Phases in binary system

Figure 7.20 Empirical relationship between the number of intermetallic phases in binary systems and the enthalpy of formation of AB [8].

Types of Phases in Binary Systems.—A two-component system, like a system with a single component, can exist in solid, liquid, and gaseous phases. The gas phase, of course, is perfectly simple it is simply a mixture of the gas phases of the two components. Our treatment of chemical equilibrium in gases, in Chap. X, includes this as a special case. Any two gases can mix in any proportions in a stable way, so long as they cannot react chemically, and we shall assume only the simple case where the two components do not react in the gaseous phase. 

Coquerel, G. Review on the heterogeneous equilibria between condensed phases in binary systems of enantiomers. Enantiomer 2000, 5, 481 98. 

Number of transfer units for the vapor phase in binary system [ - ]... 

The derivative of the surface tension with respect to temperature at the interface between condensed phases in binary systems can be either positive, or negative, or even change its sign when the temperature changes, which makes it different from the vapor-liquid interface in a one-component system. Within a certain approximation one may assume that in binary systems, as in single-component ones, the value r = -do/dT is the excess of entropy within the discontinuity surface. Consequently, for the interface between condensed phases, the excess of entropy can not only be positive (as it was with singlecomponent systems), but also negative. This situation is especially typical for the interface between two mutually saturated liquid solutions. 

FIGURE 14.4 Cu sorption to the solid phase in binary systems hematite-fulvic acid at three different ionic strengths. Experimental data ( ) 0.1 M (O) 0.03 M (A) 0.01 M, and corresponding model calculations (lines) based on the additivity assumption. (Reprinted from Geochimica et CosmochimicaActa, 65, Christl, I. and Kretzschmar, R., Interaction of copper and fulvic acid at the hematite-water interface, 3435-3442. Copyright 2001, with permission from Elsevier.)... 

Oligooxyethylene esters of this acid also display enantiotropic hexagonal columnar mesophases [312]. Brienne etal. [313] found hexagonal columnar phases in binary systems of non-mesogenic compounds, due to the formation of hydrogen bonded complexes. 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

L termination, 62-63 Lewis fugacity rule, 144-145 Liquid-liquid equilibria in binary systems, 184-190 in ternary systems, 194-203 phase diagram, 196-202... 

Ic. Ternary Systems Consisting of a Single Polymer Component in a Binary SolventMixture.—Three conditions must be satisfied for equilibrium between two liquid phases in a system of three components. In place of the conditions (1) we have... 

In the field of solid-state chemistry an important group of substances is represented by the intermetallic compounds and phases. In binary and multi-component metal systems, in fact, several crystalline phases (terminal and intermediate, stable and metastable) may occur. A few introductory remarks about these substances will be presented in relation to the mentioned figures. 

Trends in the formation capability of binary compounds. A few general comments about the formation of intermediate phases in binary alloy systems can be made by using maps similar to those previously employed in Fig. 2.8 in order to give a summary of the mutual solubility. 

Figure 2.22. Compound formation capability in binary systems. The different element combinations are mapped on Mendeleev number coordinates and those systems are indicated in which the formation of intermediate phases has been observed (either from the liquid or in the solid state). Blank boxes indicate systems for which no certain data are available. Notice that the compound-forming alloys are crowded in a region corresponding to a large difference in the Mendeleev numbers of the elements involved (for instance, basic metals with semi-metals).

In the preceding paragraphs we have seen a few examples of phase equilibria occurring in binary systems represented by means of 2D diagrams built, at constant pressure (isobaric), on temperature/composition axes for which the phase rule... 

Figure 5,9 Phase stability relations in binary systems Mg2Si04-Fe2Si04 (A) and Mg2Si04-Co2Si04 (B) at T = 1000 °C.

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

Uphill diffusion in a binary system is rare and occurs only when the phase undergoes spinodal decomposition. In multicomponent systems, uphill diffusion occurs often, even when the phase is stable. The cause for uphill diffusion in multicomponent systems is different from that in binary systems and will be discussed later. 

Three-Phase Transformations in Binary Systems. Although this chapter focuses on the equilibrium between phases in binary component systems, we have already seen that in the case of a entectic point, phase transformations that occur over minute temperature fluctuations can be represented on phase diagrams as well. These transformations are known as three-phase transformations, becanse they involve three distinct phases that coexist at the transformation temperature. Then-characteristic shapes as they occnr in binary component phase diagrams are summarized in Table 2.3. Here, the Greek letters a, f), y, and so on, designate solid phases, and L designates the liquid phase. Subscripts differentiate between immiscible phases of different compositions. For example, Lj and Ljj are immiscible liquids, and a and a are allotropic solid phases (different crystal structures). 

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