Distances to compositional equilibrium

Geochemical samples can be restricted to be on a locus in the sample space. When this occurs there is a chemical equilibrium of some kind. Typical examples are chemical equilibrium regulated by the mass action law or stoichiometry given by the structure of crystals. These equilibria can correspond to linear restrictions in the simplex, for which the restriction is on a linear manifold (hyperplane) or, more generally, restriction is on a general manifold (warped hypersurface). Exact equilibrium is seldom observed in geochemistry and so the focus is shifted to measuring distances or deviations from equilibrium. A linear equilibrium locus is defined by a constant logcontrast. When this logcontrast is evaluated on a sample, the difference between the equilibrium constant and the value obtained for each sample is a deviation from equilibrium. It is—in absolute values—the Aitchison distance to equilibrium. The non-linear case is more involved. Here, a linearization technique is proposed. It consists of adding terms to the composition so that the deviation or distance to the equilibrium locus reduces to the linear case. These techniques are illustrated with some examples: chemical reactions producing bicarbonate ions in water (linear), the weathering of microcline and the formation of kaolinite (non-linear), both concerning stream water composition at a European scale. Stoichiometric behaviour of olivines (non-linear) is also analyzed. Finally, a discussion on methods for discovering unknown equilibria in a sample is presented.