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

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}DNiol/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}DNiol/liq for 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}lnDNimolar=-Δr(1)HTref,Pref∘RT+Δr(1)STref,Pref∘R-lnXMgOliqXMgSi0.5O2ol. 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}DNiol/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}-Δr(1)HTref,Pref∘/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}-Δr(1)HTref,Pref∘/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}Δr(1)STref,Pref∘/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}-Δr(1)HTref,Pref∘/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}Δr(1)STref,Pref∘/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}DNiol/liq applicable 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}DNiol/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.

075 ± 0.120, a set of coefficients that leads to a predictive equation for D ol/liq Ni applicable 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 D

Introduction
Unlike most other minor and trace elements, Ni is compatible in olivine (ol) over a broad range of temperatures, pressures, and silicate liquid (liq) compositions (i.e., D ol/liq Ni = NiO ol /NiO liq is greater than one, where NiO ϕ refers to the concentration of NiO in phase ϕ by weight). One consequence of the compatibility of Ni in olivine and other mantle phases (e.g., Mysen 1978) is that the NiO contents of residual lherzolites are insensitive to low degrees of partial melting; this is consistent with the observed narrow distribution of the NiO contents of olivines from spinel lherzolites: 0.37 (median) ± 0.03 [mean absolute deviation (MAD)], 308 analyses (Korenaga and Kelemen 2000;Jun Korenaga, personal communication, 2011) and 0.37 ± 0.01, 172 analyses . Thus, unless the degree of melting is very high (e.g., >50%; Herzberg et al. 2016), one might reasonably expect that the first olivines to crystallize from a partial melt of a lherzolitic source would recover, within ~8%, the NiO content of olivine in the initially unmelted source (Herzberg et al. 2016). However, olivine phenocrysts from ocean islands often have NiO contents exceeding 0.5 wt% (e.g., Clague et al. 1991;Sobolev et al. 2005Sobolev et al. , 2007. Possible explanations for these elevated NiO concentrations in olivine-and the melts from which they are derived-include an olivine-free component in the mantle produced by metasomatism of peridotite by silicic partial melts of recycled oceanic crust (Sobolev et al. 2005(Sobolev et al. , 2007, Ni-enrichment in the mantle source due to interaction with the Ni-rich core (Ryabchikov 2003;Herzberg et al. 2013), or a D ol/liq Ni that is a function of temperature (T) and/or pressure (P), in addition to composition (Leeman and Lindstrom 1978;Mysen and Kushiro 1979;Li and Ripley 2010;Putirka et al. 2011;Matzen et al. 2013).
Our ability to discriminate among these hypotheses depends on knowing D ol/liq Ni and, specifically, how D ol/liq Ni is affected by variables such as temperature, pressure, oxygen fugacity (fO 2 ), and olivine and liquid compositions. Experiments in most studies measuring D ol/liq Ni for a given bulk composition have been performed at a single pressure; thus, any change in temperature results in a change in liquid composition as olivine is added or subtracted from the liquid. Interpreting the results of such experiments is not straightforward because changes in liquid composition, olivine composition, and temperature, or a combination of these factors could result in the observed changes in D ol/liq Ni (Arndt 1977;Hart and Davis 1978;Takahashi 1978;Wang and Gaetani 2008;Putirka et al. 2011). Matzen et al. (2013) isolated the effects of pressure and temperature from those of composition by performing experiments in which pressure and temperature were changed in concert; this yielded coexisting olivine-liquid pairs with roughly constant olivine Mg#s (100 × Mg/[Mg + Fe], molar) of ~90, which we refer to as Fo 90 , and liquid compositions of ~18 wt% MgO. These experiments showed for a picritic liquid that temperature has a significant effect on D ol/liq Ni . Here, we present the results of similar series of experiments designed to determine whether the temperature dependence of D ol/liq Ni is also a significant function of liquid composition, as predicted by Hirschmann and Ghiorso (1994).

Experimental and analytical methods
Run conditions are given in Table 1 and shown graphically in Fig. 1a. We used the same experimental methods and materials as Matzen et al. (2013;see their Table 1 for a description of starting materials). Briefly, we performed high-pressure experiments by surrounding a small chip of fused Juan de Fuca MORB glass with powdered Kilbourne Hole olivine in a Pt-graphite double capsule. Experiments were run in two stages: (1) a filled capsule was sintered at a temperature below the estimated solidus of the basalt [based on the Pertermann and Hirschmann (2003) parameterization], effectively forming a low-permeability, polycrystalline olivine crucible; (2) the temperature was then increased to the final run temperature, followed by a pressure increase to the final run pressure. Except for 1 GPa experiments, sintering was conducted at pressures 0.1-0.35 GPa below the desired run pressure. For experiments at 1 GPa, we hot-pressed the capsule at 1.4 GPa, but in an effort to retain the relative sense of piston motion (i.e., hot piston-in), we slowly lowered the pressure from 1.4 GPa to below 1.0 GPa before the final temperature ramp, such that when the temperature was increased to its final value, the pressure would remain slightly below the desired value; finally, pressure was increased to the final value for the run. Note that in the first of two experiments where we employed this method (Run 51), the pressure was not lowered enough before the final temperature ramp; upon reaching the final run temperature, the pressure was too high and had to be lowered to its target value (hot pistonout). One-atmosphere experiments were conducted using methods similar to Wang and Gaetani (2008): mixtures of MORB glass and powdered Kilbourne Hole olivine were placed in a crucible fabricated from a single crystal of San Carlos olivine and suspended in a flowing mixture of CO 2 and H 2 that produced an fO 2 ~1.7 log units below the QFM buffer, an fO 2 similar to those measured in high-pressure graphite-capsule experiments (Médard et al. 2008); fO 2 s for all one-atmosphere experiments are listed in Table 1. The temperatures and pressures shown in Fig. 1a were selected so that the resulting liquids would have approximately 12, 15, and 21 wt% MgO (hereafter referred to as the ~12, 15, and ~21 MgO liq series). We were not entirely successful in meeting these target liquid compositions; all of our MgO liq series show decreasing MgO liq with increasing temperature (Fig. 1b). We conducted mostly forward experiments (downward pointing triangles in Fig. 1b) in which low-Ni glass (<0.03 wt% NiO) was equilibrated with Nibearing olivine (~0.37 wt% NiO). The four reversal experiments (upward pointing triangles in Fig. 1b; run numbers appended with an R in Table 1) used starting glasses doped with 1 wt% NiO (i.e., higher than in the olivine).
