3.13.2 Mixed electronic ionic conduction in MgO

Here we demonstrate mixed ionic conduction in MgO. For working this out, we need to start with certain parameters. Assuming the temperature is 1600^oC, for MgO, we can estimate

• concentration of Schottky defect ≈ 1.4*10¹¹cm³

• concentration of electronic defects ≈ 3.6*10⁹cm^-3

• Vacancies present are V_Mg^'' and V₀^'' and V_Mg^'' having higher mobility than V₀^'' .

Diffusion coefficient of magnesium vacancies is estimated as

At 1600^oC, one can calculate the mobility from the Nernst-Einstein Equation i.e

However, at 1600^oC

So, even though the vacancy concentration is larger than electron or hole concentration, conduction is dominated by electrons or holes simply because their mobility is orders of more than 6 order of magnitude higher.

However, in reality, MgO is prone to having impurities such as Al₂O₃ with Al concentrations of the order of 400 mole ppm or 2*10¹⁹cm^-3. Using the defect reaction, one can write

Again we assume that the conduction is via Magnesium vacancies. Hence, Ionic conductivity is

However, electronic conductivity can be electron or hole dominated depending upon pO₂ You can prove yourself that electrons dominate under reducing conditions while holes dominate under oxidizing conditions. For example, in normal atmosphere i.e. air (pO₂ = 0.21atm), holes dominate. Hole concentration can be determined using the following defect reaction:

Here,  from the mass conservation, we can see that  n_h = 2 V_Mg^''   and hence the equilibrium constant is

Using the above equation, n_h can be determined at 1600^oC air

So, the total conductivity is

Hence, we can now work out the ionic transference number as

• The system shows mixed electronic and ionic conduction even when vacancy concentration is 10⁵ times higher than electronic ( 2*10¹⁹cm^-3 vs 5*10¹³cm^-3).

• p-type conduction can change to n-type as the pO₂ decreases.