2.13 Defect Structures involving Oxygen Vacancies and Interstitials

Depending upon the partial pressure of oxygen, an oxide may be oxygen deficient (or metal excess) or metal deficient (or oxygen excess).
Let us consider the following conditions in an oxide MO:

• Low pO₂ i.e. oxygen vacancies dominate.

• High pO₂ i.e. oxygen interstitials dominate.

• At intermediate pO₂ i.e. oxide is stoichiometric.

Assuming that both oxygen vacancies and oxygen interstitials are doubly charged (fully ionized), the defect reactions can be written as follows:

• At low pO₂

The defect reaction can be written as

+ [] + 2e'

The corresponding reaction constant, assuming [M_M] and [O_O] =1, would be

[]

(2.50)

• At high pO₂

The defect reaction is

and hence the reaction constant is

(2.51)

• At intermediate pO₂

Stoichiometric defects are likely to prevail i.e. either via intrinsic ionization or Anti-Frenkel defects.

• Intrinsic ionization of electrons and holes

  and corresponding reaction constant is

  (2.52)

• Similarly formation of oxygen Frenkel defects (Anti-) leads to with reaction constant as
  

  .[]

  (2.53)

• From the above four relations, we can write
  

  (2.54)