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melt partitioning
CHEMICAL GEOLOGY ISOTOPIC ( ; E O S ( "lE.\( 'I'.
ELSEVIER
Chemical Geology 117 (1994) 57-71
Systematics and energetics of trace-element partitioning between olivine and silicate melts: Implications for the nature of mineral/melt partitioning Paul Beattie Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK Received 29 October 1993; revision accepted 31 March 1994
Abstract
Olivines are structurally simple and provide an ideal phase with which to examine what controls the variation in partition coefficients between different elements. Electron probe analysis and secondary ion mass spectrometry have yielded high-precision in situ measurements of partition coefficients for alkaline earths, transition metals and rare-earth elements for olivine-glass pairs produced in experiments. Partition coefficients for these elements range from < 10 -s to > 1. The variation in divalent partition coefficients can be accurately modelled in terms of the strain energy associated with the expansion of the oxygen octahedra to accommodate a large cation, calculated using the olivine bulk modulus taken from the literature. No deviations from Henry's law are observed for trivalent cations between concentrations of 0.05 ppm to > 1%, thus local charge balance for the partitioning of trivalent cations into olivine is maintained by a coupled REE, Mg- '-A1,Si- i substitution rather than by the creation of vacancies or interstirials. The bulk modulus required to model the trivalent cations is much larger than that for the divalent cations and probably reflects the local decrease in compressibility of the oxygen lattice near sites where Si has been replaced by the larger AI ion. The ability to calculate the partition coefficients for these elements demonstrates that the substitution mechanism for the very incompatible cations is indistinguishable from that for Mg or Cr. and is now well understood. The partition coefficients between clinopyroxene, orthopyroxene, garnet or amphibole and silicate melts exhibit similar dependencies on ionic radius and charge. This similarity suggests that mineral/melt partitioning generally occurs by substitution onto crystallographic sites in crystalline phases and that the partitioning of trivalent cations is charge balanced by a coupled substitution of A1 for Si.
1. Introduction
The study of the nature of mineral/melt partitioning requires high-quality partitioning data for crystalline phases that are structurally simple: olivine-melt pairs were therefore chosen for this study. The olivine/melt partition coefficients for the compatible elements are fairly well
known (e.g., Bird, 1971; Leeman, 1974), largely as the result of electron-probe analyses of experimental mineral-melt pairs. However, electron probe microanalysis (EPMA) is not sufficiently sensitive to allow the measurement of partition coefficients for the very incompatible elements. It is these incompatible elements that are of most interest petrologically, as information on the na-
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58
P. Beattie / Chemical Geology 117 (1994) 5 7-71
ture of the melting process can be extracted most easily from the concentrations of elements whose bulk partition coefficients are of the same order as the melt fraction involved. Several studies have obtained mineral/melt partition coefficients for incompatible elements by analysing phenocryst-matrix pairs using more sensitive techniques such as instrumental neutron activation analysis (INAA) (e.g., Onuma et al., 1968; Higuchi and Nagasawa, 1969; Schnetzler and Philpotts, 1970; Matsui et al., 1977 ). This approach has the advantage that the concentration of the elements of interest is at natural levels. Unfortunately phase separation is never perfect, and this method may give apparent partition coefficients which are several orders of magnitude too high for the more incompatible elements, as will be shown later. Furthermore, phenocryst-matrix pairs provide no information on the pressure or temperature dependence of partitioning, and may be strongly affected by the presence of inclusions in the crystalline phase, and by incomplete equilibration between the crystal and melt. In order to avoid the problems associated with the analysis of phase separates, olivine-melt pairs were grown experimentally and analysed in situ by secondary ion mass spectrometry (SIMS) and EPMA. This combination of techniques allows the intensive and extensive parameters of crystallisation to be controlled and the analysis to be made with the required sensitivity and precision. Several authors (e.g., Onuma et al., 1968; Philpotts, 1978) have noted that partition coefficients for elements of a given valency vary smoothly with ionic radius. It is the purpose of this paper to model these variations and to explore their implications for the energetics and substitution mechanisms of trace-element partitioning between olivines and silicate melts.
