Brouwer Diagrams More Complex Examples

In general, there is little problem in extending the concepts just outlined to more complex materials. The procedure is to write down the equations specifying the various equilibria point defect formation, electronic defect formation, the oxidation reaction, and the reduction reaction. These four equations, only three of which are independent, are augmented by the electroneutrality equation. Two examples will be sketched for the oxides Cr2C 3 and Ba2In2Os. 

The presence of relatively small Cr3 1 cations and the close-packed corundum structure anions suggest that Schottky defects will be preferred. Oxidation will add anions and reduction will remove anions. The four equilibria can now be written. 

These equations can now be simplified in the manner described above. The electroneutrality point is given by 

The approximations to use depend upon the pressure regime and the values of the equilibrium constants. This oxide is an insulator under normal conditions, and so, in the middle region of the diagram, Schottky equilibrium is dominant, that is, Ke and the electroneutrality equation is approximated by 

In the oxidized region, holes and cation vacancies are preferred, so the electroneutrality equation is approximated by 

---