Compositional controls on the partitioning of U, Th, Ba, Pb, Sr and Zr between clinopyroxene and haplobasaltic melts: implications for uranium series disequilibria in basalts

EPSL ELSEVIER

Earth and Planetary Science Letters 128 (1994) 407-423

Compositional controls on the partitioning of U, Th, Ba, Pb, Sr and Zr between clinopyroxene and haplobasaltic melts: implications for uranium series disequilibria in basalts C.C. L u n d s t r o m a, H.F. Shaw b F.J. Ryerson b,c D.L. Phinney d, J.B. Gill a Q. W i l l i a m s ~,e a Earth Sciences Board, University of California-Santa Cruz, Santa Cruz, CA 95064, USA b Earth Sciences Division, Lawrence Livermore National Laboratory, Licermore, CA 94550, USA c Institute of Geophysics and Planetary Physics, Lawrence Lit,,ermore National Laboratory, Livermore, CA 94550, USA d Nuclear Chemistry Division, Lawrence Lit,ermore National Laboratory, Livermore, CA 94550, USA c Institute of Tectonics, University of California-Santa Cruz, Santa Cruz, CA 95064, USA

Received 24 February 1994; accepted 13 September 1994

Abstract

The partitioning of U, Th, Pb, Sr, Zr and Ba between coexisting chromian diopsides and haplobasaltic liquids at oxygen fugacities between the iron-wiistite buffer and air at 1285°C has been characterized using secondary ion mass spectrometry. The partition coefficients for Th, U and Zr show a strong dependence on the A1 and Na content of the clinopyroxene. A good correlation between lVAl and DTh exists for all recent Th partitioning studies, providing a simple explanation for the two order of magnitude variation in DTh observed in this and previous studies [1,2]. Because mantle clinopyroxenes generally have greater than 5 wt% A1203, we suggest that the relevant partition coefficients for U and Th are between 0.01 and 0.02. While variations in A1 and Na in clinopyroxene affect the absolute value of the Th and U partition coefficients, they have no effect on their ratio, D T h / D v. Our results reinforce the inference that equilibrium partitioning of U and Th between clinopyroxene and melt cannot explain the observed 23°Th excesses in basalts. Indeed, under the oxygen fugacities relevant to MORB petrogenesis, clinopyroxene has little ability to fractionate U from Th ( D T h / D U < 2), implying that chemical disequilibrium between melt and wall rock during transport is not required to 230 . . . . preserve " Th excesses generated in the garnet stabdlty field. If the Ba partition coefficient serves as an analog for Ra and the partition coefficient of U 5+ serves as an analog for Pa 5+, then =6Ra and 231pa excesses can be generated by clinopyroxene-melt partitioning. Using compositionally dependent partition coefficients, a melting model is used to show that equilibrium porous flow can explain variations in uranium series activities from the East Pacific Rise by varying the depth of melting.

1. Introduction O b s e r v e d secular disequilibria a m o n g the uran i u m (23Su a n d 235U) decay series nuclides have recently received a great deal of a t t e n t i o n as

tracers of m a n t l e m e l t i n g processes [3-5]. Since the half-lives of the i n t e r m e d i a t e nuclides are short relative to the time-scale of m a n t l e evolution, these nuclides can be a s s u m e d to be in secular e q u i l i b r i u m at the i n i t i a t i o n of melting.

0012-821X/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 0 1 2 - 8 2 1 X ( 9 4 ) 0 0 2 0 7 - X

408

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

Thus, unlike many other isotopic and elemental tracers in basalts, which are products of processes influencing the source both prior to and subsequent to the initiation of melting, secular disequilibria among the uranium decay series nuclides are largely a function of melting and melt migration processes. To exploit fully the temporal information contained in uranium decay series disequilibria, the partitioning of parent and intermediate nuclides among the various mineral, fluid and melt phases comprising the mantle must be understood as a function of both composition and external variables. In this paper, we present new data on the partitioning of U, Th, Pb, Sr, Zr and Ba (an analog for Ra) between clinopyroxene and a haplobasaltic melt. Clinopyroxene is often considered to be the mineral phase that controls the partitioning of LIL trace elements during partial melting of the upper mantle [6]. The earliest experimental investigations of U and Th partitioning between clinopyroxene and melt demonstrated that U is less compatible than Th in clinopyroxene-melt pairs (i.e., Dvh > D u) [7,8]. In contrast, 23°Th/238U activity ratios in young M O R B lavas are typically greater than unity (excess 23°Th), implying that D v is greater than DTh. However, U can vary between the tetravalent and hexavalent oxidation states and it has been suggested that a difference in oxygen fugacity between the early experiments and the more reducing conditions relevant to mantle magma genesis could be responsible for the lower partition coefficient of U [9-11]. More recent experimental data have shown that the ratio of clinopyroxene-melt partition coefficients for Th and U (Dvh/Dtj) decreases to unity with decreasing oxygen fugacity but is never less than 1 [1,2]. Interestingly, the absolute values of the U and Th partition coefficients obtained in these recent studies vary by almost 2 orders of magnitude. It is unclear whether this disparity is the result of systematic experimental or analytical differences, or a reflection of differences in composition. This study had two major goals. The first was to evaluate further the extent to which the oxygen fugacity, and thus the valence state of U, controls the relative partitioning of U and Th. The second

was to refine the values of partition coefficients for U, Th and the Ra analog, Ba, as a function of pyroxene composition. Following the suggestion of J. Jones [pers. commun., 1992], we paid particular attention to the relationship between AI substitution in the clinopyroxene and the magnitude of the partition coefficients. The results were then used to simulate the evolution of U decay series nuclides during polybaric melting in an ascending column of mantle.

