Phase diagram for a ternary system

Figure 11-12. a) Gibbs phase diagram for a ternary system with a miscibility gap. Tie lines and reaction path between (A,B) and C are indicated, b) Possible reaction paths near and across the miscibility gap. Starting compositions of the reaction couple are indicated (o) in Figure a. (Stable and unstable morphologies see text.)... 

Figure 3.10 Example of a phase diagram for a ternary system used to create a dynamic LLC system. Components Ethanol (EtOH), Acetonitrile (ACN) and Iso-octane (2,2,4-trimethylpentane TMP). I — V nodal lines. Circles compositions determined experimentally by titration (full circles) and GC (open circles). Figure taken from ref. [315]. Reprinted with permission.

Shen H, Eisenbeig A (1999) Morphological phase diagram for a ternary system of block copolymer PS310-h-PAA52/Dioxane/H2O. J Phys Chem B, 103 9473-9487... 

H. Shen and A. Eisenberg, morphological phase diagram for a ternary system of block copolymer PS3io-fo-PAA52/dioxane/H20 /. Phys. Chem. B., 103, 9473-9487 (1999). 

A ternary system is one with three components. We can independently vary the temperature, the pressure, and two independent composition variables for the system as a whole. A two-dimensional phase diagram for a ternary system is usually drawn for conditions of constant T and p. 

Figure 4.23 Synthesis space diagram for a ternary system composed of tetraethylorthosilicate (TEOS), cetyltrimethylammonium bromide (CTAB), and sodium hydroxide (H, hexagonal phase [MCM-41] C, cubic phase [MCM-48] L, lamellar phase [MCM-50] H20/Si02 = 100, reaction temperature 100°C, reaction time 10 days). (Reprinted from Science, Vol. 267, A. Firouzi, D. Kumar, L.M. Bull, T. Besier, R Sieger, Q. Huo, S.A. Walker, J.A. Zasadzinski, C. Glinka, J. Nicol, D.l. Margolese, G.D. Stucky, B.F. Chmelka, Cooperative Organization of Inorganic-Surfactant and Biomimetic Assemblies, pp. 1138-1143. Copyright 1995. With permission of AAAS.)...

To determine the complete phase diagram of a ternary system as a function of temperature, at least a three-dimension diagram is necessary. Such diagrams are unfortunately quite difficult to visualize and it is often preferable to reduce the diagrams to two dimensions by keeping the concentration of some of the components constant. Some results for the BE-H2O phase diagram as a function of temperature for fixed quantities of DEC are shown in Fig. 4. In this diagram the mole fraction of BE refers to the binary system... 

Meijering was probably the first person to attempt the calculation of a complete ternary phase diagram for a real system such as Ni-Cr-Cu (Meijering 1957). This... 

Figure 11.6 shows an example of the phase diagram for a reactive system, in which a compound C is formed from components A and B. An isothermal cut and the polythermal projection are also shown. Such a phase diagram can be obtained via a reaction invariant projection of a higher-dimensional simple eutectic phase diagram. AS and BS are binary nonreactive eutectics, since their presence is not affected by the reaction, while ACSb and BCSa are ternary reactive eutectics. Similar... 

The phase diagram of a ternary system in which the three species do not form solid solutions with each other and the constituent binary systems form eutectics, is shown in Figure 4(b). The temperatures A B and Tc correspond to the melting points of A, B, and C, respectively. The vertical faces of the prism represent the temperature-concentration behavior of the three binaries. Note that the behavior of each binary system is that shown in Figure 2d. The solidus lines are not shown for the sake of clarity. Points E g, E j. are the eutectic points of the three binary... 

Conditions for the thermod3mamic stability of an acid salt, MHXg, are usefully systematized in the isothermal phase-diagram for the ternary system HgO—HA—MX. When there is no stable acid salt, the triangular diagram takes on the form shown in Fig. 1 (a). The point A represents the solubility of the acid in water, and the curve AB the effect on this solubility of adding the salt MX to the solution C represents the solubility of this salt in water and CB the effect of added acid on this solubility. 

Fig.l Phase diagram for a ternary symmetric A + B + AB blend from Monte Carlo simulations of the bond fluctuation model as a function of the incompatibility parameter XN and the homopolymer volume fraction chain length of aU three species is equal, N = 32 corresponding to = 91. 20 denotes a region of two-phase coexistence between an A-rich and a B-rich phase, 30 one of three-phase coexistence between an A-rich, a B-rich, and a lamellar phase. Slice through the three-dimensional system of linear dimension L = 4.7J e and three periodic images are shown on the left hand side. From [60]... 