Measurements of all phase compositions are reported in Table 2. Glass and olivine compositions were measured on Caltech's JEOL JXA-8200 using analytical and data processing procedures described by Matzen et al. (2013). Pyroxenes were analyzed on Oxford's JEOL 8600, using an accelerating voltage of 15 keV, a 40 nA beam current, and a 1 μm beam at locations ~10 μm from the edge of each pyroxene grain, utilizing a set of metal (Ni), oxide (Cr 2 O 3 ), and mineral (wollastonite, rutile, jadeite, hematite, rhodonite, periclase, orthoclase) standards. On-peak counts were collected for 30-60 s with high and low backgrounds counted for half of the on-peak time. Pyroxene data acquired at Oxford were processed using the PAP matrix correction (Pouchou and Pichoir 1988). Pyroxenes from some of the runs were also analyzed at Caltech (processed using a modified ZAF correction: CITZAF, Armstrong 1988); for the Caltech data, most of the average pyroxene compositions overlap at one sigma with those obtained from the Oxford analyses and, in all cases, they overlap at two-sigma.
In a reversal experiment, the NiO content of the starting glass is higher than that of a silicate melt in equilibrium with the surrounding olivine. The mass of olivine is large compared to the mass of liquid and NiO diffuses from the liquid into the surrounding olivine over the course of the experiment. Olivines that crystallize from the Ni-rich melt at the start of an experiment will have high NiO contents, but the Ni content at their rims decreases with time as the melt continues to lose Ni to the surrounding olivine. Our experiments were never run long enough to fully homogenize all phases, so olivines in contact with a melt pool are strongly zoned near their rims. In an effort to capture the equilibrium partition coefficient, we performed a series of analyses with 1-2 μm step sizes approaching the olivine-glass interface and interpreted the equilibrium NiO ol to be the last point that showed no contamination from the glass (e.g., Matzen et al. 2013). No such procedure was conducted for the pyroxenes; reported NiO concentrations in pyroxenes from reversal experiments are most likely overestimates of the equilibrium values and they should not be used in the calculation of equilibrium partition coefficients.

Phase compositions
Glass Matzen et al. (2013) produced a set of experiments with ~18 wt% MgO liq . In this work, we produced three additional series of experiments, each with a roughly constant  Matzen et al. (2013). a Pressure as a function of temperature. Filled circles and associated dashed lines correspond to series with similar glass compositions. b Symbols denote concentration of MgO (wt%) in glass as a function of temperature; multiple symbols at a given temperature for a specific MgO series reflect forward and reverse experiments at those P-T conditions (for this study, downward and upward pointing triangles, respectively); dashed lines associated with each MgO series are weighted least-squares fits. Low-Ca (L) and high-Ca (H) pyroxenes are indicated, where present in the run products. Error bars in this and succeeding figures are one sample standard deviation, unless otherwise stated, and are shown where larger than the size of the symbol. The large error bars on the 1575 °C experiment (~21 wt% MgO series) are a consequence of quench crystallization   (6) 0.015 (4) 11.05 (9) 0.16 (3) 11.76 (7) 9.15 (4) 3.46 (11) 0.27 (1) 0.28 (2) (6) 0.010 (1) 12.01 (7) 0.19 (2) 14.15 (7) 9.20 (5) 2.82 (5) 0.22 (1) 0.27 (4) 0.279 (6) 99.00  (1) 11.31 (9) 0.20 (3) 15.91 (6) 8.99 (5) 1.76 (4) 0.10 (1) 0.13 (3) 0.062 (4) 100.45 65 ol 10 40.98 (9) 0.017 (8) 0.019 (5) 0.024 (4) 10.77 (4) 0.153 (7) 48.52 (12) 0.22 (3) ---0.373 (9) 101.09 3 Page 6 of 18 liquid composition but offset from the next series by ~3-4 wt% MgO. Experiments were conducted at 1 atm and 1-3 GPa and spaced at 25-50 °C intervals (see Table 1; Fig. 1a). All of our experiments produced glasses with MgO contents within 1.2 wt% of their specified target value, but there are within-series variations. For example, in the ~12 wt% MgO liq series, the 1-atm experiment produced a glass with 13.2 wt% MgO because the selected run temperature was too high, whereas other glasses from this series (11.8-12.2 wt% MgO) are much closer to the target of 12% (Fig. 1b). Similarly, Run 70 in the ~21 wt% MgO liq series produced a glass with 21.9% MgO, higher than the others in the series (20.4-21.3 wt%). Below, we discuss the extent to which these deviations impact our evaluation of whether or not the temperature dependence of D ol/liq Ni is a significant function of composition. As shown in Fig. 1b, MgO liq decreases in all three experimental series (this study) with increasing temperature. In addition, the ~12 and ~15 MgO liq series (and the ~18 wt% MgO liq series; Matzen et al. 2013) all exhibit increases in incompatible element concentrations and decreases in SiO 2 contents with increasing pressure (Table 2). Some variation in melt chemistry within an MgO liq series reflects deviations in the run conditions from those needed to produce the desired melt composition in a run saturated with olivine. As discussed in Matzen et al. (2013), however, we infer that changes in silica largely reflect the crystallization of progressively larger amounts of pyroxene, which has higher SiO 2 contents than the pyroxene-free glasses, (51-56 vs. 47-50 wt%), as the pressure of the experiments increases (see Table 2; Fig. 1b). Pyroxene crystallization is also likely at the root of increasing concentrations of incompatible elements in the melt with increasing pressure and temperature (see Matzen et al. 2013). As MgO in the liquid is lowered, pyroxene saturation occurs at progressively lower temperatures and pressures. For example, the 2.0 GPa run (1400 °C) in the ~12 wt% MgO liq series crystallized 31.5 wt% low-and high-Ca pyroxene, whereas the 3.0 GPa run (1600 °C) in the ~21 wt% MgO series had only olivine and melt.

