and Microscale Thermophysical Engineering, 2019
Sangyeop Lee, Xun Li, Ruiqiang Guo
Phonon transport in crystalline materials has been often discussed between ballistic and diffusive limits depending on sample size. The ballistic regime occurs when sample size is much smaller than the mean free path of internal phonon scattering such that the internal phonon scattering can be ignored. The diffusive regime occurs when umklapp scattering (U-scattering), which do not conserve phonon crystal momentum, is the most dominant scattering mechanism. For the diffusive regime, sample size should be larger than the mean free paths (MFPs) of U-scattering. There is another regime of phonon transport, called hydrodynamic regime, which rarely occur compared to the ballistic and diffusive regimes. The hydrodynamic phonon transport occurs when most internal phonon scattering processes are a momentum conserving type (i.e., normal scattering and hereafter N-scattering) and thus do not directly cause thermal resistance. The hydrodynamic regime was predicted and experimentally observed several decades ago [1–4].
Hydrodynamic Phonon Transport Perpendicular to Diffuse-Gray Boundaries
Published in Nanoscale and Microscale Thermophysical Engineering, 2019
Runqing Yang, Shengying Yue, Bolin Liao
Phonons are major carriers of heat in semiconductors and insulators, and the scattering between phonons is usually the main source of thermal resistance in single crystals of these materials [1]. Phonon–phonon scattering can be classified into two types: the momentum-conserving normal scattering processes and the momentum-destroying Umklapp scattering processes. It is understood [2] that Umklapp scatterings act as momentum sinks in the bulk of a material and directly contribute to the thermal resistance. Whereas normal scattering processes do not directly create thermal resistance per se, they perturb the phonon distributions and indirectly affect the thermal transport in presence of Umklapp processes [3, 4]. In different materials and under different external conditions, the dominating phonon–phonon scattering mechanism can vary, giving rise to distinct regimes of heat conduction [5–7]. When the characteristic size of the sample is smaller than the intrinsic phonon mean free path due to phonon–phonon scatterings, as is relevant in microelectronic devices [8] and nanostructured thermoelectric materials [9], the extrinsic phonon-boundary scattering dominates and the phonon transport approaches the ballistic regime [10, 11]. In macroscopic samples, where the intrinsic phonon–phonon scattering becomes the leading phonon scattering channel, the relative strength of the normal processes and Umklapp processes determines the characteristics of the phonon transport. In most three-dimensional bulk materials above their Debye temperature, the Umklapp processes prevail and the phonon transport is diffusive, where no net drift flow of phonons can be established and maintained due to the constant dissipation of the phonon momenta, leading to the familiar Fourier's law of heat conduction.