The predominant-defect generalization

As Wagner did with binary compounds, in a more complex solid, it is possible to take account only of the defects deemed to be predominant and describe the solid in view only of those defects. 

Let us take the example of metal oxy-hydroxides such as boehmite (AlOOH). We can describe the ideal solid using the following structure elements  

True boehmite exhibits defects in relation to the sites of the hydroxyl groups. The defect of an oxygen ion in substitution of OH (which must not be confused with an oxygen ion in the oxygen position) is taken to be the predominant defect. So that electrical neutrality is respected, thus results in the presence of vacancies of OH ions, such that we have  

Because of the conservation of the sites of the OH ions, we need the relation  

for the description of the properties of boehmite linked to the loss of water, we do not need to worry about the aluminum ions and oxygen ions placed in their normal positions. The departure of the water is expressed by the reaction  

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