The binary systems treated in the preceding sections were either ideal (melting-solidification) or deviated positively from ideality according to regular solution theory (phase separation). These simple types are rarely found in real binary systems. First, there may be more than one solid phase, each with a distinct crystal structure, just as there are in pure substances (see Sect. 5.6). Second, the liquid phase and the solid phase(s) are generally nonideal. The extent of deviation from ideality is usually different in each phase, and may not be adequately represented by regular solution theory. Very negative deviations from ideal solution behavior, indicative of strong A-B interaction, often lead to the formation of distinct compounds that appear in the phase diagram (e.g., AB2, A2B, AB). The increased physical complexity of such systems renders analytic calculation of the phase diagram amenable only to analysis by computer codes.
Irrespective of the complexity of the nonideal behavior of the phases involved, the phase diagram can always be constructed if the free energy Vs composition curves for each phase can be drawn. The link between the two graphical representations is the common-tangent rule. Because of the wide variations in the shapes of free-energy curves, the types of phase diagrams deduced from them reaches zoological proportions. In this section, a common variety called the eutectic phase diagram5 is developed by the graphical method.
The prototypical eutectic system consists of one liquid and two solid phases, labeled a and p. The a phase has the crystal structure of pure solid A and the P phase that of pure B. The two structures are usually different, as opposed to the phase-separation system, in which solids A and B have the same structure (see Figs. 8.6 and 8.7).
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