3.13.3 Ionic conduction in cubic ZrO₂

Zirconia, ZrO₂, is made stable in cubic form by doping with small amounts, ~8-10%, of aliovalent CaO or type of impurities. Cubic ZrO₂ is considered as a very good and fast ion conductor. Oxygen vacancies, the prevailing defects in Cubic ZrO₂ are created according to

Small energy of migration (Z_i)e of oxygen vacancies results in an unusually high diffusion of oxygen vacancies in ZrO₂.

Example: Take the case of Ca_0.14 ,Zr_0.86, O_1.86 . Bandgap of ZrO₂ is ~5.2 eV.

At high temperatures, the diffusion coefficient is given as

From the defect reaction

You can show that 14% molar concentration of CaO in ZrO₂ gives rise to an oxygen vacancy concentration of ∼ 3.9*10²¹ cm^-3.

Now, ionic conductivity can be written as

Mobility can be derived by using Nernst-Einstein equation as the following

Hence, ionic conductivity is

Electronic conductivity is calculated as

At 1823 K, electron concentration, n_e , using band model, is estimated to be 1.32*10¹³ cm^-3 and electron mobility, μ_e , is 24 cm²/V.s

Hence, the electronic conductivity is

• From the above analysis it turns out that σ_ionic >> σ_elec .

• σ_ionic increases only until about 12-13% of CaO doping and then decreases due to increased defect interactions.