2. Experimental methods If experimental data are to be used in modelling magmatic evolution, care should be taken to use partition coefficients measured from experiments in which the temperature and composi-
tion of the melt phase approximated that of the magma to be modelled, as the value of mineral/ melt partition coefficients are dependent on these factors (Irving, 1978; Beattie et al., 1991; Beattie, 1993b). Experiments were therefore performed at temperatures ranging from 1190 ° to 1500°C, and with melt compositions ranging from basalt to komatiite. I suggest that the partition coefficients measured in experiment B 7 be used for modelling fractional crystallisation of basalts, and that the data from experiment C10 should be used in models of partial melting. The samples used were natural or synthetic rock powders to which a mixture of oxides, carbonates and sulphates of di- and trivalent cations were added in proportions chosen to ensure that the concentrations of the elements of interest were above detection limits for SIMS in both the glass and crystalline phases. These samples were attached to Pt hooks following Biggar (1978). Iron loss to the Pt wire was minimised for all experiments other than C10 by mounting an aliquot of sample on each hook and allowing it to equilibrate with the wire for at least 24 hr at the run temperature, as suggested by Walker et al. (1979). The hook was then recovered and the experiment performed using a second aliquot of the same sample. The experiments were conducted at atmospheric pressure in vertical quench furnaces. The furnace temperatures were measured using PtPt87Rhl3 or Pt95Rhs-Pts0Rh2o thermocouples, calibrated against the melting points of gold and diopside. The oxygen fugacity of each run was maintained at about the Ni-NiO buffer by a CO2 and H2 mixture (Deines et al., 1974). Ideally, partition coefficients should be measured in reversed experiments to ensure that a close approach to equilibrium has been attained. Unfortunately, the diffusivities of the large trace elements of interest are far too low to allow crystals of a size sufficient for analysis to equilibrate with any other phase on experimental timescales. The experimental procedure was therefore chosen such that the crystals would grow from small nuclei during the experiment. As long as the crystal growth rate is small compared with the diffusion rate in the melt the crystal will grow
P. Beattie / Chemical Geology I 17 (I 994) 57- 71
59
Table 1 Run conditions of the partitioning experiments Experiment
Temperature
Duration
Fugacity
Composition
Products
B7 CI CIO CI1 F6 L2
1,250 1,400 1,495 1,495 1,450 1,190
336 336 24 24 284.5 720
- 7.1 -5.5 -4.7 -4.7 - 5.1 - 7.6
50/0.33 152 I52 152 KIA WY2
G1 +O1 GI+O1 GI+OI GI+OI GI+OI G I + O1 + Cpx
Run temperature (in ° C), duration (hours) and oxygen fugacity (log~o fo2 ) for the experiments. The experimental procedure was as described in the text, except for runs CIO and C l l which were isothermal. 50/0.33 is a synthetic sample largely CaOMgO-FeO-A1203-SiO2; 152 is a komatiite from the Belingwe greenstone belt; K1A is a kimberlite; and WY2 is an alkali basall from Wyoming, U.S.A.