2. Experimental methods The haplobasaltic starting composition used was the same as that used by Watson et al. [11]. A nominally trace element free, vitreous starting material was produced by repeated (three times) fusion and grinding of reagent grade oxide and carbonate powders. The bulk composition of this starting material was: 52.04 wt% SiO2; 0.97 wt% TiO2; 12.13 wt% A1203; 0.21 wt% Cr203; 11.14 wt% MgO; 21.11 wt% CaO; and 2.40 wt% Na20. A trace element enriched glass was prepared by adding UO 2, ThO 2 and BaCO 3 (at the 0.5 wt% level) to a split of the undoped glass, followed by additional grinding and fusing. These two materials were mixed to produce intermediate trace element concentrations ( ~ 600, 300, 150 and 75 ppm). Experiments run in air had elevated U contents (3000 ppm) to allow measurement of the small U concentration in the crystals. A powdered glass, containing 2 wt% Pb and 1 wt% U, from a previous study [11] was used for experiment Tr4B. Because of the large partition coefficients for Sr and Zr, no additional doping of these elements was required. Electron probe, ion probe and optical analyses showed no detectable inhomogeneities in the starting materials. Experiments were run in Deltech vertical quench furnaces on loops made from 0.010" diameter platinum wire using C O - C O 2 gas mixtures to control oxygen fugacity. The single Pbbearing experiment was performed in a sealed Pt capsule to prevent Pb volatilization. Typical sampies weighed 50 mg. Temperatures were monitored using P t / P t l 0 % R h thermocouples calibrated against the melting point of Au and posi-

-7.54 glass 20.70 12.0l 0.96 cpx 2 3 . 7 4 18.19 0.32

-8.00

-8.00

-8.00

-8.00

-8.19

-8.70 glass 21.11 10.03 1.01 cpx 2 4 . 4 7 18.33 0.29

-8.72 glass 21.27 10.00 cpx 2 4 . 0 9 18.31

-9.76

-9.76

-10.72 glass 21.09 10.40 0.87 cpx 2 4 . 5 4 18.44 0.37

- 0 . 6 8 glass 19.65 9.43 1.05 sealed core 24.51 16.91 0.37 rim 2 4 . 6 9 17.86 0.25

TrlA

Tr2B

Tr2D

Tr2C

Tr2A

Tr8

Tr9

Tr7

Tr6B

Tr6A

Tr3A

Trl0

21.12 10.21 1.12 2 4 . 7 4 18.26 0.31

1.08 0.27

1.01 0.28

13.12 52.67 2.98 52.87

13.16 52.18 2.72 53.77

0.30 0.40

0.26 0.29

0.07 0.04

bdl 1.22

0.09 0.79

0.26 0.28

0.50 0.48

0.03 0.12

12.97 52.85 bdl 2 . 8 2 5 4 . 2 9 1.56 1.41 56.21 0.26

13.28 53.25 bdl 1.96 5 5 . 3 8 0.20

13.21 52.87 bdl 1.36 5 5 . 1 0 0.41

13.37 52.55 bdl 1.96 5 3 . 5 3 0.54

13.70 53.09 2.12 54.92

13.15 52.70 1.89 53.61

11.93 5 2 . 6 4 0.15 2 . 7 4 5 2 . 8 3 1.47

ball 1.29

0.11 1.69

0.07 1.49

98.83 glass(ppm) 100.10 DCpx/I

100.25 glass(ppm) 101.23 DCpx/I

99.31 glass(ppm) 9 9 . 5 7 DCpx/I

99.40 glass(ppm) 100.63 D C p x / 1

0.10 0.04

2.52 98.47 glass(ppm) 0.21 100.7 DCpxcore/1 0 . 1 5 100.8 DCpx rim/l

0.73 99.62 glass(ppm) 0 . 1 3 101.02 DCpx/I

1.15 0.17

235 0.0023 -+2

390 0.0015 +3

3014 0.00007_+2

425 0.00020 -+4

870 0.00028 +_25

876 0.00019_+4

U Ba 2821 797 0.00011 _+2 0.00020-+3

571 0.0047 +_3

7018 0.00021 0.0038

382 0.0036 +4

523 0.0014-+2

292 0.0030 +6

7.46 0.0061+_7

86 0.0029+10

184 0.00008 -+2

775 0.00020_+4

442 901 0.0014+_2 0.00010+__3 315 0.0035 +5

Pb (ppm)=7000 0.0090 _+ 12

Sr

93.6 0.068+9

34.3 0.095+_4

123 94.1 33.7 0.00017_+3 0.075 +- 13 0.089_+4

268 431 0.0022-+3 0.00016 +_5

422 0.0038_+3

78 0.0020+_5

Zr

805 85.3 31.6 0.00046 +_14 0.124+_7 0.115+7

496 818 0.0022-+2 0.00024 +_13

130 119 0.0055_+9 0.0019 +_2

85.3 79 125 0.0080-+8 0.0033_+7 0.00017 +15

268 0.0048 +7

476 0.0029 +_5

598 0.0044_+3

Th 535 0.010+1

99.69 glass(ppm) 518 477 99.42 D C p x / 1 0.0072+_28 0.0038 +_7

100.03 glass(ppm) 100.75 DCpx/I

99.83 glass(ppm) 99.44 DCpx/1

99.70 glass(ppm) 100.14 DCpX/1

100.27 glass(ppm) 100.97 DCpx/I

1.10 99,47 glass(ppm) "0.21 9 9 . 5 5 DCpx/I

1.11 0.30

1.22 0.19

1.91 0.21

1.75 bdl

1.77 0.21

1.84 0.16

1.31 0.40

1.63 100.95 glass(ppm) 0 . 3 5 101.84 DCpX/1

2.26 0.16

5.53 100.66 glass(ppm) 0 . 5 7 100.16 DCprdl

total 99.25 glass(ppm) 9 8 . 9 4 DCpx/I

1.03

1.00

1.37

1.61

1.45

1.90

2.14

2.89

2.42

2.09

1.93

DTh/Du 90.9

For major elements, representative lo- errors are given at the bottom and are the average error on each experiment produced by calculating 1 sample standard deviation on 5-10 analyses. Trace element concentrations are _+15%, as given in text. Partition coefficients represent the average trace element content of the clinopyroxenes (based on 2-4 analyses) divided by the average trace element content of the glass (based on 2-4 analyses).

