Stability boundary in a mineral activity diagram

A pairwise equilibrium line restricted to conditions where both minerals are stable against the other allowed phases. Compute the Gibbs energy of reaction for independent conversions to compare them. A pairwise line can continue into a region where a third mineral is favoured; this continuation is a metastable equilibrium relation, rather than a boundary of stable fields.

Suppose two dissolution reactions to a reference mineral $C$ have been normalized to the same amount of a conserved reference component. After division by the same positive energy factor, let their Gibbs energies of reaction be $y-{\ell }_1(x)$ and $y-{\ell }_2(x)$. Their relative thermodynamic potentials can then be written as displayed. The stable mineral has the smallest potential.

It follows that $C$ is stable below $y=\min ({\ell }_1,{\ell }_2)$, mineral 1 is stable where ${\ell }_1<{\ell }_2$ and $y>{\ell }_1$, and mineral 2 is stable where ${\ell }_2<{\ell }_1$ and $y>{\ell }_2$. The two nonreference minerals coexist stably where ${\ell }_1={\ell }_2<y$. Their equality below that height is a metastable continuation. This comparison proves the stable lower envelope and selects which portions of the pairwise mass-action lines belong on the mineral activity diagram.