New model for thermal conductivity across boundaries / by Zainab Fouad Alameh.

Abstract

We have developed a theoretical model to predict the thermal conductivity across the boundary between two solids. Our approach is based on solving Boltzmann equation taking into account all the physical aspects of the phonon scattering mechanisms. Distinction between normal processes which tend to displace the phonon distribution from its equilibrium one and resistive processes which restore it back is emphasized in our analysis. Lattice vibration parameters that enter in the thermal conductivity calculation, the Debye temperature and the Gruneisen parameter, are taken to be temperature dependent. At the boundary, we consider that transmission of phonons can be diffusive or specular, the probability of each depends on incident phonon characteristics such as its incidence angle and wavelength, as well as the interface roughness. With this theoretical model in hand, the thermal conductivity of polycrystalline materials can be calculated. This model confirms the different trend of the variation of the lattice thermal conductivity for polycrystalline materials, as compared to bulk, reported by precise experiments. For bulk materials, thermal conductivity is expected to rise as T┬│ for very low temperatures, then a maximum is reached, beyond which thermal conductivity drops again. In the case of polycrystalline materials, a deviation from the cubic law is revealed for samples of small sizes at low temperatures, then the trend followed is similar to that of the specific heat, i.e. thermal conductivity increases as temperature increases. As a second application of our new model, we employ our approach to predict materials that can be used in the form of nanostructured superlattices to obtain systems of extremely low thermal conductivity. Such systems will be very effective in the design of fast heat removals, or alternatively, high efficiency thermoelectric devices.