Representative glass I c errors cpx

glass 20.91 10.19 1.07 cpx 2 4 . 9 0 18~43 0~26

glass cpx

glass 21.00 11.05 epx 2 4 , 3 8 17.51

ball 1.46

bdl bdl

0.06 1.97

13.03 5 2 . 4 4 0.18 2.90 53.82 1.74

13.25 52.40 2.98 54.80

13.29 52.02 2 . 8 2 54.12

glass 20.90 10.03 1 . 1 0 13.23 53.02 cpx 2 4 . 6 2 17.65 0.33 2.45 54.41

glass 20.88 10.21 1.07 cpx 2 4 , 3 4 17.07 0.28

glass 21.06 10.32 1.07 cpx 24.21 17.41 0.38

glass 21.47 10.69 1.15 cpx 2 4 . 1 2 17.63 0.36

- 0 . 6 8 glass 20.44 9.77 1.05 cpx 24.61 17.93 0.46

Tr4C

13.57 51.47 3 . 2 5 52.52

CaO MgO TiO2 Al20 3 SiO2 Cr20 3 Na20 19.73 11.68 1.13 12.49 51.94 bdl 2.28 2 4 . 5 4 17.86 0 . 3 7 2.20 53.74 ball 0.23

- 0 . 6 8 glass 19.65 9.53 1.05 sealed cpx 2 4 . 0 6 17.29 0.50

log f(O2) - 0 . 6 8 glass cpx

Tr4B

Tr4A

Table 1 Major, and trace element concentrations, along with partition coefficients and oxygen fugacities for all experiments

4~

t~a

J

% ,,.q

410

C.C. Lundstrom et aL / Earth and Planetary Science Letters 128 (1994) 407-423

the N i - N i O and iron-wiistite transitions [12]. Samples were heated to 12°C above the predetermined liquidus (1291°C) and held for 24 h to

tioned at the same vertical level as the sample holder. Oxygen fugacity was monitored with a doped zirconia oxygen sensor calibrated against

(b) 0.50

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~.5

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100 Microns

I

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140

o

liO

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B

Fig. 1. (a) Reflected light photomicrograph showing a portion of a typical experimental charge (Tr2A). The field of view is 0.64 mm across and shows a pyroxene crystal and coexisting glass, with epoxy to the upper left. (b) A traverse across the same crystal shows the reverse zoning of AI, Na and Ti and normal zoning of chromium, discussed in the text. Errors are based on the counting statistics of the electron probe measurement.

C.C. Lundstrom et al. /Earth and Planetary Science Letters 128 (1994) 407-423

allow redox equilibration of the sample [11]. The temperature was then dropped to the liquidus temperature for 12 h to allow nucleation of clinopyroxene, which grew as the sample was cooled at l ° / h to 1285°C. The samples were then held at 1285°C for 1-4 days. To assess the degree to which our charges approached equilibrium, we performed a reversal experiment (Trl0) in which we equilibrated Thfree clinopyroxene crystals with a Th-bearing melt. Clinopyroxene crystals were hand picked and adhering glass removed by dissolution in a 5% H F solution. They were then placed in a clinopyroxene-saturated melt containing 0.7 wt% Th at 6 ° below the liquidus for 2 months and allowed to return towards equilibrium. The resuiting charge was then mounted with a shallow dipping glass-crystal interface, allowing ion probe analysis on a wider portion of the rim, facilitating a core versus rim comparison of the Th content. Major and minor element analyses were performed on the JEOL-733 electron microprobe at Lawrence Livermore National Laboratory (LLNL) using an accelerating voltage of 15 kV. X-ray intensities were reduced using the B e n c e - A l b e e reduction scheme [13]. Results are reported in Table 1 and reflect averages of at least 3, but generally 5-10 analyses of each phase per experiment. Several pyroxene traverses were analyzed to assess zonation; Fig. lb gives one example. Correlations of the partition coefficients with the AI content of the pyroxene were obtained by surrounding each ion probe crater with 4 - 8 electron probe analyses and averaging the values to determine the composition at the spot. Trace element analyses were performed on the Cameca IMS-3f ion microprobe at LLNL. Polished sample mounts were bombarded with a 5-70 nA O - primary beam with a net energy of ~ 17 keV. The primary beam was typically rastered over an area of 30-100 /~m on a side. Positive secondary ions were extracted and accelerated to - 4 . 5 keV. A field aperture allowed only ions from the central, ~ 60/~m area of the imaged field to enter the mass spectrometer. For each sample, 2 - 5 spots on each phase were analyzed and the results for each phase were averaged. Our reported errors in Table 1 and Fig. 2

i0 -I

. . . . . .

i

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0

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A

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/~

/~

DTh

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,

,

i 6

,

,

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-log f(02)

i 8

,

,

,

i 10

o

,

,

12

Fig. 2. Partition coefficients for Th, U and Ba measured in this study as a function of oxygenfugacity. Each symbol is the average for one experiment (Table 1). Error bars represent lovariability on 2-4 clinopyroxeneanalyses and 2 4 glass analyses. are 1 standard deviation calculated from repeated analyses of each phase, or the counting statistics error, whichever was greater. The standard deviation ranged from slightly less than, to 10 times greater than, the counting statistics, demonstrating that the compositional variations within crystals exceed analytical error. Isobaric molecular interferences were minimized using a 32.5 eV window centered on an 80 eV offset from the peak of the secondary ion energy distribution [14,15]. These conditions reduced molecular interferences to less than a few percent. Trace element concentrations were determined by calibration against the S°Si-normalized count rates on a suite of silicate mineral and glass standards. We estimate an error of _+ 15% on the concentrations. Partition coefficients were calculated by dividing the average S°Si-normalized count rates of each measured isotope in the clinopyroxene by the corresponding count rates in the glass and correcting for the slight difference in Si contents of the two phases. We assume that the secondary ion yields are identical for the glass and the clinopyroxene. We did not observe a difference in trace element ion yields between glass and crystalline phases, in accord with a study of the relative ion yields from glasses and crystalline matrices [16]. Any errors introduced by this assumption are insignificant relative to the other sources of uncertainty.

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

412

3. Results

The experiments produced euhedral, inclusion-free chromian diopsides, up to 800 /xm in diameter, co-existing with glass. A representative reflected light image is shown in Fig. la, and the average major element compositions of the run products are given in Table 1. Table 2 gives Na and Al contents and D values for individual spots within the clinopyroxenes, along with the average glass compositions. Mass balance and visual inspection document that less than 10% crystallization occurred in all experiments. Qualitatively, the color of the clinopyroxene was sensitive to the oxygen fugacity (f(02)) during crystallization: samples run in air and under i r o n wiistite (IW) conditions were a paler green than those formed at intermediate oxygen fugacities. Although we consistently used the same starting material (with one exception), the liquid composition varied from run to run, due to the loss of Cr and Na from the charges. In experiments conducted in air and under IW, the Cr contents are extremely low (sometimes below detection limits, cf. Table 1). Close inspection by transmitted light microscopy and backscattered electron images shows no indication of any other phases.

