The Butler equation (1932) is a more convenient way to model the surface tension of multi-component liquids, compared to the classical Gibbs (1876) equation. In the present paper the two methods are shortly described and compared. Also, a modification is introduced into the Butler equation, based on the composition dependence of the excess molar volume of the alloy.
The Butler equation (equally as the Gibbs equation) can only be applied to actual calculations of the surface tension of multi-component liquid alloys, if the excess Gibbs energy of the surface is described by a model. According to the method, generally applied in the literature, the surface excess Gibbs energy and the bulk excess Gibbs energy are connected by a single geometric parameter, based on a broken bond model. This approach will be further discussed, and theoretical model parameters will be derived.
When there are associates in the liquid alloy, those associates might be surface active, and thus, the surface tension isotherms can not be described properly without taking that fact into account. The Butler equation is modified for the case of the associated solution model. Calculations are performed for the Al-Ni system, taking into account AlNi associates in the Al-Ni liquid alloy.
In systems with very positive heat of mixing values, surface phase transformation can occur. Such a phenomenon was modeled by the Butler equation on an example of the Fe-O system. It is shown that at an oxygen content, being much lower than the bulk solubility of oxygen, a first order surface phase transformation occurs, leading to the appearance of a nanometer thin FeO layer at the liquid/gas interface.