Olivine
One feature of our experimental design is that the mass of an experimental charge is dominated by the starting olivine (Table 1); as a result, Mg#s of the olivine in our experiments are expected to vary little from that of the starting olivine (~90; see Table 1 in Matzen et al. 2013). If, however, the melt interacts with a relatively smaller volume of olivine directly adjacent to the melt (e.g., in the 1-atm experiments), the Mg#s of the near-melt olivine are more strongly influenced by the melt composition; for example, at 1 atm, the ~12 and ~15 wt% MgO liq series melts are in equilibrium with olivines with slightly lower Mg#s (87.5 and 88.7, respectively). In all series, the Al 2 O 3 contents of near-melt olivines increase with increasing temperature and pressure; for example, in the ~21 wt% MgO liq series, Al 2 O 3 contents increase from 0.04 at one atmosphere and 1450 °C to 0.14 at 3.0 GPa and 1600 °C. Olivine-liquid Al partition coefficients measured in our experiments agree well with the predictions of Agee and Walker (1990).

Pyroxene
Low-calcium pyroxene (1.8-2.5 wt% CaO) is observed in the ~12 and ~15 wt% MgO liq series experiments, appearing at and above 1.0 and 1.5 GPa, respectively (see Table 1; Fig. 1b). Subcalcic pyroxenes (6.2-10.4 wt% CaO) are also present in the ~12 wt% MgO liq series above 1.0 GPa and in the ~15 wt% MgO liq series above 2.0 GPa. Na 2 O contents of low-Ca pyroxenes increase from 0.1 to 0.3 wt% with increasing temperature and pressure. The Al 2 O 3 contents of both low-and high-Ca pyroxenes also increase with increasing temperature and pressure, from 2 to 8 wt% in the ~12 wt% MgO liq series and from 3 to 7 wt% in the ~15 wt% MgO liq series. These changes in the Na 2 O and Al 2 O 3 contents in the pyroxenes are consistent with previous experimental measurements of the pressure and temperature dependence of Na 2 O and Al 2 O 3 partitioning between pyroxene and silicate melt (e.g., Blundy et al. 1995;Frei et al. 2009). As mentioned briefly above, the SiO 2 contents of the pyroxenes (51-56 wt%) are higher than those of liquids from pyroxene-free experiments in each series (47-50 wt% SiO 2 ). Thus, the crystallization of pyroxene acts to reduce the SiO 2 content of the glass.

Mass balance
As described in Matzen et al. (2013), phase proportions in our experiments were determined using the nonlinear approach of Albarède and Provost (1977) and account for the variable amount of interaction between melt and the enclosing olivine; results are given in Table 1. All mass balance solutions are acceptable at the 95% confidence level (e.g., Press et al. 1992), suggesting that variations in liquid composition are well explained by the observed phases and their compositions (Table 2). Table 1 includes the calculated change in bulk NiO for the forward experiments. For our piston-cylinder experiments, NiO was conserved in the central melt poolchanges range from −4.2 to +2.1% relative (negative number indicates a decrease). Losses of NiO in 1-atm experiments were larger (−4.7 to −11.5%). We did not mass balance NiO in the reversal experiments as olivines in contact with melt are strongly zoned with respect to Ni.

Attainment of equilibrium
To demonstrate a close approach to equilibrium, we conducted forward and reversal experiments. As in Matzen et al. (2013), a forward experiment is conducted with a low-NiO glass (<0.03 wt% NiO) embedded in olivine (0.37 wt% NiO). Thus, at the beginning of the experiment, the apparent D ol/liq Ni is high, and over the course of the experiment, Ni moves from the olivine into the liquid (measured glasses from these experiments have 0.05-0.15 wt% NiO)  Matzen et al. (2013), which are represented by the solid black line (a weighted least-squares fit). Downward and upward pointing triangles represent forward and reversal experiments, respectively; error bars are propagated from the analytical uncertainties reported in Table 2. The open symbol is for a run (#68) deemed to have too magnesian a liquid composition to be included with the ~12 wt% MgO series experiments (see Supplemental Information for further discussion). Dashed lines are weighted least-squares fits to each respective series from this study. As discussed in the text, the slopes of all four lines are the same within uncertainty 3 Page 8 of 18 and, thus, the apparent D ol/liq Ni decreases toward the equilibrium value (and, thus, these forward experiments are indicated by downward pointing triangles in Figs. 1, 2). The reversal experiments were conducted using a glass doped with ~1 wt% NiO, similarly surrounded by powdered olivine with 0.37 wt% NiO. In these experiments, the initial apparent D ol/liq Ni is low, and over the course of the experiment, NiO moves from the melt into the olivine so that the apparent D ol/liq Ni increases (reversals are shown as upward pointing triangles in Figs. 1, 2). Where forward and reversal experiments were conducted at the same nominal temperature and pressure, the measured D ol/liq Ni values overlap at one sigma, suggesting that the olivine-liquid Ni partition coefficients reported here closely approach equilibrium values (Fig. 2).
As stated in the Introduction, a goal of this work is to evaluate whether or not the temperature dependence of D ol/liq Ni along the join MORB-Fo 90 olivine is a significant function of composition. Such a dependency would be manifested in a different slope for D ol/liq Ni versus temperature for each of the constant composition series. Figure 2 shows D ol/liq Ni values of the ~12, ~15, and ~21 wt% MgO series experiments from this study (Tables 1, 2) along with weighted regression lines for each of these series and the ~18 wt% MgO series of Matzen et al. (2013). The reason for not including the lowest temperature run (open triangle) in the ~12 wt% series regression is discussed in detail in Supplemental Information.
Qualitatively, Fig. 2 reinforces the well-known observation that as MgO liq increases, D ol/liq Ni decreases (e.g., Hart and Davis 1978;Kinzler et al. 1990). However, the salient feature of Fig. 2 for present purposes is that the slopes of all four lines (~12, ~15, ~18, and ~21 wt% MgO liq ) are statistically identical at 2 standard errors (SE): −0.70 ± 1.63/100 °C, −0.76 ± 0.21/100 °C, −0.63 ± 0.10/100 °C, and -0.37 ± 0.14/100 °C, respectively (listed uncertainties are 1 SE). The much larger uncertainty associated with the ~12 wt% MgO liq series reflects the relatively larger errors in D ol/liq Ni and the limited range in temperature. The statistical overlap among the four slopes suggests that, for bulk compositions along the join MORB-Fo 90 olivine, the temperature dependence of D ol/liq Ni is consistent with being independent of composition, although the progressive decrease in slope in going from liquids with ~15 to ~21 wt% MgO could reflect a small compositional dependence that would be broadly consistent with the calculations of Hirschmann and Ghiorso (1994) on the activity coefficient of NiSi 0.5 O 2 in silicate liquids. Keeping in mind that increasing temperature can be associated with increasing pressure, the results shown in Fig. 2 also confirm the conclusion of Matzen et al. (2013) that, for constant liquid and olivine compositions, D ol/liq Ni decreases with increasing temperature and pressure. In the following section, we fit our partitioning data using a thermodynamically inspired model that accounts for temperature and compositional effects on D ol/liq Ni and we show that all but one of the 28 experiments that comprise the four MgO series are consistent with a single regression line in 1/T (K) space.

