Theoretical modeling to access the surface phenomenon of liquid ternary alloys

Abstract

The Redlich-Kister (R-K) polynomial was used to optimise the linear temperature dependent interaction energy parameters for excess Gibbs free energy of mixing of binary subsystems of Fe–Si–Ti, Al–Sn–Zn and Al–Cu–Fe ternary liquid alloys using experimental data for excess entropy of mixing and enthalpy of mixing. The optimised parameters of binary subsystems were then used in the Chou equation (General Solution Model) for the excess Gibbs free energy of mixing of ternary liquid alloys to evaluate the partial excess free energy of mixing of components. These partial excess free energies of components of ternary liquid alloys were then used in the Butler equation to compute the surface concentrations of components and surface tensions of these ternary systems from the corner of each element at cross-sections of 3 : 1, 1 : 1 and 1 : 3. In addition, the excess surface tension of the binary subsystems at four different temperatures was used to compute the temperature dependent coefficients of the R-K polynomial for the binary subsystems of the previously mentioned ternary alloy. These coefficients were then used in the Kohler, Toop, and Chou equation to obtain the surface tension of the ternary alloys at different temperatures and concentrations. The obtained values of surface tension using these geometrical models were then compared with those obtained using the Butler equation. It was found that the component with the lowest surface tension leads to the highest surface concentration and the surface concentration of components increases as their bulk concentration increases and vice versa. Furthermore, it was observed that the the interaction between the binary pairings affected the surface concentration of a component in these ternary alloys. All three binary subsystems of Fe–Si–Ti ternary system were found to be ordering in nature and the surface concentration of the components was also affected by the interaction between these binary pairs. The surface concentration of Ti was found to increase with the decrease of its bulk concentration at the low content of Ti in the alloys. This unusual behaviour was observed due to the higher interaction energy between Fe and Si than between Fe and Ti in Fe–Si–Ti ternary liquid alloys. It was observed that the surface concentration of each component in Al–Sn–Zn ternary liquid alloy increased with increasing the respective bulk concentration at all crosssections. In this case, surface concentration was determined by the surface tension of the individual components, as all the binary sub-systems of this ternary alloys were of segregating nature. In case of Al–Cu–Fe liquid ternary alloys, binary sub-systems Al–Cu and Al–Fe are of ordering in nature while Cu–Fe is strongly segregating. When observed from the Fe corner, the surface concentration of Cu increased from 0.060 to 0.081 while the bulk vii concentration decreased from 0.225 to 0.088 at the cross-section x Al : x = 3 : 1. This unusual trend of increasing surface concentration of Cu with the decrease of its bulk concentration may be due to the ordering tendency of Fe with Al and the segregating nature of Fe with Cu. The surface concentration of components changes towards the ideal value (bulk concentration) at elevated temperatures. The surface concentration of Fe and Ti was found to increase while that of Si was found to decrease when the temperature of the alloy was increased from 1873 K to 2173 K. The surface concentration of Fe and Ti were found less than their respective bulk concentration and mole fraction concentration of Si in the surface was found to be much higher than the bulk phase. Similar results were noticed for the variation of surface concentration with temperature in the case of Al–Sn–Zn and Al–Cu–Fe ternary liquid alloys. The surface tension of liquid ternary alloys was found to decrease rapidly with the rise in bulk concentration of the component having the least surface tension in pure state. The value of temperature coefficient of surface tension was found to vary with composition of the alloys. The surface tension of all ternary liquid alloys studied in this work decreased linearly with increase in temperature, regardless of composition.