Olivine fractionation equations for basaltic and ultrabasic liquids

Abstract

Exact equations are derived for fractionation curves of basaltic and ultrabasic liquids. The ideal fractionation equation has the form y = ax^K while equilibrium crystallisation has the form (1/y) = Km₁(1/x) + b₁ . (1 – K), and batch fractionation, y = Km₂ + b₂ · (1 – K). A ratio transformation as in Pearce diagrams allows natural data to be analysed to determine if a constant distribution coefficient fits the data: K may also be determined directly. Published data for a series of liquids fractionated from a lunar picrite parent have been analysed using the equilibrium equation. The average K value is K = 0.323 with a linear correlation coefficient, R = 0.996. The reported olivine analyses yield a K = 0.321 for the same set of experiments. Using the ideal fractionation equation, the liquid line of descent can be calculated and constraints placed on the primitive liquids which produced a given mafic rock by olivine fractionation.