With these preliminaries, the metal oxidation example used in the preceding section is modified by dissolving reactant metal M in another metal P that is inert and does not react with oxygen. To account for the presence of M in this alloy, the equilibrium reaction reads:
Using Eq (9.43) for the chemical potential of M, Eq (9.32) is replaced by:
aM is related to the mole fraction of M in the alloy and its activity coefficient according to Eq (8.35). However, for simplicity of notation, the activity is retained. Solving the above equation for the oxygen pressure gives the solution forms of Eq (9.33):
or, in terms of the oxygen potential:
RTlnpO =AGo -RTlnaM (9.46b)
In these equations, the meaning of AGo is the same as given by Eq (9.34).
Since the activity of M in the alloy must be less than unity, Eq (9.46) shows that the oxygen pressure, or the oxygen potential, is increased by dilution of M with the inert species P.
Although the solvent metal P is inert chemically, it constitutes an additional component as far as the phase rule is concerned. Applying Eq (9.35) with P =3 (as before) but changing C to 3 (M, P, and O) gives F = 3 + 2 - 3 = 2. The two degrees of freedom are temperature and composition, the latter being the mole fraction of M in the alloy. The stability diagram in Fig. 9.7 for oxidation of M in the alloy consists of a family of lines lying above but parallel to the line for pure M. Each line represents a different activity (i.e., mole fraction) of M in the M-P alloy.
~ decreasing xM
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