Prediction of surface and interfacial tension based on thermodynamic data and CALPHAD approach

Abstract

In this article, following a brief introduction concerning experimental measurements of surface and interfacial tensions, methods for calculating surface tension and surface segregation for binary, ternary, and multicomponent high-temperature melts based on Bulter's original treatment [1] and on available physical properties and thermodynamic data, especially excess Gibbs free energies of bulk phase and surface phase versus temperature obtained from thermodynamic databases using the calculation of phase diagram (CALPHAD) approach, with special attention to the model parameter β, have been described. In addition, the geometric models can be extended to predict surface tensions of multicomponent systems from those of sub-binary systems. For illustration, some calculated examples, including Pb-free soldering systems and phase-diagram evaluation of binary alloys in nanoparticle systems are given. On the basis of surface tensions of high-temperature melts, interfacial tensions between liquid alloy and molten slag as well as molten slag and molten matter can be calculated using the Girifalco-Good equation [2]. Modifications are suggested in the Nishizawa's model [3] for estimation of interfacial tension in liquid metal (A)/ceramics (MX) systems so that the calculations can be carried out based on the sublattice model and thermodynamic data, without deliberately differentiating the phase of MX at high temperature. Finally, the derivation of an approximate expression for predicting interfacial tension between the high-temperature multi-component melts, employing Becker's model [4] in conjunction with Bulter's equation and interfacial tension data of the simple systems is described, and some examples concerning pyrometallurgical systems are given for better understanding.