Discussion
Modeling D ol/liq Ni : ideal exchange reaction Following Matzen et al. (2013) and many others (e.g., Hart and Davis 1978;Leeman and Lindstrom 1978;Kinzler et al. 1990), we fit our data using a Ni-Mg exchange reaction: for which we write the following expression: where � r(1) G • T ,P , the standard-state Gibbs free energy change of reaction (1) at temperature (T, in Kelvin) and pressure (P, in bars), is independent of composition. X ϕ i and γ ϕ i are the mole fraction and activity coefficient of the ith component in phase ϕ, using the molar components of Matzen et al. (2013), and R is the gas constant. One of the benefits of an exchange reaction is that, over moderate ranges in temperature and pressure, � r(1) C • p and � r(1) V are small enough to be safely neglected in the computation of � r(1) G • T ,P , so that the standard-state changes in enthalpy and entropy for reaction (1) can be approximated as constants and the effect of pressure on D ol/liq Ni is small [see Matzen et al. (2013) for a more detailed exposition of this important point]. Furthermore, at high temperatures, olivine can be treated as an ideal solution (e.g., Nafziger and Muan 1967;Campbell and Roeder 1968) and, as discussed by O'Neill and Eggins (2002) which is presented as Eq. (5) in Matzen et al. (2013). They fit their data and data from the literature to Eq. (3) and showed that the Ni-Mg exchange reaction has a significant temperature dependence. Although not discussed here, exchange reactions between Mg and other divalent cations (e.g., Mn and Fe 2+ ) show little temperature dependence (Roeder and Emslie 1970;Matzen et al. 2011Matzen et al. , 2013, making Ni unusual in this respect. Since previous work suggested a strong effect of liquid composition on activity coefficients of the NiSi 0.5 O 2 component in silicate melts (Hirschmann and Ghiorso 1994), we seek to determine the extent to which compositional contributions to the temperature dependence of the Ni-Mg exchange reaction can be ignored (i.e., that the ratio of MgO liq and NiO liq activity coefficients is approximately constant). plotted against inverse temperature for experiments from this work and Matzen et al. (2013). Although the exchange reaction is calculated using molar units (Figs. 3 and 4), using oxide weight percents yields identical values because the conversion factors for moles to weights cancel, a point that we return to in the context of Eqs. (4) and (5) below. The solid blue line in Fig. 3 is a weighted least-squares fit to all of the data (dashed curves represent the 95% confidence bounds). The data clearly define a nonzero slope, which can be equated (3) so that the Ni-Mg olivine exchange reaction is temperature dependent. Significantly, all of the data, with one exception (see Fig. 3), overlap the best-fit line at 2σ (75% of the 28 points overlap at 1σ), indicating that the experimental data (with MgO liq contents that vary by nearly a factor of two) are consistent with single values of −� r(1) H •   Table 2 (this work) and Table 3 of Matzen et al. (2013). Solid blue line is a weighted least-squares fit to all of the data; dashed blue curves are the 95% confidence interval on the regression. Values of the slope and intercept for the blue line are 3641 ± 396 and −1.597 ± 0.229, respectively 2013), all overlap at 1 SE: 2161 ± 2598; 5000 ± 1075; 3943 ± 712, and 4248 ± 1166 (K), respectively). In our discussion of Fig. 2, we separated out the lowest temperature experiment in the ~12 MgO liq series, but this is included in Fig. 3 because differences in MgO content of the melt are accounted for by the term that includes X liq MgO in Eq. (3). Note also that the slope reported here for the ~18 wt% MgO liq experiments of Matzen et al. (2013), 3943 ± 712, differs from that reported by Matzen et al. (2013), 4375 ± 1050. Here, fits are weighted by errors on K ol/liq D,Ni−Mg , whereas Matzen et al. (2013) used an iterative, bisquare-weighted least-squares fit. When the errors on all data are known, using weights that are proportional to the inverse square of the compositional errors should result in superior estimates of the fit parameters (including uncertainties), compared to a bisquare-weighted fit. As noted above, the blue line in Fig. 3  (3) are correct, we expect that the standard-state parameters obtained from fitting individual constant composition series will be identical to each other within uncertainty and, as noted above, this expectation is met.
In Fig. 4, our results are plotted together with a compilation of literature data. The Filter-B data set (from Matzen et al. 2013), which uses analytical totals (98.5-101.5 wt%) and Ni loss (<65%) as filtering criteria, has been updated to include data from this study; we refer to this amended data set as Filter-B′. Fitting the exchange reaction to the Filter-B′ data set (using an iterative, bisquare-weighted least-squares technique since not all studies report compositional uncertainties) gives a temperature dependency (4321 ± 190 K; 183 experiments; red line in Fig. 4) that overlaps within 2 SE of the slope obtained for the highprecision data shown in Fig. 3 (3641 ± 396 K; 28 experiments; the blue line in Fig. 4).
