Ternary Solid-Liquid Equilibria

The combination of Eqs. (24)-(27) with the equation for the solid-liquid equilibrium provides a relation for the solubility of a solute forming a dilute solution in a ternary mixture. 

Equilibrium calculations for electrolyte solutions include speciation equilibrium, vapor-liquid equilibrium, solid-liquid equilibrium, and liquid-liquid equilibrium. As an example of the first three types of equilibria, we will consider the ternary H2O-NH3-CO2 system. 

Fig. 13.10. Solid-liquid equilibrium surfaces for Ternary System forming eutectic (p = constant).

Sandro RPdR, Olivera JVd, Avila SGD. A three-phase ternary model for CO2-solid-liquid equilibrium at moderate pressures. J Supercrit Fluids 1996 9 ... 

Solid-Liquid Equilibrium in Ternary Group III-V Semiconductor Materials... 

AC or BC, which melts at a higher temperature than either of the pure elements (except for the InSb-Sb case). The binary phase diagram consists of two simple eutectic systems on either side of the compound (e.g., the A-AC and the AC-C systems). The third binary phase diagram represents solid-liquid equilibrium between elements from the same group. In Figure 1 the A-B portion of the ternary phase diagram is depicted as being isomorphous... 

The solid-liquid equilibrium state of the A-B-C ternary system is calculated by equating the temperature and pressure of each phase as well as the chemical potentials of each of the species present in both phases. In addition to these equations, a constraint of stoichiometry is placed on the solid solution the sum of the mole fractions of the Group III elements must be equal to the sum of the mole fractions of the Group V elements. Because of this constraint, the chemical potentials of the three species are not independently variable in the solid. The ternary solid solution A B C can be treated as if it were a binary solution of components and BC. The requirement of equal chemical potentials of each of the species present in both phases then becomes... 

P8.10 Determine the solid-liquid equilibrium temperature of the ideal ternary system m-xylene (l)-o-xylene (2)-p-xylene (3) for a composition ofxi = 0.1 and X2 =0.1 with the help of the melting temperatures and enthalpies of fusion given in Example 8.4 in the textbook. Which component will crystallize ... 

Figure 26 shows the ternary phase diagrams (solubility isotherms) for three types of solid solution. The solubilities of the pure enantiomers are equal to SA, and the solid-liquid equilibria are represented by the curves ArA. The point r represents the equilibrium for the pseudoracemate, R, whose solubility is equal to 2Sd. In Fig. 26a the pseudoracemate has the same solubility as the enantiomers, that is, 2Sd = SA, and the solubility curve AA is a straight line parallel to the base of the triangle. In Figs. 26b and c, the solid solutions including the pseudoracemate are, respectively, more and less soluble than the enantiomers. 

Heteroepitaxy. Heteroepitaxy (e.g., deposition of Al Ga As on GaAs) is somewhat different, because the solid and liquid cannot initially be in equilibrium, that is, a chemical potential difference exists across the solid-liquid interface. In compound semiconductors, the chemical potential of each element is constrained by compound stoichiometry. For example, for a ternary solid (A B C) in equilibrium with a ternary liquid, the conditions of equilibrium are given by equations 8 and 9 ... 

The ternary-phase diagrams presented here illustrate only a small sample of the variety of equilibrium behaviors observed in solid-liquid equilibria in three-component systems. This subject, along with kinetic considerations make up much of the subject matter of a variety of fields, including metallurgy and... 

The two liquids thus formed are immiscible, but in thermodynamic equilibrium. Therefore, we may speak of a dynamic system of two immiscible phases. Figure 3.10 shows an example of a practical system applied to create a dynamic LLC phase system. A practical phase system can be created by pumping a mobile phase through a column, the composition of which corrresponds to a ternary mixture that is in dynamic equilibrium with another mixture (the two mixtures can be connected by a nodal line). If the mobile phase is the more polar one of the two ternary mixtures in equilibrium, then a non-polar (hydrophobic) solid support must be used and a reversed phase system can be generated. If the mobile phase is the less polar of the two mixtures in equilibrium, a polar support is required. 

Figure 25 Comparison of predicted liquid mole fraction X3 of different solid solutes for ternary S-L equilibrium with CO2 dissolution from PMVF of solvent in binary mixtures by Eq. (50) with experimental mole fractions of (a) naphthalene in toluene solution at 298 K (56), (b) phenanthrene in toluene solution at 298 K (56), (c) p-carotene in ethyl acetate solution at 298 K (52), (d) p-carotene in toluene solution at 298 K (50), (e) cholesterol in acetone at 308 K (53), (f) cholesterol in acetone solution at 318K (53), (g) acetaminophen in n-butanol solution at 298 K (50), (h) salicylic acid in 1-propanol solution at 303 K ( sA = 0.132), experimental (58), (i) salicylic acid in 1-propanol solution at 288 K (XsA = 0.132) (58), (j) salicylic acid in 1 -propanol solution with at 288 K (XsA = 0.144) (58).

Mukhopadhyay M, Dalvi SV. A new thermodynamic method for solid-liquid-vapor equilibrium in Ternary systems from binary data for antisolvent crystallization. Proceedings of the 6th International Symposium, France, April 2003. 

In Figure 1 a simplified process scheme of the antisolvent crystallization of sodium chloride is displayed. The process is divided into three steps the crystallization, the solid-liquid separation and the antisolvent recovery or liquid-liquid separation. In the first step sodium chloride is crystallized by mixing the feed brine with an antisolvent. The crystallization is carried out at temperatures below the liquid-liquid equilibrium line in the single liquid phase area (see Figure 2). In the second step the crystals are separated from their mother liquor, e.g. by filtration or in a centrifuge. In the third and final step the antisolvent is separated from the water phase at a temperature above the liquid-liquid equilibrium line in the two liquid phase area, in which the ternary amine-water-salt system splits up into an amine and an aqueous phase. The recovered antisolvent is recycled within the process and most ideally the water phase is reused for the dissolution of crude sodium chloride. In this paper the crystallization and the liquid-liquid separation steps will be treated. 

Since concentrations xj, X2, X3 represent equilibrium values (i.e. concentrations in the bulk phase after adsorption takes place) it is impossible to prepare the original samples of ternary solutions in such a way that the X2/X3 ratio stays constant without prior knowledge of the adsorption isotherm. This is the reason that adsorption isotherms seem to depend on the solid/liquid ratio in the system. An increase in the amount of the solid phase increases the total amount of surfactants adsorbed, which results in a change of X2/X3 ratio and a shift of the experimental point on the adsorption isotherm surface. Obviously, this effect is more pronounced in systems with large differences in individual surfactant adsorption characteristics. 

It is clear that Xj falls between zero and one (1 > X/ > 0). When x/= 1, we have unity for the transformed variable X/ = 1 and, similarly, x = 1 gives X/ = 0. Consider the ternary space in Figure 6.16a where the solid line represents the chemical equilibrium line and the dashed line is the corresponding vapor line (in vapor liquid equilibrium with liquid composition in the chemical equilibrium line). The transformation of... 

---