Three-component systems, phase diagrams

The method of construction of this type of diagram will be illustrated using the general case of the three component system metal-sulphur-oxygen (M-S-O) whose values of AG for the reactions between the various condensed phases are given in Talile 7.37 on page 7 191. 

Fig. 123.—(a) Phase diagram calculated for three-component systems consisting of nonsolvent [1], solvent [2], and polymer [3] taking Xi==X2=l and Xz equal to 10 (dashed curve), 100 (solid curve), and °° (dotted curve) xi2 = xi3 = 1.5 and X23 =0. All critical points (O) are shown and tie lines are included for the xs = 100 curve. (Curves calculated by Tompa. ) (b) The binodial curve for a 3 = 100 and three solvent ratio lines. The precipitation threshold is indicated by the point of tangency X for the threshold solvent mixture. 

For the purpose of investigating solubility relations at a given temperature in three-component systems of the type discussed above, the proportion of nonsolvent which must be added to produce incipient precipitation may be observed as a function of the polymer concentration. Isothermal phase diagrams like that shown in Fig. 123 may... 

Figure 6. Phase diagram of a three-component system consisting of one binary and one ternary compound. Boundary curves are solid and composition lines are dashed. The arrows indicate the direction of falling temperature.

Figure 9. Phase diagram for the three-component system sodium octanoate-n-decanol-water at 20°C (1). Concentrations expressed as weight percent.

Solubilization. Phase Diagrams of Three-Component Systems... 

Fig. 2.20. Phase diagram (at 25 °C) from the work by Ekwall and co-workers (cf. Refs.8 86)) for the three-component system hexadecyltrimethylammonium bromide (CTAB) - hexanol -water. Li denotes a region with water-rich solutions L2 a region with hexanol-rich solutions D and E are lamellar and hexagonal liquid crystalline phases, respectively. In the figure are also schematically indicated the structures of normal (Lj region) and reversed (L2) micelles as well as of the liquid crystalline phases. (From Ref.9Sb...

This process is illustrated in a solubility phase diagram of three-component system as shown in Fig. 7.2b... 

A number of binary systems form sohd compounds of fixed stoichiometry. The phase diagram for an A-B system, which forms a compound A2B, is shown in Fig. 11. Although there are three possible components A, B, and A2B, in this system, they are connected by a chemical equilibrium relationship, and so there are only two independent components. The phase diagram looks like two separate... 

The ternary-phase diagrams presented here illustrate only a small sample of the variety of equilibrium behaviors observed in solid-liquid equilibria in three-component systems. This subject, along with kinetic considerations make up much of the subject matter of a variety of fields, including metallurgy and... 

According to the lever rule, phases A and C will first compose phase F and then phase F decomposes according to the lever rule into phases B and D. The quadrangle rule applies especially in phase diagrams of three-component systems with the formation of a congruently melting compound and in the phase diagrams of reciprocal systems. 

The isobaric phase diagrams of three-component systems are determined by four variables three concentration coordinates and the temperature. With regard to the condition that the sum of mole or mass fractions equals one, it is possible to show these phase diagrams in three-dimensional space, where the concentration coordinates are shown in the x-y plane and the temperature on the z axis. 

Consider the phase diagram of a three-component system of water, ionic surfactant and medium-chain alcohol, as described in Figure 15.4. At the water comer... 

Figure 1 describes three representative phase diagrams for a two-component system [3]. Diagram a has a eutectic point E and the region Z is a homoge-... 

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