The Filter-B′ data set displays considerable scatter in Fig. 4. Some of this may be due to analytical errors or disequilibrium, but it is important to emphasize that this data set spans a large compositional range. For example, glass SiO 2 , Al 2 O 3 , FeO* (all Fe as FeO), CaO, and Na 2 O contents range from 40.5 to 68.8, 0 to 21.5, 0 to 37.2, 0 to 29.1, and 0 to 11.1 wt%, respectively, and olivine Mg#s range from 36 to 100. In comparison, glasses from this study and Matzen et al. (2013) are more restricted: SiO 2 , Al 2 O 3 , FeO*, CaO, and Na 2 O contents range from 44.4 to 50.2, 9.1 to 14.8, 9.3 to 12.4, 6.3 to 10.4, and 1.4 to 3.5 wt%, respectively, and olivine Mg#s ranging from 86 to 91. Given the broad range in bulk and phase compositions, it is possible, indeed likely, that the simplifications we made in arriving at Eq. (3)-especially that the ratio of activity coefficients for MgO liq and NiO liq is constant-do not hold for all of the literature experiments. Ghiorso and Sack (1995) commented on this issue when they stated that "… workers who have focused their effects on thermodynamic modeling of simple melt systems (see Berman and Brown 1987, for a synthesis and review) have demonstrated that quite complicated models are required to achieve the same level of data reproducibility as simpler formulations… provide in magmatic [natural] liquids." Unfortunately, quantifying the extent to which the ratio of MgO liq and NiO liq activity coefficients varies for all the experimental liquids in the Filter-B′ data set is difficult. Although there has been substantial work on determining how NiO liq activity coefficients vary with temperature and liquid composition, most of the experiments have been conducted using the 1-atm diopside-anorthite eutectic as a base composition, and thus, it is unclear whether a global fit to those data (e.g., Wood and Wade 2013) is applicable to the much wider range of liquid compositions encompassed by the Filter-B′ compilation. A similar situation exists for estimating MgO liq activity coefficients; the activity model of Snyder and Carmichael (1992) is calibrated on natural silicate melts, and the activity models of Berman (1983) are tied to compositions in the system CaO-MgO-Al 2 O 3 -SiO 2 (CMAS). Motivated by Ghiorso and Sack (1995), we note that many of the outliers in Fig. 4 are experiments from systems where Al 2 O 3 or CaO are either absent or present at very low concentrations, <2 wt%, in the liquid (open symbols in Fig. 4). Therefore, we also show a refit to the Filter-B′ data set (black line; Fig. 4) after removing those 53 experiments where the bulk composition did not contain at least CMAS + NiO and the liquid ≥2 wt% each of Al 2 O 3 and CaO (labeled Complex Filter-B′ on Fig. 4). Note that the scatter is reduced (the mean percent error on D ol/liq Ni for the Complex Filter-B′ data set is 9.6% compared to 11.3% for Filter-B′), but the slope of the line (4505 ± 196; 130 experiments) overlaps at 1 SE with that based on the entire Filter-B′ data set (4321 ± 190) and at 2 SE for the fit obtained from the experiments in this study combined with those of Matzen et al. (2013), 3641 ± 396. Since our goal is to generate a simple predictive tool to model D ol/liq Ni in natural olivine-bearing liquids as a function of temperature and melt composition, we prefer the Complex Filter-B′ fit in Fig. 4. In the Supplemental Information, we provide a more detailed discussion of the quality of the fit of Eq. (3) to the experimental data as well as a comparison with the temperature-independent D ol/liq Ni model of Beattie et al. (1991). Finally, although Matzen et al. (2013) concluded that ∆V for the exchange reaction (Eq. 1) was small enough to ignore, we briefly revisited Page 11 of 18 3 this issue by explicitly including a ∆V term in our fit to the Complex Filter-B′ data set ( C • p was assumed to be zero). Consistent with the conclusions of Matzen et al. (2013), ∆V is small, −0.024 ± 0.015 J/mol, and the improvement in the fit is not statistically significant at the 95% confidence level.
Rearranging Eq. (3) Ni , provided we have estimates of temperature and the MgO contents of the olivine and melt. Generally, the composition of the melt and the Mg# of olivine are known or assumed, and therefore, the corresponding temperature is readily determined using expressions explicit in temperature (e.g., Beattie 1993;Putirka et al. 2007) or any of a number of petrological programs, including MELTS (Ghiorso and Sack 1995) and Petrolog3 (Danyushevsky and Plechov 2011).

The influence of lithospheric thickness on the NiO contents of olivine phenocrysts
In this section, we explore the influence that a temperaturedependent D ol/liq Ni has on olivines erupting onto lithosphere of varying thickness. McKenzie and Bickle (1988), Ellam (1992), and Fram and Lesher (1993) provided early discussions of the potential influence of lithospheric thickness on the composition of erupted magmas. More recently, Sobolev et al. (2007) noted that lavas from areas with thick lithosphere (>70 km, e.g., Hawaii) tend to have magnesian olivines with higher NiO concentrations than those erupted onto thin lithosphere (e.g., Iceland) and to have higher concentrations than the values in mantle olivine (e.g., ~0.37 wt%; Korenaga and Kelemen 2000;Herzberg et al. 2013). They rationalized these observations as being a consequence of adiabatically rising parcels of mantle consisting of thermally (but not chemically) equilibrated packages of eclogite/pyroxenite and peridotite. As the mantle adiabatically ascends, the more fertile eclogite domains are the first to extensively melt (e.g., Hirschmann and Stolper 1996;Stolper and Asimow 2007;Lambart et al. 2016) and the resulting silica-rich liquids react with the surrounding peridotite to produce zones of olivine-poor to olivine-free, Ni-rich metasomatic pyroxenites. With continued upwelling, both the pyroxenite and the peridotite partially melt (although with different productivities) resulting in primary lavas that are mixtures of liquids originating from these two lithologies. The lithosphere limits the final pressure of partial melting so MgO ol that melts produced beneath a thick lithosphere are dominated by those from the metasomatic pyroxenite; partial melts of these pyroxenites are Ni rich both because the pyroxenites are rich in Ni relative to most known mantle-derived pyroxenites (e.g., France et al. 2015) and also because these olivine-poor source rocks have low bulk D Ni values, and thus, the olivines that precipitate from these melts are consequently predicted to be anomalously Ni rich. In contrast, partial melts produced beneath a thin lithosphere are diluted by more extensive contributions of melt from the peridotite, thus diluting the influence of the Ni-rich melts produced by melting of pyroxenite and resulting in olivine phenocrysts from shallow melting that are Ni poor relative to those from deeper melting. In the Sobolev et al. (2007) model, the composition of the mantle source (i.e., the relative amounts of pyroxenite), the mantle potential temperature, and the thickness of the lithosphere all influence the NiO contents of olivine phenocrysts crystallized from mantle-derived basalts. It is important to stress that this model, in the context of Ni contents of magnesian olivine phenocrysts, is driven by the assumption that D

ol/liq
Ni is a function only of composition-given such an assumption, it is difficult to generate olivine phenocrysts with Ni contents significantly higher than those of olivine in the mantle source by low degrees of high-pressure partial melting followed by low-pressure crystallization.
