Systems, ternary

Ternary phase diagrams relate the phases to temperature in a three-component system, and the four variables to be considered are temperature. 

To those familiar with topographical maps, height and temperature are analogous. 

Once the compatibility triangles are known, both the phases present at equilibrium and their relative amounts can be determined. Refer once more to Fig. 8.10c . At equilibrium, composition X would comprise the phases MO, 2AO MO, and AO BO in the following proportions  

Note that in going from a ternary to a binary representation, a dimension is lost planes become lines and lines become points. Thus a quaternary phase is a point, and the edges of the triangles represent the corresponding binary phase diagrams (compare Fig. 8.10a and c). 

Ternary Systems. The crystal structures of several ternary systems containing at least one Group IV element have been elucidated that of EuMg - 

Gcg has been shown to be orthorhombic, of space group Cmcm, a = 4.485, b = 30.60, c = 4.485 A, and is thought to belong to a new type derived from 

Chatillon-Colinet, A. Percheron, and J.-C. Mathieu, Compt. rend., 1972,275, C, 921. 

Voitkov, G. M. Gaiduchuk, and 1.1. Brodin, Soviet Phys. Cryst., 

Representation of a ternary composition. The dot in the upper triangie represents a composition of 30% A, 50% B, and 20% C, as shown in the iower triangie. 

The ternary eutectic is thus an isobaric invariant point, and no temperature change can take place until the liquid is all used up, at which time the crystals will resume cooling. 

The simple ternary eutectic system discussed above represents just a beginning to the general subject of ternary phase diagrams. Features such as solid 

The difference lies in the fact that the granite system is not the dry system q-ab-or, but the wet system q-ab-or-H20. The presence of water at high 

Phase diagrams are a kind of concise representation of the equilibrium relationships between phases as a function of chosen intensive variables, such as temperature, pressure, composition, pH, oxidation potential, activity ratio, and so on. They are extremely useful, not only in representing what is known about a system, but in thinking about processes involving phase changes. Most of the 

For the modeling of ternary systems(the topic of the next section), the applicability of (26) to mixtures of low molecular weight liquids would be very helpful, because of the possibility to describe all subsystems by means of the same relation. First experiments [29], presented in Sect. 4, show that this is indeed possible. This means that (26) remains physically meaningful upon the reduction of the number of segments down to values that are typical for low molecular weight compounds. With respect to X one must, however, keep in mind that this parameter loses its original molecular meaning. 

The segment molar Gibbs energy of mixing for three component (indices i,j, and k) with Ni, Nj, and segments, respectively, as formulated on the basis of the Flory Huggins theory reads in its general form  

The first three terms stand for the combinatorial part of the Gibbs energy, the next three terms represent the residual contributions stemming from binary interactions, and the last term accounts for ternary contacts. 

The double-indexed g parameters are for binary interaction parameters. The first line of the above relation represents the combinatorial part, and the second line the residual part of the reduced segment molar Gibbs energy of mixing. This relation also contains a ternary interaction parameter tij that accounts for the expectation that the interaction between two components of the ternary mixture may change in the presence of a third component. 

Because of the well-documented composition dependencies of the individual binary interaction parameters, an unmindful use of (56) would lead to totally unrealistic results. This feature requires twofold adaption. 

Sn and Pb dissolved in liquid Na have been investigated using resistivity techniques.780 At the concentrations studied ( 2 atom % total solute), no interactions were observed. The ternary phase diagram of the Sn-Cd-Hg system has been determined at constant Sn concentrations (20, 40, and 70 atom % Sn).779 

As mentioned in the introduction, hydrates may crystallize in either of two frameworks. When discussing ternary systems A+ 13+H20 it is useful to discriminate between systems in which only hydrates of one structure (I or II) are. formed, and those in which hydrates of both structures are formed. 

