Multiphase Rayleigh fractionation

Abstract

When olivine crystallizes by itself from a mafic magma, it rapidly fractionates Mg/Fe on its own binary loop, depleting Mg and enriching Fe with fractionation progress F. Pure fractionation on such a loop is easily calculated with the standard Rayleigh distillation equation. The crystallization process also rejects all other components until another phase, for example plagioclase, saturates the liquid. Such cotectic fractionation has no direct effect on the mafic olivine loop, but it operates strongly to diminish F, and hence the fractionation progress of Mg/Fe is damped. The binary component of the liquid evolves more slowly when non-participating solid phases separate from the melt. This effect is also easily calculated with the Rayleigh equation, simply by multiplying the Rayleigh exponent by the fraction of the binary solution phase in question relative to all other crystallizing phases that do not fractionate Mg/Fe. Similar principles apply to fractional melting. Calculations of both melting and crystallization by stepwise iteration are simplified by the use of linear partitioning equations with constant or variable intercepts. Such formulations operate on the mole or weight fraction, and all partition coefficients are limited to less than unity. Calculations that ignore this multiphase damping effect have led to erroneous results in the literature. Proof of the multiphase effect is easily shown with a ternary phase diagram. When the results are applied to cumulates in layered mafic intrusions they help to clarify the principles by which these rocks crystallized and solidified. The effect of trapped liquid on a minor binary solution in a cumulate is to mimic the fractionation of the pure phase in some degree, whereas the frequent recharge of unmodified magma tends to mimic an over-abundance of the passive, non-participating phase.