Recently, a number of authors (Li and Ripley 2010;Niu et al. 2011;Putirka et al. 2011;Matzen et al. 2013) have suggested an alternative explanation for high-NiO olivine phenocrysts in localities such as Hawaii. These authors proposed that the crystallization of such olivine from basalts at low-pressure results from a temperature (and/or pressure) dependent D ol/liq Ni . In this class of models, a thick lithosphere imposes a large difference in temperature and pressure between a partial melt equilibrating with the mantle (generally presumed to be peridotitic) and the near-surface environment in which olivines begin to crystallize. Thus, it is the effect that lithospheric thickness has on the temperature and pressure difference between the conditions of melt segregation in the mantle and the cooler near-surface conditions at which forsteritic olivine phenocrysts grow that controls their NiO contents and that larger temperature differences lead to higher NiO contents in early crystallized olivines.
As noted above, Matzen et al. (2013) showed that the effect of pressure on D ol/liq Ni is negligible for depths down to ~100 km (i.e., from 0 to 3 GPa)-a depth range that encompasses much of the variations in thickness of the oceanic lithosphere (e.g., Artemieva 2011). With our new olivine-melt partitioning data, we can test the hypothesis that a temperature-dependent D ol/liq Ni and partial melting of a peridotitic source control the NiO contents of near-surface olivine phenocrysts. To compute an expected difference between the NiO content of a primary olivine phenocryst and lithospheric thickness, we use after Eq. (8) from Matzen et al. (2013), except that here, NiO ol is in weight units. This equation is derived from two statements of Eq. (3) for D ol/liq Ni involving two different temperatures: one for a primary olivine-saturated melt in the mantle source at a temperature of T m , and a second, for the same melt, at its 1 bar olivine-saturated liquidus, T 1-bar , both converted to a weight basis. Given the temperature at which olivine begins to crystallize at low pressure (T 1-bar ) and assuming: (1) the Ni content of mantle olivine in the source region; (2) that the mantle melt last equilibrated at the base of the lithosphere; and (3) that the melt composition remained constant between the source and the site of phenocryst growth (and thus that the initial lowpressure olivine has the same Mg# as that in the mantle source, i.e., the olivine-liquid Fe 2+ -Mg exchange reaction is not a strong function of P and T; Toplis 2005), we can obtain T m using the slope of the olivine-saturated liquidus (55 °C/GPa, Sugawara 2000). Equation (5) can then be used to predict the NiO content of initially crystallizing near-surface olivines as a function of lithospheric thickness. As discussed in Matzen et al. (2013), the slope of the olivine-saturated liquidus estimated by Sugawara (2000) is very similar to values derived from MELTS (Ghiorso and Sack 1995) and calculations from Eq. (4) of Putirka et al. (2007); temperatures at 3 GPa obtained by applying the polynomial "pressure-correction" of Herzberg and O'Hara (2002) to the 1-atm olivine-liquid geothermometer of Beattie (1993) are within 15 °C of those calculated using Sugawara's 55 °C/GPa.
We assume that mantle olivines in the source region have 0.37 ± 0.03 wt% NiO (median ± MAD, mean absolute deviation; data for spinel lherzolites from Korenaga and Kelemen 2000;Jun Korenaga, personal communication, 2011), a value that overlaps with that for olivines from abyssal peridotites, 0.38 ± 0.03 (median ± MAD) (Hamlyn and Bonatti 1980;Shibata and Thompson 1986;Bonatti et al. 1992;Edwards and Malpas 1996;Ghose et al. 1996;Stephens 1997;Hellebrand et al. 2002;Brunelli et al. 2003;Seyler et al. 2003;Rampone et al. 2004;Warren and Shimizu 2010). Note that the spinel lherzolites considered by Herzberg et al. (2013) have an identical median but a smaller uncertainty (MAD = 0.01); in the following discussion, we use the error calculated using the Korenaga and Kelemen (2000) data set, as it is based on nearly twice as many analyses and reflects near global coverage. For a lithospheric thickness of zero, there is no temperature contrast between source and surface, so Eq. (5) recaptures the NiO content of the mantle olivine (i.e., 0.37 wt% NiO). With a thicker lithosphere, there is a temperature (5) NiO ol @T 1−bar difference between the source and olivine saturation near the surface and our calculations predict that these lowpressure olivines will have higher NiO than those present in the mantle source region. Although it is the difference between T m and T 1-bar in Eq. (5) that leads to differences in the Ni contents of the low-pressure olivines that crystallize from primary melts, it is inverse temperatures that appear in Eq. (5) and this means that variations in the 1-bar liquidus temperature (reflecting variations in primary melt  Table S1). The maximum NiO ol content for each suite was calculated by substituting the Mg# for the most Mg-rich olivine at a given locality into the equation for a linear or power law fit to the Mg# ol versus NiO ol data for that suite; coefficients are reported in Table S2. Sites are differentiated by type of volcanism (tholeiitic, alkalic, or uncertain when the assignment was ambiguous; see notes to Table S1)  composition, principally MgO content) have, as we show below, only a small effect on calculated Ni in low-pressure olivines. We used estimates of mantle potential temperature, T P , at mid-ocean ridge and hot-spot settings (~1325-1570 °C; Iwamori et al. 1995;Kinzler 1997;Ito et al. 1999;Asimow and Langmuir 2003;Courtier et al. 2007;Herzberg and Asimow 2008;Lee et al. 2009;Brown and Lesher 2014;Gale et al. 2014;Shorttle et al. 2014) (but see Putirka et al. 2007 for much higher estimates) and the expression from Herzberg and Asimow (2015) relating T P to a 1-bar liquidus temperature to acquire an estimate for the range in T 1-bar values, 1266-1447 °C (with a midpoint of 1356 °C), which most likely covers the vast majority of low-pressure liquidus temperatures for primary basaltic and picritic magmas (e.g., Herzberg et al. 2007). In Fig. 5, the solid black line was obtained using the above midpoint 1-bar liquidus temperature, 1356 °C in Eq. (5)  . The average calculated increase in the expected low-pressure olivine NiO content due to lithospheric thickness controlling the depth at which the primary magma separates from its mantle source coupled with the temperature dependence of D ol/liq Ni is ~0.114 wt% per 100 km.
