## Cd Mole fraction Zr (component B ), x

Fig. 8.3 Phase diagram of a binary system with ideal behavior in both liquid and solid

Mole fraction Zr (component B ), x

Mole fraction Zr (component B ), x

Fig. 8.3 Phase diagram of a binary system with ideal behavior in both liquid and solid

Example In the right-hand plot, horizontal and vertical lines are superimposed on the phase diagram in order to illustrate important characteristics of the melting process. If the solid solution with a composition xB = 0.4 is heated, the intersection of the vertical line with the solidus (at point A) shows that the first liquid appears at 1630 K and has a composition xBL = 0.21 (at point B). As the temperature is increased to 1700 K, the system lies at point P. Here a liquid phase with composition xBL = 0.31(point C) and a solid phase with xBS = 0.49 (point D) coexist. The fraction of the mixture present as liquid at point P is obtained from the mole balance known as the lever rule3:

Fraction liquid at point P = = = ——-— =-= 0.50

Upon heating from point P, the last solid disappears at T = 1790 K (Point E on the liquidus). Melting of this binary system at this particular overall composition is spread over a 160 K temperature range.

Problem 8.6 provides additional practice in applying ideal-melting theory to the MnO-FeO binary system. The effect of even slight deviations from ideal solution behavior can result in phase diagrams that are distorted or qualitatively different from the diagram shown in Fig. 8.3. Problems 8.8, 8.9 and 8.16 explore the nonideality effect on this type of phase diagram using regular solution theory for the solid and liquid phases. 