Types of 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 binary system lead-thallium shows an unusual type of phase diagram. Fig. 1, taken from Hansen (1936), represents in the main the results obtained by Kumakow Pushin (1907) and by Lewkonja (1907). The liquidus curve in the wide solid-solution region has a maximum at about 63 atomic percent thallium. The nature of this maximum has not previously been made clear. 

On an atomic basis, Li is much more soluble in K than vice versa (0.07, 0.43, 1.29 and 1.99 mol% Li compared with 0.007, 0.02, 0.05 and 0.07 mol% K). Although these solubilities are larger than those given by eqs. (a) and (b), both investigations point to a two-immiscible-liquid-type of phase diagram with a consolute T > 1000°C, and with the consolute composition being on the Li-rich side as in the Li-Na system. 

An equilibrium exists between a liquid and its vapor. This is just one of several equilibria that exist between the states of matter. A phase diagram is a graph representing the relationship of all the states of matter of a substance. One type of phase diagram relates the states to temperature and pressure. This type allows us to predict which state of matter will exist at a certain temperature and pressure combination. Figure 11-1 shows a general form of a phase diagram. 

Partial pressure as a variable. As mentioned in 2.1, many types of thermodynamic variables may be used in the construction of phase diagrams. The various rules of construction, based on the laws of chemical thermodynamics, which apply to the different types of phase diagrams have been discussed in several books and papers (for instance, Pelton and Schmalzried 1973, Okamoto 1991, Pelton 1991). Following a classification proposed by Pelton, the various, bidimensional, phase diagrams may be subdivided into three types as follows ... 

Two types of phase diagrams, which are of great technological importance, derive from the simpHfication that the interaction parameter varies Hneary with the inverse of temperature ... 

Connections to other types of phase diagrams can be obtained if order parameters are exchanged for intensive variables. Figure 17.2 is replotted with the order parameter V as the ordinate in Fig. 17.36. The diagram predicts the phases that would exist for a molar volume fixed by a rigid container at different temperatures. The tie-lines connect equilibrium molar volumes at the same temperature... 

We may extract a considerable amount of information from this type of phase diagram. Let s consider the case represented by the pointp in the following figure. We know that this point is in the primary field of A in which pure solid A coexists with liquid. When an isothermal line passing the point of interest (p) is constructed, the point r represents the composition of the liquid phase which exists in equilibrium with pure solid A represented by the point q. The isothermal line qr which connects the compositions of the two phases that coexist in equilibrium is called the tie line. 

Now we consider another type of phase diagram as shown below ... 

Liquid-crystalline solutions and melts of cellulosic polymers are often colored due to the selective reflection of visible fight, originating from the cholesteric helical periodicity. As a typical example, hydroxypropyl cellulose (HPC) is known to exhibit this optical property in aqueous solutions at polymer concentrations of 50-70 wt%. The aqueous solution system is also known to show an LCST-type of phase diagram and therefore becomes turbid at an elevated temperature [184]. 

Fig. 3.13 Schematic drawing of two different types of phase diagram of a lipid membrane caused by foreign molecules. Type I Substantial freezing-point depression and a wide...

Finally, we refer the reader to Fig. 3.15.9 for a study on how the diagram of part (f) arises. More complex types of phase diagrams will not be explored here, but the general methodology should be clear from the preceding examples. 

Phase behavior of solution systems depends on the nature of the interactions between the two components. Although numerous types of phase diagrams can be found in nature (and foods), many systems of importance in foods exhibit eutectic... 

Figure 11. Examples of various types of phase diagrams which would produce much different mobility control effects.

In conclusion, the same phase behavior is evidenced when we change the alcohol or the W/S ratio in a quaternary system, and the oil in a ternary system. This behavior can be characterized by two types of phase diagrams. In the first type no critical point occurs. In this case, the inverse micellar phase is bounded by a two-phase region where it is in equilibrium with a liquid crystalline phase. 

The consequence of the above considerations is that binary systems of alkali metal halides form different types of phase diagrams, starting with the simple eutectic ones through the solid solution eutectic ones, the phase diagrams with the formation of a binary compound up to those with complete solid solubility. Tables 2.4 and 2.5 summarize the main features of individual phase diagrams. 

System Type of phase diagram Compound System Type of phase diagram Compound... 

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