Three-component phase diagram: examples

Naturally, the results can be represented by a diagram similar to a three-component phase diagram, as shown in Fig. 5.10. Several interesting features are worth noting. First, when the m = 0 or state dominates, a large, positive enhancement is expected. The condition for a substantial enhancement is quite broad. For example, when the condition > 1.21 Di -i- 0.21D21 is satis-... 

The temperature-composition phase diagrams of these PEO + PDMS mixtures all show an upper consolute temperature and selected examples are given in Figure 3.4. Figure 3.5, on the other hand, shows selected examples of the three-component phase diagrams, with toluene as component 3, at a fixed temperature of 30 C. 

Three-Phase Transformations in Binary Systems. Although this chapter focuses on the equilibrium between phases in binary component systems, we have already seen that in the case of a entectic point, phase transformations that occur over minute temperature fluctuations can be represented on phase diagrams as well. These transformations are known as three-phase transformations, becanse they involve three distinct phases that coexist at the transformation temperature. Then-characteristic shapes as they occnr in binary component phase diagrams are summarized in Table 2.3. Here, the Greek letters a, f), y, and so on, designate solid phases, and L designates the liquid phase. Subscripts differentiate between immiscible phases of different compositions. For example, Lj and Ljj are immiscible liquids, and a and a are allotropic solid phases (different crystal structures). 

Take the silica-alumina system as an example. It is convenient to treat the components as the two pure oxides SiOj and AI2O3 (instead of the three elements Si, A1 and O). Then the phase diagram is particularly simple, as shown in Fig. 16.6. There is a compound, mullite, with the composition (Si02)2 (Al203)3, which is slightly more stable than the simple solid solution, so the alloys break up into mixtures of mullite and alumina, or mullite and silica. The phase diagram has two eutectics, but is otherwise straightforward. 

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... 

An interesting example of a one-component systems is SiOa, which can exist in five different crystalline forms or as a liquid or a vapor. As C = 1, the maximum number of phases that can coexist at equilibrium is three. Each phase occupies an area on the T P diagram the two-phase equilibria are represented by curves and the three-phase equilibria by points. Figure 13.1 (2, p. 123), which displays the equUi-brium relationships among the sohd forms of Si02, was obtained from calculations of the temperature and pressure dependence of AG (as described in Section 7.3) and from experimental determination of equUibrium temperature as a function of equilibrium pressure. 

Much of what we need to know abont the thermodynamics of composites has been described in the previous sections. For example, if the composite matrix is composed of a metal, ceramic, or polymer, its phase stability behavior will be dictated by the free energy considerations of the preceding sections. Unary, binary, ternary, and even higher-order phase diagrams can be employed as appropriate to describe the phase behavior of both the reinforcement or matrix component of the composite system. At this level of discussion on composites, there is really only one topic that needs some further elaboration a thermodynamic description of the interphase. As we did back in Chapter 1, we will reserve the term interphase for a phase consisting of three-dimensional structure (e.g., with a characteristic thickness) and will use the term interface for a two-dimensional surface. Once this topic has been addressed, we will briefly describe how composite phase diagrams differ from those of the metal, ceramic, and polymer constituents that we have studied so far. 

Figure 3.4 shows the water-methanol mobile phase example of a mixture problem. A three-component mixture that must add up to 100% can be represented on a triangular graph, also called a ternary or trilinear diagram (see figure 3.5). When a system is optimized, it is important to be alert for... 

Physical measurements are directly input to the statistical thermodynamics theory. For example three-phase hydrate formation data, and spectroscopic (Raman, NMR, and diffraction) data were used to determine optimum molecular potential parameters (e,o,a) for each guest, which could be used in all cavities. By fitting only a eight pure components, the theory enables predictions of engineering accuracy for an infinite number of mixtures in all regions of the phase diagram. This facility enables a substantial savings in experimental effort. 

The various porcelain types fall into three regions of the phase diagram and will be discussed in turn typical properties are summarized in Table 5.3 and examples of components are illustrated in Fig. 5.19. 

A promising way to create LLC systems with sufficient stability is the use of immiscible ternary mixtures to create what is called a dynamic (or solvent-generated ) LLC system. The principle of such a phase system is illustrated in figure 3.9. This figure shows an example of a thermodynamic phase diagram of a mixture of three components (A, B and C). Both the binary mixtures A + B and A + C are miscible in all proportions. 

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