Chapter 26 - Thermal and Electrical Conductivities

Abstract

Thermal conductivity and electrical conductivity are transport properties analogous to mass diffusion. The heat equation has the same mathematical form as the diffusion equation. As such, the solutions to the heat equation are identical to solutions of the diffusion equation, replacing concentration with temperature and replacing the diffusion coefficient with the thermal conductivity. In metals, thermal conductivity is dominated by free electrons and is therefore proportional to electrical conductivity. In non-metallic materials, thermal conductivity is governed by phonons. Single crystals have the highest thermal conductivities, since defects such as dislocations and grain boundaries lead to phonon scattering, which reduces thermal conductivity. Similarly, the thermal conductivity of non-crystalline materials is significantly less than that of their crystalline counterparts. Other mechanisms for thermal conduction include convection in fluid phases and radiation at high temperatures. Electrical conductivity varies by many orders of magnitude across materials. Metals have high electrical conductivities due to the high mobility of their valence electrons. Ceramics can exhibit highly nonlinear variations in resistivity, as in varistors and thermistors. A varistor is a material where the resistivity varies significantly with the applied voltage. In thermistor materials, the resistivity is a strong function of temperature. Thermistor materials may have different regimes exhibiting positive or negative temperature coefficients.