Table 2 I n d i v i d u a l spot d a t a for f o u r e x p e r i m e n t s

Experiment Tr6B cpxl 2 3 glass Tr9 cpxl 2 3 glass Tr8 cpxl 2 3 glass Tr2B cpxl 2 glass

DTh 0.0035 0.0024 0.0028 0.0020 0.0026 0.0039 0.0096 0.0063 0.0046 0.0037 0.0068

DZr DSr Na20 0.077 0.093 0 . 1 9 0.060 0.090 0 . 2 0 0.065 0.097 0 . 2 2 I.I0 0.059 0.091 0 . 1 7 0.076 0.085 0 . 2 0 0.085 0.088 0.21 1.22 0.121 0.117 0 . 3 9 0.128 0.109 0 . 4 8 0.114 0.110 0 . 3 9 1.91 0.24 0.23 1.31

DNa Al203 DAI 0.17 2.01 0 . 1 5 0.18 1.95 0 . 1 5 0.20 1.88 0 . 1 4 13.37 0.14 1.50 0.11 0.16 1.80 0 . 1 4 0.17 2.22 0.17 13.15 0.20 2.62 0.22 0.25 2.68 0.23 0.21 2.48 0.21 11.93 0.18 2.52 0.19 0.18 2.85 0 . 2 2 13.03

IVAI 0.067 0.063 0.065 0.059 0.045 0.067 0.070 0.081 0.074 0.067 0.063

Partition coefficients for Th, Zr, and Sr are c a l c u l a t e d by dividing an individual c l i n o p y r o x e n e ion p r o b e analysis by the a v e r a g e of the ion p r o b e analyses for the glass of t h a t experiment.

Energy dispersive analysis of the Pt wire loop in the IW charge shows a very small Cr peak, suggesting that alloying with the Pt may be responsible for the loss of Cr under reducing conditions. To examine the behavior of Cr in air, isocompositional charges were run simultaneously on a Pt wire loop and in a sealed Pt capsule for 3 days. The resulting charges differed visually; the sealed charge maintained its green appearance while the platinum loop charge was clear. Electron probe analysis confirmed that the initial 0.2 wt% Cr was retained in the sealed capsule, but lost in the loop experiment. It appears that Cr volatilizes in air. Such volatilization is probably associated with the presence of Cr 6+ in the sample and the resultant formation of transient CrO 3 molecules, which have been shown to volatilize readily [17,18]. Sodium is also lost under reducing conditions in platinum loop experiments [19]. Under the most reducing conditions, Na loss from the glass was as high as 70% (Tr3A, Table 1). Because Na may play an important role in the coupled substitution of the large, high valence actinide ions in clinopyroxene, we took particular care to characterize the Na content of both the glasses and pyroxenes, analyzing each spot with the ion probe. The crystals are normally zoned in Cr because of its large partition coefficient (apparent Dcr varies from 10 to 20) [18]. Although a quantitative assessment of Dcr is impossible (because Cr is lost), Dcr qualitatively decreases under reducing conditions (Tr3A, Tr6A, Tr6B, Table 1). The maximum amount of zoning (exclusive of reversal experiment Trl0) occurred in samples with cores containing 2.3 wt% Cr20 3 and rims with 1.4%. This zoning of Cr (plausibly entering M1) exerted a strong control over the other pyroxene sites, resulting in higher concentrations of Na, A1 and Ti in crystal cores. Fig. lb shows this effect for the clinopyroxene of Fig la. Although a depletion of Cr in a boundary layer formed at the surface of the growing crystal could explain the Cr zoning pattern, it cannot explain the zoning of the incompatible elements Na, Ti and A1. Failure to maintain a constant composition boundary layer would result in higher concentrations of these elements in the rims relative to the cores, oppo-

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

site to what we observe. Major element zoning within the glass adjacent to a crystal face was undetectable in an experiment quenched within 6 h of the crystal growth phase. It is this pyroxene zoning, combined with the variation in liquid composition, that allows us to sample a large range of clinopyroxene compositions, despite the use of a constant composition starting material. The partitioning results for Th, U and Ba are presented in Fig. 2. Each point represents the average trace element concentration in clinopyroxene, divided by the average tracer concentration in the glass in each experiment. It is clear that the partition coefficients decrease in the order Da-h > D v > DBa. The average values are consistent with this order: DTh = 0.0050 ± 0.0024, D U = 0.0025 + 0.0009 (for experiments of log f ( O 2) < - 7 ) , and DBa = 0.00022 + 0.0001. The average partition coefficient for Sr is 0.10 _+ 0.013, while the average Zr partition coefficient is 0.089 _+ 0.030. Our single determination of the Pb partition coefficient yielded a value of 0.009. The effect of trace element concentrations on the partition coefficients was evaluated by comparing the results from four runs performed at log f ( O 2) = - 8 containing different trace element concentrations (experiments T r 2 A - T r 2 D , Table 1). The average DTh for each experiment is 0.0047 _+ 3 (lo- variation in the last decimal place), 0.0048 + 7, 0.0055 + 2 and 0.0080 + 8, respectively, as the thorium concentration in the glass decreased from 571 ppm to 85 ppm. Although the DTh of the most dilute experiment lies outside the errors of the others, we believe this reflects the substantially higher Na content (as measured by ion probe) of this charge. This confirms that our dopant levels are sufficiently low that partitioning is consistent with Henry's law behavior. Averaging the trace element concentration of zoned clinopyroxenes to compute the partition coefficients obscures any compositional controls on the partitioning of these elements. However, the DTh calculated between a particular spot in a zoned clinopyroxene and the average melt composition has a strong dependence on the clinopyroxene composition (Figs. 4 and 5). The partition coefficients calculated in this way are meaningful because: (1) the crystals maintained interfacial

