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For a mixture with phase compositions $x_1,x_2$, its molar <Gibbs free energy> is the straight-line combination $g=(1-f)g_1(x_1)+fg_2(x_2)$ at overall $x=(1-f)x_1+fx_2$. Minimizing over phase compositions gives equal slopes and equal tangent intercepts: the <common-tangent construction> expresses equality of both component <chemical potentials>. The equilibrium curve is the lower <convex envelope> of the candidate phase curves. Phase fractions follow the <lever rule>.
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