Changes in element and isotope ratios upon closed-system crystallization

3 Changes in element and isotope ratios upon closed-system crystallization 

If we are dealing with major elements, partition coefficients Dt may be expected to vary with many parameters, including temperature or liquid chemistry. For some elemental pairs and particularly for isotopes for which activity coefficients are correlated, there is a better chance, however, that the ratio of two partition coefficients Dn and Di2 shows lesser variations. We therefore subtract the distillation equation (1.5.3) for element or isotope il from that for i2 as 

We sometimes want to track the change in the concentration of a species i3 as a function of an index ratio i2/il. Dividing equation (1.5.3) for i=i3 by equation (1.5.4), the appropriate equation is 

Equation (1.5.9) has been derived by Irvine (1977) and Pearce (1978) in the case of olivine fractionation from magmas and is also found in fluid-magma systems (Candela, 1986). 

Dividing equation (1.5.8) for the pair i3-il by the equation for the pair i2-il gives 

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