Schematic phase diagram binary system

Simple schematic phase diagrams of binary alloy systems are shown in Fig. 2.18 in which the formation of one intermediate solid phase may be noticed. In these... 

Figure 7 A schematic phase diagram of a binary system...

FIG. 141, Schematic phase diagram of a binary system with a miscibility gap (curve/), with indicated region of spinodal decomposition (curve s). 

Figure 27.1 shows a schematic phase diagram for binary blends showing the relationship between free energy of mixing AG ) and blend composition cp). For sample A, an immiscible system is obtained (AG j > 0), for sample B a fully miscible system is obtained in which AG < 0, and C represents a partially miscible system that satisfies AG < 0 for all compositions, but d AG Idcpi is lower than 0 at certain compositions, indicating that at these compositions the blend will be immiscible. 

Figure 42 Schematic phase diagram of the amphiphile-water binary system.

For simplicity, we consider here only a binary mixtures (A, B) and do not discuss the complications posed by extensions to multicomponent systems. Figure 1 shows a schematic phase diagram in the plane of variables temperature T and concentration c of species B. Kinetics of phase separation in bulk fluid mixtures is triggered by a rapid quench (at time t = 0) from the one-phase region into the miscibility gap. The initial equilibrium state (f < 0) is spatially homogeneous, apart from small-scale concentration inhomogeneities. The final equilibrium state towards which the system ultimately evolves (t oo) consists of... 

Fig. 1.11 Schematic phase diagram for a binary system having a miscibihty gap. The phase boundary is shown solid while the spinodal is dashed. The labeled temperatures and compositions correspond to those in Figure 1.10.

For simplicity, we consider here only a binary mixtures (A,B), and do not discuss the complications posed by extensions to multicomponent systems. Figure 1 shows a schematic phase diagram in the plane of variables tem-... 

Figure 11.25 Schematic phase diagram of a binary system surfactant/water. Inverse hexagonal phase Hn, lamellar phase Lo, hexagonal phase Hj, isotropic (cubic) phases a, b, c, d.

Figure 4 Schematic phase diagram of a binary system, consisting of a polymer and a solvent of marginal thermodynamic quality. The miscibility gap is shaded. Indicated in the graph is how the compositions of the working point (WP) can be reached either by cooling a homogeneous feed solution (FD, route A) or by adding pure solvent (extracting agent, EA) to a concentrated feed solution (FD, route B). The system demixes into a polymer-rich gel phase (GL) and a polymer-lean sol phase (SL).

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

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.

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... 

Figure 11-17. a) Phase diagram of the quasi-binary system AX-BX with an extended miscibility gap. b) Schematic electrolysis cell A/AX/BX/B. Cation vacancy drift and the mechanism of interface motion are indicated. 

Figure 15.1 Effect of /3-phase particle size on the concentration, Xeq, of component B in the a phase in equilibrium with a /3-phase particle in a binary system at the temperature T. assuming that, 6 is pure B. (a) Schematic free-energy curves for a phase and three /3-phase particles of different radii, R > R2 > Rs. The free energies (per mole) of the particles increase with decreasing radius due to the contributions of the interfacial energy, which increase as the ratio of interfacial area to volume increases, (b) Corresponding phase diagram. The concentration of B in the a phase in equilibrium with the /0-phase particles, as determined by the common-tangent construction in (a), increases as R decreases, as shown in an exaggerated fashion for clarity, (c) Schematic concentration profiles in the a matrix between the three /3-phase particles.

A schematic diagram to illustrate the growth process of the ArBs layer at the interface between the ApBq and B phases at the expense of diffusion of component A is shown in Fig. 4.2. If the ApBq compound has a considerable range of homogeneity, then the content of component A in the initial phase ApBq will be assumed to be constant and equal to the lower limit of this range according to the equilibrium phase diagram of the A-B binary system. 

In this diagram, applicable mainly to binary systems, the temperature, pressure, and overall composition are the independent variables, with the pressure held constant. The diagram, shown schematically in Figure 2.2, consists of an upper curve representing dew points and a lower curve representing bubble points. The Z coordinate represents overall mole fraction of component 1, usually chosen as the more volatile component. A vertical line at Z = 0 corresponds to pure component 2, and point A represents its boiling point at the fixed system pressure. Similarly, pure component 1 is represented by a vertical line at Z = 1, and its boiling point by point B. Points above the dew point curve are in the vapor phase, and those below the bubble point curve are in the liquid phase, while the area between the two curves corresponds to the mixed phase. 

Fig. 2.4. (a) Schematic free-energy diagram of a two-component system at a temperature below solidus (b) free-energy diagram at a temperature between the solidus and liquids (c) binary-phase diagram (d) illustration of polymorphous (I and IV), primary (II), and eutectic (III) crystallization reactions from an undercooled liquid (e) the T0 (C) curves for the a and y phases... 

Figure 1.1 Schematic view of the phase behaviour of the three binary systems water (A) oiI (B), oil (B)-non-ionic surfactant (C), water (A)-non-ionic surfactant (C) presented as an unfolded phase prism [6]. The most important features are the upper critical point cpc, of the B-C miscibility gap and the lower critical point cpp of the binary A-C diagram. Thus, at low temperatures water is a good solvent for the non-ionic surfactant, whereas at high temperatures the surfactant becomes increasingly soluble in the oil. The thick lines represent the phase boundaries, while the thin lines represent the tie lines.

The binary phase diagram for typical polymer-solvent systems is shown schematically in Fig. 3.8. Nonpolar polymer solutions usually display an upper and a lower critical solution temperature. In the limit of infinite polymer molecular weight, these would correspond to an upper (6,) and lower (dj) theta-temperature. This can be readily seen as follows. 

Figure 1 Gas-liquid equilibria in binary systems schematic representation for symbols see Section 1). a, Three-dimensional representation in the p-T-x space , b, p T) projections of the phase diagrams...

Figure 27 Phase behaviour of binary CO2 systems schematic representation see text X = mole fraction), a to d, p X) projections of the phase diagrams e to k, p x) isotherms...

Figure 30 p-T-x surfaces and p(T) projections of phase diagrams for binary mixtures of HgO with hydrocarbons (HC) schematic representation see text, a and c. Type found for naphthalene + H O, biphenyl + HgO b and d, type found for benzene + HgO and aqueous solutions of methylsubstituted benzenes e, no aqueous hydrocarbon system known f, type found for cyclohexane + HjO, butane + HjO... 

Figure 8.37 Schematic illustration of the solubility of a binary fatty acid system in the form of a phase diagram, after Bailey (1950). The broken line cuts the binary fatty acid system at the eutectic composition E.

---