Nonstoichiometric solid solutions or compounds

Nonstoichiometric solid solutions are substances whose composition approximates that of stoichiometric compounds, but which have a range of compositions. The problem of applying thermodynamics to such substances is primarily how to express the composition of the solution. The simplest choice would be to use the mole fractions or atom fractions in terms of the components. In such a case the effects of the formation of the compound from the components would be contained in the values of the activity coefficients or excess chemical potentials. 

In some systems, particularly metal oxides or nitrides, different states of oxidation of the metal or metals could be assumed or actually determined. Expressions for equilibrium constants related to reactions between the atoms in different oxidation states could be set up in terms of the mole fractions of the reacting species. The expressions for the chemical potentials could also be written in terms of these mole fractions. As an example, consider the substance Uj l,Pul02 x. The question might be to determine how the pressure of oxygen varies with the value of x at constant temperature and constant y. We assume that the uranium is all in the oxidation state of +4 and that the plutonium exists in the +3 and +4 oxidation states for positive values of x. The equilibrium change of state is 

By the conditions of mass balance and electroneutrality, we determine the mole fractions to be 

With the mole fractions and the expression for the nonthermodynamic equilibrium constant for the postulated reaction, we can obtain the relation between the pressure of oxygen and x. 

For the expression for the chemical potentials, we choose to use U4+ as an example. We may write 

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