The effects of liquid composition, temperature, and pressure on the equilibrium dihedral angles of binary solid–liquid systems inferred from a lattice-like model

Dihedral angles of binary eutectic systems, such as silicate+melt systems, silicate+H2O systems, binary alloys, and binary organic systems, tend to decrease with increasing concentration of the solid component in the liquid phase. This empirical law is useful to estimate dihedral angles in the Earth’s interior from phase diagrams of solid–liquid systems. In this paper, we investigate the mechanism underlying this empirical law. By employing a lattice-like model in which the liquid phase is treated as a regular solution, we clarify the liquid composition, temperature, and pressure effects on the solid–liquid interfacial tension. It is shown that the non-ideality in chemical bonding causes a strong compositional dependence of the solid–liquid interfacial tension; due to the non-ideality in chemical bonding, the solid surface preferentially adsorbs the solid component, which results in the decrease of the interfacial tension with increasing concentration of this component in the bulk liquid phase. With this effect, the significant decrease of the dihedral angle with T observed in the SiO2–H2O system near the monotectic temperature, and the decrease with P observed in the forsterite–H2O system, can be explained semi-quantitatively.