Near mantle solidus trace element partitioning at pressures up to 3.4 GPa



[1] We present new experimental partitioning data for a range of petrogenetically important elements at pressures of up to 3.4 GPa. The experiments are designed to mimic low degrees of anhydrous melting beneath mid-ocean ridges. The available data indicate that the partition coefficients are pressure, temperature, and composition dependent. Therefore partitioning behavior over the appropriate range of pressure, temperature, and composition must be quantified, in order to model continuous extraction of melt during the adiabatic rise of mantle material. For this purpose, we have parameterized the partitioning behavior of the REE, Hf, Zr, U, and Th based on a simple thermodynamic model. Although these parameterizations cannot be used for retrieving thermodynamic constants yet, they do yield accurate descriptions of the partitioning behavior that are useful for modeling decompression melting. Our parameterizations show that the partitioning of trace elements is strongly dependent on the Ca and Al-content of the clinopyroxene (cpx) and REE are always incompatible in cpx on the peridotite solidus at pressures up to 3.4 GPa. For garnet the data indicate that the heavy REE partition coefficients decrease with increasing pressure. Our data also indicates that Pb is more incompatible than Ce in clinopyroxene; Ce and Pb have similar partition coefficients in garnet. Therefore the presence of a residual phase with high Pb partition coefficients is required to produce the near-constant Ce/Pb ratios in MORB and OIB. Sulfides are the most likely phase to buffer the Pb content in the melt. Except at small porosities (<0.3%), clinopyroxene on the peridotite solidus is unable to fractionate U from Th significantly (15% 230Th-excess), whereas garnet can fractionate U from Th effectively at porosities up to 1%. Therefore if the 230Th-excesses in mid-ocean ridge basalts are melting phenomena, then melting with garnet residual is required in order to be compatible with physical observations on porosities and upwelling rate at mid-ocean ridges. New model calculations that include the compositional dependent partitioning of the trace elements show that the predicted physical characteristics (depth and extent of melting, upwelling rate, porosity) of the MORB melting regime are similar for the Lu/Hf, Sm/Nd, and U-Th systems.

1. Introduction

[2] Our understanding of the melting process and the sophistication of the models for melting and melt transport in the mantle has significantly increased over the last years [Aharonov et al., 1997; Kelemen et al., 1995, 1997; Salters and Longhi, 1999; Spiegelman and Reynolds, 1999]. Both major and trace elements can be used to constrain the melting process and the combination of the two is even more powerful [Spiegelman and Reynolds, 1999]. However, coupling of major and trace element constrains on melting and melt transport requires accurate quantitative descriptions of both phase relations and trace element partitioning as a function of pressure, temperature, and composition. Several papers have pointed out the importance of composition on the partitioning behavior of trace elements [Blundy et al., 1998; McKay, 1989; Nielsen, 1988; Salters and Longhi, 1999], and the present paper provides additional partitioning data for olivine, garnet, orthopyroxene, and clinopyroxene at pressures up to 3.4 GPa for compositions that are relevant to low degrees of anhydrous melting of the MORB source region. This approach is designed to weight the partitioning parameterizations most heavily in the most relevant range of pressure, temperature, and composition.

[3] There are several approaches to modeling the temperature, pressure, and compositional dependence of the partition coefficients. Numerous researchers [Gaetani and Grove, 1995; Hack et al., 1994; Nielsen et al., 1992] have employed variations of the thermodynamic approach in which a complex partition coefficient incorporates both the simple partition coefficient and liquid composition terms. Recently, in a series of papers, Wood and Blundy described a different type of partition model dependent on the fit of an ion in the crystal lattice. We have parameterized trace element partitioning using both types of models and have evaluated their performances. We have also applied these parameterizations to models of magma genesis beneath mid-ocean ridges in order to identify the compositional characteristics of different sources. Estimates of phase compositions and rate of melting can be calculated from the MELTS program [Ghiorso and Sack, 1995] as well as the model described by Longhi [1992] but updated with recent experiments [Longhi, 2002].

2. Experimental Techniques

[4] Starting materials in all experiments began as oxide mixtures that were fused, doped, and then partially crystallized at the QFM buffer for 2 days. High-pressure experiments were run in graphite capsules in a 1/2" piston cylinder apparatus with BaCO3 pressure medium according to the procedures described by Longhi [1995, 2002] and Fram and Longhi [1992]. However, recent measurements of the longitudinal thermal gradient show a smaller gradient (∼5°C) than previously reported (∼20°C) by Fram and Longhi [1992]. Consequently, the temperatures reported by Longhi [1995] and Salters and Longhi [1999] should be adjusted by ∼15°C. Exact information is available upon request.

[5] Recent determination of the anorthite- to spinel-peridotite transition in CMAS at 1305°C and 0.85 GPa in this lab agrees exactly with the gas apparatus determination reported by Kushiro and Yoder [1966], while an extension of the salt cell curve of the quartz coesite transition [Bohlen and Boettcher, 1982] passes through our bracketed reversals at 140 °C at 3.2 and 3.3 GPa. The reader should be aware that despite close agreement at relatively modest temperatures, substantial differences in high-temperature pressure calibration exist among experimental laboratories [Longhi and Baker, 1999]. Several that employ a single cylindrical pressure medium of BaCO3 (Lamont-Doherty Earth Observatory (LDEO)) or CaF2 (University of California, Davis, Caltech) locate the high temperature (≥1500°C) portion of the opx + cpx + sp = ol + gar equilibrium in the CMAS system at 2.1 to 2.3 GPa, whereas several that employ talc-Pyrex [Gudfinnsson and Presnall, 1996], salt-Pyrex [Klemme and O'Neill, 2000], or talc-boron nitride [O'Hara et al., 1971] concentric sleeves report pressures as high as 3.0 GPa. Although several laboratories are actively trying to resolve the discrepancies, the matter is not settled yet because there is no independently determined standard at these conditions. Preliminary results from an in situ X-ray study of the spinel-garnet transition (SGT) equilibrium that derives pressure from the MgO equation of state suggest a pressure of ∼2.6 GPa for the intersection of the SGT and the model solidus in CMAS [Walter et al., 2000]. If correct, this determination would require an approximate adjustment of +0.00145 (T −1300°)GPa for our runs and a similar correction with opposite sign for experiments run with talc-Pyrex pressure media.

