Writing defect reactions:

a$.$ Write the appropriate defect reaction for incorporation of magnesium oxide $($MgO$)$ in nickel oxide $($NiO$).$

b$.$ Write the appropriate defect reactions for formation of a Schottky defect in alumina $(A{l}_2{O}_3).$

c$.$ Write the appropriate defect reaction for the incorporation of calcium oxide $($ CaO in zirconia $(Zr{O}_2)$ using Kr$$ger$-$Vink notation. Assume that $C{a}^{+2}$ will occupy $Z{r}^{+4}$ sites.

d$.$ Write the appropriate defect reaction for the incorporation of calcium oxide $($CaO$)$ in lithia $(($:$L{i}_{2}O\}.$ Assume the $C{a}^{2+}$ substitutes for $L{i}^{+}.$

e$.$ Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.