2.11 Defect Equilibria in Stoichiometric Oxides

The defects which we usually consider in stoichiometric oxides are Schottky and Frenkel defects and following paragraphs so analysis for both these kinds of defects for an oxide MO.

2.11.1 Schottky Defects

Defect reaction in an oxide MO is written as

Equilibrium constant for this reaction is

KS = [] [VM'']

Here square brackets i.e. [ ] are used for concentration.
Equilibrium constant can be also be expressed as

(2.22)

where ΔG_S is the molar free energy of defect formation and is ΔH_S - TΔS_S, where ΔH_S is the enthalpy for defect formation and ΔS_S is the entropy change which is mainly vibrational in nature and can be assumed to be constant. This leads to

(2.23)

If Schottky defects dominate, then

[]

(2.24)

Here, as one can see, defect concentrations are independent of pO₂.

2.11.2 Frenkel defects

For an oxide MO

which leads to 

(2.25)

OR

At reasonably low defect concentrations when

Thus

If Frenkel defects dominate, then

i.e.

In a similar manner what we did above for Schottky defects, one can now write

[Mi••]=[VM'']

(2.28)

Again we can see that the defect  is independent of pO₂.