## Oxygen isobars on a phase diagram

Phase diagrams are a convenient vehicle for displaying the equilibrium oxygen pressures generated by a metal and its oxides. In elements with multiple oxidation states and/or crystal structures, the equilibrium may not involve only the metal and an oxide, as in the MO2/M couple discussed in the previous section. In particular, two-phase regions separating two different oxides are represented by reactions of the following type:

The stoichiometric coefficients w and z are determined by balances on M and O:

wm = m', or w = m'/m wn + 2z = n', or z = %(n'-nm'/m)

the integers m, n, m' and n' characterize the two oxides. The equilibrium oxygen pressure is dependent on the free energy of formation of the above reaction:

po is actually a surface in the 3rd dimension of the temperature-composition plane; it is a more complex version of the equation-of-state surface of water (Fig. 2.7). As in the case with the EOS of water, projection of the po surface onto the T, O/M plane permits semi-quantitative use of the information contained the surface.

Figure 8.14 displays the po projection onto the Fe/O phase diagram. This diagram is the two-component analog of the familiar diagrams for a single-component substance such as water (Fig. 2.8). In single-phase regions, po is a function of T and O/Fe; in the two-phase zones, po is a function of temperature only (the phase rule: add a phase, lose a degree of freedom)

The 4 two-phase zones in Fig. 8.14 control the oxygen pressure by the following equilibria:

In the iron-rich region

In the oxygen-rich region

13^Fe1—xO(wustite) + J^gy O2 — Fe304(magnetite) ^2yFe3—yO4 (magnetite) + y) O2 — Fe2O3(hematite)

The stoichiometric coefficients in the above reactions were determined by the method described at the beginning of this section. 