Ternary systems projection

Fig. 57. Projections of the crystallization surfaces of the ternary systems K.2TaF7 - KF - KCl (top). Reproduced from [306], Z. Bin-Sin, N. P. Lushnaya, V. I. Konstantinov, Zh. Neorg. Khim. 8 (1963) 389, Copyright 1963, with permission of Nauka (Russian Academy of Sciences) publishing.

Projections, linearly independent, 293 Propagation, of polymerization, 158 Propane, hydrate, 10, 33, 43, 46, 47 hydrate thermodynamic data and lattice constants, 8 + iodoform system, 99 Langmuir constant, 47 water-hydrogen sulfide ternary system, 53... 

Figure 15.5. Eutectic formation in the ternary system o-, m- and p-mtrophenol 3 a) Temperature-concentration space model b) Projection on a triangular diagram. (Numerical values represent temperatures in K)...

In petrology, the usual representation of phase equilibria in the crystalhzation process of ternary systems is based on a projection from the T axis onto the... 

Let us now treat compositional relations in the ternary system Di-An-Ab. Figure 7.14A shows the projection of the liquidus surface of the system onto the compositional plane the locations of cotectic line E -E" and of the isotherms are based on the experiments of Bowen (1913), Osborn and Tait (1952), and Schairer and Yoder (1960). 

Figure 11.7 shows a ternary system consisting of components A, B and a compound C. The presence of the reaction confines the feasible composition to the reaction equilibrium surface. Projection of the intersection between the solubility... 

Figure 2.3 (a) Isometric projection (solid diagram) for a hypothetical ternary system (b) isotherm (horizontal section) (c) binary-phase subset (d) liquidus surface. 

The ternary system furfural-water-C02 has been studied before in different research works [1,2,9]. In this project the influence of acetic arid on the distribution of furfural was determined. According to the results of the solubility measurements temperatures were adjusted at 298 and 313 K and the equilibria were investigated at pressure levels of 90, 130 and 160 bar. Furtheron the con-... 

Figure 4 (a) Ternary systems that form solid solutions, (b) Ternary systems in which the three constituent binaries exhibit eutectic behavior, (c) Projection ofliquidus curves in (b). (d) Ternary system in which two of the constituent binaries form eutectics, (e) Ternary system in which A and B combine to form AB... 

Figure 3. P-T projection for a ternary system with discontinuous four phase line.

In the ternary system, in which a congruently melting binary compound is formed, the figurative point of the binary compound AB lies in the boundary binary system A-B. The vertical projection of the phase diagram of such a ternary eutectic system is shown in Figure 3.31. 

The phase diagram of such a system has four planes. The plane pc(A) is the vertical projection of the plane of primary crystallization of the compound A, plane pc(B) represents the plane of primary crystallization of the component B, and the plane pc(C) refers to the primary crystallization of compound C. Finally, the plane pc(AB) is the projection of the plane of primary crystallization of compound AB. In the case of the congruently melting compound AB its figurative point lies inside the plane of the primary crystallization of this compound. In comparison with the simple eutectic ternary system a new boundary line, Ctj - Ct2, which represents the common crystallization of compounds C and AB, will arise. The joint AB-C divides the ternary system A-B-C into two simple... 

The phase diagram of the ternary system with the formation of an incongruently melting compound has four planes. Planes pc(A), pc(B), pc(C), and pc(A4B) are the projections of the planes of primary crystallization of the compounds A, B, C, and A4B, respectively. The figurative point of the binary compound A4B lies in the boundary of the binary... 

The vertical projection of the phase diagram of this ternary system is shown in Figure 3.33. 

Quaternary systems are composed of four components with a common ion and form four ternary and six binary systems. The concentration diagram of the quaternary system can be represented by a tetrahedron. The vertical projection of every ternary system is placed on one face of the tetrahedron. The phase diagram of the quaternary system A+, B+, C +, D + // X with the formation of the congruently melting binary compound BCX3 is shown in Figure 3.39. 

Let us consider an ideal ternary system A-B-C. In this case Eq. (3.190) must be valid for all the three components. From the integral form of Eq. (3.190) for the components A and B, the equation of a projection of the monovariant line of the simultaneous crystallization of these components, E-P in Figure (3.50), can be derived... 

Multicomponent systems can usually be considered as either pseudobinary, when only water crystallises, or pseudo-ternary, when water and a solute crystallise. When ice is the only crystallising species, the process can be adequately described with the help of a simple two-dimensional temperature-composition phase diagram, as shown in Figure la in Chapter 4. To describe in full the crystallisation and phase relationships in the ternary system, a three-dimensional phase diagram is required, but as a simplification, a triangular projection on the composition base can usually be employed. The following is a summary outline of the construction and interpretation for a model system of pharmaceutical significance, water-NaCl-sucrose, where the data were obtained from an in-depth study by DSC methods. ... 

Figure 4 Example of planar projection of the minimal energy configuration of a ternary system composed of a cellulose I schematic elementary crystallite surface, the photopol5mierizable acrylic primer tripropyleneglycol diacrylate (TPGDA), and a polyester finish. (From Refs. 72, 73.)...

The chemical composition of clinker is complex, however, it is easy to notice that the sum of four components, CaO, Si02, AI2O3 and Fe203 is as a rule higher than 95 %. The processes of Portland cement clinker phases ciystallization in the four components system can thus be presented. It is especially justified that MgO is not forming own compounds in the rich in calcium part of five-components system, but solid solutions with remaining clinker phases, or is present as periclase. However, the four-components system is seldom used, because the use of ternary systems is much more convenient. They are usually presented as the horizontal projection. 

The most frequently we use the ternary system horizontal projection, on which the most important isotherms are marked. On the Fig. 2.14 the section of this system is presented, on which, apart of earlier discussed two-component compounds, mull-ite, without practical importance for cement chemistry, is shown. However, it is present in siliceous fly ash, but it belongs to inert compounds does not reacting with calcium hydroxide in water. Furthermore two ternary phases are formed in... 

The Janecke projection (section 4.4) in Figure 8.16 shows the phase equilibria for the ternary system, ortho-, meta- and pura-nitrotoluene the three pure components are represented by the letters O, M and P, respectively, at the apexes of the triangle. Four different eutectics can exist in this system, three binaries and one ternary ... 

The series provides consistent phase diagram deseriptions for individual ternary systems. The representation of the equihbria of ternary systems as a function of temperature results in spaeial diagrams whose sections and projections arc generally published in the literature. Phase equilibria are deseribed in terms of hquidus, soUdus and solvus projections, isothermal and quasibinary sections data on invariant equilibria are generally given in the form of tables. 

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