Phase equilibria and mixing reactions

A continuous increase in the oxygen partial pressure causes /icu in CU2O to fall until CuO forms. Now, the copper potential is the same in both oxide phases. The corresponding oxygen potential is coupled to the Cu potential. This can be demonstrated in the following way For CU2O we may formulate 

Again it is possible to apply Eq. (4.29). Since, as already discussed (Eq. (4.17)), miaO in CuaO - A Ca20 we obtain the desired coupling 

It is the purpose of the next chapter, which deeds with defect chemistry, to demonstrate not only that the deviation from the Dalton composition is determined by the defect concentrations, but also that the chemical potentials of the components are determined by the chemical potentials of the defects . In many cases of interest, the latter quantities can be represented by a Boltzmann relation (Eq. (4.19a)) as a function of defect concentrations. Such simple functions do not in almost all relevant cases apply to the relationships between component potentials and component concentrations (ncu in CU2O const -1- RTln [Cu]). 

There is, however, a Boltzmann relationship (and then over the entire solubility range), if the partners are so similar that there is no heat of mixing produced and the entropy of mixing only occurs as a result of the (ideal) configuration effect. Thus moving far away from the above example, let us consider a mixture of A and B at AxBi x = C formed according to 

In the case of an ideal mixture AmU = 0 AmH and AmG = —TAmS. The simple site-statistical analysis yields AmGto = RTEkXklnXk = RT(xlnx + (1 — x)ln(l - x)) and Mk = = obtained in the Boltzmann form as 

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