Trace element partitioning coefficients between orthopyroxene and melt: Parameterizations of D variations and an improved Lattice Strain Model for rare Earth elements

Abstract

Nernst partition coefficient data (D) between orthopyroxenes with <5.5 mol% Wollastonite component and melts are compiled and interpreted to generate simple linear equations allowing ^{orthopyroxene/melt}D values to be calculated for 48 trace elements. The regression coefficients apply to melts ranging in composition from carbonatite to granite, and use commonly measured and petrologically significant variables as inputs. 2561 crystal/liquid pairs yielding 8219 individual D measurements were considered. Results from extra-terrestrial melts and synthetic (non-natural) melts often yield trends distinct from those of terrestrial melts, and were excluded from many regressions so as to tailor the parameterizations to terrestrial melts. With few exceptions ^{orthopyroxene/melt}D increases with decreasing temperature, orthopyroxene molar mg/(mg + fe^total), weight % melt MgO and MgO/(MgO + FeO^⁎); and with increasing wt% melt SiO₂ and Na₂O + K₂O contents. No strong correlations of D with melt water content were observed. Changes in oxygen fugacity affect partitioning of V, Mo, W, Re, and to a lesser extent Eu, and several of these regressions can be used as oxygen barometers. ^{orthopyroxene/melt}D_REE yield well-constrained linear functions for ratios of LnD (e.g. LnD_La/LnD_Ce) of elements with similar ionic radii. Model Nearest-Neighbour ^{orthopyroxene/melt}D_REE profiles (NN-D_REE) were constructed from these LnD/LnD ratios from a starting point at D_Yb. As D_Yb increases, the LREE-depleted NN-D_REE model profiles rise and flatten. Model NN-D_REE profiles computed at a given melt MgO or SiO₂ content resemble published partitioning data for chemically comparable melts. A series of model NN-D_REE profiles for a wide range of corresponding melt MgO and SiO₂ were fit with a Lattice Strain Model (LSM) to constrain variations of D³⁺₀ (the strain compensated partition coefficient), r³⁺₀ (the strain-free radius of the site into which REE substitute), and E³⁺_M (the elastic response of the M-site hosting REE as measured by Young's Modulus). Excellent LSM fits were obtained assuming a constant value of r³⁺₀ = 0.81 Å. Regression of experimental temperature against wt% melt LnMgO applied to the global data set was used to parameterize an internal temperature-composition function, required for application of the LSM. Values of r³⁺₀, D³⁺₀ and E³⁺_M derived from the LSM fits against multiple NN-D_REE profiles at diverse melt MgO and SiO₂ contents were regressed against melt MgO or SiO₂ to parameterize a NN-D_REE-LSM. This allows the complete ^{orthopyroxene/melt}D_REE profile to be calculated for any magma as long as D_Yb can be constrained. Here, model LnD_Yb values were calculated from regressions against melt and mineral compositions. The NN-D_REE-LSM parameterized against melt MgO content yields model D_Yb = 0.054 and D_La = 0.0009 (D_Yb/D_La = 59.2) for ultramafic melts with MgO = 25 wt%. As MgO decreases, model D_REE values rise and the NN-D_REE profiles flatten. By ∼0.5 % MgO (rhyolitic melts) D_Yb becomes compatible. The highest model D_Yb = 4.21 and D_La = 0.100 (D_Yb/D_La = 42) correspond to hyper-siliceous (SiO₂ > 80 %) melts with ∼0.1 % MgO. Trace element contents of melts in equilibrium with an orthopyroxene-rich cumulate from the Bay of Islands ophiolite were calculated as an example, yielding a trace element profile closely resembling boninitic melts. For carbonatite-kimberlite melts (SiO₂ < 30 %), NN-D_REE profiles were parameterized as a function of melt SiO₂. The lowest model D_Yb = 0.0023 and D_La = 0.000021 (D_Yb/D_La = 108) correspond to near-pure carbonatite (1 % SiO₂). As melts become kimberlitic (SiO₂ > 15 %) the model D_REE profiles rise and come to resemble magnesian silicate melt D_REE profiles.