### Thermodynamic modelling of solution and ordered phases

I. Ansara
1998 Pure and Applied Chemistry
Thermodynamic calculations are successfully used to predict multiphase equilibria or to analyse industrial processes. Different models have been used to evaluate the thennodynamic behaviour of the solution phases, non-stoichiometric compounds with different structures, or phases which present order-disorder transformations. The most common models which are used will be briefly described. The mathematical equivalences between some of them will be emphasized. Introduc tion In recent years, a
more » ... effort was made to represent the thermodynamic properties of solution substitutional phases as well as ordered ones. Many models, empirical or derived from statistical thermodynamics have been published. For solid phases, the models are more and more based on the knowledge of the crystal structure. It is not the aim of this contribution to list all of them but to discuss the mathematical equivalences which can be observed among certain of them, especially for those which have been applied to multcicomponent systems. Substitutional Solutions Power series expansions have been used to describe the thermodynamic behaviour of substitutional solutions by Margules (ref. 1). Since then Redlich and Kister (ref. 2), Esdaile (ref. 3), Sharkey (ref. 4) , Bale and Pelton (ref. 5 ) and Tomiska (ref. 6) used different fomulations listed in Table 1. Conversion matrices of the coefficients have been established (ref. 7,8). Krupkowski's (ref. 9) empirical equation presents a dissymmetry and it is equivalent to Hoch-Arpshofen's equation (ref. 10) which related the interaction parameter to the interatomic bonding strength with respect to the molar fraction of the component with smaller binding capacity. These power series have been extended to multicomponent systems. However, for such systems, Hillert (ref. 7) suggested that the following composition variable be used: m "ij = (1 + (1m ) q -&)/m (1) Its advantage is that C vij = 1 whatever the order of the system, and a certain symmetry for the j # i mole fractions is introduced. Instead of using molar fractions as composition variables, volume fractions were employed like in the equations suggested by Van Laar (ref. ll), Scatchard-Hamer (ref. 12), Flory-Huggins (ref. 13,14), Wohl(ref. 15), and Wilson (ref. 16). Van Laar, Scatchard-Hamer and Wohl equations are equivalent analytically as seen in Table I . All these equations were used to represent the thermodynamic properties of binary and ternary organic mixtures but very seldom for metallic solutions. This is also the case for the Non-Randon Two Liquid equation (NRTL) developed by Renon and Prausnitz (ref. 17). 449