For a brief reminder about free energy
curves for a single phase, click start

To go straight to an explanation about
a two phase system, click skip

The free energy decreases with increasing T

 

The free energy is in fact governed by the master equation
G = H - TS

The intercept on the vertical axis is the enthalpy, H (at 0K), which is equivalent to G (at 0K).

The gradient is the negative of the entropy, −S. The entropy is always positive, therefore the gradient is always negative, and becomes increasingly negative as T increases.

For example, in shape memory alloys the two free energy
curves represent the austenitic and martensitic phases

Above Te the austenitic phase has a lower free energy therefore it is more stable

Plot first curve
      

Plot second curve
      

Generally the two different phases have different enthalpies and entropies. This leads to an intersection of the curves
            

Where the curves intersect the phases have the same free energy and are in equilibrium (both phases are equally stable)
            

The temperature at which this occurs is the equilibrium temperature, T_e
            

Below T_e the martensitic phase has a lower free energy therefore it is favoured thermodynamically.