Quantifying garnet-melt trace element partitioning using lattice-strain theory: New crystal-chemical and thermodynamic constraints

Abstract

Many geochemical models of major igneous differentiation events on the Earth, the Moon, and Mars invoke the presence of garnet or its high-pressure majoritic equivalent as a residual phase, based on its ability to fractionate critical trace element pairs (Lu/Hf, U/Th, heavy REE/light REE). As a result, quantitative descriptions of mid-ocean ridge and hot spot magmatism, and lunar, martian, and terrestrial magma oceans require knowledge of garnet-melt partition coefficients over a wide range of conditions. In this contribution, we present new crystal-chemical and thermodynamic constraints on the partitioning of rare earth elements (REE), Y and Sc between garnet and anhydrous silicate melt as a function of pressure (P), temperature (T), and composition (X). Our approach is based on the interpretation of experimentally determined values of partition coefficients D using lattice-strain theory. In this and a companion paper (Draper and van Westrenen this issue) we derive new predictive equations for the ideal ionic radius of the dodecahedral garnet X-site, r0(3+), its apparent Young's modulus EX(3+), and the strain-free partition coefficient D0(3+) for a fictive REE element J of ionic radius r0(3+). The new calibrations remedy several shortcomings of earlier lattice-strain based attempts to model garnet-melt partitioning. A hitherto irresolvable temperature effect on r0(3+) is identified, as is a pronounced decrease in EX(3+) as Al on the garnet Y site is progressively replaced by quadruvalent cations (Si, Ti) as pressure and garnet majorite content increase. D0(3+) can be linked to the free energy of fusion of a hypothetical rare-earth garnet component JFe2 Al3Si2O12 through simple activity-composition relations. By combining the three lattice-strain parameter models, garnet-anhydrous melt and majorite-anhydrous melt D values for the REE, Y and Sc can be predicted from P, T, garnet major element composition, and melt iron content at pressures from 2.5-25 GPa and temperatures up to 2,573 K, covering virtually the entire P-T range over which igneous garnets are stable in solar system compositions. Standard deviations of the difference between predicted and observed DREE,Y,Sc range from 25% for Er to 70% for Ce, and are not correlated with trace element mass. The maximum error in D prediction (n > 300) is 218% for one measurement of DDy. This is remarkably low considering the total spread in D values of over four orders of magnitude. © Springer-Verlag 2007.