A Landau free energy is a symmetry-constrained analytic expansion in an order parameter. Its minima determine the mean-field equilibrium phases.
Two compositions coexist when one straight line is tangent to the free-energy density at both compositions. Equality of its slope gives equal chemical potentials, and equality of its intercept gives equal pressures.
The binodal is the coexistence boundary: its two branches give the compositions of phases joined by the common-tangent construction.
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