[6] The experiments were designed to generate multisaturated liquids, similar to those expected at the mantle solidus but with a much higher proportion of liquid, so as to promote rapid equilibration. Figure 1 is an example of a typical experiment. We first performed reconnaissance experiments on synthetic materials to determine which combinations of bulk composition, pressure, and temperature would yield melt saturated (or close to saturation) with the mantle peridotite assemblage - olivine, orthopyroxene, cpx, and an aluminous phase (garnet or spinel). These reconnaissance runs thus provided major element and phase relation information (including melt reactions) relevant to mantle melting [Longhi, 1995, manuscript in preparation, 2002; Longhi, 2002]. Bulk composition and P, T conditions were fine-tuned to produce relatively large proportions of melt and crystal sizes large enough for ion microprobe analyses. Nonetheless, it still proved difficult to achieve saturation with the full mantle assemblage, maintain high liquid/crystal ratios, and produce large crystals. Consequently, even though liquid compositions were very close to four-phase saturation, only two or three of the lherzolite phases were usually present and typically no more than two of the phases were large enough in a single charge to analyze with the ion microprobe.

Figure 1.

Backscattered electron image of run RD1099-2. Upper half of photo shows a mass dendritic cpx that formed from liquid during the quench. The lower half is comprised of crystals present during the run. Bright white areas are cracks and edges of crystals where charges built up. Garnets are large (300–500 microns) dark gray crystals with sharp facets against the liquid. Opx and ol are smaller black crystals. Some are entirely enclosed by garnet in the center, but others on the left side are independent grains in contact with the liquid. Cpx (also dark gray) forms irregular crystals which are molded around the garnets at the bottom of the charge and which enclose ol. There are also a few small grains of spinel included within the opx enclosed by the large garnets. Scale bar is 200 microns.

3. Analytical Techniques

[7] We doped starting materials with different combinations of elements in order to keep the total amount of dopant as low as reasonably possible. One set of starting materials was doped with 4000 ppm each of U and Th, 100 ppm each of Y, Zr, Nb, Ce, Nd, Sm, Er, Yb, Lu, and 200 ppm Hf. Two other sets were doped with 5000 ppm of U, 2500 ppm Pb, and 1000 ppm of Ba, and one of these sets also contained 1000 ppm each of Ce and Yb. The total amount of dopant was limited to ∼1 wt % of oxide, as larger additions would change the phase relations. The rare earth element (REE) used for doping were chosen to avoid light REE oxide interferences on the heavy REE. Minerals and melt were analyzed for trace element composition with the CAMECA 6f ion microprobe at the Carnegie Institution of Washington using established techniques [Johnson et al., 1990]. Two to three spots were analyzed per mineral phase and usually four spots in the melt. In most of the runs, electron microprobe analyses of cpx and garnet (typically ≥30 microns in diameter) did not show any gradation or variation in major element composition; in some cases, though, garnets were zoned and these were avoided. Subsequent to the ion microprobe analysis, we checked the sputter pits for inclusions and overlap with both an optical microscope and by backscattered electron image to ensure that the analyses pits were in a single mineral phase. Although most of the liquids quenched to masses of dendritic crystals, heterogeneities in trace elements concentrations were not observed within these quenched regions of the charges for beam diameters of ≥15 microns. Precision of the partition coefficients (D) are a direct function of the concentrations in the crystals and are in general better than 15% for D > 0.1 better than 20% for 0.1 > D > 0.005, and between 50 and 100% for D < 0.005. All concentrations are calculated using Si-normalized intensities; concentrations are matrix corrected based on well-established calibration curves. Partitioning data are presented in Table 1. Starting compositions, run conditions, and major element content and variations of all mineral phases and starting compositions are presented in Table A1. Trace element concentration data and uncertainties are reported in Table A2.

Table 1. Partition Coefficients for Individual Mineral Phasesa
  • a

    Data taken from other experiments at similar P, T and X.

P in GPa11.
T in K162316681833186118531873188318831883190619081908190819331933
Cpx GarnetGarnetOpxOlivine CpxCpx
Ba0.0004 0.00050.00070.00100.0011 0.00120.0025
Ce0.019* 0.014*0.014*0.00580.0002 0.02290.0431
Pb0.0109 0.00460.00540.00910.0035 0.00330.0135
U0.0063 0.02570.03540.00290.0013 0.00500.0106
P in GPa 2.8 2.82.8 2.82.4
T in K 1838 18581848 18551813

4. Results

[8] Although another paper [Longhi, 2002] will deal with the systematics of primary melts, the major element phase compositions of the runs (Table A1) merits a brief discussion. Seven of our runs contain the full garnet lherzolite assemblage, and one run contains the spinel lherzolite assemblage. Nonetheless, simply having an lherzolite assemblage is no guarantee that the liquid and crystal compositions will exactly match those of a given partially molten mantle peridotite. Indeed this goal can be quite elusive because trajectories of equilibrium melt compositions depend strongly on bulk composition [Bowen, 1928]. The effects of an orthopyroxene peritectic in the garnet stability field [Longhi and Bertka, 1995] complicate matters considerably. Hence it is quite difficult to intersect the melt trajectory of crystal-rich system (such as mantle peridotite) with a multisaturated liquid-rich system, as we have attempted, even with some empirical method of estimating compositions of low-degree melts [e.g., Longhi, 1992] or a series of recursive syntheses and melting experiments [Robinson et al., 1998]. Indeed, none of our runs exactly matches that of a partially molten mantle assemblage with either PUM [Hart and Zindler, 1986] or depleted PUM [Kinzler and Grove, 1992] composition. These mismatches are inferred from the presence of negative coefficients for at least one phase when the solid and liquid phase compositions from each run are mass balanced (linear least squares method) against the mantle compositions.