Let us consider the influence of alloying a binary system with a third component on the formation of the diffusion zone in a ternary system [8, 9]. We analyze a case for an Al-Cd-Mg-hke phase diagram of a ternary system (Figure 9.1). In the phase diagram there are two sohd solutions rj (diluted solution of B and C in A) and a (unlimited solubihty of B and C in each other and the negligible solubihty of A in them). There are also two binary intermediate phases p (the solubihty hmits are c L id c j ) and y (with and Cgg, respectively). The intermediate phases are in equihbrium with the y-phase and the a-phase. 

Figure 9.8 Isothermal cross section of the phase diagram for the ternary system chosen as a model of investigation.

Li and L2 can be described by considering the phase diagram of a ternary system of water-surfactant-cosurfactant system, as shown in Figure 13.20 for water-ionic sulphate-long-chain alcohol system. 

A typical phase diagram of a ternary system of water, ionic surfactant and long-chain alcohol (co-surfactant) is shown in Figure 15.5. The aqueous micellar solution A solubilizes some alcohol (spherical normal micelles), whereas the alcohol solution dissolves huge amounts of water, forming inverse micelles, B. These two phases are not in equilibrium, but are separated by a third region, namely the lamellar liquid crystalline phase. These lamellar structures and their equilibrium with the aqueous micellar solution (A) and the inverse micellar solution (B) are the essential elements for both microemulsion and emulsion stability [3]. 

Figure 17.2. A sequence of isothermal schematic phase diagrams of a ternary system L denotes the liquid microemulsion phase, W and O are essentially pure water and oil phases, respectively, while L -f O is the Winsor I, L + W is the Winsor II and W + L + O is the Winsor III equilibrium. For nonionic surfactant-water-oil systems, the sequence from (a) to (i) is obtained with increasing temperature...

Figure 2.11 Phase diagrams for the ternary systems at 20° C (a) Sodium...

Racemic Compound System Figure 56.19 shows a ternary phase diagram for a racemic system at temperature T in an achiral solvent L when no solvates are formed. Points A and A represent the binary solutions saturated with pure enantiomer S and R. respectively. Points E and E (eutectic points) correspond to the solution compositions when the three phases exist in equilibrium racemic compound (r), one enantiomer (5 or R). and the saturated solution. When the starting material, represented by point PI, has an ee lower than the eutectic ee, the desired enantiomer (5) can be enriched in the liquid phase, and the ee of the product will be the same as the ee values of the eutectic point (cceu) if the system composition remains in region rES. The highest yield (yield is defined here as the ratio of amount of desired enantiomer S in the supernatant to the amount of S in the total system) for a product with ee u is obtained when the system composition is shifted firom PI to Ml, the intersection point of lines LPl and rE. 

This concept has also been demonstrated at ambient temperature in the case of the Li-Sn-Cd system [47,48]. The composition-de-pendences of the potentials in the two binary systems at ambient temperatures are shown in Fig. 15, and the calculated phase stability diagram for this ternary system is shown in Fig. 16. It was shown that the phase Li4 4Sn, which has fast chemical diffusion for lithium, is stable at the potentials of two of the Li-Cd reconstitution reaction plateaus, and therefore can be used as a matrix phase. 

In practice, for a ternary system, the decomposition voltage of the solid electrolyte may be readily measured with the help of a galvanic cell which makes use of the solid electrolyte under investigation and the adjacent equilibrium phase in the phase diagram as an electrode. A convenient technique is the formation of these phases electrochemically by decomposition of the electrolyte. The sample is polarized between a reversible electrode and an inert electrode such as Pt or Mo in the case of a lithium ion conductor, in the same direction as in polarization experiments. The... 

A schematic illustration of the method, and of the correlation between binary phase diagram and the one-phase layers formed in a diffusion couple, is shown in Fig. 2.42 adapted from Rhines (1956). The one-phase layers are separated by parallel straight interfaces, with fixed composition gaps, in a sequence dictated by the phase diagram. The absence, in a binary diffusion couple, of two-phase layers follows directly from the phase rule. In a ternary system, on the other hand (preparing for instance a diffusion couple between a block of a binary alloy and a piece of a third... 

Experimental phase diagrams of CO2 with ethyl acetate [37] and alkyl carbonates [38] are also available. Molecular simulations that describe the binary phases diagrams of many organic solvents with CO2 were also recently published [39], Binary phase diagrams of methanol with fluoroform are also available [40], At any given pressure and temperature, fluoroform is more miscible with methanol than CO2. Ternary phase diagrams for a number of systems are also available, such as methanol/H20/C02 [41] acetonitrile/H20/C02, and methanol/H20/fluoroform [40]. 

Fig. 11.6. Ternary phase diagram for a system with compound formation.

For a ternary system, the phase diagram appears much like that in conventional liquid-liquid equilibrium. However, because a SCF solvent is compressible, the slopes of the tie lines (distribution coefficients) and the size of the two-phase region can vary significantly with pressure as well as temperature. Furthermore, at lower pressures, LLV tie-triangles appear upon the ternary diagrams and can become quite large. 

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