Module 2: Defect Chemistry and Defect Equilibria
  Defect Structures involving Oxygern Vacancies and Interstitials
 


2.13.1.3 Stoichiometric Condition, i.e., Intermediate pO2

Case - I:  Intrinsic ionization dominates i.e.

The defect reaction is

The corresponding reaction constant is
OR
[ ] and
(2.65)

Here both ne and nh are independent of pO2 while the point defect concentrations are given as from (2.50)

(2.66)

and from (2.51)
(2.67)

Case – II: Internal disorder and anti-Frenkel defects dominate i.e.

The reactions are
(2.68)
Now, since  and [] are independent of pO2 , using (2.50) and (2.51) respectively, ne and nh are given as
(2.69)
(2.70)
The above equations provide the limiting conditions of oxygen partial pressure separating three regimes of oxygen pressures with variations of defect concentration vs pO2 obtained. From this we can plot a defect concentration vs pO2 plot, also called as Brouwer’s Diagram. Such diagrams are extremely important in defect chemistry to understand the dominating defects which govern the physical processes.