Appendix B: Bulk Composition?

When does the bulk composition from MC_fit represent rock composition?

It may seem incongruous to treat bulk composition as an unknown parameter in a local-equilibrium context because bulk composition is formally undefined in local equilibria. The oxymoron arises because 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. Excepting the trivial single-phase case, this bulk composition is not unique; any positive linear combination of the compositions of the equilibrium phases will reproduce the same local equilibrium. For local equilibrium problems, MC_fit finds such a composition and this composition can be used to calculate a P–T phase diagram section to graphically assess the quality of the result. However, because the composition is not representative of the entirety of the rock within which the local equilibrium exists, the phase relations in the section cannot be used to infer how the rock would evolve as a function of P and T.

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, a complete bulk composition suitable for modelling rock phase relations can be obtained by providing an incomplete bulk composition and/or phase modes.

Bulk Composition vs Modal Data

Do not use both modal and bulk compositional data together if one set was derived from the other — they are not independent observations. Follow these guidelines:

• Bulk composition from mineral modes: If the bulk composition was calculated from observed mineral compositions and modes (e.g., via XMapTools [Lanari2019]), use only the modal data in MC_fit, as it represents the raw observations.

• Modal data from bulk composition: If mineral modes were inferred from a measured bulk composition, use only the measured bulk composition, not the inferred modes.

• Both independently measured: If modal data and bulk composition were measured independently, using both datasets is justified.