2.17 Example: Comparative Behavior of TiO₂ and MgO vis-à-vis Oxygen Pressure

Magnesium oxide in intrinsic form, primarily contains Schottky defects. However, under oxidizing conditions, defect reaction would be

with the equilibrium constant as    which is experimentally determined to be

It can be seen from the above equations that K_ox increases as the temperature increases; i.e. MgO can be oxidized at high temperatures producing extrinsic Mg vacancies and holes if no other defects are present.

Further from electrical neutrality condition,

It should be noted that though actual concentrations can be very small but they still do vary with temperature and oxygen pressure.

For example, at 80% of T_m (2480 K) in air i.e. pO₂ = 0.21 atm

which is equivalent to a deficiency of x=0.6 ppm in Mg_1-xO,
While in pO₂ of 10^-9 MPa,

which is equivalent to a deficiency level of x=0.04 ppm in Mg_1-xO.

In comparison, TiO_2-x is more non-stoichiometric and prone to having oxygen deficiency. The reduction reaction is

From the electrical neutrality condition

[]

and

The reaction constant is

= [ ]

and is experimentally determined to be  MPa.cm^-1 .
Now, at 0.8 T_m, i.e. 1690 K

In air

[] =

which is equivalent to a deficiency (x) of 93 ppm.

While at a pO₂ of 10^-9 MPa,

[] =

which is equivalent to a deficiency of x~0.27% in TiO_2-x and makes TiO_2-x an n-type semiconductor due to the resulting high electron concentration.