The temperature variation of the electrical resistivity was measured at various concentrations of binary liquid alloys, Zn-Cd, In-Tl, Sn-Pb and Sb-Bi, having the same value in the valency of their solute and solvent metals. The resistivity for these alloys obtained from the above experiments was found to be approximately changed in proportion to the concentration of solute atoms over its whole range for each alloy system.
Distribution of solute and solvent species in these liquids can be assumed to be random because of the mutual interaction being approximately unchanged between like atoms and unlike atoms having the same valency. Under the above assumption a formula for the concentration dependence of resistivity of alloys was deduced, which was composed of two terms. The first term contributes to the main part of the resistivity leading to the linear dependence upon the concentration, and the second term is a cross term depending the square of the difference between scattering potentials of solute and solvent ions, (U_A−U_B)². When the pseudo-potential obtained by Animalu and Heine is used as the scattering potential of each ion, it can be considered that such potentials of ions with the same valency are similar so that the contribution of the second term to the resistivity is small compared with that of the first term. Thus the nearly linear dependence of the resistivity upon the concentration of alloy is obtained.
Small deviations of the concentration depencence from the linearity for respective alloys was discussed from the variation of the pseudo-potential of ions caused by alloying.