Tangent Plane Distance TPD Analysis

Consider moles of a homogeneous mixture at temperature T and pressure P. The overall mole fractions are zi = Ni/ The 

Gibbs free energy of the homogeneous single-phase system (see Fig. 4.6a) is 

If AG 0 for all feasible values of x, then the original state at 1 is stable and G cannot be further reduced (that is, G is a global minimum at constant T and P). However, if AG 0 for any feasible value of x, then the original state is unstable and the single phase will split into more than one phase it may split into two phases, three phases, or more. When AG = 0, the system is said to be neutral. 

From the Gibbs-Duhem equation at constant T and P, (see Eq. (1.40), of Chapter 1) which after dividing by becomes 

Now we define the tangent plane distance (TPD) as the difference from T Xi) to ( i) at any point  

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