[9] In order to determine how close the experimental assemblages are to those of partially molten mantle peridotite, we have run a series of regressions with FeO treated as a separate phase (as in estimating Fe-loss or gain). In these calculations the phases in run RD1099-2 all have positive coefficients when regressed against both depleted-PUM (0.544 ol, 0.299 cpx, 0.126 opx, and 0.008 gar, 0.007 FeO, and 0.016 ± 0.008 liq with a residual sum of squares = 0.001), and the weight fraction of liquid is 0.0096 ± 0.0071 for depleted PUM with a residual sum of squares = 0.001 and PUM (0.031 ± 0.013 liq). These results imply that the liquid in RD1099-2 would be a 1.6 wt % melt of a peridotite similar in composition to dPUM but with 0.7 wt % less FeO or Mg # increased from 90.0 to 90.8. When similar regressions with adjustable FeO are calculated for the other runs, one or more of the phase coefficients remains negative. Comparison of the input bulk composition with those produced by the regression models shows that these mass balance mismatches are largely the result of Na2O concentrations that are too low or too high for a given pressure. Consider, however, that the liquid from run RD1099-2 that successfully fit a 1% melt at 2.8 GPa contains 1.5 wt % Na2O, whereas low-degree melts produced in the diamond aggregate experiments at 1.0 GPa contain as much as 7.4 wt % Na2O [Baker and Stolper, 1994; Hirschmann et al., 1998]. Most of this large difference in Na2O can be attributed to a systematic increase in bulk partition coefficient for Na2O in low degree melts with increasing pressure along the solidus resulting from decreasing incompatibility of the jadeite component in pyroxene with pressure (J. Longhi, manuscript in preparation, 2002). A corollary of the increasing bulk partition coefficient for Na2O is that there is relatively little change in Na2O concentration in the liquid as the melt fraction approaches zero at higher pressures. Consequently, the 1.5% Na2O in the liquid from run RD1099-2 is an approximate upper limit for Na2O in a melt of depleted PUM (d-PUM) at this pressure, and the upper limit for Na2O in runs at higher pressures should be lower still. Thus the liquid in run RD699-2, with a Na2O concentration of ∼1.9 wt %, contains slightly too much Na2O to be a melt of d-PUM at 2.8 GPa and, analogously, the liquids in runs RD1097-5 and -7 with Na2O concentrations of ∼2 wt % Na2O contain > 0.5 wt % too much Na2O to be d-PUM melts at higher pressures. These differences in liquid composition are small with respect to the differences between anhydrous mantle melt compositions and the basaltic and simple system compositions that have been employed in other partitioning studies [e.g., Hauri et al., 1994; Van Westrenen et al., 1999]. Parameterization of partition coefficients with respect to pressure, temperature, and composition provides a means of compensating for the small compositional differences that do exist.

[10] Our doped experiments have yielded 22 new mineral-liquid pairs suitable for ion-probe analysis and have extended the maximum pressure of our measured partition coefficients from 2.8 to 3.4 GPa (Table 1). The new data (Figure 2) confirm our earlier studies on U and Th partitioning which showed (1) that partition coefficients for the REE and Hf and Zr in cpx are dependent on the Wo content (molar CaO/[CaO + MgO + FeO]) in cpx, (2) that Th is more incompatible than U in garnet, (3) that the partition coefficients for U and Th in garnet are higher than those in coexisting clinopyroxene, and (4) that the partition coefficients for U and Th in clinopyroxene are equivalent within error leaving little potential for cpx to fractionate these two elements. The new REE partition coefficients also confirm our earlier observation that the REE become more incompatible in cpx on the peridotite solidus as the Wo content in cpx decreases with increasing pressure. The new REE partition coefficients for garnet show that heavy REE become less compatible with increasing pressure. This decrease in D for the heavy REE partitioning is not associated with an increase in the D for the more incompatible elements; thus the decrease is unlikely to be an artifact of liquid contamination of the analyzed spots.

Figure 2.

Spider diagrams for new weight-based partition coefficients for (a) clinopyroxene and (b) garnet. Numbers are molar CaO/(CaO + FeO + MgO + MnO) in cpx and garnet.

[11] The new measurements also reveal very little variation of the opx partitioning with P and T, which is consistent with opx having much smaller compositional variation than cpx on the peridotite solidus. As expected, measured partition coefficients for olivine are very low, implying a minor role for olivine in incompatible trace element fractionations during melting. Partition coefficients for the REE in olivine increase with mass and DCe is ∼100 times lower than DLu. Our data also indicate Nb partition coefficients are very similar in garnet and cpx, but DCe is similar to DNb in garnet and greater than DNb in cpx. Thus cpx has the dominant influence on the Ce/Nb (and La/Nb) ratio.

[12] The experiments that involved Pb partitioning were mainly conducted to confirm the two experiments of Hauri et al. [1994, p. 2790], which were the only experiments in which U, Th, Pb, and Ce partitioning were determined together. Our measurements show Pb to be more incompatible than Ce in both cpx and garnet, in general agreement, with Hauri's determinations, but the DPb for garnet (0.00012) reported by Hauri et al. [1994] seems improbably low. DPb/DCe ranges from 0.3 to 0.2 for garnet and is ~0.5 for high pressure clinopyroxene. DPb/DU ratios are <2 in cpx, which is far lower than expected. Also, DPb/DU in garnet is always less than 1 indicating that Pb is more incompatible than U in garnet.

5. Modeling of the Compositional Dependence of Trace Element Behavior

[13] Traditionally, partitioning of trace elements is modeled as a reaction (either formation or exchange). Recently, in a series of papers, the Bristol group [Blundy and Wood, 1994; Blundy et al., 1998, 1996; Van Westrenen et al., 1999; Wood and Blundy, 1997; Wood et al., 1999] has argued that the absolute value of partition coefficients is dependent on how well the ion “fits” in the lattice of the crystal. The fit is determined by the size of the ion's site (dependent on crystal composition), the rigidity of the crystal as measured by the Young's modulus (E) and the size, and valence of the substituting ion. Partition coefficients are scaled to the partition coefficient (D0) of an element whose ion has the “ideal” fit. Although this model has advanced our understanding of how the energetics of cation sites in crystals affects partitioning, it has not yet addressed the complimentary contribution of cation energetics (or structure) in the liquid, even though it has been shown that liquid structure (or composition) has an important influence on the partitioning [Watson, 1977]. Several studies [Baker and Stolper, 1994; Hirose and Kushiro, 1993; Hirschmann et al., 1999] have shown that very low degree melts at 1.0 GPa have significantly higher silica and sodium than higher degree melts or melts from higher pressures. Proper accounting of the structure or composition of these liquids is therefore important in order to predict partition coefficients correctly on the mantle solidus and an approach that takes the liquid composition into account is required. In addition, the Wood and Blundy [1997] model produces a parabolic distribution of partition coefficients plotted against ionic radius with the ideal ionic radius (r0) being the one beneath the maximum of the parabola [Blundy et al., 1998, 1996]. Parameterization of these models works best if partition coefficients are available for both sides of the parabola so that the curvature and maximum is constrained by the data. Such is the case for REE in high Ca-cpx at P ≤ 2.0 GPa, but the ionic radii of all the REE are larger than r0 in garnet as well as the r0 of higher pressure low-Ca-cpx. Consequently, the calculated r0, D0, and E of our partitioning experiments have very large uncertainties, and the model does not reproduce the data very well. For these data a different approach is required.

[14] In this study we have employed a thermodynamic approach in which the simple partition coefficient is part of a complex partition coefficient that is proportional to the ideal portion of an equilibrium constant. It can easily be shown that all simple partition coefficients in complex silicates have an explicit dependence on the liquid composition that is determined by the stoichiometry of the component that the element of interest forms in the crystal [Beattie et al., 1993]. For example, if Ce forms a Ce3Al5O12 component in garnet, DCe will depend on AlO1.5 concentration in the liquid. This compositional dependence can be removed if the concentration of another element with the same valence and substitution mechanism in the crystalline phase is known. However, in forward modeling the composition of the crystal must be calculated from the liquid composition, in which case there is little to gain from exchange reactions.

