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. However, except in 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.

In the context of a local equilibrium problem, MC_fit finds such a bulk composition, but not only is the solution non-unique, it does not correspond to the composition of the rock sample within which the local equilibrium is presumed to exist. Thus, while the bulk composition can be used to calculate a P–T phase diagram section to graphically assess the quality of a result, the phase relations predicted by MC_fit are strictly valid only at the P–T conditions of the local equilibrium, i.e., the P–T 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 abundances.

Hint

Bulk compositions computed from the modes and compositions of observed minerals, e.g., as obtained by XMapTools [Lanari2019], are not independent observations and therefore the modes and bulk composition so obtained should not be used together as observational data in MC_fit. Because MC_fit functions best with raw data, in such cases, the modal data is preferred. Conversely, if modal data has been inferred from a measured bulk composition, then the measured bulk composition is preferred over the inferred modes. When both modal and bulk compositional data have been measured independently, then the use of both data sets is justified.