What happens when the surface and bulk phases of liquid metal alloys attain the same density at equilibrium?

Abstract

Arguments supporting the prediction of a surface phase that is denser than the underneath bulk phase, when the surface-active metal in binary liquid alloys is the densest component, are presented. Butler’s thermodynamics for ideal surface phases are worked out to identify these event requirements. The two main factors leading to this situation are identified, namely the ratio between pure metal densities and the difference between their surface tensions. Expressions to estimate the composition interval where this outcome is expected to take place and to calculate the alloy surface tension under the restriction of equal surface and bulk densities are obtained. As expected, this surface tension is higher than that predicted by usual methods. Using literature data, nine different binary alloys are examined, and their interest composition ranges established. These span from very low to relatively high concentrations of the surface-active metal. The limitation of surface densities may lead to surface tensions up to 500 mN m−1 larger than those calculated without that constraint. Graphs showing these modelled features are presented. The liquid metals Pb, Tl and Bi are identified as powerful surface-active agents with high density and Al, Ti, Ga and Zr stand up as relatively low-density metals with high liquid state surface tensions. The influence of the surface phase packing factor value adopted is discussed, and it is demonstrated that it should be larger than unity for realistic modelling of liquid metal alloys. Finally, it is concluded that elaborate thermodynamic modelling of liquid alloys should impose surface densities not exceeding bulk densities.