Thermal Transport in Solids: Diffusive and Radiative Regimes.

Heat in dielectric solids consists of atomic vibrations, which may be either individual or collective, depending on the material and its temperature. At high temperature individual vibrations are abundant, whereas at low temperature collective vibrations predominate. The energy of individual vibrations is carried by a random walk through the solid, whereas collective vibrations propagate as elastic waves called phonons. The random walk process may be described by the diffusion equation, and therefore this regime of heat transport is called the diffusive regime. At very low temperature in crystalline compounds however, the mean free path of the phonons exceeds the dimensions of the sample, and the diffusive picture of heat flow is no longer valid. These conditions represent the ballistic or radiative regime, wherein the phonons are scattered primarily at the sample's outer surfaces, and the thermal transport must be described in terms of phonon blackbody radiation. Finally, at intermediate temperature, and at low temperature in disordered compounds, the heat is still carried mostly by phonons, but their mean free paths are much smaller than the sample size, and the thermal transport may again be described as a diffusive flow. We explore experimental techniques for thermal conductivity measurements in both the diffusive and radiative regimes, and discuss the results of these measurements in the context of their respective models for thermal transport. We first describe a heat-pulse technique which is used for thermal measurements at intermediate and high temperature (30 K < T < 300 K) in ceramic compounds, and compare the results to two models of diffusive thermal transport--one involving phonons and the other isolated vibration centers. For studies of the radiative regime, we present low temperature (T < 1 K) thermal conductance measurements of pure single crystals, and analyze the data using Monte Carlo simulations of phonon blackbody radiation. We confirm that phonon surface scattering is very important in the radiative regime, and find that our polished silicon surfaces are 99.87 +/- 0.01% specular at the lowest temperature (50 mK) in our experiments. The powerful Monte Carlo analysis allows us to also determine phonon transmission probabilities between two materials.