5.1. Results of Thermodynamic Modeling

[15] The appendix describes the thermodynamic model that we have employed to describe the partitioning behavior of the trace elements. We have parameterized cpx-liquid and garnet-liquid partitioning in terms of complex partition coefficients using only formation reactions. The formation reactions were based on known crystal components where possible. In some cases, however, cation site assignments are not certain, and in these cases, we tested several crystalline components for some elements and present the parameterizations that seem to fit the data best. We performed stepwise regression for each element's partition coefficient for each reaction testing the significance of each additional parameter. Goodness of fit is measured by the correlation coefficient (R2), which has a maximum value of 1.0 for a perfect fit and by the standard deviation of the model from the observed values:

display math

The number of experiments that contains partitioning information is different for each element as very few experiments provide partitioning information on all of the REE, plus U, Th, Hf, and Zr. We restricted the data to nominally anhydrous liquids. The results of these multiple regression analyses are listed in Table 2 for cpx and Table 3 for garnet. In addition, Figures 3 and 4 show measured versus predicted partition coefficients for a number of key elements. Because the values of some D may vary by more than an order of magnitude, perhaps the best appraisal of the models is to note that most of the predictions lie well within ±Dmeas/2, as is evident in the figures. In addition, we did investigate whether there are systematic variations between goodness of fit (measured as (DmeasuredDpredicted)/Dmeasured) and P, T or compositional parameters and found none. This indicates that the parametrization is robust over the P, T, &#55349;&#56499; range modeled. The variation of the regression coefficients from element to element reflects different data sets as well as lower precisions for D with lower values. Because the major element concentrations are highly correlated, a “blind” stepwise regression could assign “artificial” significance to parameters; that is, Ca and Al in cpx are correlated and perhaps Ca better parameterizes Ce behavior, whereas Al better parameterizes Sm. In order to avoid arbitrary assignment of significance, we have used for cpx DSm and DLu as the backbone of the parameterization. For both Sm and Lu the number of experiments is significantly larger than for any other element. Furthermore, in most cases we have reported only those parameters that show statistically significant correlations with more than one trivalent or tetravalent element and used only parameters that make mineralogical sense.

Figure 3.

Measured versus predicted simple mole based partition coefficients (D) for trivalent and tetravalent ions in clinopyroxene. Data are from this study and Beattie [1993a], Gaetani and Grove [1995], Gallahan and Nielsen [1992], Hart and Dunn [1992], Hauri et al. [1994], Johnson and Kinzler [1989], Salters and Longhi [1999], Wood and Blundy [1997], Wood et al. [1999], Adam and Green [1994], Green and Pearson [1985], Hack et al. [1994], and Nicholls and Harris [1980].

Figure 4.

Measured versus predicted simple mole based partition coefficients for trivalent and tetravalent ions in garnet. Data are from this study and Beattie [1993b], Hauri et al. [1994], LaTourrette et al. [1993], Salters and Longhi [1999] and Van Westrenen et al. [1999].

Table 2. Multiple Regression of Natural Logarithm Complex Clinopyroxene/Liquid Partition Coefficientsa
Trivalent dbA1000P/T10,000/T(1 − XMg)2(1 − XFe)2(1 − XDi)2R2nRSD
  • a

    X = cation mole fraction; XFM = XMg + XFe; XEn and XDi are mole fraction of enstatite and diopside component in the crystal. The n is the number of points; R2 indicates square of multiple correlation coefficient; RSD is the standard deviation of the model prediction of Ds; sd is the standard error of the coefficient; and A is the intercept.

  • b

    d = D*(M) / [XFM(XAl)*XSi]. D* is value reported in Table 1, M = Σ(ciliq /mwi)/Σcixt /mwi); c, weight % oxide; mw, 1-cation oxide formula weight.

  • c

    d = D*(M) / [XFM(XAl2)].

  • d

    d = D*(M) / [XCa(XAl2)].

Ce−9.43  3.379.880.867320.035
sd0.84  0.590.75    
Nd−11.76  4.1112.75 0.831250.036
sd1.94  0.542.34    
Sm−8.41−0.160.303.348.23 0.860860.127
Er−11.63 1.41 7.66 0.928160.087
sd1.47 0.20 2.28    
Yb−6.96  4.627.041.390.726350.143
sd1.46  0.561.310.35   
Tetravalent dcA(1 − XEn)21000/T(1 − XMg)2(1 − XFe)2(1 − XDi)2R2nRSD
Zr−10.233.910.68 6.892.810.833460.073
sd1.820.620.14 1.620.84   
Hf−4.60 1.38   0.779200.046
sd1.01 0.17      
Tetravalent ddA(1 − XEn)21000/T(1 − XMg)2(1 − XFe)2(1 − XDi)2R2nRSD
Th−3.073.29   5.800.666410.0054
sd1.111.27   1.17   
U−5.65  6.04 5.000.691410.0046
sd1.84  2.53 0.55   
Table 3. Results of Multiple Regressions of Natural Logarithm Complex Garnet/Liquid Partition Coefficientsa
Trivalent dbA10,000/T1000P/T(1 − XAl)2(1 − XCa)2(1 − XFM)2(1 − XGross)2nR2RSD
  • a

    Variables as in Table 2; XGross is mole fraction of grossular component in garnet.

  • b

    d = D*(M)/[XFM(XAl)XSi].

  • c

    d = {D*(M)/[XFM4(XSi2)]}1/2.

Ce6.36−0.80     220.3950.057
Nd−0.01  4.49  −1.04170.5360.032
sd0.66  1.13  0.50   
Sm0.57  3.13   220.8410.118
sd0.22  0.31      
Er−0.35  4.001.20  210.9720.59
sd0.16  0.480.34     
Yb−2.60  7.90 1.07 220.9770.94
sd0.60  0.55 0.38    
Lu−2.71  8.16 1.04 220.9721.51
sd0.69  0.640.45    
Tetravalent dcA10,000/T1000P/T(1 − XAl)2(1 − XCa)2(1 − XFM)2(1 − XGross)2nR2RSD
Zr9.98 1.89−21.397.06  220.9570.42
sd1.07 0.671.941.45     
Hf10.54 1.23−18.465.25  220.9690.34
sd0.86 0.541.571.17     
U7.85−2.43 4.01 10.84−1.88330.9080.044
sd2.100.56 1.83 1.650.59   
Th11.46−2.42   8.60−2.08300.8690.017
sd2.560.66   1.700.72   

[16] REE partitioning in cpx is best described by formation reactions involving cation-oxide melt components:

display math

which yield complex partition coefficients with the form

display math

whereby M converts the weight based partition coefficients to mole units and x is mole fraction of the cation-based oxide. In previous work over a limited range of composition and atmospheric pressure, Gaetani and Grove [1995] found that describing the liquid in terms of Bottinga and Weill (BW) two-lattice model [Bottinga, 1985] worked the best for their data, but as we have argued previously, BW components are not well-suited to activity approximations in a data set with a wide range of composition because of systematic discontinuities that will lead to erroneous predictions.