In Fig. 5, we compare our model 1-bar olivine NiO contents calculated as a function of the depth of primary melt segregation to observed nickel contents in olivine phenocrysts from MORBs and lavas from the Hawaiian-Emperor seamount chain (H-E), the Galápagos, the North Atlantic Igneous Province (NAIP; Iceland, West Greenland, and Baffin Island/Bay), Réunion, the Azores, and the Canary Islands (see caption for island abbreviations) plotted as a function of depth to the lithosphere-asthenosphere boundary (LAB) at the time of eruption (drawn largely from Dasgupta et al. 2010; other data sources are noted in Table S1). Olivine analyses for the Galápagos are from Vidito et al. (2013); for West Greenland and Baffin Island/ Bay, data from Herzberg et al. (2016) were combined with those of Sobolev et al. (2007); analyses for the other localities are from Sobolev et al. (2007). Our model NiO olivine contents are calculated assuming no olivine crystallization as the primary magma migrates from its source region to the surface. It is, therefore, important to compare these calculated NiO values to those in the most primitive olivine phenocrysts at each of the localities as these primitive olivines are presumably closest in Ni composition to those that crystallized from the "primary" magmas. For each locality/suite of lavas, a plot of olivine Mg# versus olivine NiO defines either a relatively linear or curved trend. In order to estimate the "average" NiO content in the most primitive (i.e., highest Mg#) olivine in each of the suites of lavas, we fit each suite of data to either a linear or power law expression by minimizing the sum of the absolute deviations (in four of the 44 suites, samples defined two coherent trends and both were fit and in six of the 44, a subset of the samples defined a much more coherent trend in Mg# ol versus NiO ol space compared to the entire suite and, in these cases, only the subset was used; see notes to Table S1). The olivine with the highest Mg# in a given suite (or subset) was then used to calculate a NiO content (NiOmax-Mg# ) based on the regression equation for that suite-in this way, the plotted NiO content for each locality/suite of lavas (Fig. 5) reflects all or a large portion of the olivines analyzed for that suite (further details concerning the sample suites, e.g., the designations "tholeiitic," "alkalic," and "uncertain" in Fig. 5, are discussed in the notes to Table S1; regression coefficients are reported in Table S2). Figure 5 shows that the NiO max-Mg# values of olivine phenocrysts from MORBs and various OIBs are positively correlated with lithospheric thickness, consistent with the observation of Sobolev et al. (2007) and, although the scatter of the data points is large, suggesting that other factors are also at work, the positive correlation between lithospheric thickness and NiO max-Mg# for the data plotted in Fig. 5 is significant at greater than the 99% confidence interval (Spearman rank-order correlation coefficient = 0.709). A weighted least-squares fit of olivine NiO max-Mg# versus depth to the LAB using only those nickel contents from localities with maximum olivine Mg#s of ≥89 yields a slope per 100 km of 0.105 ± 0.006 wt% NiO. Note that the observed change in maximum NiO with increasing depth is consistent with the slope from the model T 1-bar = 1356 °C curve in Fig. 5 (0.114 wt% NiO/100 km) and, thus, the overall trend of increasing NiO in the most magnesian olivine phenocrysts in lavas erupted above lithosphere of increasing thickness is consistent with a temperaturedependent D ol/liq Ni and a mantle source region (dominantly peridotite) with olivines that contain ~0.37 ± 0.06 wt% NiO. It is perhaps significant that both tholeiitic and alkalic basalts show a positive correlation in Fig. 5 suggesting  3 Page 14 of 18 that the same overall mechanism controls the Ni contents in both of these compositionally distinct groups of lavas. We want to emphasize that we are not asserting that source regions of the lavas shown in Fig. 5 are exclusively peridotitic in composition. The presence of pyroxene-rich lithologies has been widely invoked to account for aspects of the geochemical and isotopic variability in oceanic basalts (e.g., Hirschmann and Stolper 1996;Harpp and White 2001;Hofmann 2003;Huang and Frey 2005;Jackson et al. 2012;Lambart et al. 2013;Brown and Lesher 2014;Shorttle et al. 2014), and the presence of pyroxene-rich lithologies in the source regions may well contribute to some of the observed scatter in Fig. 5 (e.g., in samples from the Hawaiian-Emperor chain). Nevertheless, the positive correlation between NiO max-Mg# and lithospheric thickness suggests an important role for a temperature-dependent D ol/liq Ni , as does the positive correlation between olivine NiO contents and olivine-spinel temperatures calculated for MORBs and basalts from large igneous provinces (Coogan et al. 2014). Finally, based on comparisons with olivines in Hawaiian lavas, Herzberg et al. (2016) suggested that the Ni contents of olivines in West Greenland and Baffin Island Paleocene picrites are not consistent with a temperaturedependent D ol/liq Ni . However, Fig. 5 shows that both the West Greenland and the Baffin Island/Bay data are, in fact, consistent with the model curve based on Eq. (5) (see Supplemental Information for a brief discussion of the apparent contrasting conclusions of Dasgupta et al. (2010) on the depth of melt equilibration for OIBs).
Even though the correlation between olivine NiO max-Mg# and depth to the LAB is statistically significant, several of the MORB, Icelandic, and Galápagos suites plot below the dashed lower bound (−2 × MAD on the median mantle olivine NiO content). Furthermore, the y-intercept of the weighted fit to NiO max-Mg# ≥ 89 versus lithospheric thickness discussed above is 0.33 wt%, below the accepted median NiO content in peridotitic olivines (0.37 wt%), although still within two mean absolute deviations of the median value. Two possible explanations for these deviations are: (1) partial re-equilibration of the parental melts with the lithosphere as the liquids migrate to the surface and/or lithosphere erosion (both processes would move points to lower LAB depths in Fig. 5) and (2) not sampling the most primitive and thus highest Ni olivine in a suite of samples. Interactions between ascending parental melts and the lithosphere are likely. However, for Hawaii, both low-and high-silica magmas are observed (Rhodes and Vollinger 2004;Stolper et al. 2004) and compositions of melt inclusions in Hawaiian olivines are highly variable (e.g., Sobolev et al. 2000), suggesting that interactions of mantle melts with the lithosphere were insufficient to destroy their geochemical characteristics. In the remainder of this section, we focus on the second possible explanation-that of the vagaries of sampling.
