Three-Component Ternary Phase Diagrams

Three-Component (Ternary) Phase Diagrams 3.1.4.1 Composition of a Ternary Compound... 

Also, the phases formed in the course of discharge of an electrode with three or more components may be readily detected by reading the equilibrium cell voltage. As an example, the determination of the quite complex ternary phase diagram of the system Li-In-Sb is shown in Fig. 8.9. In this case, plateaux are observed in the presence of three-phase equilibria. In order to obtain the complete phase diagram it is necessary... 

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... 

FIGURE 2 Ternary phase diagram used to elucidate ME formation regions. Each of the three corners represents 100% of the individual components. Apex S = 100% w/w surfactant (0% oil and water), apex W = 100% w/w water (0% oil and surfactant), and apex O = 100% w/ w oil (0% water and surfactant). The three lines joining the corner points represent two-component systems. The area within the triangle represents all possible combinations of the three components. 

The phase behaviour of a mixed biopolymer solution is quantitatively characterized by a phase diagram, which graphically describes the boundary conditions of phase separation, the partitioning of the components between the phases and the effects of different variables (temperature, pH, salt concentration, etc.) on the phase behaviour of biopolymers. Conventionally, phase diagrams of three-component (ternary) systems are presented in triangular coordinates. However, an excess of solvent water... 

The phase diagrams for some systems are quite simple, like the solubility curve for binary mixtures, whereas for some complex mixtures, it is dilScult to define the degree of supersaturation owing to the large number of crystallizing components present. So it is necessary to make an approximation and represent a complex system on the basis of a ternary phase diagram of only three prominent components. The phase boundaries obviously depend on the number of components present, and these are explained in the sections that follow. 

Ternary phase diagrams relate the phases to temperature in a three-component system, and the four variables to be considered are temperature. 

Figure 8.10 (o) Three-dimensional representation of a ternary phase diagram. (/>) Triangular grid for representing compositions in a three-component system, (c) Two-dimensional representation of part (a) where boundary curves between two surfaces are drawn as heavy lines and temperature is represented by a series of lines corresponding to various isotherms. " (ct) Isothermal section of a ternary system that includes a ternary AO BO and a quaternary phase AO 2MO BO. The compatibility triangles are drawn with solid lines. 

Ternary-phase diagrams are roadmaps for three component systems, where the major difference between them and binary-phase diagrams lies in how the results are presented. In ternary diagrams, the apexes of an equilateral triangle represent the compositions of the pure components, and the temperature appears as contour lines. 

In the absence of special symmetry, the phase mle requires a minimum of three components for a tricritical point to occur. Symmetrical tricritical points do have such s mimetry, but it is easiest to illustrate such phenomena with a true ternary system with the necessary symmetry. A ternary system comprised of a pair of enantiomers (optically active d- and /-isomers) together with a third optically inert substance could satisfy this condition. While liquid-liquid phase separation between enantiomers has not yet been found, ternary phase diagrams like those shown in figure A2.5.30 can be imagined in these diagrams there is a necessary symmetry around a horizontal axis that represents equal amounts of the two enantiomers. 

Although much surfactant-based research has focused on dilute aqueous solutions of snrfactant micelles, they are only a small fraction of the total composition range that may be studied. Phase diagrams have been prepared for a wide range of snrfactant systems containing two or three components, binary and ternary phase diagrams. 

---