Binary Immiscibility Diagrams

6 APPLICATION OF IMMISCIBILITY DIAGRAMS 6.1 Binary Immiscibility Diagrams 

Figrue 4.8 Metastable immiscibility diagram for the sodium silicate system 

Reheating of glasses to temperatures above Tg and within the immiscibility region can often alter their micro structures. If we consider a sodium silicate glass containing 15 mol% soda formed by rapid 

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Only Eu and Yb, among the rare earths, form immiscibility gaps with Sc in the liquid and solid. The difference in valence of these two rare earths and Sc is, perhaps, the main reason of this difference of interaction. The divalent state is more typical for Eu and Yb, whereas the other rare earths are usually trivalent. The same divalent state is characteristic for aUcaline earths which are immiscible with Sc in the liquid and solid too. Therefore, it is possible to predict the same type of binary phase diagrams of Sc with alkaline metals. These elements are even more different from Sc in the valence state and other characteristics (melting temperature, electronegativity, etc.) than are the alkaline-earth metals. 

The phase diagram of a typical binary immiscible system is shown in Figure 15.6, where the spinodal and binodal lines are depicted these two lines can be calculated from the mixing free energy. The spinodal line of a binary system can be calculated from Eq. (15.4), whilst for a ternary system the spinodal line can be calculated from the mixing free energy from the equation as follows ... 

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

Case II. ai3 > oti2- In this case, the tie lines slope toward the 1-3 binary line. This could have been intuitively predicted by considering the limiting case of an immiscibility band across the phase diagram, as shown in Fig. 31C. Of necessity, the tie lines become parallel to either the 1-3 or the 2-3 binary lines in the limit of pure 1-3 binary or pure 2-3 binary, respectively. 

Fig. 11 Defay-Crisp diagram for a binary monolayer A, ideal mixing B, non-ideal mixing C, complete immiscibility. and n2 are the phase transition pressures of components 1 and 2.

All the phase diagrams reported above show a complete mutual solubility in the liquid state. The formation of a single phase in the liquid state corresponds to behaviour frequently observed in intermetallic (binary and complex) systems. Examples, however, of a degree of immiscibility in the liquid state are also found in selected intermetallic systems. Fig. 2.16 shows a few binary systems in which such immiscibility can be observed (existence of miscibility gaps in the liquid state). All the three... 

Figure 2.27. Isothermal section at 307°C of the Al-Zn-Si diagram. The boundary binary systems are shown. The isothermal section at 307°C is marked on the binary Al-Zn diagram. The corresponding single-phase (thick segment) and two-phase regions are indicated in the base edge of the triangle. By additions of Si (immiscible in the solid state in the other two elements) two- and three-phase fields are formed. ( ) = three-phase region. In the two-phase region on the left examples of tie-lines are presented.

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). 

Figure 2 shows a spin-label-derived phase diagram for binary mixtures of (II) and (IV), dipalmitoylphosphatidylcholine and dielaidoylphosphatidylcholine. It will be seen that the diagram describes miscibility of these two lipids in both the solid and solution phases. (Other binary mixtures of lipids show immiscibility in the solid as well as the fluid phases.45,54)... 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (solid line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, Ca , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are C02 -hexane and C02 benzene. More complicated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (liquid—liquid) immiscibility lines, and even three-phase (liquid—liquid—gas) immiscibility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include C02—hexadecane and C02 H20 Class IV, C02 nitrobenzene Class V, ethane— -propanol and Class VI, H20— -butanol. 

Figure 7.11 Schematic T-x phase diagram for a binary A/B solution exhibiting partial immiscibility and liquid-liquid phase separation below the consolute temperature Tc. The horizontal tie-line (heavy solid line) connects the compositions of coexisting A-rich and B-rich liquid phases (small circles) in the lower liquid-liquid coexistence dome. (See text for description of behavior along vertical dashed and dotted lines.)...

Eutectic diagrams (from Greek svtt]ktoo- easily melted ) represent the T-x melting behavior for binary systems with completely immiscible solid phases a, /3. The solid a, /3 phases often correspond to (virtually) pure components A, B, respectively, so we may treat phase and component labels (rather loosely) as interchangeable in this limit. 

A number of additional DTA experiments were undertaken with various compositions within the binary system up to 66.6 at. % S (= MoS2 composition). In Fig. 7 a phase diagram is shown in which all results are incorporated. With respect to the above-mentioned classification of sulfide systems14), the Mo—S system, as well as the Cr—S system, exhibits Type 1 two regions of immiscible liquids one field of liquid immiscibility in the metal-rich portion at high temperatures, and a second two-liquid field in the sulfur-rich region beyond MoS2 which is not shown in Fig. 7. 

Like the other systems above, the W-S system can be treated according to Kullerud s classification scheme for binary sulfides141. Two regions of liquid immiscibility should occur at high temperatures under equilibrium pressure in both the metal-rich and the sulfur-rich portions of the W—S system. This is incorporated in the schematic diagram shown in Fig. 9. 

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