Regular solution ternary

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

A fourth, and perhaps more realistic approximation for G x in a ternary solution, may he derived hy combining three suh-regular binary mixing terms, weighted in proportion to the molar composition ... 

Given a nonionic solute that has a relatively low solubility in each of the two liquids, and given equations that permit estimates of its solubility in each liquid to be made, the distribution ratio would be approximately the ratio of these solubilities. The approximation arises from several sources. One is that, in the ternary (solvent extraction) system, the two liquid phases are not the pure liquid solvents where the solubilities have been measured or estimated, but rather, their mutually saturated solutions. The lower the mutual solubility of the two solvents, the better can the approximation be made. Even at low concentrations, however, the solute may not obey Henry s law in one or both of the solvents (i.e., not form a dilute ideal solution with it). It may, for instance, dimerize or form a regular solution with an appreciable value of b(J) (see section 2.2). Such complications become negligible at very low concentrations, but not necessarily in the saturated solutions. 

It should be noted that the regular solution model has been extended to ternary alloys and applied successfully for systems for which interactions cause positive deviations from ideality (Joud et al. 1974). 

Phase diagrams are calculated from these data using regular solution or other appropriate solution models. Some of the great strengths of the CALPHAD approach are that it provides immediate, approximate diagrams for new systems of interest and that it can be readily extended to ternary and higher order systems that would be prohibitively complex and expensive to study experimentally. A comparison of the... 

As an example of the application of the above formulae let us examine the behaviour of a strictly regular solution. In a ternary regular solution we have... 

For example, if a= - 10, j8 = 0, y = 0, this equation is that of a closed curve inside the composition triangle. For these values of the coefficients, the immiscibility curve will therefore also consist of a closed ring inside the triangle. The existence of such closed miscibility gaps, which are observed for example with the Cu + Au + Ni system, can therefore be interpreted in terms of regular solution theory without introducing any specifically ternary factor. 

Barton"" " provides empirical methods based on solubility parameters for ternary solvent systems. All these methods provide only a qualitative idea on miscibility. The combination of regular solution theory and solubility parameters has been employed for predicting the partition coefficients of organic compounds between water and polystyrene and between alcohols and polyolefins. The results are useful to a first approximation. 

Here 6, = FitOi is the monolayer coverage, Fi is the adsorption, n = yo - y is the surface pressure, yo is the surface tension of solvent, n, = coj/too, and coo are the partial molar surface areas of the surfactant and solvent, respectively, bi is the adsorption constant, Cj is the surfactants concentration in the solution bulk. The Frumkin parameters ai and a2 represent the interactions of components 1 and 2 with the solvent, while the parameter ai2 accounts for interactions between the two surfactants 1 and 2 in the ternary regular mixture (see Eq. 2.32) a,=HJ,/RT aj=HJ2/RT a,2=(Ho,+Ho2-HJj)/2RT, where Hy=A,jRT. Choosing the dividing surface after Lucassen-Reynders (cf. Chapter 2), one can eliminate the contributions from the entropic non-ideality of the solvent, thus reducing Eq. (3.27) to a much simpler form... 

The first attempt to calculate phase equilibria in this system on the flrermodynamic basis (Calphad meflrod) was made by [1974Kir] who was able to reproduce the a--y equilibrium data between 750°C and 950°C based on their analysis of the previous evaluations of the Fe-Mn and Cr-Fe systems [1973Kir]. They introduced the regular solution parameters L for a and y phases of tire Cr-Mn system and parameters L for the a and y phases of the Cr-Fe-Mn system, but flrey did not attempt to evaluate tire binary parameters for the Cr-Mn system from any information on fliis binary system. They used aU four parameters to describe their experimental information which was confined to the Fe rich comer of tire ternary system. For reconciling the calculation results with experiment flrey had to introduce the temperature dependence of Are obtained parameters which is so strong that seems to be non-physical. 

MAG Maghsoud, Z., Famili, M.H.M., and Madaeni, S.S., Phase diagram calculations of water/tetrahydrofuran ly(viityl chloride) ternary system based on a compressible regular solution model, Iran. Polym. J., 19, 581,2010. 

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