Finding the Phase Assemblage

The calculation described to this point does not predict the assemblage of minerals that is stable in the current system. Instead, the assemblage is assumed implicitly by setting the basis B before the calculation begins. A solution to the governing equations constitutes the equilibrium state of the system if two conditions are met (1) no mineral in the system has dissolved away and become undersaturated, and (2) the fluid is not supersaturated with respect to any mineral. 

A calculation procedure could, in theory, predict at once the distribution of mass within a system and the equilibrium mineral assemblage. Brown and Skinner (1974) undertook such a calculation for petrologic systems. For an n-component system, they calculated the shape of the free energy surface for each possible solid solution in a rock. They then raised an n-dimensional hyperplane upward, allowing it to rotate against the free energy surfaces. The hyperplane s resting position identified the stable minerals and their equilibrium compositions. Inevitably, the technique became known as the crane plane method. 

Such a method seldom has been used with systems containing an aqueous fluid, probably because the complexity of the solution s free energy surface and the wide range in aqueous solubilities of the elements complicate the numerics of the calculation (e.g., Harvie et al., 1987). Instead, most models employ a procedure of elimination. If the calculation described fails to predict a system at equilibrium, the mineral assemblage is changed to swap undersaturated minerals out of the basis or supersaturated minerals into it, following the steps in the previous chapter the calculation is then repeated. 

Minerals that have beqome undersaturated are revealed in the iteration results by negative mole numbers nk. A negative mass, of course, is not meaningful physically beyond demonstrating that the mineral was completely consumed, perhaps to form another mineral, in the approach to equilibrium. 

Minerals that develop negative masses are removed from the basis one at a time, and the solution is then recalculated. When a mineral is removed, an aqueous species must be selected from among the secondary species Aj to replace it in the basis. The species selected should be in high concentration to assure numerical stability in the iterative scheme described here and must, in combination with the other basis entries, form a valid component set (see Section 3.2). The species best fitting these criteria satisfies 

---