A predictive surface tension model for liquid metallic solutions

Surface tension originates from the thermodynamically unstable broken bonds of atoms at a liquid surface. To minimize total Gibbs energy, the surface composition deviates from the bulk, governed by both the cohesive energies of individual atoms and their interactions. These interactions determine which species preferentially segregate to the surface. Therefore, by quantifying the thermodynamic interactions between atoms and the broken-bond energies of surface species, it should be possible to predict surface segregation and, consequently, the surface tension of liquid metallic solutions.

Surface tension of a binary liquid metal is expressed as the weighted sum of the surface tensions of pure components considering their surface concentrations. Chemical potential equilibrium was imposed between the bulk and the surface layer, with the broken-bond contribution included in the partial molar Gibbs energy of each species. From this equilibrium, effective interactions between components were extracted for each system at its composition. These interactions were then analyzed against unary surface energies and bulk thermodynamic properties to establish a predictive expression.

The model reproduced all reliable experimental surface tension data without empirical parameters. Predicted surface segregation was governed by bulk thermodynamic properties and unary surface energies, highlighting the dominant role of bulk-surface coupling. This work presents the first parameter-free surface tension model that incorporates surface energy into the chemical potential, enabling full prediction of surface tension. It also provides a clear description of how bulk interactions drive surface segregation and how competing energetic contributions determine the resulting surface composition based on relevant thermodynamic properties.