I have three components, $A,B,C$, with 3 Flory-Huggins exchange parameters: $\chi _{AB}, \chi _{BC}, \chi _{AC}$. I want to create a ternary diagram to see how such a mixture behaves and how phase separation takes place i.e find points on the ternary plot where I will see $(A+B,C), (A+C,B), (B+C,A), (A+B+C), (A,B,C)$, where $I+J$ represents a mixed phase of $I,J$ and a separation by a comma $","$ indicates the third species is in a different phase.
The ternary spinodal condition is: $$D=\frac{\partial ^2 f}{\partial \phi _B ^2}\Bigg|_{N,T,\phi_A}\frac{\partial ^2 f}{\partial \phi _A ^2}\Bigg|_{N,T,\phi _B} - \left( \frac{\partial ^2 f}{\partial \phi _B \partial \phi _A} \Bigg| _{N,T}\right)^2 = 0$$
My question is, how do I find the regions on the ternary plot indicated above? How do I find the region where two species are mixed while the third one is not?
I am not quite sure what it means when A+B is in a mixed state and when C is not. Does this mean that $\mu _A = \mu _B \neq \mu _C$?
This is basically the figure I want to make from this paper:
I would appreciate any advice you have for me.
