Gibbs-Duhem Relation for Binary Oxides

The chemical potentials of the various components in a multicomponent system are interrelated. The relationship for binary compounds, known as the Gibbs-Duhem equation, is developed here. Its applicability and usefulness, however, will only become apparent later in Chap. 7. 

In terms of the building blocks of a binary MOc compound, one can write 

Furthermore, since locally, the anions and cations are subjected to the same potential 0, it follows that for a binary oxide 

This expression is known as the Gibbs-Duhem relatiomMp and it expresses the fact that the changes in the chemical potentials of the building blocks of a binary crystal (i.e., anions and cations) are interrelated.  

In textbooks of solution thermodynamics the Gibbs-Duhem is derived as + - b = 0  

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