Gibbs free energy and non-stoichiometry

These conditions can be satisfied by drawing the common tangent to the G curves of M(O) and MO. As shown in Fig. 1.7, the chemical potentials of M and O for the M(O) phase with the composition x, are equal to those for the MO phase with the composition Xj, and the values correspond to MqMj and OgO, respectively. If the experimental conditions are similar to those described in Section 1.1, the solid phases must coexist with the gas phase. It may be adequate for the gas phase to be pure O2, because the vapour pressure of other species is very low in this case. The chemical potential of O for the gas phase is equal to OgO, which corresponds to the oxygen pressure. Thus we can understand the coexistence of the M(O) phase with Xj and the MO phase with X2 from the free energy change of composition. 

At the composition X between x, and X2, let the mixed phase M(O) -+- MO have the mole ratio of Then we have 

The number of oxygen atoms in the mixed phase is equal to the sum of that in the M(O) and MO phases  

This relation is called the lever law or lever rule (Fig. 1.8), which shows 

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In this chapter, we discuss classical non-stoichiometry derived from various kinds of point defects. To derive the phase rule, which is indispensable for the understanding of non-stoichiometry, the key points of thermodynamics are reviewed, and then the relationship between the phase rule, Gibbs free energy, and non-stoichiometry is discussed. The concentrations of point defects in thermal equilibrium for many types of defect structure are calculated by simple statistical thermodynamics. In Section 1.4 examples of non-stoichiometric compounds are shown referred to published papers. 

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