Ternary phase diagrams, complex

Ternary Alloys. Almost ah commercial ahoys are of ternary or higher complexity. Ahoy type is defined by the nature of the principal ahoying additions, and phase reactions in several classes of ahoys can be described by reference to ternary phase diagrams. Minor ahoying additions may have a powerflil influence on properties of the product because of the influence on the morphology and distribution of constituents, dispersoids, and precipitates. Phase diagrams, which represent equhibrium, may not be indicative of these effects. 

Let us now consider two real ternary systems to illustrate the complexity of ternary phase diagrams in some detail. While the first is a system in which the solid state situation is rather simple and attention is primarily given to the liquidus surfaces, the solid state is the focus of the second example. 

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 diagram shown in Fig. 9b for the schizophyllan-water system has two more phase regions the isotropic-anisotropic (cholesteric)-anisotropic triphasic region (IAA) and the anisotropic-anisotropic biphasic region (AA). This was the first observation of the complex phase diagram as had been predicted by Abe and Flory, but the diagram quantitatively departs from their prediction in the positions and sizes of the regions [76]. 

The thermodynamics of the above-elucidated SiC/C and SijN Si composites are determined by the decomposition of silicon carbide and silicon nitride, respectively, into their elements. The chemistry of ternary Si-C-N composites is more complex. If producing Si-C-N ceramics for applications at elevated temperature, reactions between carbon and silicon nitride have to be considered. Figure 18.2, which exhibits a ternary phase diagram valid up to 1484°C (1 bar N2) displays the situation. The only stable crystalline phases under these conditions are silicon carbide and silicon nitride. Ceramics with compositions in the three-phase field SiC/Si3N4/N are unknown (this is a consequence of the thermal instability of C-N bonds). Although composites within the three-phase field SiC/Si3N4/Si are thermodynamically stable even above 1500°C, such materials are rare. The reasons are difficulties in the synthesis of the required precursors and silicon melting above 1414°C. The latter aspect is of relevance, since liquid silicon dramatically worsens the mechanical properties of the derived ceramics. 

Figure 11.17 Ternary phase diagram of complex coacervation between pRE-luciferase plasmid and chitosan at 55°C in 50 mmol dm No2S04. Sodium sulfate solution was regarded as one component, since the concentration change in the experiment range was minimal. The region to the right of line the ABC depicts the conditions under which phase separation occurs. The concentration ranges in the small grid area yield distinct particles.

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. 

There is a vast body of data concerning the influence of third components on surfactant liquid crystals. Because of the potentially great complexity of the inherent mesophase behaviour, this array of data can appear to be enormously difficult to rationalize. However, if we consider the simple concepts described above (micelle formation, micelle shape/packing constraints, volume fractions and the nature of intermicel-lar interactions), then a reasonably simplified picture emerges, at least for the water-continuous phases. This present section does not attempt to be comprehensive - it simply reports selected examples of behaviour to illustrate the general concepts. The simplest way to show the changes in mesophase behaviour is to employ ternary phase diagrams. The reader should recall that the important factors are (i) the behaviour as a function of surfactant/additive ratio, and (ii) the volume... 

Tan = 1550°C the binary eutectic temperatures 1362°C (quartz-diopside), 1270°C (diopside-anorthite), and 1368°C (quartz-anorthite) and the ternary eutectic temperature of 1200 °C. The composition of the ternary eutectic is 30 mass% quartz, 33 mass% diopside, and 37 mass% anorthite (Clark et al., 1962 Osborn and Tail, 1952). The ternary phase diagram discussed above refers to high-fired calcareous UMtic clays with the four components Si02, AI2O3, CaO, and MgO, but fails to incorporate an important fifth component such as Fe203. Hence, even more complex phase relations must be considered in appropriate multicomponent (quaternary, quinary, hexanary,... multinary) systems. 

More complex changes in the ternary phase diagram with temperature will be encountered in reality as a result of more pronounced differences in the entropy of the crystalline species and numerous non-idealities such as the temperature dependence of their enthalpy and entropy or finite interaction energies in the liquid phase. As a result of this, combinations of congruent melting and incongruent dissolution or vice versa may occur (Figure 12.6). 

Fig. 6 The ternary phase diagram of polybenzyl-trimethyl-ammonium (PVBMA)-polystyrene sodium sulfonate (PNaSS) complex.

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