FeO-MgO fractionation during olivine crystallization in basalts

The Fe/Mg fractionation between olivine and basaltic liquids is independent of temperature (Roeder and Emslie, 1970) while its pressure-dependence is quite small (Ulmer, 1989). This is also the case, although to a lesser extent, between other mafic minerals and basaltic liquids (see a compilation in Warren, 1986). This remarkable property makes these two elements invaluable tools for understanding basalt genesis. The approach taken here is that of Albarede (1992). 

Olivine is assumed to be the only mineral precipitating and the fa and fo subscripts refer to pure fayalite and forsterite. Upon crystallization of the incremental amount dM i of cumulate, the incremental amount dMfa of fayalite is precipitated, and, since the iron content of fayalite is constant 

Factoring the numerator of the last term on the right-hand side gives 

Up to this point, the only assumption is that olivine is the only phase precipitating. Taking the further step that KD is constant, equation (1.5.21) can be integrated into 

Because solving the transcendental equation (1.5.23) requires iterative methods of root finding, the numerical solution to this equation is postponed to Section 3.1. o 

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