A thermodynamic study on an associated solution model for liquid alloys

Abstract

Liquid alloys with a rapid increase of component activities over a narrow composition range may be modelled by an associated solution model. Associated species with a fixed stoichiometry in that composition range are postulated in equilibrium with elemental species. Palrwise interactions among all species are described by Margules-type equations. The success of this description is, of course, not a verification of the physical existence of associated species. The thermodynamic background of this model is investigated in this study. For binary liquid alloys, the key equations governing the calculation of activities in internal equilibrium are presented graphically. Formulae for the calculation of the Gibbs energy, enthalpy and entropy of mixing in the postulated species-system are developed and related to the corresponding effects in the binary liquid alloys. The formation of very asymmetric and twin miscibility gaps is discussed. The difference between the Gibbs energy of species and real alloys at stoichiometry is pointed out. Limiting cases of weak and strong association are discussed and formulae for terminal values of activity coefficient and partial enthalpy of solution are developed. Structural related properties of Sn-Te liquid alloys are calculated and compared to experimental data. A quantitative prediction of data in ternary and multicomponent alloys is one major motivation for the precise description of binary alloys and a suitable extension of the associated solution model is presented. The model is compared to other associate models and to sublattice models. Despite the different physical picture, close phenomenological and mathematical resemblance is discovered among the associated solution and the sublattice model.