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In the 3 dimensional diagram given, when a constant pressure plane intersects with the double surface, it produces a looped curve without a maxima or minima. What is the double surface and how is the looped curve produced? And since the line joining $T_\ce{A}$ and $C_\ce{A}$ is the temperature-pressure curve of pure A and similarly for B, I cannot understand what the curve joining the 2 critical points (of A and B) means.
The liquid phase is above the surface. The vapor phase is below the surface.
The planar cut at a constant temperature is easiest to understand. The bottom curve will show the composition of the liquid phase as a function of molar fraction, and the upper curve will show the composition of the vapor phase.
Likewise for the curves of molar fraction versus temperature at a given pressure.