Given that Ni is strongly partitioned into olivine and that olivine is generally the only silicate phase on the liquidus of primitive basalts at low pressures, the scatter to low Ni values in Fig. 5 may reflect the vagaries of sampling-i.e., the most Fo-rich olivines that crystallized from the parental magmas associated with a given suite were not analyzed (most of the low NiO data points in Fig. 5 are denoted by open symbols indicating that the maximum olivine Mg# for these suites is <90). There are at least two possible explanations for these anomalously low NiO max-Mg# values that could reflect incomplete sampling: • The first possibility is that the most primitive olivines are present in the lavas, although in low abundance, but are easily overlooked. This can be understood using the HSDP2 Mauna Kea data set of Sobolev et al. (2007), which contains 3869 olivine analyses from 42 polished thin sections. In 41 of these sections, there is no olivine analysis with an Mg# within 0.5 of the maximum value of 90.99 found in section SR277-8.0, and only 74 analyses (2%) have Mg#s within 1 unit of the maximum observed value (these 74 olivines are distributed among 11 thin sections). A simple Monte Carlo calculation indicates that had only three thin sections out of the 42 been analyzed (three being the median number of samples per suite/distinct population; see Table S1), then the likelihood of "capturing" the 90.99 value falls to ~7% and the probability of analyzing an olivine with an Mg# ≥90 is ~57% (assuming that all olivine phenocrysts are analyzed in each thin section). Note that the range of olivine compositions for many of the suites plotted in Fig. 5 is based on a small number of samples and a small number of analyses (i.e., not all available olivines in the chosen sections were analyzed). Thus, for those suites where the maximum observed Mg# ol is less than ~90 and where a relatively small number of olivines were analyzed, it is plausible that the most primitive olivines present were missed. • The second possibility is that the most primitive olivines were never erupted. Large piles of cumulate olivine are thought to lie beneath Hawaiian volcanoes (e.g., Clague and Denlinger 1994), and seismic refraction studies suggest that large volumes of gabbro exist beneath ocean islands that sit on thinner lithosphere (e.g., Galápagos; Richards et al. 2013). Furthermore, petrologic and geochemical arguments have been used to argue that high-pressure fractionation is an important process for MORBs from Knipovich Ridge (labeled "K" in Fig. 5, Hellevang and Pedersen 2005), in Iceland (e.g., Maclennan 2008; Winpenny and Maclennan 2011), and in the Galápagos (e.g., Geist et al. 1998). Therefore, magma chambers may act as density filters that prevent the earliest fractionation products (i.e., high-NiO olivines) from being erupted. Alternatively, based on extensive data from Icelandic lava flows, Thomson and Maclennan (2013) suggest that the majority of olivine phenocrysts are not in chemical equilibrium with their surrounding magma and that the olivine phenocrysts have resided in cumulate mush piles at the base of crustal magma chambers, where high NiO concentrations in olivine are likely to have been muted by diffusive re-equilibration [note that deformed olivine phenocrysts in picritic Hawaiian lavas have also been used to argue that they are not directly related to their entraining magma (e.g., Garcia 1996;Baker et al. 1996;Sakyi et al. 2012)]. Thus, magma chambers may act as density filters preventing primitive olivines from erupting and/or (given sufficient residence times) serving to homogenize olivine compositions through diffusive re-equilibration.
Since olivine residence times and entrainment processes are stochastic, most basaltic suites may contain olivines whose Ni contents either reflect or approach those values expected of olivines in equilibrium with the primary (or parental) magmas that have entered the system (e.g., Fig. 5)-although, as discussed above, the number of analyses required to discover olivines with these primitive Ni values may number in the hundreds to thousands. It is our hope that by using data sets with large numbers of analyses, and focusing on the NiO contents of the most Mg-rich olivine observed, we can minimize the effect of sampling "biases" of the sort described above.
Finally, a potential test of the extent to which the various sampling and petrologic issues discussed above were operative is to plot NiO max-Mg# values versus the maximum observed olivine Mg# for a given suite. Figure 6 shows that for MORBs and tholeiites from Iceland and Hawaii-those petrologic provinces where we have the most tholeiitic suites, the maximum olivine NiO and Mg# are positively correlated. If the most magnesian olivines in these low NiO ol suites have not been sampled, the trends in Fig. 6 suggest that the low NiO max-Mg# MORB, Icelandic, and Hawaiian suites might, thereby, project to higher NiO ol values and become more consistent with the model curve of Fig. 5.
Given the factors discussed above that can skew compositions of entrained olivines in erupted lavas to lower Mg#s and nickel contents, the general agreement between the NiO contents of primitive olivine phenocrysts and the model curve shown in Fig. 5 is encouraging and consistent with lithospheric thickness controlling the depth at which melts last equilibrate with a largely peridotitic mantle.

Conclusions
We performed experiments over a range of temperatures (1300-1600 °C) and pressures (1 atm-3.0 GPa) to separate the effects of temperature from those of liquid composition on the partitioning of Ni between olivine and silicate melt. The results of these experiments are subsets of glasses with approximately constant compositions (~12, ~15, and ~21 wt% MgO) coexisting with olivine. We parameterized our partitioning data using a Ni-Mg exchange reaction and, at 2 SE, the resulting temperature dependencies overlap with each other, with the temperature dependency of the ~18 wt% MgO liq series determined by Matzen et al. (2013), and with a global set of data that spans a wide range of olivine and liquid compositions (this study, Matzen et al. 2013, and experiments from the literature). The relative  Table S2) versus the maximum Mg# ol observed at each locality. Only maximum NiO ol values from suites of olivines from tholeiitic lavas are plotted. See text for further discussion 3 Page 16 of 18 insensitivity of D ol/liq Ni obtained in this work to liquid composition makes the predictive model applicable to a wide range of natural melts.
The temperature dependence of D ol/liq Ni causes the NiO contents of primitive near-surface olivine phenocrysts to scale with the temperature contrast between mantle melting and low-pressure crystallization, and if primary melts last equilibrate with the mantle near the lithosphereasthenosphere boundary, then a correlation between NiO contents of initially crystallizing olivine and lithospheric thickness is a natural consequence of this temperature dependence of D ol/liq Ni . Our predictions compare favorably with the observed increase in NiO contents of high-Mg# olivine phenocrysts with lithospheric thickness, suggesting that these variations in observed NiO contents may reflect melting of and equilibration with mantle peridotite under lithospheric lids of varying thickness.