Quantifying garnet-melt trace element partitioning using lattice-strain theory: assessment of statistically significant controls and a new predictive model

Abstract

As a complement to our efforts to update and revise the thermodynamic basis for predicting garnet-melt trace element partitioning using lattice-strain theory (van Westrenen and Draper in Contrib Mineral Petrol, this issue), we have performed detailed statistical evaluations of possible correlations between intensive and extensive variables and experimentally determined garnet-melt partitioning values for trivalent cations (rare earth elements, Y, and Sc) entering the dodecahedral garnet X-site. We applied these evaluations to a database containing over 300 partition coefficient determinations, compiled both from literature values and from our own work designed in part to expand that database. Available data include partitioning measurements in ultramafic to basaltic to intermediate bulk compositions, and recent studies in Fe-rich systems relevant to extraterrestrial petrogenesis, at pressures sufficiently high such that a significant component of majorite, the high-pressure form of garnet, is present. Through the application of lattice-strain theory, we obtained best-fit values for the ideal ionic radius of the dodecahedral garnet X-site, r 0 (3+), its apparent Young's modulus E(3+), and the strain-free partition coefficient D 0 (3+) for a fictive REE element J of ionic radius r 0 (3+). Resulting values of E, D 0 , and r 0 were used in multiple linear regressions involving sixteen variables that reflect the possible influence of garnet composition and stoichiometry, melt composition and structure, major-element partitioning, pressure, and temperature. We find no statistically significant correlations between fitted r 0 and E values and any combination of variables. However, a highly robust correlation between fitted D 0 and garnet-melt Fe-Mg exchange and D Mg is identified. The identification of more explicit melt-compositional influence is a first for this type of predictive modeling. We combine this statistically-derived expression for predicting D 0 with the new expressions for predicting E and r 0 outlined in the first of our pair of companion papers into an updated set of formulae that use easy-to-measure quantities (e.g. garnet composition, pressure, temperature) to predict variations in E, r 0 , and D 0 . These values are used in turn to calculate D values for those garnets. The updated model substantially improves upon a previous model (van Westrenen et al. in Contrib Mineral Petrol 142:219-234, 2001), and accounts well for trivalent cation partitioning in nominally anhydrous systems up to at least 15 GPa, including for eclogitic bulk compositions and for Fe-rich systems appropriate to magmagenesis on the Moon and Mars. The new model is slightly less successful in predicting partitioning with strongly majoritic garnets, although the mismatch is much less than with the original 2001 model. Although it also improves upon the 2001 model in predicting partitioning in hydrous systems, the mismatch between model and observation is still unacceptably large. The same statistical tools were applied in a...

Trace element partitioning between ilmenite, armalcolite and anhydrous silicate melt: Implications for the formation of lunar high-Ti mare basalts

“…The only exceptions are the observed slight decreases in r 0 for divalent cations with increasing pressure for both Ilm-Gk and Arm, accompanied by small decreases in apparent site Young's moduli E. Decreases in r 0 with increasing P have been observed in partitioning data for other minerals (most notably garnet, e.g. Draper and van Westrenen, 2007;van Westrenen and Draper, 2007) and are consistent with the measured decreases in the Mg/Fe site volumes with increasing compression (e.g. Tronche et al, 2010).…”

A new method for estimating parent rock trace element concentrations from zircon

“…A complication to lattice strain modeling is that experimental and naturally determined LREE partition coefficients are commonly larger than predicted (Hanchar and van Westrenen, 2007). Under the assumption that the larger-than-expected LREE partition coefficients are in error as a result of inclusions or melt composition uncertainty, LREE partition coefficients can be "corrected" by fitting lattice strain models to the HREE and middle REE partition coefficients (Hanchar and van Westrenen, 2007;Draper and van Westrenen, 2007;Taylor et al, 2015). There are several difficulties in using lattice strain modeling to determine appropriate partition coefficients.…”

Basalt petrogenesis beneath slow- and ultraslow-spreading Arctic mid-ocean ridges

“…6). Partition coefficient data for Sm and Nd are from for peridotite, and for pyroxenite we use our measurements for Cpx partitioning and calculate Gt partition coefficients from van Westrenen et al (2001) and Draper and van Westrenen (2007). We chose source Sm and Nd concentrations for the depleted peridotite and enriched pyroxenite sources from the Workman et al (2004) and Workman and Hart (2005) inversions for the DMM and EM2 endmembers, respectively.…”

“…While our new data provide constraints on U and Th partitioning, due to the nucleation difficulties associated with Gt, our experiments lack DiGa rnet/M el values for Sm and Nd. Thus, in order to examine silica-poor garnet pyroxenite melting for these systems, we apply our measured DPCpx/Melt values for Th, U, Sm, and Nd, while our measured Di (2001) and Draper and van Westrenen (2007). Using these partitioning constraints and published partitioning data for peridotite , and applying them to forward batch and fractional melting, we find that existing Hawaii and Samoa data plot closer to the peridotite batch melting trend than that for pyroxenite or to fractional melting trends (Fig.…”