2.19 Examples

2.19.1 Intrinsic electronic and ionic defect concentrations  in MgO 

Consider that a material like MgO usually has Schottky defects with enthalpy of formation (ΔH_F)) of about 7.7 eV. Its band gap is about 7.65 eV which decreases at a rate of 1 meV per K as MgO is heated.

The question is that in case of an absolutely pure and stoichiometric MgO, which defects are likely to be created and present in higher concentrations at a temperature of say 1400°C or 1673 K?

We can calculate the Schottky defect concentration as

Electron and hole concentrations are calculated as

In MgO,

and

where m_o is the mass of free electron and is 9.1×10^­31 kg.

At 1673K, E_g = 7.85 eV – (1570*1*10^­3 ) eV = 6.28 eV .

Hence, n_e = n_h = 4.6*10¹⁰ cm^­3

Now magnesium vacancy concentration can be calculated as

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Hence, at 1400°C, despite high energy of Schottky defect formation, the vacancy concentration will be slightly larger than the electronic carrier concentration due to thermal excitation.