Formation of Point Defects by Additives

The concentrations of point defects in ionic compoxmds vary with the concentration of dopants. The defect concentrations can be predicted using defect chemistry where each defect species is considered to be a chemical species and the reactions among defects are expressed as chemical reaction equations. In expressing defect chemical reactions, some basic principles are applied. 

the mass action law must be satisfied between defect species. 

Second, the sum of effective charges on the left-hand side of any reaction equation must be the same as that on the right-hand side. Accordingly, an overall electrical neutrality condition is maintained in the sample. 

the cation to anion site ratio must be constant even for nonstoichiometry (site relation). In other words, as long as the crystal structure of an MaXb compound is maintained, the ratio a/b is invariable. However, the absolute number of sites may vary according to defect reactions. In respect of the site relation, there are species which create lattice sites, for example, 

From the above principles, we can predict the concentrations of various 

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