Surface tension of liquid mixtures and metal alloys. Thermodynamic conditions for the occurrence of a positive temperature coefficient

Abstract

The atypical increase of surface tension when the temperature of a liquid alloy increases, is addressed using Butler’s thermodynamic model for an ideal surface phase. A rigorous expression for this temperature coefficient at fixed bulk alloy composition, requiring only pure-metal density and surface tension data and no arbitrary simplifying assumptions, is worked out. This theoretical development predicts the occurrence of positive temperature coefficients whenever a combination involving large difference of pure-metal surface tensions, temperatures close to the alloy melting point and molar surface area of the surface-active metal larger than that of the other component, is met. The proposed method is applied to the alloys Cu–Sn, Cu–In, Ag–Bi, Ag–Pb and Ag–Sn for which experimentally measured positive temperature coefficients have been reported. An acceptable agreement between theoretical and experimental values is documented. This theoretical approach predicts a negative temperature coefficient of the surface tension at fixed surface-phase composition, which is in fact the typical behaviour for this dependence. It is concluded that the temperature and composition ranges over which a certain binary alloy may exhibit positive temperature coefficient of the surface tension can be established beforehand using the proposed methodology.