Understanding the resistivity and absolute thermoelectric power of disordered metals and alloys

Abstract

We recall definitions of the electronic transport properties, direct coefficients like electrical and thermal transport conductivities and crossed thermoelectric coefficients like the Seebeck, Peltier and Thomson coefficients. We discuss the links between the different electronic transport coefficients and the experimental problems in measuring these properties in liquid metals. The electronic transport properties are interpreted in terms of the scattering of electrons by 'pseudo-atoms'. The absolute thermoelectric power (ATP), thermopower or Seebeck coefficient is known as the derivative of the electrical resistivity versus energy. The key is to understand the concept of resistivity versus energy. We show that the resistivity follows approximately a 1/E curve. The structure factor modulates this curve and, for a Fermi energy corresponding to noble and divalent metals, induces a positive thermopower when the free electron theory predicts a negative one. A second modulation is introduced by the pseudopotential squared form factor or equivalently by the squared t matrix of the scattering potential. This term sometimes introduces an anti-resonance (divalent metals) which lowers the resistivity, and sometimes a resonance having an important effect on the transition metals. Following the position of the Fermi energy, the thermopower can be positive or negative. For heavy semi-metals, the density of states splits into an s and a p band, themselves different from a free electron E(0.5) curve. The electrons available to be scattered enter the Ziman formula. Thus if the density of states is not a free electron one, a third modulation of the [Formula: see text] curve is needed, which also can change the sign of the thermopower. For alloys, different contributions weighted by the concentrations are needed to explain the concentration dependent resistivity or thermopower. The formalism is the same for amorphous metals. It is possible that this mechanism can be extended to high-temperature crystalline alloys or even disordered semiconductors since we can separate the transport coefficients between the effect of the number of charge carriers and a scattering term linked to carrier mobility.

Electrical and thermal conductivities and Seebeck coefficient of liquid copper–bismuth alloys

“…More details are given in [14]. properties in the framework of the extended Faber-Ziman theory has been published by Gasser [15].…”

Electronic transport properties of liquid zinc and zinc–germanium alloys: Theory versus experiment

“…The melting point of liquid germanium (940°C) is well above the boiling point of liquid zinc (906°C). A very interesting temperature dependence of the absolute thermoelectric power of liquid zinc is observed which can be understood in the frame of the generalized formalism presented in a review article by Gasser [30]. The concentration dependence behavior has been reasonably described using ab initio muffin-tin potentials derived from the (LDA) density functional approach.…”

A limit model for thermoelectric equations

“…From the regularity theory for the Robin-Laplace problem and by virtue of the existence of a solution θ ∈ W 2,pn/(p+n) (Ω) we proceed as in (30) (27) with ξ replaced by θ and using (33) we conclude (21). Choose η = θ ∈ W 1,p (Ω) as a test function in (18). Then applying the Hölder inequality and using the assumptions (H1)-(H4) it follows…”