Eutectic isotherm

Figure 1.8 presents the phase equilibria in a hypothetical binary eutectic system similar to that in Figure 1.7, represented on each of the three types of diagrams. This diagram is similar to those for the Ag-Cu and Ni-Cr systems. The plot of T versus ub is a Type 1 diagram and the three-phase equilibrium a-L-(3 is represented by a point. The plot of T versus Ab is a Type 2 diagram and the a-L-(3 equilibrium is represented by three points on a line, the eutectic isotherm. The plot of S versus Xb is a Type 3 diagram and the a-L-(3 equilibrium is represented by an area. Note that the forms of these diagrams correspond to those for the unary system in Figure 1.4. (Numerous examples of the three types of phase diagrams are given for unary, binary and ternary systems in Chapter 13 of Reference [2], Reference [5] and Chapter 2 of Reference [8].

The metastable eutectic equilibium occurs at a lower temperature than the stable eutectic isotherm. 

Often, the horizontal solidus line at is called the eutectic isotherm. 

The third case involves solidification of the eutectic composition, 61.9 wt% Sn (C3 in Figure 9.13). Consider an alloy having this composition that is cooled from a temperature within the liquid-phase region (e.g., 250°C) down the vertical line yy in Figure 9.13. As the temperature is lowered, no changes occur until we reach the eutectic temperature, 183°C. Upon crossing the eutectic isotherm, the liquid transforms into the two a and [3 phases. This transformation may be represented by the reaction... 

This means that the compositions of all three phases—as well as the temperature —are fixed. This condition is met for a eutectic system by the eutectic isotherm for the Cu-Ag system (Figure 9.7), it is the horizontal line that extends between points B and G. At this temperature, 779°C, the points at which each of the a, L, and phase fields touch the isotherm line correspond to the respective phase compositions namely, the composition of the a phase is fixed at 8.0 wt% Ag, that of the liquid at 71.9 wt% Ag, and that of the f3 phase at 91.2 wt% Ag. Thus, three-phase equilibrium is not represented by a phase field, but rather by the unique horizontal isotherm line. Furthermore, all three phases are in equilibrium for any alloy composition that lies along the length of the eutectic isotherm (e.g., for the Cu-Ag system at 779°C and compositions between 8.0 and 91.2 wt% Ag). 

A primary (or pre-eutectic) phase and the layered eutectic structm-e are the solidification products for all compositions (other than the eutectic) that he along the eutectic isotherm. 

Figure 24 shows the ternary phase diagram (solubility isotherm) of an unsolvated conglomerate that consists of physical mixtures of the two enantiomers that are capable of forming a racemic eutectic mixture. It corresponds to an isothermal (horizontal) cross section of the three-dimensional diagram shown in Fig. 21. Examples include A-acetyl-leucine in acetone, adrenaline in water, and methadone in water (each at 25°C) [141].

Fig. 24 Isothermal solubility diagrams for a racemic conglomerate, i.e., a eutectic system of the two opposite enantiomers. The appearance of the tie lines is shown in (b). Symbols are defined in the text. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., New York, from Ref. 141, p. 178.)...

For the alloy marked 1 , on cooling, the liquidus curve was intercepted at a relatively high temperature and there was a fair temperature interval during which for the Mg crystals it was possible to grow within the remaining part of liquid. The solidification finally ended at the eutectic temperature. At this temperature the eutectic crystallization occurs (L (Mg) + Cu2Mg) in isothermal conditions, where the simultaneous separation of the two solid phases results in a fine mixture... 

Transition Region Considerations. The conductance of a binary system can be approached from the values of conductivity of the pure electrolyte one follows the variation of conductance as one adds water or other second component to the pure electrolyte. The same approach is useful for other electrochemical properties as well the e.m. f. and the anodic behaviour of light, active metals, for instance. The structure of water in this "transition region" (TR), and therefore its reactions, can be expected to be quite different from its structure and reactions, in dilute aqueous solutions. (The same is true in relation to other non-conducting solvents.) The molecular structure of any liquid can be assumed to be close to that of the crystals from which it is derived. The narrower is the temperature gap between the liquid and the solidus curve, the closer are the structures of liquid and solid. In the composition regions between the pure water and a eutectic point the structure of the liquid is basically like that of water between eutectic and the pure salt or its hydrates the structure is basically that of these compounds. At the eutectic point, the conductance-isotherm runs through a maximum and the viscosity-isotherm breaks. Examples are shown in (125). 

Any appearance of secondary phases can be easily taken into account in this approach with the assumption that no back-diffusion is involved. Therefore all transformations can be handled, including the final eutectic solidification. This approach is based on a series of isothermal steps but, as the temperature step size becomes small, it provides results which are almost completely equivalent to those which would be obtained from continuous cooling. 

As an example, liquefied mixtures are easily formed by using some amino acids protected with acetyl, Boc-, Fmoc- and Z-groups. Some authors have called the resulting systems eutectic mixtures , but this term should be reserved for the textbook definition as the composition of minimum melting point that freezes isothermally at the eutectic temperature. Hence we refer to them as eutectic melts . 

Fig. 16. Calculated liquidus isotherms (solid lines) and solid isoconcentration lines (dotted lines). The labels on the isotherms are in degrees Celsius. The numbers along the InSb-GaSb section label the solid isoconcentration lines and are the mole fraction GaSb in the GaSb-InSb solid solution. The dashed line across the upper part of the figure is the calculated eutectic valley.

First, we discuss a simple ternary eutectic system without solid solution as shown above. The following figures show isothermal sections at a number of different temperatures ... 

Polythermal projections of the liquidus discussed in section 4.3.2. do not provide information on the compositions of solid phases if solid solutions or non-stoichiometric compounds are formed at equilibrium. For providing this information, the method of isothermal section is particularly useful. The following figure represents a simple ternary eutectic system with terminal solid solutions formed. 

Figure 11.6 shows an example of the phase diagram for a reactive system, in which a compound C is formed from components A and B. An isothermal cut and the polythermal projection are also shown. Such a phase diagram can be obtained via a reaction invariant projection of a higher-dimensional simple eutectic phase diagram. AS and BS are binary nonreactive eutectics, since their presence is not affected by the reaction, while ACSb and BCSa are ternary reactive eutectics. Similar... 

Jefremov and Khaibashev [60] have also investigated melts of TNT with other nitro compounds. They observed deep minima on the isotherms of plastic flow of mixtures of TNT and picric acid, trinitroxylene or 1,8-dinitronaphthalene. corresponding to eutectic mixtures. Unlike those the corresponding curves for mixtures of TNT and 2,4-dinitrotoluene, m- dinitrobenzene, and tetiyl, showed an additive character. 

Hydrogen-Absorption Isotherms. The isotherms for the 25 weight % uranium alloy constitute a family of curves closely resembling each other. Seven of the 13 isotherms which were measured are plotted in Figure 3. Isotherms intermediate between each adjacent pair were omitted to reduce the complexity of the plot. The isotherms at 572° C. (not shown) and at 601° C. cross only two phase boundaries, because they are below the eutectic temperature. 

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