Ideal Binary Eutectic Phase System

If the liquid phase is ideal, but the solid phase only consists of a pure crystalline component, we have a eutectic system. These phase systems allow crystallization of a pure component in a single step, until the point of eutectic composition is reached, where the solid and the liquid phase have the same composition. Hence, 

In this case, Eq. (3.3.91) simplifies (x = 1 for the compound that crystallizes)  

For a binary system, the composition of the liquid phase has to fulfill the condition  

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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). 

Many binary systems, both ideal and nonideal, have phase diagrams of the simple eutectic type. The phase diagram, water-salt, is the simple eutectic type if the salt does not form a stable hydrate. The diagram for H20-NaCl is shown in Fig. 15.10. The curve ae is the freezing-point curve for water, while efis the solubility curve, or the freezing-point curve, for sodium chloride. 

Although this equation (due to the simplifications made) just applies to ideal systems, it can be used to predict the liquidus curve as a first approximation from the melting temperature and heat of fusion of the substance which are easily accessible from a DSC measurement. After calculating the liquidus lines for both components of the binary system, the eutectic composition in the phase diagram can be derived from the intersection of the two liquidus lines. To account for deviation from ideality. Equation 3.8 can be modified by re-introducing the activity coefficient Y replacing x by(x y). 

Figure 13.2 shows two temperamre-composition phase diagrams with single eutectic points. The left-hand diagram is for the binary system of chloroform and carbon tetrachloride, two liquids that form nearly ideal mixmres. The solid phases are pure crystals, as in Fig. 13.1. The right-hand diagram is for the silver-copper system and involves solid phases that are solid solutions (substimtional alloys of variable composition). The area labeled s is a solid solution that is mostly silver, and s is a solid solution that is mostly copper. Tie lines in the two-phase areas do not end at a vertical line for a pure solid component as they do in the system shown in the left-hand diagram. The three phases that can coexist at the eutectic temperature of 1,052 K are the melt of the eutectic composition and the two solid solutions.

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