A method to calculate equilibrium surface phase transition lines in monotectic systems

When a surface active component (B) is being gradually added to a component with a higher surface tension (A) at any constant temperature (being lower than the so-called surface critical point, Tcr∗) in any A-B system with a miscibility gap, the first order surface phase transition (SPT) will occur at a certain bulk concentration of component B, within a one-phase, A-rich liquid region of the phase diagram. This SPT is connected with an abrupt change of the surface concentration of component B from a low value to a high value, i.e. with the formation of a thin film of a B-rich layer on the surface of the A-rich bulk liquid alloy. In this paper a general method is developed, based on the Butler equation, to calculate the equilibrium SPT line for any monotectic system, using optimized CALPHAD thermodynamic properties of the liquid alloy and the surface tension and molar volume values of the pure components, as initial data. This new SPT line should be included in all equilibrium phase diagrams with miscibility gaps, for which the Tcr∗ point appears in the A-rich one-phase liquid region of the diagram. The behavior of liquid alloys is expected to be qualitatively different on the two sides of the SPT line. The temperature coefficient of the surface tension is shown to change its sign from negative to positive in the vicinity of the SPT line, which has a serious impact on the Marangoni convection of the alloy. The method is validated on the Ga-Pb system, for which a reasonable agreement is found between the calculated SPT line and the experimentally determined points, as published in 1998 by Chatain, Wynblatt and co-workers. The method of calculation is shown to be applicable for multi-component liquid alloys and solid solutions, as well.