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We report the results of experiments designed to separate the effects of temperature and pressure from liquid composition on the partitioning of Ni between olivine and liquid,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$D_{\text{Ni}}^{\text{ol/liq}}$$\end{document}    D   Ni   ol/liq. Experiments were performed from 1300 to 1600 °C and 1 atm to 3.0 GPa, using mid-ocean ridge basalt (MORB) glass surrounded by powdered olivine in graphite–Pt double capsules at high pressure and powdered MORB in crucibles fabricated from single crystals of San Carlos olivine at one atmosphere. In these experiments, pressure and temperature were varied in such a way that we produced a series of liquids, each with an approximately constant composition (~12, ~15, and ~21 wt% MgO). Previously, we used a similar approach to show that    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$D_{\text{Ni}}^{\text{ol/liq}}$$\end{document}    D   Ni   ol/liqfor a liquid with ~18 wt% MgO is a strong function of temperature. Combining the new data presented here with our previous results allows us to separate the effects of temperature from composition. We fit our data based on a Ni–Mg exchange reaction, which yields    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\ln \left( {D_{\text{Ni}}^{\text{molar}} } \right) = \frac{{ -\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{RT} + \frac{{\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{R} - \ln \left( {\frac{{X_{\text{MgO}}^{\text{liq}} }}{{X_{{{\text{MgSi}}_{ 0. 5} {\text{O}}_{ 2} }}^{\text{ol}} }}} \right).$$\end{document}    ln    D   Ni   molar    =    -   Δ   r  (  1  )HT  ref   ,   P  ref∘R  T    +Δ   r  (  1  )ST  ref   ,   P  ref∘    R   -  lnX   MgO   liq    XMgSi   0.5O  2ol.Each subset of constant composition experiments displays roughly the same temperature dependence of    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$D_{\text{Ni}}^{\text{ol/liq}}$$\end{document}    D   Ni   ol/liq(i.e.,   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R$$\end{document}    -   Δ   r  (  1  )HT  ref   ,   P  ref∘   /  R) as previously reported for liquids with ~18 wt% MgO. Fitting new data presented here (15 experiments) in conjunction with our 13 previously published experiments (those with ~18 wt% MgO in the silicate liquid) to the above expression gives    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R$$\end{document}    -   Δ   r  (  1  )HT  ref   ,   P  ref∘   /  R = 3641 ± 396 (K) and    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R$$\end{document}Δ   r  (  1  )ST  ref   ,   P  ref∘   /  R = − 1.597 ± 0.229. Adding data from the literature yields    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R$$\end{document}    -   Δ   r  (  1  )HT  ref   ,   P  ref∘   /  R = 4505 ± 196 (K) and    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R$$\end{document}Δ   r  (  1  )ST  ref   ,   P  ref∘   /  R = − 2.075 ± 0.120, a set of coefficients that leads to a predictive equation for    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$D_{\text{Ni}}^{\text{ol/liq}}$$\end{document}    D   Ni   ol/liqapplicable to a wide range of melt compositions. We use the results of our work to model the melting of peridotite beneath lithosphere of varying thickness and show that: (1) a positive correlation between NiO in magnesian olivine phenocrysts and lithospheric thickness is expected given a temperature-dependent    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$D_{\text{Ni}}^{\text{ol/liq}} ,$$\end{document}D   Ni   ol/liq   ,and (2) the magnitude of the slope for natural samples is consistent with our experimentally determined temperature dependence. Alternative processes to generate the positive correlation between NiO in magnesian olivines and lithospheric thickness, such as the melting of olivine-free pyroxenite, are possible, but they are not required to explain the observed correlation of NiO concentration in initially crystallizing olivine with lithospheric thickness.   Electronic supplementary material  The online version of this article (doi:10.1007/s00410-016-1319-8) contains supplementary material, which is available to authorized users.

The effect of liquid composition on the partitioning of Ni between olivine and silicate melt