Systems that Exhibit Eutectic Behavior

The thermodynamic relationships along the liquidus curves are given by 

Equation (7) is obtained from Equation (2) by noting that the solid phase is pure, and therefore the mole fraction and activity coefficient in the solid phase are both unity. The ratio of pure-component fugacities can be obtained from any one of Equations ((3) to (6)), and the activity coefficient in the liquid, Ji, must be estimated. The composition-temperature behavior along the liquidus curves may then be calculated. The eutectic point is found from the intersection of the two liquidus curves. 

If the solution is dilute (i.e. the liquidus curve exists over a narrow concentration range near the pure solvent axis), then the activity coefficient of the solute in the liquid solution can be replaced by its value at infinite dilution. Furthermore, a simple relationship may be employed for the temperature-dependence of the infinite-dilution activity coefficient as follows  

The liquidus curves can be obtained by solving the thermodynamic relationship already presented above, since pure solid A, pure solid B, or pure solid AB is in equilibrium with a liquid phase in each of the instances described. The fugacity of pure subcooled liquid AB may be obtained by considering the reaction equilibrium in the liquid phase, so that 

The standard Gibbs energy may be obtained from the standard Gibbs energies of fusion and dissolution of solid AB. 

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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... 

The distribution-coefficient concept is commonly applied to fractional solidification of eutectic systems in the ultrapure portion of the phase diagram. If the quantity of impurity entrapped in the solid phase for whatever reason is proportional to that contained in the melt, then assumption of a constant k is valid. It should be noted that the theoretical yield of a component exhibiting binary eutectic behavior is fixed by the feed composition and position of the eutectic. Also, in contrast to the case of a solid solution, only one component can be obtained in a pure form. 

The eutectic reaction, upon cooling, is similar to solidification for pure components in that the reaction proceeds to completion at a constant temperature, or isothermally, at Te- However, the solid product of eutectic solidification is always two solid phases, whereas for a pure component only a single phase forms. Because of this eutectic reaction, phase diagrams similar to that in Figure 9.7 are termed eutectic phase diagrams components exhibiting this behavior make up a eutectic system. 

In Chapter 8, the simple case of totally immiscible solids, exhibiting a minimum melting eutectic, was discussed. There are a variety of other behaviors that can be demonstrated in solid-liquid equilibria. For example, a solid solution may be formed. In a solid solution, the arrangement of atoms shows some degree of randomness on the molecular level. This occurs in a substitutional solid solution, where the components are very similar and can substitute for each other in the solid lattice. Although the lattice is regular, which atoms in the lattice are substituted is random. (If the substitution were periodic, the system would be a compound.) Copper and nickel illustrate this behavior and form a substitutional solid solution at all concentrations. Another type of solid solution is an interstitial... 

The polymorphic nature of the multicomponent TAG systems is related to phase behavior that is affected by molecular interactions among the component TAGs. The fat crystals in a miscible phase may exhibit simple polymorphic properties. By contrast, the immiscile eutectic phase may show complicated polymorphic properties as a superposition of the polymorphic forms of the component TAGs. Furthermore, if the molecular compound is formed by specific TAG components, the polymorphic behavior becomes complicated, as shown for the case of POP-OPO (see Section 5.2). Therefore, knowing the phase behavior of the principal TAG components is a prerequisite for precise understanding of the polymorphism of natural fats. 

The Pb-Bi alloy system exhibits behavior of an eutectic between an hep intermetaUic fi phase and the Bi terminal phase at 56.5 wt% Bi and 125 °C. Both Pb and Bi have low cross sections for neutron absorption such that these alloys are attractive in heat transfer applications in nuclear reactor systems [1.299]. 

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