Free-Energy Composition and Temperature Diagrams

The previous sections dealt with various types of phase diagrams and their interpretations. What has been glossed over, however, is what determines their shape. In principle, the answer is simple the phase or combination of phases for which the free energy of the system is lowest is by definition the equilibrium state. However, to say that a phase transformation occurs because it lowers the free energy of the system is a tautology, since it would not be observed otherwise — thermodynamics forbids it. The more 

The objective of this section is much less ambitious and can be formulated as follows If the free-energy function for all phases in a given system were known as a function of temperature and composition, how could one construct the corresponding phase diagram In other words, what is the relationship between free energies and phase diagrams Two examples are considered below polymorphic transformation in unary systems and complete solid solubility. 

Congruent melting of a compound, or any of the polymorphic transformations discussed earlier, is a good example of this type of transformation. To illustrate, consider the melting of a compound. The temperature dependence of the free-energy functions for the liquid is 

Gj-ijq is steeper than Gj because the entropy content of the liquid is larger (more disorder) than that of the solid. The salient point here is that at the temperature above which the lines intersect, the liquid has the lower energy and thus is the more stable phase, whereas below that temperature the solid is. Not surprisingly, the intersection temperature is the melting point of the solid. 

The free-energy versus composition diagram for a system that exhibits complete solid solubility is shown in Fig. 8.11. The components of the diagram are the two vertical axes that represent pure AO (left) and pure 

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