Systems, binary, diagram types

The P-V Diagram for a Multicomponent System. For a relatively volatile multicomponent system, a gasoline for example, an isotherm on the P-V diagram is similar to its counterpart for a binary system (Figure 23). However, it is commonly found that at the dew point the break in the P-V isotherm is not very pronounced in multi-component systems. Consequently, for systems of this type, it may be very difficult to fix the dew point in this manner. This experimental difficulty can be overcome by using a windowed cell and observing the pressure and volume when traces of liquid appear in the system. 

Representative phase diagrams for the most common types of binary systems are shown in Figure 12.6, along with example systems. For each type, phase diagrams are presented in two ways T vs. X and y, and y vs. x. Typical isothermal curves of activity coefficients for binary systems are illustrated in Figure 12.7. 

Figure 7.1 Typical phase diagrams Types of binary organic systems according to Matsuoka (1977) and data from ICT.

Figure 2 Critical phenomena in binary systems where gas-liquid and liquid-liquid equilibria interfere schematic representation for symbols see Section 1). a, b, and c, p T) projections of the phase diagram d, p x) isotherm for T = const. = Ti of binary systems corresponding to type 2b or 2c...

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... 

Fig. 2.3-4 Phase diagram of a eutectic binary system with total immiscibility in the two sohd phases left), phase diagrams of various types of binary systems with perfect (Type I) or partial (Type II -V) miscibility in the solid phase (right)...

There are two types of lipid-water phase diagrams. The first type, discussed above, is obtained from polar lipids, which are insoluble in water (i.e. the solubility is quite small, monolaurin for example has a solubility of about 10 m). Fig. 8.12 illustrates the principles of phase equilibria in this type of lipid-water system. The second type of binary system is obtained when the lipid is soluble as micelles in water. Examples of such lipids are fatty acid salts and lysolecithin. An aqueous soap system is illustrated in Fig. 8.13. When the lipid concentration in the micellar solution is increased, the spherical micelles are transformed into rod-shaped micelles. At still higher lipid concentrations the lipid cylinders are hexagonally arranged and the liquid-crystalline phase Hi is formed. The lamellar liquid-crystalline phase is usually formed in the region between Hi and the anhydrous lipid. Excellent reviews of the association behaviour of amphiphiles of this type have been published (Wennerstrom and Lindman, 1979 Lindman and Wennerstrom, 1980). 

A selection of phase diagram type for given system from the possible versions obtained by the theoretical derivation (based only on the information about phase behavior in binary subsystems) can be made using an additional experimental data on the ternary phase equilibria. It is clear that the munber of experimental measmements needed for a selection of the right phase diagram type is significantly lower than in the case of experimental way without any theoretical derivations beforehand. 

Similarly to the phase diagrams for binary systems, the main types for fluid phase diagrams of ternary mixtures should not have an intersection of critical curves and inunis-cibUity regions with a crystallization surface in them. Combination of four main types of binary fluid phase behavior la, lb, Ic and Id (Figure 1.2) for constituting binary subsystems gives six major classes of ternary fluid mixtures with one volatile component, two binary subsystems (with volatile component) complicated by the immiscibility phenomena and the third binary subsystem (consisted from two nonvolatile components) of type la with a continuous solid solutions. These six classes of ternary fluid mixtures can be referred as ternary class I (with binary subsystems Ib-lb-la), ternary class II (with binary subsystems Ic-lc-la), ternary class III (with binary subsystems Id-ld-la), or ternary class IV (with binary subsystems Ib-ld-la), ternary class V (with binary subsystems Ib-lc-la) and ternary class VI (with binary subsystems Ic-ld-la). 

Fig. 1. Predicted reaction pressure versus temperature curves for the systems MCI-XCI4, where M is an alkaline earth metal and X is one of the reactive metals Ti, Zr, or Hf. The analysis is only applicable to a binary system of this type which is described by a simple eutectic-type phase diagram and in the absence of solid solubility.

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Binary Alloys. Aluminum-rich binary phase diagrams show tliree types of reaction between liquid alloy, aluminum solid solution, and otlier phases eutectic, peritectic, and monotectic. Table 16 gives representative data for reactions in tlie systems Al—Al. Diagrams are shown in Figures 10—19. Compilations of phase diagrams may be found in reference 41. 

Three types of binary equilibrium cui ves are shown in Fig. 13-27. The y-x diagram is almost always plotted for the component that is the more volatile (denoted by the subscript 1) in the region where distillation is to take place. Cui ve A shows the most usual case, in which component 1 remains more volatile over the entire composition range. Cui ve B is typical of many systems (ethanol-water, for example) in which the component that is more volatile at lowvalues of X becomes less volatile than the other component at high values of X. The vapor and liquid compositions are identical for the homogeneous azeotrope where cui ve B crosses the 45° diagonal. A heterogeneous azeotrope is formed with two liquid phases by cui ve C,... 

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. 

The binary oxides and hydroxides of Ga, In and T1 have been much less extensively studied. The Ga system is somewhat similar to the Al system and a diagram summarizing the transformations in the systems is in Fig. 7.13. In general the a- and y-series have the same structure as their Al counterparts. )3-Ga203 is the most stable crystalline modification (mp 1740°) it has a unique crystal structure with the oxide ions in distorted ccp and Ga " in distorted tetrahedral and octahedral sites. The structure appears to owe its stability to these distortions and, because of the lower coordination of half the Ga ", the density is 10% less than for the a-(corundum-type) form. This preference of Ga "... 

In conclusion, we have presented a new formulation of the CVM which allows continuous atomic displacement from lattice point and applied the scheme to the calculations of the phase diagrams of binary alloy systems. For treating 3D systems, the memory space can be reduced by storing only point distribution function f(r), but not the pair distribution function g(r,r ). Therefore, continuous CVM scheme can be applicable for the calculations of phase diagrams of 3D alloy systems [6,7], with the use of the standard type of computers. 

The binary system lead-thallium shows an unusual type of phase diagram. Fig. 1, taken from Hansen (1936), represents in the main the results obtained by Kumakow Pushin (1907) and by Lewkonja (1907). The liquidus curve in the wide solid-solution region has a maximum at about 63 atomic percent thallium. The nature of this maximum has not previously been made clear. 

An alloy is said to be of Type II if neither the AC nor the BC component has the structure a as its stable crystal form at the temperature range T]. Instead, another phase (P) is stable at T, whereas the a-phase does exist in the phase diagram of the constituents at some different temperature range. It then appears that the alloy environment stabilizes the high-temperature phase of the constituent binary systems. Type II alloys exhibit a a P phase transition at some critical composition Xc, which generally depends on the preparation conditions and temperature. Correspondingly, the alloy properties (e.g., lattice constant, band gaps) often show a derivative discontinuity at Xc. 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

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