8.7 Detecting Fractional Crystallization - Exchange Coefficients

Minerals other than olivine can be separated from a magma by fractional crystallization. Each mineral has its own chemical composition and the change in melt composition will reflect the combined effects of removing all the fractionated minerals. Data from Mauna Loa (blue) is shown again in Figure 8.09 along with data from a Pacific MORB suite (orange) from PetDB, and data from a Sierra Nevada batholith suite (red) from the PETROS dataset. Each data set shows a roughly linear trend, but the lines are not the same. How can we determine possible fractionating mineral combinations that could produced the observed trends? Or is some other process responsible for the compositional variations?

One way to do this is to choose a starting bulk composition, to subtract the compositions of crystallizing minerals in various proportions, and to plot the resulting liquid compositions on a variation diagram. This is relatively simple algebra once the compositions and proportions of the fractionation minerals are chosen. For solid solution minerals, one needs to know the composition of the mineral as a function of the melt composition (see for example the olivine melting diagram). To a first approximation, the relationship between melt composition and the composition of a two-component solid-solution mineral (e.g. olivine) can be expressed as an exchange coefficient, K_D. K_D is defined as:

(1)     K_D = (n₁/n₂)^S / (n₁/n₂)^L

where n_i is the number of moles of component i, S marks values for the solid, and L marks values for the liquid. By convention, component 1 is the low-melting component. For example, the olivine K_D is

(2)     K_D = (n_Fa/n_Fo)^Oliv / (n_Fa/n_Fo)^Melt

where Fa is fayalite (Fe₂SiO₄) and Fo is forsterite (Mg₂SiO₄). Details of this relationship and major element exchange coefficients for some common minerals can be found in Morse (2015). On the next page, exchange coefficients are used to create fractionation model diagrams.

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