Calculating activities from the phase diagram involving an intermediate compound using its entropy of formation
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I.
INTRODUCTION
CALCULATING activities from phase diagrams is one method to obtain activity data. 1'2 This method has made some progress during the past several decades. In the early stages, the calculation of activities from phase diagrams was limited to simple eutectic systems. 3'4 In 1940, Hauffe and Wagner 5 extended this method to phase diagrams containing intermetallic compounds. Chipman 6 used their formula to calculate activities of silicon in iron-silicon alloy. However, it was not accurate and could be used only for compositions near the compound. About ten years later, Richardson 7 offered another method for this kind of phase diagram. He used the BzO3-CaO system as an example and calculated activity values, from which it may be seen that this method is not precise and requires having a series of intermediate compounds which should be closer to each other. Those requirements prevent us from applying his method extensively. Two advances were made in 1964 for this kind of phase diagram. One was contributed by Chou, 8 who suggested a method to calculate activity coefficients based on the Gibbs energy of formation of the compound. Another was offered by Steiner, Miller, and Komarek. 9 Both methods worked well under different known conditions. However, the former has some inherent integration difficulty, and the latter needs more information about partial molar enthalpy of components; besides, the procedures for evaluation of dT/dN2 at phase boundaries may introduce large errors. In order to overcome the inherent integration difficulty appearing in Chou's method and extend this method to fit any type compound, in 1965, one of the present authors m developed a method that requires the Gibbs energies of formation of the compounds to be known. The procedures are also cumbersome. In this paper, a new method for calculating activities from phase diagrams involving a series of intermediate compounds is presented, in which temperature is used as the integral variable, and the entropy of formation of the
KUO-CHIH CHOU (Zhou Guo-zhi) is Professor, Department of Physical Chemistry, Beijing University of Iron and Steel Technology, Beijing, People's Republic of China. JIAN-JUN WANG, former Student in the Department of Physical Chemistry, Beijing University of Iron and Steel Technology, Beijing, People's Republic of China, is Assistant Engineer of Ma-Tou Aluminium Factory, Han-Dan, Hao-Bei Province, People's Republic of China. Manuscript submitted February 5, 1985. METALLURGICALTRANSACTIONSA
compounds is taken as known instead of other thermodynamic functions.
II.
DERIVATION OF F O R M U L A
For a binary system A-B which contains an intermediate compound A,~B~ (Figure 1), the standard Gibbs energy of formation is equal to AG ~ = RT In X~X~ + RT In y ~ y ~
[1]
where Yl, Y~ indicate the activity coefficients of components A and B, respectively, at the composition X~, Xz (mole fraction) along the liquidus (Figure 1). Assuming that the dependence of activity coefficients on temperature T observes the regular solution
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