[17] The regressions show that REE partitioning in cpx is mostly dependent on P, T, the diopside component in the cpx, and the MgO, FeO, and SiO2 contents of the liquid. The dependence of REE partition coefficients on the diopside (or wollastonite) component in pyroxene is well known [e.g., McKay et al., 1986]. Since these parameters are all related to each other to some degree, not all of these components occur in all final regressions, but all these parameters show significant correlations with the complex partition coefficients. It has been observed that the M2 site decreases in size as the Mg or Al content in the M1 site increases. Incorporation of the AlO1.5 term in the complex coefficient effectively adds a dependence on the Al-content of the clinopyroxene that has been observed in some previous studies that used a subset of the data set that we have analyzed [Blundy et al., 1998; Gaetani and Grove, 1995; Nielsen et al., 1992], but we have not observed this dependence in the large data set. We expected that the coefficients would vary systematically from the light to the heavy REE. Inspection of Table 2 shows that this is not the case. This lack of systematic variation shows that the parameterizations are not yet the full and correct descriptions of the partitioning behavior out of which thermodynamic data can be extracted. Therefore the description, at the moment, is an accurate description of the partitioning behavior but has undetermined thermodynamic significance.

[18] Initially, we attempted to fit all of the tetravalent high field strength elements (HFSE) according to the same component. However, we observed that models with the highest correlation coefficients for Hf and Zr have very low coefficients for U and Th, whereas models with the highest correlation coefficients for the more incompatible elements have low coefficients for Hf and Zr. Consequently, we present regressions for two different components with similar formation reactions: CaOliq + UO2liq + Al2O3liq:→ CaUAl2O6cpx and (Fe,Mg)Oliq + ZrO2liq + Al2O3liq:→ Zr(Fe,Mg)Al2O6cpx. Ionic radii provide a rationale for these two different components. U4+ and Th4+ have larger radii than Ca2+, which in turn is much larger than Mg2+ and Fe2+; whereas Zr4+ and Hf4+ are similar in size to Fe2+ [Shannon, 1976]. It is plausible therefore that the larger HFSE require the largest possible major element, Ca, to expand the structure. However, given the similarity of Hf4+ and Zr4+ to Fe2+, the presence of Fe2+ (and Mg2+) facilitates the substitution of the smaller HFSE. As expected, (1 − XDi)2 was the highest ranked variable for the Hf and Zr regressions. Even though a different variable ranked highest for each of the larger 3 HFSE, (1 − XDi)2 in each case ranked only a few points behind, suggesting that the larger errors associated with more incompatible elements may have slightly obscured the true compositional dependences. Alternatively, these elements may have more than one substitution mechanism.

[19] Although the existence of YAG-type garnets (Y3Al2Al3O12) provides a clear guide how to formulate components for the REE in garnet, several studies suggest multiple substitution mechanisms (and thus components) for the tetravalent HFSE. In calcic environments Zr-rich garnets appear to have a kimezite component Ca3Zr2(Al2Si)O12 [Milton et al., 1961]. However, Mössbauer spectra of such garnets show both octahedrally and tetrahedrally coordinated Fe2+ [Dowty, 1971], which is consistent with two components Ca3(Zr(Fe, Mg))Si3O12 and Ca3Zr2((Fe, Mg)Si2)O12. In another Mössbauer study of Ti-rich garnets, Huggins et al. [1977] found that ferrous iron was approximately equally distributed between octahedral and tetrahedral sites. Given that Mg2+/Fe2+ is likely to be higher on tetrahedral than octahedral sites, we suspect that the Ca3Zr2((Fe, Mg)Si2)O12 component is more appropriate to magnesian garnets. Furthermore, since peridotitic and basaltic garnets are relatively low in grossular component (0.10–0.25), it is not surprising that we found a (Fe, Mg)3(Zr2)((Fe, Mg)Si2)O12 component to produce the best correlations for all of the HFSE. Even though Van Westrenen et al. [1999] showed that D for REE between garnet and liquid varied systematically along the pyrope-grossular join, (1 − Xgross)2 does not appear as a significant variable for most of the REE and HFSE complex coefficients in Table 3. The reason is that for many of the elements the major compositional variation among the crystals and liquids is not along the pyrope-grossular join, but between peridotitic and basaltic melts, as reflected in the appearance of (1 − XAl)2 as a variable for a majority of elements in Table 4. In most instances (1 − Xgross)2 was highly correlated with the partition coefficient but also was correlated with a more highly ranked variable, such as (1 − XAl)2 and so did not improve the fit sufficiently to be chosen as a secondary variable.

6. Consequences of the Modeling on the Trace Element Fractionations

[20] Do we still need garnet to explain the Lu/Hf and 230Th-excesses in MORB? It has been suggested that the heavy REE are compatible in high Al-clinopyroxene and that these high partition coefficients in cpx are sufficient in the absence of garnet to explain the relatively large fractionations in Lu/Hf between mid-ocean ridge basalts and their source [Blundy et al., 1998; Walter and Gudfinnson, 1999]. Some experiments [Wood et al., 1999] also indicate that Th is more incompatible than U in high-Al cpx. According to the equations of Wood et al. [1999], higher Al produces a smaller M2 site radius (r0), which in turn implies a lower U/Th ratio in the melt. However, it is unclear whether these high Al-cpx, which were not in equilibrium with the full lherzolite assemblages are appropriate to the solidus of MORB mantle. The assessment of the presence of garnet requires the answer to two questions: what is the composition of clinopyroxene on the mantle solidus at 1.5–2.4 Gpa, and what are the partition coefficients associated with these compositions? The following section will answer those two questions.

[21] We have calculated magma compositions produced along a variety of melting paths and compared them to MORB compositions. We modified a version of the batch melting program described by Longhi [2002] to simulate fractional melting (FFTHERM) of lherzolite and have applied our parameterization of the compositionally dependent partition coefficients of key trace elements in cpx and garnet to the output of FFTHERM. In the calculations we present here melt is generated in response to steps of 0.1 GPa decompression; and any melt in excess of a 1% background porosity is removed and aggregated. The mineral and melt compositions and phase proportions, output from the major element melting models at each pressure, are used to calculate the partition coefficients for each element in each phase for this pressure interval as well as the bulk partition coefficients from the parameterizations given above. In this way, the calculations automatically account for the changing composition of the residue and the changing stoichiometry of the melting reaction. A more complete description of the major element model is given by Longhi [2002].