413

equilibrium with the melt at all times; (2) the composition of the melt at the interface was not significantly different from that of the melt far from a growing crystal; and (3) the concentration of trace elements in the melt did not change significantly during the time the clinopyroxene was growing. Our reversal experiment provides evidence for equilibrium in these experiments. The rims of an originally trace element-free 'seed' clinopyroxene incorporated Th and yielded a partition coefficient (0.0038) similar to that expected for a pyroxene of that composition. The core did not completely re-equilibrate and produced an apparent partition coefficient more than an order of magnitude lower than our other measurements (0.00021). The approach to equilibrium during the reversal probably reflects dissolution and reprecipitation rather than solid-state diffusion because the Cr20 3 content changes abruptly between the rim and the core. However, any boundary layer of melt produced by the dissolution of the original seed crystals would be depleted in trace elements and, if the melt were not well mixed, the newly recrystallized rims would have apparent partition coefficients lower than those measured for a 'forward' crystallization experiment. This is not the case, providing primary evidence that the bulk composition is reflected in our observed partition coefficients. Because the partition coefficients for Th, U and Ba are very small, the concentration of these trace elements in the bulk melt can only have increased over the course of the experiment by 10% or less (the extent of crystallization), much smaller than the variation in the partition coefficients observed in different spots. Further, the partition coefficients decrease towards the rims, opposite to that expected if the trace element concentration of the bulk melt increased during crystallization, or an incompatible element enriched boundary layer existed at the crystal-melt interface. Partition coefficients have been retrieved successfully from zoned crystals before. Beckett et al. [20] determined the partition coefficients for a number of elements from zoned melilite crystals grown during controlled cooling rate experiments

414

C.C. Lundstrom et a l . / E a r t h and Planetary Science Letters" 128 (1994) 407-423

similar to ours. Using trace element analysis of the zoned crystal, calculated melt compositions and an experimentally determined relationship between melilite composition and melt fraction, they derived the partition coefficient. Given the small temperature interval over which the clinopyroxenes in our experiments were grown, the relatively small range in clinopyroxene composition and the varying amounts of sodium and chromium loss, we cannot derive an expression relating clinopyroxene composition and melt fraction, preventing determination of the trace element concentration in the melt coexisting with a particular clinopyroxene composition. Given the highly incompatible nature of the elements considered and the small degree of crystallization in our experiments, we can use the final melt composition to calculate the partition coefficients, resulting in no more than a 10% error in the partition coefficient. The most important aspect of any partition coefficient determination is that interfacial equilibrium is maintained and that crystal growth is slow enough to maintain a constant reservoir composition at the boundary layer adjacent to the crystal face. The zoning of our clinopyroxenes implies that the cores are no longer in equilibrium with the liquid analyzed at the end of the experiment. However, because of the good agreement between our results (in a comparable compositional range) with the Ostwald ripening re-

'

10 2

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I

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'

,

,

I

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Effect of oxygen fugacity

,

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+

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Rangeof MORB glasses

1 O

I

,,,,,,

,

0

2

,

4

6 8 -log f(02)

,

,

i

*,, 10

2

Fig. 3. Dependence of D T h / D U on oxygen fugacity. Compositional effects have been removed by taking the ratio of the partition coefficients. Each symbol represents one experiment.

suits of Beattie [1], the systematic trends in our data and our reversal experiment, we believe interfacial equilibrium was maintained between each spot in our crystals and the homogenous, co-existing liquid.

4. Discussion

Our results generally agree with those of Beattie [1] and LaTourrette and Burnett [2] with respect to both the relative Th and U partitioning between clinopyroxene and melt and the general dependence of U partitioning on oxygen fugacity. D T h / D U decreases steadily under increasingly reducing conditions, ultimately converging on unity near log f ( O 2) = - 9 . 7 (Fig. 3). This convergence on unity reflects the similar ionic radii of Th (1.12 A) and U (1.08 ~,) [21] in the + 4 oxidation state, and suggests that U is largely, if not entirely, tetravalent under these conditions [22]. Although there is no systematic change in DTh o v e r our experimental range of f(O2), D U varies by almost two orders of magnitude (Fig. 2). This is due to the variation in U valence between +4, + 5 and + 6, depending on oxygen fugacity [22], while Th remains exclusively quadrivalent. The magnitude of our U and Th partition coefficients at specific oxygen fugacities fall between those of other recent studies. Beattie [1] has argued that the lower partition coefficients measured in his experiments are more accurate than the higher values obtained from track counting methods [2], as deviations from equilibrium and analytical errors will tend to produce partition coefficients closer to unity. Our data show that the discrepancy between these two studies may be reconciled by the strong compositional dependence of the partition coefficients. DTh and the tetrahedral Al content of the clinopyroxene for all recent results define an excellent correlation (Fig. 4). Here, we have plotted the partition coefficients calculated from ion probe analyses of individual spots on clinopyroxene grains (not the average values for a grain), along with other recent data [1,2]. The experiments of LaTourrette and Burnett [2] have clinopyroxene compositions with A120 3 contents between 3 and 4 wt%

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

whereas most of the clinopyroxenes of Beattie [1] have A1 contents less than 2 wt%. Thus, neither differences in analytical technique nor in degree of equilibration need be invoked to explain the discrepancy between prior results; when the effect of AI is considered all the data are completely consistent. Our data also show a strong compositional dependence of DTh on the Na content of the pyroxene, consistent with an earlier investigation (Fig. 5) [2]. Since the magnitude of the partition coefficients increases with both Na and tetrahedral A1, we infer that DTh must increase dramatically as the solubility of jadeite and Tschermak's molecule increases at higher pressures. The correlation between DTh and the Na and A1 content of the pyroxene indicates that pyroxene composition plays a crucial role in the partitioning behavior. Because only tetrahedral A1 (not octahedral) can charge balance the Th 4+ substitution, we suggest that actinide partitioning depends on tetrahedral A1 content, in agreement with previous studies of rare earth element partitioning [23]. However, since the A1 contents of both sites are interdependent because of the Ca-Tschermak's substitution [24], total A120,~ px

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(or DA1) has a similarly strong correlation with OTh.

