Line, equilibrium eutectic

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].

At the eutectic point the three phases are in equilibrium. The compositions of the two new phases are given by the ends of the line through the eutectic point. 

Below the equilibrium lines, but above the eutectic temperature, a liquid and solid are in equilibrium. Under line ac, solid benzene, and liquid Li, whose composition is given by line ac, are present. Under line be, the phases present are solid 1,4-dimethylbenzene and liquid Li, whose composition is given by line be. Below point c, solid benzene and solid 1,4-dimethylbenzene are present. In the two phase regions, one degree of freedom is present. Thus, specifying T fixes the composition of the liquid, or specifying X2 fixes the temperature.cc Finally, at point c (the eutectic) three phases (solid benzene, solid 1,4-dimethylbenzene, and liquid with x2 = vi.e) are present. This is an invariant point, since no degrees of freedom are present. 

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

Fig. 22 Dissolution fates of various griseofulvin and gri-seofulvin-succinic acid samples as determined by the oscillating bottle method. , griseofulvin, crystalline A, griseofulvin, micronized , eutectic mixture 0> physical mixture at eutectic composition , solid solution A, physical mixture at solid solution composition. The dashed line indicates the equilibrium solubility of griseofulvin in water. (From Ref. 41.).

On the other hand, if the enantiomeric purity of the original solid is less than that of the eutectic (as in the case of M2 in Fig. 25b), crystallization results in a decrease in enantiomeric purity. For example, when sufficient solvent has been added to correspond to point P2, the tie line shows that the solid N2 contains less of the predominant enantiomer D than M2 and is in equilibrium with E, which corresponds to a saturated solution of the eutectic solid, e. When the system reaches the composition represented by point Q2, the solid that crystallizes out is the racemic compound, R, which is in equilibrium with the saturated solution, U2, containing the racemic compound and enantiomer D. 

If solvent is added to either of the solid eutectics represented by e or e in Fig. 25a or b, the undissolved solid retains this composition while the saturated solution maintains the composition E or E, respectively. Again, Gibbs phase rule [145,146] can provide further insight into these systems. If the solid enantiomers are solvated, the compositions of the equilibrium solids are displaced symmetrically along the DS or LS axes to an extent determined by the stoichiometry of the solvates. Similarly, if the racemic compound is solvated, the stoichiometry of the equilibrium solid is displaced from R along the line RS to an extent determined by the stoichiometry of the solvate. 

The temperature of the eutectic equilibrium is called the eutectic temperature and is shown as a horizontal line in Figure 4.1. 

In the present case there are no ternary invariant equilibria in the system, partly due to the complete solid solubility of the A-B system. In a ternary system composed from three binary eutectic sub-systems, three univariant lines would meet in a ternary eutectic equilibrium ... 

Figure 2.36. Au-Sb system. The continuous line represents the (equilibrium) phase diagram containing the peritectic melting AuSb2 compound and a eutectic equilibrium (Es). Dotted lines represent equilibria (and phases) which may be observed on rapid cooling. The sequence of phases (C, AuSb2, it) detected in fast-quenched alloys and their composition ranges are shown in the...

For the niobium-copper system different phase diagrams of the simple eutectic type (with the eutectic point very close to Cu) have been proposed, either with an S-shaped near horizontal liquidus line or with a monotectic equilibrium. It was stated that the presence of about 0.3 at.% O can induce the monotectic reaction to occur, whereas if a lesser amount of oxygen is present no immiscibility gap is observed in the liquid. 

Crystallization, by definition, implies that the initial structure be a glass, followed by the nucleation and growth of a crystalline phase, be it the equilibrium one or a metastable phase. The process is a first-order transformation and involves atomic diffusion, or at least atomic shuttles. Types of crystallization reactions that occur include polymorphous crystallization, which is a composition invariant transformation such as that in Fe-B, and eutectic crystallization, T, in FeNiPB glass, where line lamellae of iron-nickel austenite and mclastable (FeNiJj PB phases grow cooperatively. 

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