[22] Our calculations predict an Al-content in the cpx on the lherzolite solidus at pressures between 1.5 GPa and 2.5 GPa of up to 9 wt % Al2O3. These values are significantly lower than the values asserted by Wood et al. [1999] (12–14 wt % Al2O3). The most sodic 1.5 GPa melt (3.5% Na2O) of MPY-90-40 from Falloon et al. [1988] coexisted with a full lherzolite assemblage and its cpx contained 9.1 wt % Al2O3. Furthermore, experiments by Kinzler [1997] in the range of 1.5–1.9 GPa produced full lherzolite assemblages with melts in the range of 4–5 wt % Na2O and cpx with 9–10 wt % Al2O3. Calculations using MELTS [Ghiorso and Sack, 1995] also indicate less aluminous pyroxenes. Consider that the Wood and Blundy experiments [Wood et al., 1999] ostensibly produced analogs of low degree melts of a “fertile MORB pyrolite” with a bulk Na2O of 0.5 wt %. The two melts from these experiments (1.5 and 1.9 GPa) were highly sodic (each contained 7.4 wt % Na2O) and were highly aluminous (20.5–20.7 Al2O3). Most estimates of undepleted upper mantle are ∼ 0.3 wt % Na2O [Hart and Zindler, 1986], so low-degree melts of even “fertile” MORB mantle are likely to contain considerably less Na2O than those produced by Wood et al. [1999]. Similarly, Al2O3 content for the undepleted mantle is 4.0 wt %. With minimum estimates for the amount of spinel (2 modal%, 50 wt % Al2O3) and opx (25 modal%, 6 wt % Al2O3) the Al2O3 content in cpx (18 modal%) cannot be higher than 9 wt %. Thus it is unlikely that cpx with 12–14 wt % Al2O3 exist on the mantle solidus.

[23] Figures 5 and 6 shows the results of trace element fractionations for melting paths calculated with the FFTHERM model for the major elements. We choose to use only the FFTHERM results because the MELTS model allows only spinel as a host for Cr, which stabilizes aluminous spinel at the expense of garnet on the solidus well into the garnet field (cpx, opx, and garnet take up significant amounts of Cr and Cr affects the details in the cpx composition). Melting paths begin at 2.0 and 3.0 GPa and trace element compositions in aggregated melts along each path are modeled in terms of cylindrical and triangular geometries [Langmuir et al., 1992]. The melting curves in black are melts from triangular melting regimes, while the melting curves in red are aggregated melts from a single melting column. With melting starting at 3.0 GPa, 4% melt is generated in the garnet stability field between 3.0 and 2.4 GPa. Both FFTHERM model as well as MELTS predict extremely limited melt production after exhaustion of cpx. In MELTS the initial melting rates are slower than in FFTHERM, but the pressures of the cpx exhaustion are very similar: when melting begins at 3.0 GPa cpx is exhausted at ∼20% melting at 0.8 GPa; when melting starts at 2.0 GPa cpx is exhausted after 16% melting at ∼0.7 GPa.

Figure 5.

A δ(Lu/Hf) versus δ(Sm/Nd) diagram with various melting curves for the different trace element parameterization compared with the data for MORB and OIB. Melting curves are the aggregated melts from the complete melting regime. Except for where noted melting curves are for triangular melting regime. Green curves are old models [Salters and Hart, 1989], numbers at tick marks on left most green curve is extend of melting (in percent) for a peridotite unit that has undergone the largest degree of melting in the melting regime (i.e., ascended directly under a ridge). Black curves use the trace element parameterization presented in this study combined with the Longhi model for fractional melting at decreasing pressure. Tick marks are at 1% melt increments of the peridotite unit that has undergone the largest degree of melting in the melting regime. Red curves are the same as the black curves but for Wood and Blundy [1997] parameterization for cpx partitioning. The experimental database for both cpx partitioning models was the same. Fractional melting model used 0.1% increments to calculate the trace element fractionations and the matrix had a constant residual porosity of 1%. Data sources for OIB and MORB with black symbols from [Salters, 1996], red MORB symbols from [Chauvel and Blichert-Toft, 2001].

Figure 6.

Contours of 230Th-excesses for melts generated using the cpx and garnet parameterizations of this study for a range of upwelling velocities (0.1–1 cm/yr) and a range of initial porosity (0.1–10%). Melting model used is that of Spiegelman and Elliott [1993], using the Web-based program Usercalc [Spiegelman, 2000]. Lines in red are the 15% 230Th-excess, which is the average excess of MORB. When melting starts at 3 Gpa, 15% excess can be created at porosities that are up to 1% and matrix upwelling velocities of between 2 and 7 cm/yr. In contrast, if melting starts at 2 GPa, i.e., no garnet present, 15% excess can only be created at porosities less than 0.3% and upwelling velocities of less than 2 cm/yr.

6.1. Sm/Nd and Lu/Hf Fractionations

[24] Lu, Hf, Sm, Nd fractionations were calculated in 0.1% melt intervals to mimic continuous melt extraction as best as possible. For the melting trajectory starting at 2 GPa, we were able to use both the Wood and Blundy [1997] parameterization as well as those listed in Tables 2 and 3 for the Sm and Lu partitioning. Because much more data is available for Sm than for Nd, we modified our parameterization to obtain greater consistency between Sm and Nd. We calculated a simple linear regression of DNd versus DSm and then calculated DNd from the DSm predicted by our or the Blundy and Wood parameterization. Similarly, since the data set for Zr is larger than for Hf, we used the Zr parameterization and simple linear regression to predict DHf from DZr. Trace element evolution paths calculated from the partition coefficients derived from our model have slightly larger Sm/Nd and Lu/Hf fractionations than do the same paths calculated with the Wood and Blundy parameterizations (see Figure 5). These differences in path reflect small differences in the parametrization, but in general both parameterizations lead to roughly similar partition coefficients for cpx. Neither our nor the Wood and Blundy parameterization produced partition coefficients for the heavy REE in cpx larger than 1, and the highest calculated DLu is ∼0.7. Thus although Lu can be compatible in cpx [Wood and Blundy, 1997], the Al2O3-content of cpx on the mantle solidus is too low to make the heavy REE compatible in cpx.

