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

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 crystalchemical 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 rareearth garnet component JFe2Al3Si2O12 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.