There are several possible explanations for the effect of Na and A1 on actinide partitioning. The most simple is that coupled substitution mechanisms involving Na or Al charge balance the high-valence actinide ions, allowing greater solubility of these elements in the clinopyroxene structure. Although charge balance must be maintained in the pyroxene structure, consideration of all of our partitioning data suggests more complicated explanations may be needed. For instance, Ti and Sr both partition more strongly into the aluminum-chromium-rich portions of the pyroxene. A more encompassing explanation is that changes in the major element chemistry of the pyroxene alter the geometry and energetics of the available sites in the growing crystal so that they are more 'favorable' to trace elements. For instance, incorporation of Cr into the M1 site is likely to cause local expansion of the M2 site [25], allowing large ions such as Th to be accommodated more readily. Therefore, both charge balancing and site size play important roles in partitioning. Since the major element composition of the pyroxene is determined by the temperature, pressure and composition of the system, it should be possible to relate the partition coefficients to the pyroxene composition so as to account for the combined effects of all these variables. In essence,

416

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423 -0.5

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this is what has been done in Fig. 4, in which partition coefficients derived from experiments conducted at varying temperature, pressure and bulk composition are shown to correlate well with the single parameter, WA1. Zirconium partitioning is also strongly correlated with clinopyroxene composition, indicating that the increased incorporation of high valence ions with enhanced A1 content is a general phenomenon. However, there is a significant difference between the effect of clinopyroxene A1 content on Th partitioning and its effect on Zr partitioning. The slope of the correlation between log DTh and log DAI (Fig. 6) is approximately 2, documenting that the Th content of the clinopyroxene depends on the square of the clinopyroxene A1 content (glass A1 concentrations are relatively constant). This suggests that the ability of Th to substitute into the M2 site requires two tetrahedral AI ions in close proximity to satisfy local charge balance constraints. In contrast, the smaller Zr 4+ ion (0.80 A) [21] plausibly substitutes into the M1 site and the slope shown in Fig. 6 suggests that only one tetrahedral A1 is required for substitution of Zr. In the case of Zr 4+, local charge balance is achieved via simultaneous substitution of Na + into the M2 site: this latter substitution is not available to the larger Th ion (1.12 ~,) which must reside in the M2 site itself. These substitutions might therefore be represented by the components ThMgAl206 and NaZrA1SiO 6. Thus, it is the different site prefer-

ences of Zr and Th which modulate their behavior with respect to AI content. We conclude that both clinopyroxene composition and oxygen fugacity affect U - T h partitioning between clinopyroxene and liquid. Substitution of non-quadrilateral components into the pyroxene structure can affect the partition coefficients for these elements by at least an order of magnitude but not the ratio of D T h / D v. Variations in oxygen fugacity affect D U independently of DTh, and therefore alter D T h / D v. For our Fe-free system, the U valence increases and shifts D T h / D v to values greater than 1 at log f ( O 2) values above - 9.7. Our values for DBa agree with those of Beattie [1] and show Ba to be at least an order of magnitude less compatible than Th in clinopyroxene. We see no dependence of Ba partitioning on oxygen fugacity; this is in accord with Ba always being present in the + 2 valence state. If Ba (1.50 A) represents a valid analog for the next larger alkaline earth, Ra (1.56 A)[21], then DBa plausibly represents an upper limit o n ORa. Our results for Dsr, Dzr and Dpb also agree well with previous results. A study within the A b - A n - D i system yielded composition-dependent Sr partition coefficients ranging from 0.077 to 0.136 [26], compared to our average value of 0.10. Previous Zr partition coefficients range from 0.05 to 0.22 [27,28]. Because of the strong dependence on A1 content of the pyroxene, our determinations of Dzr range from 0.059 to 0.128, with Dzr increasing as a function of A1 content. The result of our single Dpb determination (0.009) agrees well with the results of Watson et al. (Dpb = 0.010) [11] who used the same composition starting material, but analyzed their run products by differential dissolution isotope dilution mass spectrometry. o

4.1. The role of clinopyroxene in observed U series disequilibria Clinopyroxene in spinel lherzolite is commonly considered to be the mineral that controls the partitioning behavior of most incompatible trace elements during M O R B petrogenesis. However,

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

since uranium is never more compatible than thorium in clinopyroxene/basaltic melt pairs, equilibrium partitioning between clinopyroxene and melt cannot produce the observed 23°Th excess in MORB. Although melting of garnet peridotite can produce excess 23°Th [29,30], the role of clinopyroxene both in modulating this excess and in influencing other p a r e n t - d a u g h t e r pairs must be assessed. We have demonstrated that the A1 and Na contents of clinopyroxene have large effects on the absolute values of the U and Th partition coefficients. The Al content of most mantle clinopyroxenes exceed 5.0 wt% (in garnet or spinel peridotite [31,32]), greater than the experiments plotted in Fig. 4. Therefore, we estimate cpx/IDTh within the garnet peridotite field to be 0.015. Within the spinel peridotite field, we suggest cpx/IDTh will be near 0.015 at 60 km and decrease to less than 0.01. In addition, the modal abundance of clinopyroxene in the source will decrease with higher degrees of melting [33]. Therefore, the contribution of cpx/IDTh to the bulk partition coefficient will steadily decrease as the source reaches shallower depths and becomes more depleted. The observed excess of (226Ra) o~er (23°Th) in M O R B [34] agrees with the sense of fractionation implied by DBa/DTh for clinopyroxene. D B a / D x h varies from 0.1 for low-Al clinopyroxene to values of 0.02 for more aluminous pyroxenes. Therefore, the large 226Ra disequilibria could easily result from equilibrium partitioning in the spinel peridotite stability field, even at our lowest DTh values, as long as the mantle porosity is of similar magnitude to the partition coefficient of Th [10]. Our results may also provide constraints on the disequilibria of (231pa)/(235U). Since no Pa partition coefficients have yet been measured, an analog to this + 5 cation with a radius near 0.99 [21] must be used to estimate its value. Pentavalent U is likely to be a suitable analog because it is similar in charge and size (1.04 A) to Pa [21]. Nb 5+ has an ionic radius of 0.72 ,~ [21] and is likely to be a less appropriate analog as it would probably reside in the M1 site of clinopyroxene. We suggest D p a / D v will be less than 0.1 for clinopyroxene under mantle conditions, based

417

on our measurements of U partitioning in air, while U is pentavalent or hexavalent. Comparison of the observed isotopic disequilibria within M O R B and the fractionations implied by the clinopyroxene partition coefficients shows an intriguing correlation. 226Ra and 231pa are enriched relative to their parents in M O R B by up to 200% [34-37] and have analog p a r e n t / d a u g h t e r partition coefficient ratios that are greater than 10 for clinopyroxene. 23°Th, which is not significantly fractionated from 238U by clinopyroxene, has a correspondingly small excess, of 10-20%, in most MORB. 4.2. Influence o f melt migration on U series disequilibria

Observation of 20% excess 23°Th and up to 200% excess 226Ra and 231pa in young MORBs has contributed to a re-evaluation of the processes involved in basalt genesis [34-38]. Two end-member models of the equilibrium melting and extraction process have been proposed: fractional melting and equilibrium porous flow. The major element chemistry of M O R B and abyssal peridotites suggests fractional melting [33,39]. However, the degree to which fractional melting or porous flow processes explain the U series observations in M O R B has not been determined. The power of U series data stems from the ability to use three different p a r e n t - d a u g h t e r fractionations (226R a - 23oTh, 23l P a - 235U, 23oT h 238U) to constrain melting and transport processes. All three should be explicable by a single model if all the excesses are solely magmatic in origin. The most attractive aspect of a model incorporating melt transport processes is that it can explain secular disequilibria for these three systems by different processes (melting vs. transport), or different locations within the melting column (bottom vs. top). The longer lived isotopes (Z3°Th and 231pa, but not 226Ra) should preserve fractionations generated throughout the melting column [4] and should, therefore, carry information about the relative column length, whereas the shorter lived isotopes only give information about the upper portion of the melting column.