[25] The δ(Lu/Hf) - δ(Sm/Nd) diagram is best at distinguishing between garnet-present and garnet-absent melting at relatively low degrees of melting. At higher degrees of melting, all of the incompatible trace elements are extracted from the solid, and distinction between garnet absent and garnet present melting is less clear. Relatively few MORB lie near the 2.0 GPa curve in the δ(Lu/Hf) - δ(Sm/Nd) diagram and thus can be explained by melting in the absence of garnet as only few lie near the 2.0 GPa curve. Most of the MORBs lie around the 3.0–0.5 GPa melting curve and thus, irrespective of the degree of melting, the majority of MORB require melting in the presence of garnet. MORBs with δ(Sm/Nd) higher than the 3 GPa melting curve require less melting in the presence of garnet. The samples below the curve require a melting curve that either starts at higher pressure than the 3.0 GPa curve, as this curve starts at a similar position as the 3.0 GPa curve, but extends to lower δ(Sm/Nd) before significant decreases in δ(Lu/Hf). Samples with negative δ values are most likely from a younger source. Some MORBs with lower δ values fall along the 3.0 GPa melting curve of a one dimensional melting regime (single column under the ridge) indicating that variation in the shape of the melting regime exists.

[26] Figure 5 also compares these latest melting models with the older and much simpler non-modal fractional melting model of Salters and Hart [1989] shown in green. In this model melt reactions for garnet peridotite and spinel peridotite were constant and partition coefficients were independent of P, T, and X. The 2.0–0.5 GPa melting curves of our present model shows fractionations of Sm/Nd similar to the old model but fractionations of Lu/Hf that are significantly larger due to higher partition coefficients for cpx at lower pressures.

[27] Comparison of the 3 GPa melting curve with the previous model is a bit more difficult as each individual path in the old model has a constant ratio of amount of melt generated in the spinel stability field (FS) over amount melt generated in the garnet stability field (FG). In the recent model FG/FS varies is 8 for melting between 3.0 and 2.4 GPa (lower limit of garnet stability field) and decreases to FG/FS = 0.35 at the point of cpx exhaustion. The low degree melts on the curve with FG/FC = ∞ in the old model can be compared with the low degree melts from the 3 GPa curve. The smaller Lu/Hf fractionations in the new model are due to the smaller amount of garnet in the source for the new model (8% versus 10%) as well as the decreased D for REE and Hf in the high-pressure-low-Ca cpx.

6.2. What is Compositional Effect on U-Th Partitioning?

[28] Typical MORB have a 10–15% 230Th excess. It has been argued that significant 230Th-excesses can be created by melting at low pressure in the absence of garnet and that cpx is able to significantly fractionate Th from U [Turner et al., 2000; Wood et al., 1999]. As discussed above, the partition coefficients on which these arguments are based upon coexisting cpx and liquid that are far too aluminous and sodic to be present in the MORB source. Thus for MORBs where the source is thought to be even more depleted than bulk silicate earth there is no indication that clinopyroxene can generate the 230Th-excesses observed in MORB. We have calculated 230Th excess for aggregate melts as functions of upwelling rate and porosity using the Usercalc model [Spiegelman, 2000] for garnet-present (3.0 GPa) and garnet-absent (2.0 GPa) melting paths (Figure 6). The partition coefficients used in this model are derived from our model and are composition dependent. Although cpx is not instrumental in creating large 230Th-excesses the parameterization does indicate that small excesses can be created in the presence of only cpx. Figure 6 shows that for mantle upwelling rates between 2 and 7 cm/yr and 1% porosity, 230Th-excesses up to 45% can exist in melts from peridotite that started melting at 2.0 GPa. Only for porosities of 0.2–0.3% and upwelling velocities less than 2 cm/yr will garnet-absent melting of peridotite produce excesses of the size that are observed in MORB.

[29] If melting starts in the garnet stability field at 3.0 GPa 230Th excesses of the magnitude observed in MORB (10–15% 230Th excesses) are easily created. Because Th is slightly more incompatible that U in cpx (Table 1), the Th-excesses created in the garnet stability field are not eradicated during melt transport at reasonable porosities and upwelling rates. This typical excess for MORB can be created at upwelling rates of 2–7 cm/yr at porosities of ∼0.5–1%. The 1% porosity was taken as most reasonable as the MELT experiment has shown that 1% melt can be present in the melting region beneath a ridge [Team, 1998]. It is interesting to note that the 3 GPa melting curves also passes through the middle of the MORB field on the δ(Lu/Hf)- δ(Sm/Nd) diagram showing some convergence for the two estimates for degree and depth of melting. It thus seems that melting models which include compositionally dependent partitioning of the trace elements produce similar constraints for both the δ(Lu/Hf)- δ(Sm/Nd) and the 230Th-excesses. The modeling presented here is far from unique, but it is reassuring to know that similar constraints on MORB melting can be obtained from these independent models.

6.3. Implications for Ce/Pb Ratios

[30] Despite its obvious importance in isotope systematics, very few literature data exists for Pb [Beattie, 1993a, 1993b; Hauri et al., 1994]. Our determinations of Pb cpx/liquid and garnet/liquid partition coefficients are within the range observed by these other studies. The relatively constant Ce/Pb ratios in oceanic basalts [Hofmann, 1988] require that Ce and Pb have similar bulk partition coefficients. Yet, the data presented here, as well as the available data from the literature, indicate that Pb is more incompatible than Ce in both cpx and garnet. Our partitioning data also shows that Ce, as a REE, behaves systematically within the REE group and its compatibility is between La and Nd. Therefore it does not seem that DCe for cpx and garnet is different than expected at first glance. It is DPb that is lower than expected. According to all available data Pb is significantly more incompatible in cpx and garnet than Ce for the P, T range of all experiments. DPb in olivine and orthopyroxene is slightly higher than DCe, but with reasonable mantle mineralogies the calculated bulk D is 0.010 for Ce and 0.006 for Pb. The available partitioning data suggests that a phase in which Pb is more compatible exists and is residual during melting. Sulfide is a candidate phase that would make Pb more compatible while having no significant effect on DCe. The presence of sulfide is consistent with primitive mantle melts being saturated with respect to sulfur [Mathez, 1976].

7. Conclusions

[31] We have extended the P-T-X range of partition coefficient measurements and parameterizations for REE, Hf, Zr, U and then combined the parameterization for the trace elements with a model for major element partitioning during melting in order to calculate trace element fractionations during decompression melting. The parameterization shows that all REE are incompatible in cpx on the peridotite solidus at pressures up to 3.4 GPa. The highest D values for cpx are those for Lu and have a maximum of 0.7. The models show that although melting in the spinel stability field can significantly fractionate Sm/Nd and Lu/Hf, the fractionations observed in most MORB are larger and require some melting in the garnet stability field. Similarly, cpx in combination with olivine and orthopyroxene on the peridotite solidus is not able to produce the observed Th/U fractionations; melting has to start in the garnet stability field. Thus coupled major and trace element modeling in two independent systems, Lu/Hf-Sm/Nd and U/Th, are consistent with melting beneath mid ocean ridges beginning in the garnet stability field. In addition the constraints on degree and depth of melting, porosities are similar from both systems and these constraints as well as constraints on upwelling rate at mid-ocean ridges are consistent with physical observations.