in equilibrium with the melt, even if the effects of diffusion within the crystal are negligible. Large crystals can be readily grown if the sample is cooled from above its liquidus. On cooling, no crystals will grow until the melt is supercooled sufficiently for homogeneous nucleation to occur. All subsequent olivine precipitation occurs around these few nuclei. However, the rate of crystal growth may be rapid owing to the high degree of supersaturation required for homogeneous nucleation, often generating large, skeletal crystals. This technique has been avoided in this study, as the rate of crystal growth associated with this technique may be large compared to the low diffusivities of the large cations being studied. In this study samples were never taken above their liquidi, thus ensuring that many small nuclei exist for heterogeneous nucleation at all times. Large degrees of supersaturation and rapid crystal growth are thus avoided, allowing chemical equilibrium to be maintained during crystal growth. Unfortunately this procedure also precludes the growth of large crystals making analysis difficult and time consuming, but at least this procedure ensures that as close an approach to equilibrium as possible is attained. Preliminary experiments of identical run conditions to those of CI1 show that all phases other than olivine dissolve in the melt within the first 5 min, at which time the largest crystals are < 1% of an analysable size. After this time crystal growth continues slowly by Ostwald ripening. Thus almost all of the analysed material is precipitated in
equilibrium with a melt after all phases other than olivine have been dissolved. The procedure used to grow the crystals analysed in this study was to lower the samples into the hot spot of the furnace set 20°C above the run temperature. Preliminary experiments were conducted to check that the sample was never above its liquidus at this stage. The samples were held at this temperature for 24 hr and then cooled at 1 ° C h r - 1 for 20 hr to encourage the growth of large ( > 40 #m ), homogeneous crystals (Colson et al., 1988 ). Run durations were between 24 and 720 hr [which is an order of magnitude longer than the comparable experiments of McKay (1986)] to ensure equilibration. The charges were dropped from the hot spot into water to ensure a rapid quench: no evidence of quench crystallisation was observed in any of the samples. Run temperatures, oxygen fugacities and durations are shown in Table 1. All SIMS analyses were made with the Cam6ca ® ims-4f at the University of Edinburgh, using a beam of O - ions and counting positive secondary ions. The mounted samples were polished and gold-coated to prevent sample charging or sputtering from the periphery of the beam. The low concentrations of the elements analysed prevented the use of high mass resolution, and energy filtering (using a 77-V offset) was therefore used to reduce molecular interferences and matrix effects. Ions were sputtered using a 1.252-nA beam with a secondary accelerating voltage of 10.7-13.23 kV to minimise spot size and
60
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
Table 2 Olivine and glass compositions
Na20 MgO AlzO3 SiO2 K20 CaO Sc203 TiO2 Cr203 MnO FeO Fe203 Co SrO Y2O3 BaO La203 Ce203 Pr203 Sm203 Tb203 Ho203
Yb203
Experiment B 7
Experiment C1
Experiment CIO
Experiment CI 1
Experiment F6
Experimenl L2
glass
glass
glass
glass
glass
glass
0.44 8.58 14.02 48.44 1.33 1.70 0.10 0.06 0.05 0.08 15.75 1.15 0.00 0.59 0.2t 0.82 0,88 0.59 0.36 0.53 0.46 0.30 0.08
olivine
37.73 (1,683) 37.36 (638) (383) (603) (917) 0.09 23.09 (158) (0.4) (26.0) (0.0) (0.1) (0.1) (0.2) (2.9) (19.0) (35.3) (38.2)
n.d. 18.29 7.98 47.81 0.01 8.18 0.15 0.31 0.02 0.20 6.02 0.46 n.d. 0.72 0.28 n.d. 1.12 0,83 0.53 0.71 0.64 0.39 0.24
olivine
53.30 (822) 41.48 (1,571) (182) (28) (203) 0.15 5.86 n.d. (0.7) (15.3) n.d. (0.3) (0.3) (0.3) (2.4) (12.6) (19.2) (37.7)
n.d. 24.88 6.01 47.18 0.05 6.26 0.16 0.34 0.17 0.23 6.24 0.46 0.03 0.73 0.21 0.98 1.03 0,63 0.45 0.56 0.53 0.36 0.14
olivine
53.27 (764) 41.22 (901) (197) (317) (1,094) 0.14 4.08 (404) (1.0) (15,3) (0.2) (0.2) (0.3) (0.4) (3.5) (14.5) (22.9) (26,2)
n.d. 24.58 6.04 46.77 0.02 6.16 0.01 0.38 0.13 0.18 8.85 0.68 n.d. 0.15 0.05 0.24 0.22 0.16 n.d. 0.12 0.19 2.61 n.d.
olivine
51.85 (760) 40.89 (801) (10) (407) n.d. 0.08 5.80 n.d. (0.4) (3.7) (0.0) (0.0) (0.1) n.d. (0.7) (5.9) (181.2) n.d.
