Mineral activity diagram

A diagram of stable mineral assemblages as functions of specified aqueous thermodynamic activities, at fixed temperature and pressure. The coordinates often use logarithmic activity ratios. Mass-action equations give pairwise coexistence lines; a line segment is stable only when no omitted mineral has a lower relevant thermodynamic potential under the same imposed chemical potentials.

Suppose a reference mineral $C$ can dissolve to either $G$ or $K$, with the same conserved solid component, and normalized Gibbs energies of reaction ${\Delta }_r{G}_G/A=y-{\ell }_G(x)$ and ${\Delta }_r{G}_K/A=y-{\ell }_K(x)$ for $A>0$. Choose relative solid potentials ${\Phi }_C=0$, ${\Phi }_G=y-{\ell }_G$ and ${\Phi }_K=y-{\ell }_K$. The stable state minimizes $\Phi$. Thus $C$ is stable above $y=\max ({\ell }_G,{\ell }_K)$; $G$ is stable below ${\ell }_G$ where ${\ell }_G>{\ell }_K$; and $K$ is stable below ${\ell }_K$ where ${\ell }_K>{\ell }_G$. The $G$–$K$ coexistence line is stable below their triple intersection and metastable above it. These inequalities follow directly from the sign of each forward dissolution reaction. Reversing reaction directions reverses the corresponding sign convention, so one must establish the reaction direction before choosing an upper or lower envelope.

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.