Appendix: Parametric Dependence of Partition Coefficients

[32] Consider a simple equilibrium that relates liquid and crystalline components:

display math

where I, J, and K are simple one-cation oxides, IεJϕKγxt is the crystalline component, and α = δ(ε), β = δ(ϕ) and χ = δ(γ). The equilibrium constant is

display math

where [ ] denote activity and x is mole fraction. If element i mixes only on the Iε site, and either there is no mixing on the other sites or the mixing that does occur is coupled to the substitution of i, then the activity term for the crystalline component becomes [Xi δ(ε) ] = [Xiα]. The concentration of the oxide of i in the crystal may be related to the concentration of the i component by a stoichiometric constant, η (e.g., XNiOol = 0.667 XNi2SiO4ol). The ideal portion of the equilibrium constant thus becomes

display math

and contains both the simple molar partition coefficient for oxide i,D*i, and the complex coefficient, di, as defined by Beattie et al. [1993]

display math

[33] The weight partition coefficient (D) can be related to the simple partition coefficient and, hence, to the complex coefficient by a ratio of the gram molecular weights of the liquid and crystal. Thus Di = Di*/M, where M = Σ[Xi(mwi)]liq/Σ[Xi(mwi)]xt, and mwi is the gram molecular weight of oxide i. The equilibrium constant has both ideal and nonideal portions

display math

where γi is the activity coefficient for component i. From basic thermodynamics

display math

where the Δ terms, which are assumed to be constant over the range of P and T covered by the data, are the differences between the molar enthalpies, volumes, and entropies of the pure end-members of the reactant and product components. Substituting (A4) and (A5) into (A6) and rearranging terms yields

display math

where υn is the stoichiometric coefficient of the nth component in equilibrium (A1) and γn is the component's activity coefficient. We then have a relation of the form ln d*i = A + B/T + CP/T + Σ(Dnlnγn) that lends itself to multiple regression analysis. The activity coefficients, which describe the departure from ideal mixing between the different components, can be fit by Margules or other interaction parameters. The formal description leads to a large number of potential parameters even when only binary interactions are considered [e.g., Ghiorso and Carmichael, 1980]. There are, however, insufficient data at this time to justify regressions against dozens of parameters. To simplify matters as much as possible, Gaetani and Grove [1995] noted that in the simplest binary case lnγn is proportional to (1 − Xn)2, and thus employed standard pyroxene components and 2-lattice liquid components in the form (1 − Xn)2 as proxies for the activity coefficients. Sack et al. [1980], faced with a similar situation, chose simple oxides mole fractions (Xn) as proxies. In this paper we have chosen cation mole fraction for the liquid and CaO/(CaO + MgO + FeO) for both pyroxene and garnet in the form (1 − Xn)2 as the proxies. Regardless of the proxy, however, at this point the regression equation departs from a strict thermodynamic formalism and the regression coefficients have uncertain thermodynamic significance. Nonetheless, this empirical approach remains faithful to the thermodynamic requirement for an explicit dependence of simple partition coefficients on liquid composition, yet easily accommodates dependence on crystal composition.

[34] Finally, because of the limited P, T, x range of the experiments used in the regressions, the regression coefficients of pressure and/or temperature sometimes have no statistical significance and hence are rejected. Such a lack of significance may be due to intrinsically low values of the volume and/or enthalpy of the formation equilibria or an otherwise significant correlation between P or T and the partition coefficient may be masked by a strong correlation between P or T and a compositional parameter that correlates even more strongly with the partition coefficient than does pressure or temperature. Conversely, compositional parameters that have statistically significant coefficients may be overemphasized. As the database of partition coefficients expands and correlations between P, T, and compositional parameters diminish, regressions should yield more robust and informative coefficients.

Table A1. Run Conditions and Major Element Compositions of Experimental Phases in Wt % Oxides
  • a

    Number of spots or areas analyzed. The … indicate element not analyzed.

  • b

    Run temperature, first temperature is “homogenization temperature.”

  • c

    Run pressure.

  • d

    Run duration, first time interval is time given for homogenization (at the higher temperature).

  • e

    Sum of the squares of the residuals to phase proportion regression.

  • f

    qu, liquid quenched to dendritic crystals.

  • g

    Phase proportions in weight fraction.

  • h

    Units in parentheses are 1 standard deviation of replicate analyses in terms of least unit(s) cited.

  • i

    Olivine not analyzed; analysis is average of RD1097-3 and -4.

RD1097-1, 1580° Cb, 2.8 GPac, 20.7 hrd, 0.060e
RD1097-2, 1588°C, 2.8 GPa, 22.5 hr, 0.029
RD1097-3, 1550°/1595°C, 2.4/3.2 GPa, 0.25/24 hr, 0.063
RD1097-4, 1560°/1615°C, 2.4/3.2 GPa, 0.25/24 hr, 0.041
RD1097-5, 1625°C, 3.2 GPa, 24 hr, 0.043
RD1097-6, 1633°C, 3.2 GPa, 23 hr, 0.041
RD1097-7, 1650°C, 3.4 GPa, 23 hr, 0.048
RD1097-8, 1580°/1675°C, 3.4 GPa, 0.25/19 hr, 0.058
RD699-1, 1620°/1580°C, 2.8 GPa, 0.75/21.5 hr, 0.119
RD699-2, 1650°/1600°C, 2.8 GPa, 1/23.5 hr, 0.017
RD1099-1, 1650°/1590°C, 2.8 GPa, 0.5/22 hr, 0.054
RD1099-2, 1650°/1582°C, 2.8 GPa, 0.5/20 hr, 0.101
RD1099-3, 1600°/1535°C, 2.4 GPa, 0.5/23 hr, 0.069
TM0500-1, 1410°C, 1.5 GPa, 23.2 hr, 0.085
TM0500-3, 1430°/1350°C, 1.0 GPa, .5/46 hr, 0.094
Bulk Compositions in Wt % Oxides
Table A2. Trace Element Concentrations of Mineral Phases of the Experimental Run Productsa
  • a

    All concentrations are in ppm.



[35] Erik Hauri and Jianhua Wang are thanked for being the perfect host during the visits to the DTM ion microprobe. This research was supported by grant OCE 9633778 and OCE 0084098 and to J. Longhi and OCE 9633683 and OCE 0083794 to V. J. M. Salters.