Nonstoichiometry Equilibria with Gaseous Phase

Whilst the above-mentioned disordering processes do not disturb the crystal stoichiometry, the effects of interaction between the crystal and its environment must be taken into account, especially at elevated temperatures [9, 15-19]. In particular, this becomes necessary when one or several lattice constituents are volatile, for example, in the case of oxides, sulfides, and halides. In a heterogeneous system, the condition of phase equilibria is expressed by the equality of chemica] potentials of a given component in both phases  

Let us now consider binary oxide MOi g equilibrated with gaseous phase at constant temperature. The process of oxygen exchange between the solid and gaseous phases can be represented by the following reaction  

In order to simplify the task, we should accept several assumptions (i) that the predominant atomic defects are vacancies in the metal and oxygen sublattices (ii) that metal M is nonvolatile in the conditions under investigation (iii) that the concentration of different defects in the crystal lattice is small enough, so that the atomic fraction ofatoms in regular positions can be taken as [M ] w 1, [Oq] w 1 and interaction of defects can also be neglected and (iv) that the vacancies are completely ionized. Accordingly, the disordering processes can be presented as  

One important task here is to express each defect concentration as a function of the oxygen partial pressure at a given temperature. Hence, the set of nonlinear Equations (3.30)-(3.33) should be solved using the approximation method. The whole range of the oxygen chemical potentials can be tentatively divided into three regions  

Region 2. In this intermediate range of the oxygen partial pressure, there are no dominating reactions and, therefore, the concentrations of metal and oxygen vacancies are comparable. As a consequence, the composition of the oxide phase is nearly stoichiometric. This allows the electroneutrality condition to be approximated by using two altemative expressions  

---