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

418

Spiegelman and Elliot [4] have previously considered the consequences of melt transport for U series disequilibrium in young lavas. We use their model (eq. 23 of [4]) to calculate 23°Th, 231pa and 226Ra excesses as a function of upwelling velocity and mantle porosity. We assume that permeability is a second-order function of porosity (n = 2) and use a linear dependence of the degree of melting on depth (Fig. 7). The expression describing melt composition is numerically integrated, with porosity calculated at each step from their eq. (7) [4] by a root bisection algorithm [40]. We present two models of M O R B petrogenesis. In the first, melting is initiated at 100 km depth, in the second, at 80 km depth. The partition coefficients and parameters used are given in Table 3 and shown in Fig. 7. Within the garnet lherzolite stability field, we assume a constant mode consisting of 12% garnet and 8% clinopyroxene (the remainder olivine and orthopyroxene) and use our estimate of cpx/IDTh = 0.015 and c°×/~DU = 0.010, along with previously determined garnet partition coefficients [30]. Therefore, the bulk partition coefficients are constant from the depth of melt initiation to the garnet peridotite-

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Dpa 0.00067 0.00067 0.00013

lI. Spinel lherzolite : (variable bulk D)

Dyh = 0.00225 - 0.0075* F D U = DTh / 1.5 Dpa = D U / 15 Bulk D (Mode x cpx/ID) 60 km 0 km DTh N-MORB (80 km) 0.0019 0.00075 DTh E-MORB (100 km) 0.0015 0.00038 DU N-MORB 0.0013 0.00050 D U E-MORB 0.0010 0.00025 Dpa N-MORB 8.6e -5 3.3e -5 Dpa E-MORB 6.7e -5 1.7e -5 DRa is assumed to be 1.0 e -5 throughout the melting column

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Table 3 M a t c h o f results f o r o u r m o d e l with o b s e r v e d d i s e q u i l i b r i a f o r N - M O R B a n d E - M O R B [ 3 4 - 3 6 ] , a l o n g with p a r a m e t e r s a n d p a r t i t i o n c o e f f i c i e n t s u s e d in this c a l c u l a t i o n

0.25

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spinel peridotite transition at a depth of 60 km [41]. The bulk partition coefficients in the spinel lherzolite field reflect the effect of: (1) increasing degrees of melting on the clinopyroxene mode; and (2) decreasing clinopyroxene A1 contents on cpx/ID. To assess these effects, we first use data from abyssal peridotites [33] to constrain the bulk partition coefficient at the top of the melting column. At 0 km depth, we assume cpx/IDTh to be 0.010 and the clinopyroxene mode to vary from 8% to 4%, depending on the degree of melting. At a depth of 60 km, cpx/IDTh is 0.015 and the mode varies between 12.5% and 10% (due to different degrees of anatexis for melting initiated at 80 vs. 100 km). The variation of the bulk partition coefficient with depth (Table 3) is a linear fit to bulk partitioning data at these two depths (0 and 60 kin), with D T h / D v = 1.5 and D v / D p a = 15. Partition coefficients for all of the

419

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

n u c l i d e s are a s s u m e d to be z e r o for olivine, ort h o p y r o x e n e a n d spinel [1]. B e c a u s e the c a l c u l a t i o n s of (Z31Pa)/(235U) a n d (226Ra)/(Z3°Th) a r e m o s t sensitive to the p a r t i tion coefficients of the p a r e n t nuclides, the p o o r c o n s t r a i n t s on t h e b u l k p a r t i t i o n coefficients of R a a n d P a do not significantly lessen the a p p l i c a -

Depth of melt initiation:

bility of o u r model. W e e s t i m a t e gt/IDpa to be ~ 7 × 10 4 ( b a s e d on a large p e n t a v a l e n t ion's p r e s u m e d i n c o m p a t i b i l i t y ) a n d use 1 × 10 -5 t h r o u g h o u t the m o d e l for t h e b u l k p a r t i t i o n coefficient o f Ra. If g t / l D p a = 8 X 10 -5 is used, (231pa)/(235U) is i n c r e a s e d by only 5 % for the s a m e p a r a m e t e r s used in T a b l e 3.

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420

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

The disequilibria produced by this model for each isotopic system as a function of the maximum porosity and upwelling rate for two different starting depths are shown in Fig. 8 and reveal several important aspects of the nature and origin of U series disequilibria. First, 23°Th enrichments created by melting within the garnet peridotite field can be preserved during ascent through the spinel peridotite field at a relatively slow melt velocity (< 5 m/yr) even if the melt maintains equilibrium with the solid throughout its ascent. Because the bulk partition coefficients for Th and U are small within the garnet peridotite field, these elements are stripped from the solid and reside almost entirely in the melt upon arrival in the spinel peridotite field. The 23°Th excess created by ingrowth due to U retention in garnet lherzolite during melting will be reduced by a chromatographic effect within the spinel peridotite field but this effect is small because DTh/D U is not very different from 1 and the half-life of 23°Th is relatively long. Thus, although the 23°Th excess is unsupported during transport in the spinel peridotite field, because DTh/Dtj is the wrong sense for a transport effect, spinel peridotite can do little to decrease the excess already generated in the garnet peridotite field. Furthermore, because the (23°Th)/(Z38u) excess can be explained by either dynamic [9,10,29] or porous flow [4] melting processes, it cannot be used to distinguish the actual MORB melting process. As (226Ra)/(23°Th) excesses are produced by very different phenomena in the two models, it is more useful for resolving whether fractional or batch melting occurs. Second, enrichments predicted by our melting and transport model show better qualitative agreement with observations of disequilibria in MORBs than do dynamic melting models with instantaneous transport. 226Ra and 231pa excesses in MORBs are large (up to 200%), while 23°yh excesses remain small (10-20%), in agreement with the fractionation implied by the parent and daughter partitioning in clinopyroxene. This contrasts with the pooled melt analysis of slow dynamic melting, which suggests that maximum enrichments in 23°Th and 231pa occur at slower melting rates (10-7/yr) than 226Ra (10 6/yr) and,

