Understanding the resistivity and absolute thermoelectric power of disordered metals andalloys

Abstract

We recall definitions of the electronic transport properties, direct coefficients like electricaland thermal transport conductivities and crossed thermoelectric coefficients like theSeebeck, Peltier and Thomson coefficients. We discuss the links between the differentelectronic transport coefficients and the experimental problems in measuring theseproperties 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 Seebeckcoefficient is known as the derivative of the electrical resistivity versus energy. The key is tounderstand the concept of resistivity versus energy.We show that the resistivity follows approximately a1/E curve. The structure factor modulates this curve and, for a Fermi energycorresponding to noble and divalent metals, induces a positive thermopower when thefree electron theory predicts a negative one. A second modulation is introducedby the pseudopotential squared form factor or equivalently by the squaredt matrix of the scattering potential. This term sometimes introduces an anti-resonance(divalent metals) which lowers the resistivity, and sometimes a resonance having animportant effect on the transition metals. Following the position of the Fermi energy, thethermopower can be positive or negative. For heavy semi-metals, the density ofstates splits into an s and a p band, themselves different from a free electronE0.5 curve. The electrons available to be scattered enter the Ziman formula. Thus if thedensity of states is not a free electron one, a third modulation of the curve is needed, which also can change the sign of the thermopower.For alloys, different contributions weighted by the concentrations are needed to explain theconcentration dependent resistivity or thermopower. The formalism is the same foramorphous metals. It is possible that this mechanism can be extended to high-temperaturecrystalline alloys or even disordered semiconductors since we can separate the transportcoefficients between the effect of the number of charge carriers and a scattering term linkedto carrier mobility.