n.d. 21.46 5.85 47.67 0.03 6.42 0.18 0.38 0.03 0.25 7.84 0.61 0.03 0.72 0.25 1.03 1.08 0,88 0.50 0.59 0.57 0.39 0.17
olivine
52.07 (591) 40.64 (1,772) (242) (41) (314) 0.15 5.63 (329) (0.7) (17.2) (0,0) (0,1) (0,2) (0,4) (2,6) (15.5) (24.7) (32.4)
0.41 8.99 10.11 43.81 0.43 12.88 0,13 3.61 0.05 0.26 5.76 0.55 0.02 1.85 0.29 2.51 1.17 0.95 0.49 0.65 0.59 0.40 0.21
olivine
48.98 (2,245) 40.03 (3,799) (169) (491) (593) 0.28 8.29 (431) (0.7) (14.2) (0,1) (0.0) (0.1) (0.1) (1.6) (9.6) (19.1) (37.9)
Composition of olivines and glasses (in weight percent), as determined by electron probe. Data in parentheses are concentrations in parts per million (weight) calculated from the partition coefficients measured by SIMS.
counting times. Counting times at each mass varied from 5 s for major elements to > 600 s for low-abundance isotopes. The number of counts per second for each isotope was corrected for mass overlaps and normalised to that of 28Si. The partition coefficient for each element was calculated from these data as the ratio of oxide concentration in the crystal to that in the glass phase using the SiO2 content of each phase determined by EPMA. It was assumed that there is no difference in high-energy secondary ion yields between phases (Bottazzi et al., 1991 ). The sputtering of the glass around one crystal in experiments C1 and B 7 gave rise to anomalously high and constant partition coefficients for the very incompatible elements; these analyses were discarded. The Fe 2+ concentration in the melt phases were calculated from the total Fe content, oxy-
gen fugacity, run temperature and melt composition using the equation ofKillinc et al. ( 1983 ). All partition coefficients for Fe were calculated from the Fe2+O concentrations alone.
3. Results
The composition of each phase (as measured by EPMA) and the olivine/melt partition coefficients calculated from the SIMS data are shown in Tables 2 and 3. These data are presented in weight percent, as this is the basis on which partition coefficients are generally used in petrogenetic models. The partition coefficients can be converted to molar partition coefficients by multiplying them by the factor F shown in Table 3. The standard errors of the partition coefficients are calculated by propagating the variances of the
P. Beattie / Chemical Geology 117 (1994) 57- 71
61
Table 3 Olivine/melt partition coefficients B7
CI
CIO
MgO 4.44(0.04) AI?O3 1.20(0.13)-10 -2 SiO2 0.77 CaO 3.75(0.12).10 -2 Sc203 0.38(0.01) Cr203 1.85(0.13) MnO 1.07(0.02) Fe(total ) 1.55(0.03) FeO 1.44(0.02) Co 3.56(0.05) SrO 7.17(0.46)-10 -5 Y203 1.25(0.06)'10 -2 BaO 4.09(0.71)'10 -6 ka203 1.20(0.24)-10 -5 Ce203 2.42(0.40)'10 -5 PrzO 3 6.05(1.61).10 -5 Sm203 5.49(0.55)-10 -4 Tb203 4.15(0.43)-10 -3 Ho203 1.18(0.12).10 -2 Yb203 4.69(0.39).10-'-
3.23(0.21) 1.03(0.09)-10 2 0.87 1.92(0.28).10 -2 0.12(0.01) 1.02(0.14) 0.61(0.08) 0.58(0.06) 0.54(0.06) 1.50(0.01 ) 1.03(0.23)-10 -4 5.45(0.35)'10 -3 3 . 2 5 ( I . 1 5 ) ' 1 0 -s 2.67(0.54).10 -5 3.57(1.03).10 -5 5.57(1.37).10 -~ 3.33(0.60)'10 -4 1.97(0.26).10 -3 4.93(0.57).10 -3 1.57(0.23)-10 -2
2.17(0.02) 1.27(0.19).10-2 0.87
