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Phase Diagram

Fig. 8.10 Phase diagram derived from Fig. 8.9 (after Ref. 1)

Temperature T6 is the melting point of pure A, and is the first temperature at which a solid phase appears from the liquid. At this point, the free energy-composition plot shows that gL = ga. For the entire composition range, the liquid is the stable phase because its free energy is lower than that of either of the two solid phases. Transferring this information from the T6 plot in Fig. 8.9 to the T6 isotherm in the phase diagram of Fig. 8.10 shows a liquid-to-solid a transition at point a. Only liquid is present over the composition range 0 < xB < 1.

At temperature T5, point b is the melting temperature of pure B in the P crystal structure. In addition, the a and L curves are joined by a common tangent at points c and d. At all compositions to the left of c, solid solutions of B in A with the a crystal structure exist. Between c and d, the system's lowest free energy lies along the common tangent. In this interval, liquid of composition at point d and solid a of composition c coexist. For compositions larger than that at d, liquid is the lowest free energy phase. Translating points b, c, and d to the T5 isotherm in the phase diagram shows the phases indicated by the free energy curves.

At temperature T4, the liquid free energy curve has risen relative to the solid curves to the extent that two common tangents can be drawn, one to the a curve and the other to the P curve. This implies that both a+L and P+L two phase zones are present in the phase diagram at this temperature.

T3 is a unique temperature because a single common tangent links the three free energy curves in Fig. 8.8. When transferred to the phase diagram, the isotherm at T3 shows that three phases coexist at equilibrium: a and P solid solutions with compositions at points j and l, respectively, and a liquid with composition at point k. This point is called the eutectic point, meaning that it corresponds to the lowest-temperature point in the phase diagram at which the system is all liquid.

At the two temperatures T2 and Ti below the eutectic temperature, common tangents join the two solid phases. In Fig. 8.10, A-rich solid solutions with crystal structure a are stable up to mole fractions of B corresponding to points m and o. Further addition of B to the system results in precipitation of a B-rich P phase at the corresponding compositions n and p. The two-branch curve omj/acej is called the terminal solubility of B in a-A. Similarly, the counterpart on the B-rich side of the phase diagram is the terminal solubility of A in P-B.

Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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