There is a considerable patent art concerning preparation of transparent mixtures of water with low molecular weight silicone oils using polymeric silicone surfactants. Some representative early references are Keil [47], Gee [48, 49], Gum [50] and Terae [51]. These compositions are called micro emulsions in the patents in the sense of being transparent mixtures of water, surfactant and oil - but note that they are transparent because of small particle size or because of index of refraction matching. 

Silicone surfactants containing polyoxyalkylene groups are usually soluble in ethers, alcohols, esters, ketones, and aromatic and halogenated solvents. Unlike hydrocarbon nonionic surfactants they are not very soluble in alkanes. Polymeric silicone surfactants are not miscible with polymeric silicone oils [13]. 

Mixtures of low molecular weight silicon-based surfactants and cosurfactants have been used to prepare a self-dispersing microemulsion of silicone agents applied to building materials to impart water repellency [54, 55]. The structure of the surfactants used was not disclosed but they are described as being themselves reactive so that they bind to the surfaces of the building materials and become part of the water-repellancy treatment. 

Silicone surfactants are specialty surfactants that are primarily used in applications that demand their unique properties. Most applications are based on some combination of their (a) low surface tension, (b) surface activity in nonaqueous media, (c) wetting or spreading, (d) low friction or tactile properties, (e) ability to deliver silicone in a water-soluble (or dispersible) form, (f) polymeric nature or (g) low toxicity. The major applications will be discussed briefly in following sections. 

Certain comb-type silicone surfactants have been shown to stabilize emulsions in the presence of salts, alcohol and organic solvents that normally cause failure of emulsions stabilized using conventional hydrocarbon surfactants and a study by Wang et al. [66,67] investigated the cause of this stability. Interaction forces due to silicone surfactants at an interface were measured using AFM. Steric repulsion provided by the SPE molecules persisted up to an 80% or higher ethanol level, much higher than for conventional hydrocarbon surfactants. Nonionic hydrocarbon surfactants lose their surface activity and ability to form micelles in 

As first pointed out by Gibbs the composition of a solution containing three components may be represented by a point in an equilateral triangle whose vertices A, B and C represent the three pure components. If the side of the triangle is taken as unity, then the mole fractions Xj, Xb and Xq in the solution under consideration are given by the distances, measured along lines parallel to the sides of the triangle, 

This is easily shown by reference to fig. 13.9 (6), from which it is seen that the sum of the three lengths which represent and Xq is equal 

Furthermore we see that the sides of the triangle represent the binary systems (A + B), (B + C) and (C + A) and the vertices represent pure components. 

To represent the variation in some property of a solution which is a function of the composition we employ a three-dimensional diagram the base of which is a triangle the height of the representative point above the base is proportional to the property under consideration. 

Let us consider a solution of three substances A, B and C which do not react together, and suppose the solution is in equilibrium with one of the solid components. Then c = 3, r = 0, j = 2 whence — 3 and the system is trivariant. We can thus consider the pressure and composition of the solution (p, Xj, x ) and see how the equilibrium temperature changes with these variables. Let us take the pressure as constant, 

FIGURE 1.17 The ethanol-benzene-water system (Example 1.13). 

The relative quantity of the phase with composition A to the phase with composition C equals the ratio of segments CD to DA, according to the lever rule. 

Since ternary diagrams represent one temperature and one pressure, a set of diagrams would be required to describe the effects of temperature and pressure, as well as the effect of composition. A three-dimensional diagram could be constructed to describe the phase compositions-temperature relationship at a fixed pressure. 

Martin-Garin, M. Gomez, P. Bedon, and P. Desre, J. Less-Common Metals, 1975, 41, 65. 

Chatillon-Colinet, J.-L. Deneuville, J.-C. Mathieu, and E. Bonnier, J. Chim. phys., 1975, 72, 878. 

Fischer, R. Kirchheim, and E. Gebhardt, J. Less-Common Metals, 1974, 38, 201. 

