The theory of the thermal conductivity of metals and alloys is reviewed. There are two components: electronic and lattice. The electronic component is related to the electrical conductivity by the Lorenz ratio. Deviations from the Sommerfeld value of the Lorentz ratio are discussed. At high temperature deviations are due to incomplete degeneracy of the electron gas (Fermi smearing), at low temperatures deviations are due to the inelastic nature of the electron-phonon interactions and to the electron-electron interactions. The lattice conductivity is discussed as a function of temperature, point defects, and electron density. The predictions of the theory are compared with measured thermal conductivities. For the elements, the effects of the lattice component can be distinguished from deviations of the electronic component from the Lorenz ratio. Three representative alloy systems are discussed. In aluminium alloys the lattice component is small, and the electronic component well behaved. In titaniu...

Thermal conductivity of metals and alloys

Thermal Conductivity of Metals

The low-temperature DC electrical and thermal resistance of nearly-free-electron metals, such as the alkali metals and aluminium, are ideal for testing one's understanding of the basic scattering processes of electrons and phonons in a metallic environment. The greatly improved experimental capabilities of the past decade facilitated measurements, the results of which made clear that the traditional models were at least incomplete. Significant progress has hence been made in understanding the role of electron-electron and electron-phonon scattering, both normal and Umklapp; their sample dependence; other deviations from Matthiessen's rule; the influence of the lattice thermal conductivity on the transport tensor elements; the linear magnetoresistivity, and related fields. Yet, crucial questions like the existence of a charge density wave ground state in the alkali metals remain open, and new ones show up.

https://iopscience.iop.org/article/10.1088/0034-4885/48/6/003/pdf

Simple transport properties of simple metals: classical theories and modern experiments

A simple approximation for the scattering rate is shown to yield values for the electron-electron contribution to the thermal resistivity that are in good agreement with experiment in simple metals These metals have been modelled by a uniform electron gas with a modified mass and electron-electron interaction to account approximately for crystalline effects The scattering function was approximated by using an exact expression for the forward-scattering limit in terms of the model-system Landau parameters with scattering events of finite momentum transfer accounted for by the s-p approximation given by Dy and Pethick Estimates of the contribution from electron-electron scattering to the electrical resistivity based on the same scattering function have also been calculated for the alkali metals

https://iopscience.iop.org/article/10.1088/0305-4608/10/4/019/pdf

Electron-electron scattering and the thermal resistivity of simple metals

An analysis of the temperature dependence of the coefficient Aee of the T2 term due to the electron-electron scattering contribution to the electrical resistivity defined by rho ee(T)=AeeT2, is presented for the alkali metals. In contrast to the standard theory, which predicts a temperature-independent value for Aee, there are two different contributions to the temperature dependence of Aee, there are two different contributions to the temperature dependence of Aee, one arising from anisotropic electron-dislocation scattering and the second arising from the electron-phonon interaction. It is shown that the temperature dependence of Aee is significantly different for each of three classes of metals. The first contribution to the temperature dependence of Aee is large only for the alkali metals, but small for the noble and simple polyvalent metals, whereas the second contribution is large only for the simple polyvalent metals, but small for the noble and alkali metals.

Correlation between high-temperature and low-temperature electron-electron scattering for the alkali metals

The electrical resistivity ρ, thermal conductivity κ, and thermoelectric power S have been measured for two bare K specimens between 80 and 330 K. The data fully support the main conclusions of an earlier, preliminary study by Cook and Laubitz. The Lorenz function L = κρ/T does not approach the Sommerfeld value L0 with increasing temperature. Both the magnitude and temperature dependence of L–L0 indicate the presence of an added term Wee in the thermal resistivity, due to electron–electron scattering. Such scattering also affects S. It is shown that the data for K, together with published values of B = Wee/T for Na, Rb, and the noble metals, form a consistent picture of electron–electron scattering in the monovalent metals above the Debye temperature.

J. G. Cook

Papers

Electron-electron scattering in potassium