This repository is for the distribution of the Equilibrated Major Element Assimilation and Fractional Crystallisation (EME-AFC) spreadsheet-based model discussed in:
Burton-Johnson, A., Macpherson, C. G., Ottley, C. J., Nowell, G. M. & Boyce, A. J. (2019). Generation of the Mt Kinabalu granite by crustal contamination of intraplate magma modelled by Equilibrated Major Element Assimilation with Fractional Crystallisation (EME-AFC). Journal of Petrology.
The EME-AFC model is distibuted as two files: a blank template for completion by the user, and, for illustrative purposes, a completed spreadsheet showing the modelling of the Mt Kinabalu intrusion of Burton-Johnson et al. (2019). For first order approximations of your system the calibrations used for Mt Kinabalu may be reasonable, but it is best to modify the model to represent your chosen system.
The EME-AFC model is based on the approach of Grove and Donnelly-Nolan (1986) but developed to model expected variation of all major and minor elements of each fractionating phase whilst simultaneously modelling the trace elements and isotopic compositions of the fractionating assemblage, evolving melt and bulk cumulate composition.
The liquid line of descent is calculated iteratively at 1% changes of F (the remaining melt fraction) and at each stage the composition of the chosen fractionating phases is calculated to be in equilibrium with the melt based on experimental two-component partition coefficients (refer to the "Major Kd Values" tab). The relative abundances for major and minor elements not determined by stoichiometry or two-component partition coefficients are calculated according to the equations in the "Calculations" tab. The formulae for each phase and the sites in to which elements can substitute are determined from Deer et al. (1966) and the ionic charge of each element. The liquid composition is converted from molar masses to atomic abundances prior to the equilibration calculations and the mineral composition is calculated in this manner to conform to the stoichiometric constraints of each mineral.
AFC differentiation of trace elements and isotopes are calculated at each increment according to the equations of DePaolo (1981). At each increment, oxygen isotope fractionation coefficients are recalculated for each fractionating phase based on their mineral-mineral coefficients and SiO2 derived temperature (empirical relationship derived by linear regression to ±63oC σ based on experimental data). To better simulate the mafic to felsic evolution of a melt the model is divided in four, with the first modelling basalts, the second modelling basaltic andesites, then andesites and finally dacites/rhyolites. These changes occur at 52, 57, and 63 wt.% SiO2 by default although these brackets can be modified.
In addition to the melt evolution, the evolution of the fractionating assembalge and bulk cumulate composition are also calculated and output.
This geochemical approach to modelling has specific advantages to thermodynamic models of melt evolution (e.g. MELTS; Ghiorso and Sack, 1995). In particular, the ability to model felsic systems and those dominated by the fractionation of hydrous mineral phases (e.g. hornblende); inputs can be easily modified to achieve a target composition; and most importantly by allowing complete control of the fractionating system and its parameters it is easy to explore the particular effects each parameter or input has on the liquid line of descent (LLD). The effects of pressure, water content and oxidation state of the system are accounted for by calibrating the model to your mineral separate data.