Appendix B: Bulk Composition?

Note

When is the bulk composition from MC_fit macroscopically meaningful?

It may seem incongruous to refer to bulk composition as an unknown parameter in the local equilibrium context where bulk composition is formally undefined. The explanation for this oxymoron is that the free energy minimization problem is formulated in terms of bulk composition, and there is a bulk composition that will predict the phases of any local equilibrium. However, except in the trivial single-phase case, the bulk composition that predicts a local equilibrium is not unique, i.e., the local equilibrium is predicted by any bulk composition that is a positive linear combination of the compositions of the equilibrium phases.

In the context of a local equilibrium problem, MC_fit finds such a composition, but the composition has no macroscopic meaning. Even when MC_fit is applied to the phases of a bulk equilibrium, for which a definite bulk composition exists, the issue of non-uniqueness may persist if the bulk composition is treated as an unknown parameter. In the bulk equilibrium case, unless some bulk compositional constraints are provided, a unique, macroscopically meaningful, bulk composition is only obtained by inversion when mineral proportions are included in the observational data.