Phase diagram representation

The thermodynamic equilibrium between anionic copolymer/cationic copolymer/aqueous medium are given in classical triangular representation. Only the diluted and semidiluted (up to 10% in weight for the total polymer concentration) are studied. 

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With the explicit formula (12.75) for the y coefficients, (12.78)-(12.80) become convenient formulas for the slopes of coexistence"6oundaries in various phase-diagram representations (including those with an extensive axis). Notice in particular that the derivatives (12.78) involving only intensive variables (as plotted in conventional phase diagrams) can be evaluated solely in terms of the 7 coefficients (i.e., in terms of extensive... 

Fig. 23 Phase diagram representation of the crystallite size and yttria concentration dependency of the tetragonal-to-monoclinic transformation temperature [87] (reprinted with permission)...

Sch2] Schultz, A., Chuang, Y.-Y, Chang, Y.A., Three-Dimensional Phase Diagram Representation , Bull. Alloy Phase Diagrams, 6(4), 304-316 (1985) (Calculation, Thermodyn., 20) [1985Spe] Spencer, R, Hack, K., Moser, Z., Zakulski, W., Calculation of the Fcc/Liquid Phase Equilibria in the Cu-Fe-Ni System , Calphad, 9(2), 191-198 (1985) (Thermodyn., Assessment, 31)... 

Figure 2.15 The ternary phase diagram representation. Point M represents the liquid composition with 59% of A, 9% ofB and 32% of C (total 100%). The percentage can be mass, volume or mole percentages.

The relations between the compositions of Pordand cements and some other common hydrauhc cements are shown in the CaO—Si02—AI2O2 phase diagram of Figure 2 (5). In this diagram, Fe202 has been combined with AI2O2 to yield the Al O content used. This is a commonly appHed approximation that permits a two-dimensional representation of the real systems. 

Figure 7.1 Representation of the phase diagram for a pure fluid such as water. The shaded area is the continuum tlirough wliich we can continuously vary the properties of the fluid. The liigh-pressure and liigh-temperature limits shown here are arbittary. They depend only on the capabilities of the experimental apparatus and the stability of the apparatus and the fluid.

Figure 12. A schematic representation of a section of the Li-Mn-O phase diagram (adapted from Ref. (1301).

Figure 3.17. Phase-plane representations of reactor stability. In the above diagrams the point -I- represents a possible steady-state solution, which (a) may be stable, (b) may be unstable or (c) about which the reactor produces sustained oscillations in temperature and concentration.

Fig. 61 a Schematic representation of phase diagram of blend of PS-rich (a) with Pi-rich (/S) PS-fc-PI block copolymer in parameter space of a, and T. Expected morphologies of blend specimen are also sketched at b low and c high temperatures. Note phase diagram is effective only for American Chemical Society... 

Figure 4.12 (a) Gibbs energy representation of the phases in the system Zr02-Ca0 at 1900 K. McaO - MzrO = TSZ n°t deluded for clarity, (b) Calculated phase diagram of the system Zr02 Ca0. Thermodynamic data are taken from reference [9]. 

Non-stoichiometry in solid solutions may also be handled by the compound energy model see for example a recent review by Hillert [16]. In this approach the end-member corresponding to vacancies is an empty sub-lattice and it may be argued that the model loses its physical significance. Nevertheless, this model represents a mathematically efficient description that is often incorporated in thermodynamic representations of phase diagrams. 

Figure lb. Representation of type II and type III systems in the usual ternary phase diagram. 

Figure 2.9. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the liquid state and, at high temperature only, in the solid state. By lowering the temperature, however, the continuous solid solution decomposes into two phases. In (d) a schematic representation of NiAu or PtAu type diagrams is shown as formed by two generic components A and B.

Fig. 5.12 Two different 3-D representations of the phase diagram of 3-methylpyridine plus wa-ter(H/D). (a) T-P-x(3-MP) for three different H2O/D2O concentration ratios. The inner ellipse (light gray) and corresponding critical curves hold for (0 < W(D20)/wt% < 17). Intermediate ellipses stand for (17(D20)/wt% < 21), and the outer ellipses hold for (21(D20)/wt% < 100. There are four types of critical lines, and all extrema on these lines correspond to double critical points, (b) Phase diagram at approximately constant critical concentration 3-MP (x 0.08) showing the evolution of the diagram as the deuterium content of the solvent varies. The white line is the locus of temperature double critical points whose extrema (+) corresponds to the quadruple critical point. Note both diagrams include portions at negative pressure (Visak, Z. P., Rebelo, L. P. N. and Szydlowski, J. J. Phys. Chem. B. 107, 9837 (2003))...

Phase diagrams are often constructed to provide a visual picture of the existence and extent of the presence of solid and liquid phases in binary, ternary and other mixtures of substances. Phase diagrams are normally two-component (binary) representations but multicomponent phase diagrams can also be constructed. Interactions between active substances and excipients can often be evaluated using phase diagrams. 

In a reduced-phase diagram for a two-component system, T = 2 for a single phase and an area is the appropriate representation. F = 1 for two phases in equilibrium, and a curve that relates the two variables is the appropriate representation. As the composition of the two phases generally is different, two conjugate curves are required. 

Figure 5 BaO-CuO-YOj 6 ternary phase diagram (1) ( 950-1000°C). Various compounds and compositions require various oxygen activities so that a complete rigorous representation of the diagram should include an additional dimension related to Poz.

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