The effect of associates with an arbitrary stoichiometry on mixing thermodynamics in liquid alloys

Abstract

The model of an ideal association solution is one of the models successfully used in calculating thermodynamic characteristics of multicomponent liquid systems. Traditionally, the model is applied to solutions that have stable compounds in their solid phases. In this case, it is usually assumed that a melt consists of individual atoms of initial components and of one or several associates with a fixed stoichiometry and a minimum size. The equilibrium constants responsible for a reaction of the formation of the associates from initial components and, often, the stoichiometries of associates are adjustable parameters [1‐4]. The possibility of the existence of associates composed of individual atoms was considered in the general theory of an ideal association solution [1, 5, 6]. However, only recently, a number of studies have appeared in which the existence of self-associates was taken into account in calculating particular systems [7, 8]. In [9‐14], it was shown that the consideration of the self-association, even in the case of allowance for only the configurational contribution into entropy, is sufficient to qualitatively explain features of the thermodynamic properties of the process of melting metals and of thermodynamic characteristics of melting and mixing liquid eutectic alloys. The successful use of self-associates in calculating properties of pure metals and simple eutectics makes it possible to assume that, in multicomponent melts, associates with an arbitrary stoichiometry can also exist. If we admit the existence of such associates, then, evidently, their effect must first of all be manifested in systems characterized by infinite solubility in the solid and liquid phases. However, for both simple eutectics and systems containing a stable compound in the solid phase, the consideration of associates with an arbitrary stoichiometry may, in principle, affect the magnitudes of calculated properties, as well as the qualitative pattern of their behaviors. The goal of this study is to develop a general scheme that takes into account associates with an arbitrary stoichiometry in the model of an ideal association solution and to analyze the effect of these associates on the behavior of the thermodynamic characteristics of mixing and on a position of the liquidus line. We now consider a binary system A c B 1 — c whose components in the liquid phase form a solution with the complete mutual dissolution. We present this solution as an ideal solution consisting of the A n ( i ), B n ( j ) , and A n B m ( i , j , q ) associates. (Here, n and m are the numbers of corresponding atoms in the complex and i , j , and q are, respectively, the numbers of nearest-neighbor pairs of the AA, BB, and AB types in the complex.) Next, we assume that the energy of the complex is determined by the sum of energies of the nearest-neighbor pairs and restrict our consideration by only configurational contributions into the entropy. Then, the molar fractions of the complexes are related to each other by the following equations [10]: