A new generation solution model for predicting thermodynamic properties of a multicomponent system from binaries
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TRODUCTION
IN thermodynamic properties, there is an increasing need for various kinds of solutions. It is anticipated that most of the thermodynamic data of ternary and multicomponent systems will come from a theoretical calculation rather than a direct experimentation because of the difficulty of experiments. The solution model used to estimate thermodynamic data could be divided into two categories, a physical model and a semiempirical model. The former model can offer a clear physical picture for the practical solution; however, its application will be limited in a very narrow range because of too many unknown factors and an unclear physical nature. It is still a long way from readiness for practical use, especially for multicomponent systems. The latter model does not concern the exact physical nature; instead, it combines both theoretical considerations and practical thermodynamic data together under a theoretical guidance to develop an applicable model, so that it can give more reasonable data and be suitable for more systems with larger concentration ranges. In the semiempirical model, the method that predicts ternary and multicomponent thermodynamic properties based on the binary ones is the most attractive approach. It is simple, effective, and employs more reliable binary sources that are easily obtained experimentally and theoretically. It is well known that the thermodynamic properties available in ternary and multicomponent systems are incomparable with those in binary systems. This gap will not be getting smaller with the application of new experimental techniques. Therefore, this approach will be particularly meaningful in predicting ternary and multicomponent thermodynamic data. In fact, in past decades it has already KUO-CHIH CHOU and SHOU-KUN WEI, Professors and members, Chinese Academy of Sciences, are with the Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China. Manuscript submitted May 17, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS B
been used extensively in estimating thermodynamic properties and calculating phase diagrams for ternary systems. From 1960 to 1987, around seven examples of this kind of model were introduced.[1–8] They have been summarized by Hilert[7,11] and Ansara[9,10] and can be divided into two categories: symmetrical and asymmetrical models (Figure 1).[7] Along the same lines, from 1987 to 1989, Chou and his group developed many dozens of models.[12–19] A complete summary was given by Chou and Chang,[20] in which they stated that this kind of model can express ternary thermodynamic properties of mixing as a combination of all binaries with an assigned probability weight, as follows: E E E DG E 5 W12DG 12 1 W31DG 31 1 W23DG 23
[1]
where DGE and DGEij represent the ternary and binary excess Gibbs free energies (or other thermodynamic properties) of mixing, respectively, and Wij indicates the weight probability for the corresponding binary, which can be calculated in terms of the following form: Wij 5
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