Theory for the Electrical Resistivity of Liquid Metals

With respect to the transport properties of conduction electrons in liquid metals; two theories are available to explain electrical resistivity of liquid metals. In 1961, Ziman proposed "how the conduction electrons are scattered by ions" which is known as the Ziman theory. In 1962, Takeuchi and Endo proposed "how the fluctuation of ion's assembly, in other words, the density fluctuation of component ions, affects to the scattering of conduction electrons." The Ziman theory was widely accepted by many researchers, but Takeuchi-Endo theory was very limited. Are there appreciable differences between two theories? In the present work we modified the Takeuchi-Endo theory to achieve the Ziman's result. It is interesting to conclude that "Takeuchi and Endo assumed the scattering of conduction electrons is caused by the averaged value of density fluctuation, which means the scattering is related only to the structure factor S(q) of liquid metals at q = 0."