Clinopyroxene–melt trace element partitioning and the development of a predictive model for HFSE and Sc

Clinopyroxene–melt trace element partitioning experiments were carried out in the system Na2O–CaO–MgO–Al2O3–SiO2 at pressures of 1, 2.3 and 3 GPa and temperatures of 1508 to 1811 K, to investigate the effects of temperature (T), pressure (P) and composition (X) on partition coefficients. Of particular interest were elements entering the octahedral M1-site. Ion probe analyses of run products produced crystal–melt partition coefficients (D) for 16 elements (Na, Ca, Al, Cl, Sc, Ti, Fe, Zr, In, La, Ce, Nd, Sm, Ho, Yb and Hf). With the exception of DNa, partition coefficients for all elements studied decrease with increased P and T, despite the concomitant increase in the Al content of the T-site. Fitting partition coefficients for isovalent series of cations to the elastic strain model of Blundy and Wood (1994) produced values for the site radius (r0), effective elastic modulus (E) and strain-free partition coefficient (D0). At each pressure, E values for the M1 and M2-sites increase with increasing Al concentration in the T-site \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {X_{\text{Al}}^{T} } \right) $$\end{document}. For a given bulk composition, E values decrease with increased T. The decrease in E with increasing T accounts for the remarkable constancy of the degree of fractionation between chemically similar elements, e.g. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ D\left( {{\frac{\text{Zr}}{\text{Hf}}}} \right) $$\end{document}, over the range of pressures studied here. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ E_{{{\text{M}}1}}^{4 + } $$\end{document} for our experiments is found to be higher than predicted by the Hazen and Finger (1979) relationship between elastic moduli and interatomic distance. This is explained by deformation of the M1-site polyhedron leading to relative displacement and kinking of the clinopyroxene T-site chains. We developed expressions for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ E_{{{\text{M}}1}}^{4 + } $$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ r_{{0,{\text{M}}1}}^{4 + } $$\end{document}, DSc and DTi as functions of P, T and composition. We show the feasibility of using calculated DTi values in the prediction of DZr and DHf. Scandium and Ti partition coefficients were modelled based on the thermodynamic description for the crystal–melt exchange reaction and in terms of the energetics of the different charge-imbalanced configurations produced by insertion of a heterovalent trace cation. The resulting equations produce values of DSc and DTi that are within a factor of 2 of other experimentally determined values. Fits of the equations along the lherzolite solidus show that DSc remains compatible in clinopyroxene at high pressure and that ratios of Zr/Hf and Ti/Eu should vary subtly with the pressure at which melting occurred.