Eutectic Behavior

Eutectic diagrams (from Greek svTJ]KToa easily melted ) represent the T-x melting behavior for binary systems with completely immiscible solid phases a, (3. The solid a, f3 phases often correspond to (virtually) pure components A, B, respectively, so we may treat phase and component labels (rather loosely) as interchangeable in this limit. 

The diagram shows the homogeneous liquid (melt) region (with /= 2) as well as the three distinct two-phase regions (each with /= 1). The junction of these regions is the eutectic point (triangle), a triple point (with /= 0). 

In each hatched two-phase region, the lever rule (Section 7.3.2) can be used as usual to determine the relative amounts of the two phases at opposite ends of the tie-line. However, the quantity of precipitated solid a and/or f3 is usually of less interest than the composition of the melt, so the principal focus is on the two liquidus lines that meet at the eutectic point. These liquidus lines are also called solubility curves or freezing-point depression curves, in that they map both the saturation-solubility limits (horizontal variations) as well as the freezing-point depression of the liquid (vertical variations). 

The dashed lines in (7.90) illustrate an expected cooling path for a liquid chosen to be of initial concentration jc = jcb — 0.1. As cooling proceeds (1), the first precipitate of solid a appears when the cooling path meets the a-liquidus curve. Thereafter, as solid a proceeds to freeze out of solution, the melt is successively depleted of component A and moves down the a-liquidus curve (2) toward the eutectic point. At this point, the remaining liquid freezes to a mix of solid a and (3 (in proportion to eutectic composition), and the mix of solids 

Binary systems exhibiting simple eutectic behavior are rather common, including metallic pairs such as Bi/Cd or Pb/Sb, inorganic saline solutions such as NaCl/H20, and organic systems such as naphthalene/benzene. 

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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. 

Some mixtures of organic substances may be separated advantageously by cooling and partial crystallization. The extent of such recovery is limited by the occurrence of eutectic behavior. Examples 16.2 and 16.8 consider such limitations. Sometimes these limitations can be circumvented by additions of other substances that change the phase equilibria or may form easily separated compounds with one of the constituents that are subsequently decomposed for recovery of its constituents. 

The shape of the DCB curves show within the measuring area the expected eutectic behavior (Figure 4). Because of the similar structure of para and meta DCB the charts under different atmospheres are parallel. 

Eutectic behavior is seen where the SFC of a mixture falls below the SFC for either of the two individual components, as seen between 30% and 70% milkfat in Figure 7. Isosolids diagrams allow phase compatibility to be studied (4), but they do not provide a thermodynamic measure of driving force for crystallization. Again, because the crystal phase composition may be different at different temperatures (and mixture ratios), isosolids diagrams do not represent true phase diagrams. 

Impurities are measured, which have an eutectic behavior (i.e., solubles in the liquid phase and insolubles in the solid phase). 

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... 

Both Te and i//c vary widely among solutes. Further details of the phase diagram can also vary. For instance, it is seen in the figure that fructose has two crystalline phases (with and without water), but other systems are different, being either simpler or having more phases. Some mixtures do not show eutectic behavior see Section 15.4.3. 

Mixture studies between various derivatives of 142 were unremarkable, showing a linear dependence of the SmA clearing point with composition and eutectic behavior in the melting point. ... 

Less than 1% of racemic species are pseudoracemates, which show typical phase diagrams of continuous solid solutions. Figure 2c shows the three types of melting phase diagrams of pseudoracemates, which comprise ideal solid solutions, solid solutions with positive deviations from ideality, and solid solutions with negative deviations from ideality, respectively [13]. In real systems, the enantiomers and the racemic compound may display a small mutual solubility, even if they show eutectic behavior, which corresponds to terminal solid solutions for which the phase diagrams are shown in Figs. 2d and 2e. 

When the rate of drug absorption is controlled by the dissolution rate, the bioavailability of a drug increases with an increase of its dissolution rate. The dissolution rate is proportional to the solubility, regardless of dissolution mechanism. The solubilities of the two enantiomers are identical in an achiral solvent. The theoretical ternary solubility phase diagrams of racemates are represented by Fig. 6. The solubility phase diagram of a conglomerate (Fig. 6a) shows eutectic behavior. 

Figure 13.3. Melting points of copolymers of hexamethy-lene adipamide and terephthalamide, and of hexamethylene sebacamide and terephthalamide (Billmeyer, 1962, pp. 213-214 Edgar and Hill, 1952). Adipamide copolymer with terephthalamide forms isomorphous crystals, whereas seba-camide-terephthalamide copolymers result in more normal melting-point depression curves, which superficially resemble curves characteristic of eutectic behavior.

Construct the SLE diagram for the ternary system o-xylene-m-xylene-p-xylene assuming eutectic behavior. Since isomer compounds are considered, ideal behavior in the liquid phas can be assumed. 

Calculate the solubility of solid carbon dioxide in propane with the help of the group contribution equations of state PSRK and VTPR assuming simple eutectic behavior. Compare the results with the results assuming ideal behavior and the experimental data that can be downloaded from the textbook page on ivww.ddbst.com. All required parameters can be found in Appendix A. 

Estimate the enthalpy of fusion of benzene (1) by regressing the following solubility data of benzene in toluene assuming ideal (yi = 1) and simple eutectic behavior. 

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