Multicomponent systems, phase diagrams

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

The unary phase diagram is seldom used in solid state syntheses. However, the unary diagram forms the basis for the phase diagrams of multicomponent systems. Since there are no composition variables, the only externally controllable variables in a unary system are simply the temperature and pressure. For this... 

Knowledge of the expressions for the chemical potentials of each of the components allows theoretical prediction of the critical concentration boundaries of the phase diagram for ternary solutions of biopolymeri + biopolymer2 + solvent. According to Prigogine and Defay (1954), a sufficient condition for material stability of this multicomponent system in relation to phase separation at constant temperature and pressure is the following set of inequalities for all the components of the system ... 

While classical phase diagrams provide a powerful methodology for grasping the thermodynamic behavior of few-component systems, it is evident that the restricted 2D or 3D realm of human graphical intuition cannot adequately cope with the complexities of many-component systems. Hence, it is important to find generalized analytical techniques that can accurately represent many-component phase behavior for arbitrary values of c. Such techniques will be considered in the metric geometric representation of multicomponent phenomena (Chapter 12). 

Liquid-Solution Models. The simple-solution model has been used most extensively to describe the dependence of the excess integral molar Gibbs energy, Gxs, on temperature and composition in binary (142-144, 149-155), quasi binary (156-160), ternary (156, 160-174), and quaternary (175-181) compound-semiconductor phase diagram calculations. For a simple multicomponent system, the excess integral molar Gibbs energy of solution is expressed by... 

Paints, adhesives and lubricants are typically multicomponent polymer systems. The behavior of phase-separated blends in the bulk after quenching into the unstable region of the phase diagram is variable. In the bulk, the concentration fluctuations... 

In multicomponent systems, compounds are frequently formed between components. The following phase diagrams are for ABC ternary system forming a binary compound AB which melts congruently, as it is stable at its melting point ... 

Because of its high dimensionality, it is difficult - or even impossible - to view the phase diagram of a multicomponent system in its entirety. For example, an isobaric phase diagram for four components would involve a four-dimensional space. To... 

As demonstrated in the previous section, it is advantageous to obtain a deeper understanding of how to perform projections and cuts for multicomponent reactive systems. A single projection or cut captures only part of the system under consideration. However, the user can form a mental picture of the phase diagram in its entirety by making a sequence of such projections and cuts [6],... 

Pressure-temperature diagrams offer a useful way to depict the phase behaviour of multicomponent systems in a very condensed form. Here, they will be used to classify the phase behaviour of systems carbon dioxide-water-polar solvent, when the solvent is completely miscible with water. Unfortunately, pressure-temperature data on ternary critical points of these systems are scarcely published. Efremova and Shvarts [6,7] reported on results for such systems with methanol and ethanol as polar solvent, Wendland et al. [2,3] investigated such systems with acetone and isopropanol and Adrian et al. [4] measured critical points and phase equilibria of carbon dioxide-water-propionic acid. In addition, this work reports on the system with 1-propanol. The results can be classified into two groups. In systems behaving as described by pattern I, no four-phase equilibria are observed, whereas systems showing four-phase equilibria are designated by pattern II (cf. Figure 3). 

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