2.10(0.01) 1.96(0.03) 1.26(0.11).10 2 1.01(0.03).10 2 0.87 0.85 2.76(0.03).10 2 0.12(0.00) 0.15(0.00) 0.13(0.00) 0.63(0.04) 0.94(0.01) 1.13(0.17) 0.52(0.02) 0.50(0.02) 0.56(0.02) 0.53(0.02) 0.51(0.01) 0.57(0.02) 0.49(0.02) 0.48(0.01 ) 0.53(0.02) 1.18(0.03) 1.10(0.04) 1.29(0.05) 1.38(0.11).10 4 2 . 5 6 ( 0 . 7 5 ) . ! 0 - 4 9.13(2.93).10-5 7.19(0.31).10 3 7.54(0.40).10-3 6.77(0.31).10-3 2.30(0.15)-10 -5 n.d. 1.39(0.46)-10 -6 2.18(1.26).10 -5 2.16(2.63).10 -5 6.69(1.17).10 6 4.51(1.06).10 s 7.61(1.90).10 5 2.63(0.13).10-5 8.45(4.32)-10 -5 6.80(4.94).10 -5 7.19(0.36).10 -5 6.36(0.23)-10 .4 6.33(3.36)'10 -4 4.35(0.64)-10 -4 2.75(0.12).10 -3 3.09(0.44)-10 -3 2.72(0.16)-10 -3 6.43(0.24).10 -3 6.94(0.55).10 -3 6.27(0.35).10 3 1.88(0.11).10 -2 2.12(0.33)-10 -2 1.87(0.15).10 2
3.75(0.35) 2.22(1.06).10-2 0.91 2.95(0.71).10-2 0.13(0.01)
n F
5 0.85
3 0,84
2 0.83
3 0.90
CII
3 0.84
F6
3 0.85
L2
0.82(0.10) 0.90(0.12) 0.82(0.11 ) 2.24((1.28) 3.94(0.65).10-5 4.94(0.15).10-3 2.09(1.98).10 ~ 3.77(0.12).10-6 1.02(0.13).10-5 2.61(0.32)-10 -5 2.44(0.35)'10 -4 1.63(0.08).10 3 4.72(0.15)-10 3 1.84(0.09).10 2
Data in parentheses are one standard error of the partition coefficient, calculated by propagation of the variance of crystal and glass concentrations. Electron probe was used to measure D °~/L for all experiments and n* J Ot/L for experiments B 7, C 10 and C l 1: Mg all other partition coefficients were measured using SIMS. n is the number of cD'stals analysed for each experiment: F is the ratio of molar to weight partition coefficients and is identical for all elements.
concentration of each component in each phase, as this source of error is much larger than that associated with counting statistics. EPMA traverses across the crystals demonstrate that a close approach to equilibrium has been attained, at least for the major elements. More than one hundred analyses were made of the olivines in experiment CIO, which had the shortest equilibration time (24 hr), giving a Mg number of 0.900_+ 0.0013. Thus the analytical error of the electron probe is greater than one standard error of the variation in crystal composition. Thus no significant disequilibrium is observed in the major-element compositions of the crystals. The homogeneity of the trace-element concentrations in the olivines cannot be checked by EPMA due to their low concentrations (0.1-100 ppm). The degree of trace-element equilibration in these experiments can be assessed only by ex-
amining the variability of analyses of different crystals in a given experiment. The partition coefficients calculated from five different crystal-glass pairs in experiment C1 are shown in Fig. 1. The standard errors of the concentrations measured for the five different crystals are < + 20% of the average concentrations for all but the most incompatible trace elements, where peripheral sputtering of glass may become significant. Similar small variations in compositions within a single experiment is seen in many partitioning experiments (e.g., Watson et al., 1987). It is clear from Fig. 1 that the small variation in concentrations of the different crystals is negligible compared to the difference between the partition coefficients of the different elements studied, which varies by more than five orders of magnitude. The lack of large variations in the calculated
62
P. Beattie / Chemical Geology 117 (1994) 57- 71
Five Olivine/Glass Pairs Experiment CI, 1400°C
each of the other experiments, owing to the long analysis time and high cost of SIMS. The lack of variation between the different crystal-glass pairs of experiment C1 demonstrates that each crystal-glass pair gives an accurate measurement of the equilibrium partition coefficient; the measurement of three crystal-glass pairs for each experiment is therefore sufficient to allow the value of the partition coefficients to be determined with adequate precision.
