Calculation of surface tension using CALPHAD software as a Zero Phase Fraction line of ""surface"" phase

Abstract

A new approach for calculation of surface tension of solutions is presented. Based on the proposal of Butler (Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 135 (1932) 348 [3]), a surface phase was assumed to be in equilibrium with a corresponding bulk phase. Following the proposal of Pajarre et al. (Calphad 30 (2006) 196 [71), a surface area element (X) was introduced, only in the surface phase. The surface tension can be obtained by Constrained Gibbs Energy Minimization (CGEM) under a constraint of constant surface. The equilibrium chemical potential of the surface element, X, was interpreted to be proportional to the surface tension. According to the present author (Calphad 50 (2015) 23 [9]), the surface tension calculation by the CGEM can be interpreted as if the bulk phase and the surface phase are in equilibrium with each other, and the chemical potential of the area element is obtained as a result of the equilibrium. It was shown that a geometrical relationship among the molar Gibbs energies of the bulk phase and the surface phase, the surface tension, and the surface concentration is found. In the present study, further improvement was made in such a way that the chemical potential of the area element can be simply obtained by combining the CGEM with Zero Phase Fraction (ZPF) line in Type II phase diagram, where the chemical potential of the area element is used as an axis variable. Such phase diagram can be easily calculated using conventional CALPHAD softwares. The proposed approach was validated for a number of binary and ternary systems. (C) 2015 Elsevier Ltd. All rights reserved.