Chapter 2 explains the concepts behind T–c phase diagrams, which are maps of the phases that exist in an alloy of chemical composition c at temperature T. A T–c phase diagram displays the phases in thermodynamic equilibrium, and these phases are present in the amounts f, and with chemical compositions that minimize the total free energy of the alloy. The emphasis in this chapter is on deriving T–c phase diagrams from free energy functions F(c, T). The constraint of solute conservation is expressed easily as the “lever rule.” The minimization of the total free energy leads to the more subtle “common tangent construction”, which selects the equilibrium phases at T from the F(c) curves of the different phases. For binary alloys, the shapes of F(c) curves and their dependence on temperature are used to deduce eutectic, peritectic, and continuous solid solubility phase diagrams. Some features of ternary alloy phase diagrams are also discussed.

If atoms occupy sites on a lattice throughout the phase transformation, free energy functions can be calculated with a minimum set of assumptions about how different atoms interact when they are brought together. Because the key features of phase diagrams can be obtained with general types of interactions between atoms, systems with very different types of chemical bonding, e.g., both oil in water and iron in copper, can show similar phase transitions.