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The greatest convex function lying below a given function, when such an envelope is considered in the specified domain. A convex combination of phase compositions and their Gibbs free energies constructs candidate mixtures; the equilibrium free energy is their lower convex envelope. For two differentiable coexisting branches, the supporting line is a common tangent.

At $100{}^{\circ }\mathrm{C}$, the stable sequence is $(\mathrm{Bi})$, $(\mathrm{Bi})+(\beta \mathrm{Sn})$, $(\beta \mathrm{Sn})$. The stable two-solid common tangent lies below the liquid curve. There is no stable liquid interval, although a metastable extrapolated liquid Gibbs free energy can still be drawn.