Intermetallic phase Ref. a Intermetallic phase Ref a Intermetallic phase Ref a 

The preparation and characterization of the two phases Caio- Si,2-2 As,(, and Caio, Si]2- Pi6 (0.66 X 2.50) have been described.Their structures are isotypic and crystallize with monoclinic symmetry, of space group they may be related to a slightly distorted NaCl-type. Their unit-cell parameters are included in Table 27. A comparison of the different methods of crystal growth of ZnSiP2, ZnSiAs2, and CdGeAs2 (chalcopyrite structures) has also been undertaken.  

In addition to temperature changes, changes in composition brought about by the addition of a third component, a nonsolvent can also cause demixing. Under these circumstances 

The initial procedure for membrane formation from such ternary systems is always to prepare a homogeneous (thermodynamically stable) polymer solution. This will often correspond to a point on the polymer/sol vent axis. However, it is also po.ssible to add nonsolvent to such an extent that all the components are still miscible. Demixing will occur by the addition of such an amount of nonsoivent that the solution becomes thermodynamically unstable. 

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In the next three sections we discuss calculation of liquid-liquid equilibria (LLE) for ternary systems and then conclude the chapter with a discussion of LLE for systems containing more than three components. 

In ternary systems, we distinguish between two common types. In type II, two binaries are partially miscible and the third binary is completely miscible in type I, only one binary is partially miscible. (A third type, where all three binaries are only partially miscible, is relatively rare and not considered here.)... 

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

Unfortunately, good binary data are often not available, and no model, including the modified UNIQUAC equation, is entirely adequate. Therefore, we require a calculation method which allows utilization of some ternary data in the parameter estimation such that the ternary system is well represented. A method toward that end is described in the next section. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

Using the method outlined above, calculations were performed for ten ternary systems. All binary parameters are shown in Table 4. Some typical results are shown in Figures 16 to 19. 

Two further examples of type I ternary systems are shown in Figure 19 which presents calculated and observed selectivities. For successful extraction, selectivity is often a more important index than the distribution coefficient. Calculations are shown for the case where binary data alone are used and where binary data are used together with a single ternary tie line. It is evident that calculated selectivities are substantially improved by including limited ternary tie-line data in data reduction. 

Figure 4-19. Calculated selectivities in two ternary systems show large improvements when tie-line data are used to supplement binary VLB data for estimating binary parameters.

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

Figure 4-21. Parameters obtained for the furfural-benzene binary are different for the two ternary systems. An optimum set of these parameters is chosen from the overlapping confidence regions, capable of representing both ternaries equally well.

In the absence of special syimnetry, the phase mle requires a minimum of tliree components for a tricritical point to occur. Synnnetrical tricritical points do have such syimnetry, but it is easiest to illustrate such phenomena with a tme ternary system with the necessary syimnetry. A ternary system comprised of a pair of enantiomers (optically active d- and /-isomers) together with a third optically inert substance could satisfy this condition. While liquid-liquid phase separation between enantiomers has not yet been found, ternary phase diagrams like those shown in figure A2.5.30 can be imagined in these diagrams there is a necessary syimnetry around a horizontal axis that represents equal amounts of the two enantiomers. 

In block copolymers [8, 30], long segments of different homopolymers are covalently bonded to each otlier. A large part of syntliesized compounds are di-block copolymers, which consist only of two blocks, one of monomers A and one of monomers B. Tri- and multi-block assemblies of two types of homopolymer segments can be prepared. Systems witli tliree types of blocks are also of interest, since in ternary systems the mechanical properties and tire material functionality may be tuned separately. 

Zulauf M and Eicke FI 1979 Inverted micelles and microemulsions in the ternary system Fl20/aerosol-OT-isoctane as studied by photon correlation spectroscopy J. Phys. Chem. 83 480... 