1 01
Mg
'
"
'
1 0° 10-1
E
.=o
Sc'~
~ ,
Ca
10-2 10-3 10 -4 i 10-5 10-6 0.06
Smpr ~
~
a
Ce La
3.1. Henry's law 0.08 0.1 0.12 Ionic Radius (nm)
0.14
Fig. 1. Graph showing the partition coefficients calculated from the analyses of five olivine-meltpairs in experiment C 1 plotted against ionic radius (in nm). The partition coefficients are calculated on a weight percent basis. Separate trends are shown for the divalent and trivalent cations. There is little variation in the partition coefficients for any given element between the different crystal-glass pairs. It is therefore clear that a close approximation to equilibrium has been attained. The low partition coefficients for Ba and the LREE demonstrates that the effects of contamination of crystals during polishing and sputtering of peripheral glass during analysis changes the measured partition coefficients by <3.10 -5"
partition coefficients between the different crystal-glass pairs demonstrates that a close approach to equilibrium has been obtained in these experiments, even for the low-diffusivity trace elements. This conclusion is supported by the similarity of the partition coefficients for experiments F6 and CIO, despite a difference in equilibration times of more than an order of magnitude (284.5 and 24 hr, respectively). Partition coefficients for the very incompatible elements are difficult to measure, due to the contamination of the crystals during polishing of the sample, the finite background of the electron multiplier and the sputtering of small amounts glass around the periphery of the beam. The partition coefficients for all elements will be equally increased by these effects. The upper limit for the errors introduced by these effects is therefore equal to the lower of nOl/L and is JL"Ba and nOl/L .tJLa therefore < 3" 10- 5 in all the experiments. Only three olivine-glass pairs were analysed in
Experiment C l l was performed to test the validity of Henry's law in olivine-melt systems. The Ho concentration in sample C l l is approximately six times higher than that in CIO and the concentration of all other trace elements is lower by about a factor of 4; the Y / H o ratio in the olNines differs by a factor of 20. As can be seen from Table 3 and Fig. 2, the partition coefficients for each element are identical in the two experiments to within two standard errors, and vary by less than one standard error for all elements other than Ce. Thus no deviations from Henry's law are observed for elements whose concentration in the olivines range from 0.05 to 180 ppm, even though heterovalent substitutions are required for these trivalent cations. Henry's law will be violated if the dominant partitioning mechanism changes with concentration. No definitive proof exists in the literature for deviations from Henry's law at concentrations of < 1% for trace elements which substitute for another cation of the same valency (Beattie, 1993a). Deviations from Henry's law are therefore most likely to be observed in the partition coefficient systematics of the trivalent cations, as the trivalent cations must substitute for either Mg or Si in olivines.
3.2. Comparison with previous data There have been several studies in the past that have attempted to measure the mineral/melt partition coefficients for incompatible elements in olivine or orthopyroxene. Olivine/melt partition coefficients were measured by Schnetzler
P. Beattie / Chemical Geology l 17 (1994) 57- 71 Olivine/meh Partition Coefficients
Experiments C10 and C11 1495°C 1 0 .2
I
.,~
[
"5 ° 10-3
L
.......
'
........
~ Y'
°°
.
.
.
.
.
Ho .
.
.
63
1
o
{'I1:~
0°
10-1 10-2
oSm •
©
L) ©
i
10-5 [ 0.01
0[,3.0
....... , 0.1 1 10 1 O0 Concentration in Olivine (ppm)
O
10-3
e~
10 -4
Sm~
i
i
1000
Fig. 2. If trivalent cations were charge balanced by the creation of vacancies or interstitials then the partition coefficient would cease to be independent of the concentration of the trace components. Thus deviations from Henry's law are more likely for heterovalent than for homovalent substitutions. Here the measured partition coefficients for the trivalent cations are plotted against the concentration of these elements in the olivines. Despite changes in Y / H o ratios of almost a factor of 20 there are no significant differences in the partition coefficients of any of these elements between experiments C 10 and C I 1 ( hollow and solid symbols, respectively ). Inspection of Table 3 demonstrates that partition coefficients for the two experiments differ by less than two standard errors for all the elements analysed, and by less than one standard error for all elements other than Ce. Thus no deviations from Henry's law are observed in these experiments, even for heterovalent substitutions. Error bars represent one standard error of the partition coefficients.