therefore, should not produce similar sized excesses of 226Ra and 231pa [42]. Furthermore, all 231pa and 23°Th excesses measured thus far in MORB are positively correlated with one another [36], while 226Ra excesses are, if anything, inversely related to the other excesses [34,37]. Our model reproduces these qualitative trends. The extent of (231pa)/(235U) and (23°Th)/(Z38U) disequilibria cannot both be explained by dynamic or batch melting processes by varying the degree of melting [36]. However, both disequilibria can be reproduced in melting with equilibrium transport by varying the depth of melt initiation using reasonable values for the Pa partition coefficients (Table 3). Fig. 8 shows that 231pa excesses, like those of 23°Th, are generally sensitive to upwelling velocities, due to its relatively long half-life. However, the observed excesses of the three parent-daughter pairs are best matched in the area where 231pa and 23°Th excesses are sensitive to the maximum porosity as well as the upwelling velocities (boxes in Fig. 8). This emphasizes the importance of considering all three parent-daughter pairs simultaneously when drawing constraints on both magma equilibration processes and upwelling rates. High precision mass spectrometric data for MORBs [34-37] show that E-MORBs have higher (23°Th)/(238U) (and (231pa)/((235U)) than NMORBs, resulting in a positive correlation between (23°Th)/(232Th) and (238U)/(232Th). This suggests a systematic relationship between melting behavior (measured by (23°Th)/(238U)) and source heterogeneity (measured by T h / U ) for a given ridge. Several authors have suggested that the larger U series excesses in E-MORBs result from mixing of small degree melts with normal MORB [3,34]. However, this is contrary to what is expected if E-MORBs represent melting of more enriched source material. Such a source should undergo larger degrees of melting, with its solidus intersecting the geotherm at a deeper level. Our preferred explanation for E-MORB formation invokes a deeper initiation of melting and, therefore, longer residence times within the garnet peridotite stability field. Such a model straightforwardly creates the larger 23°Th and 231pa excesses. Further evidence for substantial variation

C.C. Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

in the depth of melt initiation comes from recent mass spectrometric observations of (23°Th)/(238U) < 1 in very depleted MORBs [37,38]. In our interpretation, these samples represent melts produced totally within the spinel lherzolite stability field. Global ridge systematics show that more enriched segments have higher Fe contents, indicative of deeper melting [39], and consistent with our suggested origin of EMORB. In Table 3, we show the agreement between our model results and observed disequilibria for a typical N-MORB and E - M O R B from 9°N on the EPR [34-36]. For melting initiating at 80 km depth, our results closely match the isotope systematics of N-MORBs from 9°N. Using the same parameters and simply changing the depth of initial melting to 100 km provides a good match to the observed E-MORB systematics from 9°N. The solution is not unique but this is the first model to calculate accurately the quantitative extent of 23°Th, 231pa and 226Ra disequilibria. This model is also testable as it predicts small but measurable 228Ra excesses of approximately 40%, providing a possible signature of shallow equilibration. Because we use a higher value for D x h (based on the AI content of mantle clinopyroxene) than the value recommended by Beattie [1], the mantle porosity required to match the observed 226Ra excesses is raised to 0.1%. The evidence favoring fractional, rather than equilibrium, melting include abyssal peridotite studies [33] and major element parameterizations [39]. We have shown that treating the mantle as chemically heterogeneous can explain U series data for MORB. Evidence for fractional melting derived from abyssal peridotites is substantially weakened when source heterogeneity is considered. The wide variation in trace element concentrations observed can as easily be explained by wide concentration variations in the starting source material. The upwelling rate given in Table 3 suggests that the width of the melting region is greater than the depth. Expanding to two dimensions could make this model more compatible with the fractional melting character observed in the major element chemistry [39].

421

5. Conclusions Our experiments document that U and Th partitioning between basaltic melt and clinopyroxene is strongly dependent on clinopyroxene composition. This compositional dependence explains the order-of-magnitude discrepancy between recent experiments on the clinopyroxenebasalt system. Na and tetrahedral A1 contents appear to control the partitioning behavior of the actinides and Zr. The small fractionation of U and Th by clinopyroxene suggests that if 23°Th excesses originate by melting in the garnet stability field, disequilibrium transport of melts is not required to preserve these excesses. The size of observed excesses in 226Ra, 23°Th and 231pa match the size and sense of the fractionation implied by p a r e n t - d a u g h t e r partition coefficients within clinopyroxene, using Ba and U 5+ as an analogs for Ra and Pa, respectively. A model using our compositionally dependent clinopyroxene partition coefficients with previously determined garnet partition coefficients [30] demonstrates that equilibrium porous flow [4] is a viable explanation for the magnitudes and differences of U series disequilibria between N-MORBs and E-MORBs from the East Pacific Rise. Indeed, unlike previous modeling, we are able to explain quantitatively the magnitudes of all the U series excesses using geophysically reasonable parameters. Moreover, the 231pa-Z3°yh correlation may provide a first-order constraint on the depth at which melting commences beneath different ridges.

Acknowledgements James Brenan is thanked for help in the laboratory and many useful discussions. We thank Bob Anderson for help with the computer modeling, and James Wong for computational and electronics support in the ion probe laboratory. Bruce Watson kindly donated samples of his starting materials. This work benefited from reviews by T.Z. LaTourrette and P.D. Beattie and comments from C.H. Langmuir. This work was supported by funds from the Department of Energy's Office of

422

c . c . Lundstrom et al. / Earth and Planetary Science Letters 128 (1994) 407-423

Basic Energy Sciences (H.F.S.) and LLNL's Institute of Geophysics and Planetary Physics and NSF (Q.W. and C.C.L.). This work was performed under the auspices of the U.S. Departm e n t of E n e r g y by L L N L u n d e r c o n t r a c t n u m b e r W-7405-ENG-48.

This

is c o n t r i b u t i o n

#235

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[16]

of

t h e I n s t i t u t e o f T e c t o n i c s at U C S C . [CL] [17] [18]

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