Military. The single-component explosives most commonly used for military compositions are TNT, RDX or HMX, nitrocellulose, and nitroglycerin. The last two are used almost exclusively to make propellants. The production volume of TNT far exceeds that of any other explosive. It is used as manufactured, as a base of biaary slurries with other high melting explosives, or ia ternary systems generally containing a biaary mix and aluminum. 

Table 14. Properties of Explosive Mixtures Based on Ternary Systems Containing TNT and Aluminum ...

An even wider range of wavelength, toward the infrared, can be covered with quantum well lasers. In the Al Ga As system, compressively strained wells of Ga In As are used. This ternary system is indicated in Figure 6 by the line joining GaAs and In As. In most cases the A1 fraction is quite small, X < 0.2. Such wells are under compressive strain and their thickness must be carefully controlled in order not to exceed the critical layer thickness. Lasers prepared in this way are characterized by unusually low threshold current density, as low as ca 50 A/cm (l )-... 

The GdAlgB O QiCe ", Tb " is synthesized by a soHd-state firing of the rare-earth coprecipitated oxide plus boric acid and MgCO at 900° C in a slightly reducing atmosphere. As in the case of the lanthanum phosphate phosphor, a flux is usually used. The synthesis of this phosphor is further comphcated, however, by the fact that it is a ternary system and secondary phases such as gadolinium borate form and must then react to give the final phosphor. 

In the Ee—Al—Si ternary system, alloys close to the 9.5 Si, 5.6 A1 composition exhibit very low magnetostriction and anisotropy. As a result, these show very high values of initial and maximum permeabiHty. However, the ternary alloys are very britde, a factor which limits their general usefiilness. 

Selected physical properties of various methacrylate esters, amides, and derivatives are given in Tables 1—4. Tables 3 and 4 describe more commercially available methacrylic acid derivatives. A2eotrope data for MMA are shown in Table 5 (8). The solubiUty of MMA in water at 25°C is 1.5%. Water solubiUty of longer alkyl methacrylates ranges from slight to insoluble. Some functionalized esters such as 2-dimethylaniinoethyl methacrylate are miscible and/or hydrolyze. The solubiUty of 2-hydroxypropyl methacrylate in water at 25°C is 13%. Vapor—Hquid equiUbrium (VLE) data have been pubHshed on methanol, methyl methacrylate, and methacrylic acid pairs (9), as have solubiUty data for this ternary system (10). VLE data are also available for methyl methacrylate, methacrylic acid, methyl a-hydroxyisobutyrate, methanol, and water, which are the critical components obtained in the commercially important acetone cyanohydrin route to methyl methacrylate (11). 

Thermo dynamic data for nitric acid are given ia Table 2. Properties for the ternary systems sulfuric acid—nitric acid—water (5,14) and magnesium nitrate—nitric acid—water (11,15—17) used ia processes for concentrating nitric acid are available. 

The possibiHties for multidimensional iastmmental techniques are endless, and many other candidate components for iaclusion as hyphenated methods are expected to surface as the technology of interfacing is resolved. In addition, ternary systems, such as gas chromatography-mass spectrometry-iafrared spectrometry (gc/ms/ir), are also commercially available. 

Cellulose Solvent. Although DMSO by itself does not dissolve cellulose, the following binary and ternary systems are cellulose solvents DMSO—methylamine, DMSO—sulfur trioxide, DMSO—carbon disulfide—amine, DMSO— ammonia—sodamide, DMSO—dinitrogen tetroxide,... 

Phase Behavior. One of the pioneering works detailing the phase behavior of ternary systems of carbon dioxide was presented ia the early 1950s (12) and consists of a compendium of the solubiHties of over 260 compounds ia Hquid (21—26°C) carbon dioxide. This work contains 268 phase diagrams for ternary systems. Although the data reported are for Hquid CO2 at its vapor pressure, they yield a first approximation to solubiHties that may be encountered ia the supercritical region. Various additional sources of data are also available (1,4,7,13). 

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