Resistivity of the liquid gallium-lead miscibility gap system

Abstract

We present our electrical resistivity measurements of the gallium-lead system which shows a very large miscibility gap between 2.4 and 94.5 at. % lead with a critical temperature of $606\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ and composition of 40 at. % lead. A small negative deviation of the experimental temperature coefficient of the resistivity (TCR) appears near the critical composition of the alloy. The resistivity of the alloys is interpreted and discussed in terms of the extended Faber-Ziman formula using the $t$-matrix formalism with hard-sphere and experimental (for pure metals only) structure factors. An approach is proposed, taking into account the information given by the experimental density of states which allowed us to explain the resistivity of pure lead and that of the liquid gallium-lead alloys. As a conclusion it was shown that two electrons in the conduction band of liquid lead better explain the experimental resistivity than four electrons.