Stability condition and miscibility based on first-order deviations from SI solutions

6 Stability condition and miscibility based on first-order deviations from SI solutions 

In this section we discuss the stability conditions of a mixture with respect to material flow. There are several ways of expressing the condition of stability. The simplest is in terms of the derivatives of the chemical potential. 

Basically, this condition means that if a fluctuation occurs at some region in the system such that xA increases relative to the bulk composition, then the corresponding chemical potential in that region must increase. As a result of this, A will flow out of the region, and the equilibrium composition in this region will be restored. 

Another way of expressing the stability condition is in terms of the Gibbs energy of the system. If G is the Gibbs energy of the mixture, then 

Taking the second derivative with respect to xA and using the Gibbs-Duhem relation, we obtain 

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