Recent progress and frontier issues in thermal transport theory of metals

Abstract

Metal is one of the most widely used engineering materials. In contrast to the extensive research dedicated to their mechanical properties, studies on the thermal conductivity of metals remain relatively rare. The understanding of thermal transport mechanisms in metals is mainly through the Wiedemann-Franz Law established more than a century ago. The thermal conductivity of metal is related to both the electron transport and the lattice vibration. An in-depth understanding of the thermal transport mechanism in metal is imperative for optimizing their practical applications. This review first discusses the history of the thermal transport theory in metals, including the Wiedemann-Franz law and models for calculating phonon thermal conductivity in metal. The recently developed first-principles based mode-level electron-phonon interaction method for determining the thermal transport properties of metals is briefly introduced. Then we summarize recent theoretical studies on the thermal conductivities of elemental metals, intermetallics, and metallic ceramics. The value of thermal conductivity, phonon contribution to total thermal conductivity, the influence of electron-phonon interaction on thermal transport, and the derivation of the Lorenz number are comprehensively discussed. Moreover, the thermal transport properties of metallic nanostructures are summarized. The size effect of thermal transport and the Lorenz number obtained from experiments and calculations are compared. Thermal transport properties including the phonon contribution to total thermal conductivity and the Lorenz number in two-dimensional metals are also mentioned. Finally, the influence of temperature, pressure, and magnetic field on thermal transport in metal are also discussed. The deviation of the Lorenz number at low temperatures is due to the different electron-phonon scattering mechanisms for thermal and electrical transport. The difference in thermal conductivity among metals is induced by the difference in pressure among different metals and is related to the electron state at the Fermi level as well. The effect of magnetic field on thermal transport is related to the coupling between the electron and the magnetic field, therefore the electron distribution in the Brillouin zone is an important factor. In addition, this review also looks forward to the future research directions of metal thermal transport theory.