Contributions to Mineralogy and Petrology
, Volume 154, Issue 6, pp 731746
First online:
Quantifying garnetmelt trace element partitioning using latticestrain theory: assessment of statistically significant controls and a new predictive model
 David S. DraperAffiliated withInstitute of Meteoritics, 1 University of New Mexico Email author
 , Wim van WestrenenAffiliated withFaculty of Earth and Life Sciences, Vrije Universiteit
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As a complement to our efforts to update and revise the thermodynamic basis for predicting garnetmelt trace element partitioning using latticestrain 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 garnetmelt partitioning values for trivalent cations (rare earth elements, Y, and Sc) entering the dodecahedral garnet Xsite. 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 Ferich systems relevant to extraterrestrial petrogenesis, at pressures sufficiently high such that a significant component of majorite, the highpressure form of garnet, is present. Through the application of latticestrain theory, we obtained bestfit values for the ideal ionic radius of the dodecahedral garnet Xsite, r _{0}(3+), its apparent Young’s modulus E(3+), and the strainfree 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, majorelement 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 garnetmelt Fe–Mg exchange and D _{Mg} is identified. The identification of more explicit meltcompositional influence is a first for this type of predictive modeling. We combine this statisticallyderived 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 easytomeasure 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 Ferich 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 an attempt to predict tetravalent partitioning as well, because latticestrain based techniques are not applicable to such partitioning. However, no statistically significant predictive relationships emerged from that effort. Our analyses show that future efforts should focus on filling the gap in partitioning data between ∼10 and 25 GPa to evaluate more closely the gradual transition of garnet to majorite, and on systematically expanding the hydrous partitioning database to allow extension of our model to waterbearing systems.
 Title
 Quantifying garnetmelt trace element partitioning using latticestrain theory: assessment of statistically significant controls and a new predictive model
 Journal

Contributions to Mineralogy and Petrology
Volume 154, Issue 6 , pp 731746
 Cover Date
 200712
 DOI
 10.1007/s0041000702353
 Print ISSN
 00107999
 Online ISSN
 14320967
 Publisher
 SpringerVerlag
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 David S. Draper ^{(1)}
 Wim van Westrenen ^{(2)}
 Author Affiliations

 1. Institute of Meteoritics, 1 University of New Mexico, MSC032050, Albuquerque, NM, 87131, USA
 2. Faculty of Earth and Life Sciences, Vrije Universiteit, De Boelelaan 1085, 1081 HV, Amsterdam, The Netherlands