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Thermal conductivity of solids to high temperatures

Abstract:

The search of new materials for the design of the next generation of Thermal Barriers Coating (TBC) focuses on materials with very low thermal conductivity (λ) to high temperatures (T ≥ θD where θD is the Debye's temperature). The dependence of the thermal conductivity with the temperature can be divided in four regions. In region I, at low temperature (T < 20 K), the thermal conductivity is determined by the physical dimensions of the material, the size of the grain and the spacing among dislocations. The thermal conductivity in this region increased quickly with the temperature, being proportional to T3. In region II, the thermal conductivity reaches a maximum value, which usually happens at T ≈ θD / 20. In the region III, the lack of harmony (anharmonic effect) of the phonons begins to be significant and the thermal conductivity diminishes with T-1. Finally at very high temperatures (T ≥ θD) in the region IV, the thermal conductivity becomes independent of the temperature. Due to the absence of a rigorous theory that can explains the behavior of thermal conductivity in regions III and IV, in terms of the fundamental physical processes that happen, in this work we present and review the existent models to estimate the values for the thermal conductivity of materials to high temperatures. It was found that the fundamental physical process responsible for the decrease in thermal conductivity in region III is the phonons dispersion through the u-process or «umklapp» of phonons. In region IV, the behavior of the thermal conductivity is due to phonons whose means free path is of the order of an interatomic spacing. Also, we present the requirements that should satisfy a material showing low values of thermal conductivity to high temperatures.