and Philpotts (1970) and Matsui et al. (1977) using INAA; by McKay and Weill (1977), McKay (1986) and Colson et al. (1988) using EPMA; and by Kennedy et al. (1993) using SIMS. Fig. 3 shows the olivine/melt partition coefficients for trivalent cations taken from the literature together with the data from experiment CI which is representative of the data from this study. The different studies all found similar values of the partition coefficients for the heavy rareearth elements (HREE) and yet the values of the light rare-earth elements (LREE) partition coefficients vary by up to three orders of magnitude. The INAA data and the EPMA data of McKay and Weill (1977) all show concave-upward trends on Fig. 3, indicating that the large parti-
i
Pr 10-5 0.06
0.07
0.08 0.09 Ionic Radius (nm)
! 0.1
0.11
Fig. 3. Graph of partition coefficients for trivalent cations against ionic radius allowing comparison of the olivine-melt data of this study (solid circles= experiment C 1) with data from the literature: hollow circles are the data of McKay ( 1986 ) and Colson et al. (1988) (experiment 115b ); hollow squares are the EPMA data of McKay and Weill ( 1977 ); hollow triangles are the data of Matsui et al. ( 1977 ); and hollow diamonds the data of Schnetzler and Philpotts (1970). The dashed lines shows the apparent partition coefficients that would be obtained if 0.3% or 1% of glass were incorporated in the material analysed as crystal. The correspondance between these lines and the LREE partition coefficients measured by INAA or routine EPMA suggests that imperfect isolation of the crystalline phase can give rise to partition coefficients that are in error by more than two orders of magnitude.
tion coefficients for the LREE may be a reflection of a small amount of glass being analysed during the analysis of the crystal, as proposed by McKay (1986). The dashed lines in Fig. 3 are the apparent partition coefficients that would be produced if the crystal analyses of experiment C1 were contaminated by 1% and 0.3% glass fluorescence. The excellent correspondence between these lines and the partition coefficients measured by INAA suggests that the high apparent partition coefficients of the LREE may be due to the incorporation of glass in the crystalline material analysed. Spurious partition coefficients of the order of 10 -2 may be produced even for perfectly incompatible cations because of imperfect phase separation. The EPMA data of McKay and Weill (1977) can also be modelled by a 1% contamination of
64
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
Experiment B7, 1250°C.
Experiment C1, 1400°C
1 01
1 0~ 1
0°
1
.
Sc
10-1
S c ~ ' ~ , ,
10-2
y Ho
O 10-3 c~ t0 .4
Ca ", ~,
i
Ce
10-6 0.06
0.08
'
Cr
Co '
T
" % ~'-.,..
10-1
Sm~
10 5
00
',
0.1
Yb~
g 10-2 L~ r~ 10-3 o
v,\.o
0.14
Ced' ~
10-6 0.06
0.08
100
' '
Tb
1 0~
' ~
5 10-1 i 10-2 L) 10-3
x
10 .4
't Sr
Pr~,c e
~"S
1o-
\.,,
0.06
. . . . 0.08
0.1
\,.
0.12
"; Ba~ 1
"i 0.14
10 -4 10 .5 ~ 1 0.6 ~(d) 0.06
Ionic Radius (nm) Experiment F6, 1450°C
101
'
Mg CO'Fe
10-1
10 -2 [
t-, 0
0.14
~.
! 10-41
~_
'
!
~ La ,,
Sr
\, \',
l . I
\°a I
0.08 0.1 0.12 Ionic Radius (nm)
0.14
1 01 0°
~.
10-1
Ho "%,~a
10-2
Sm S%L~
~
Experiment L2, 1190°C
1
{J
0.12
10°
e., o
"5
0.1
Experiment C11, 1495°C
5
lO
~ , , Ba,
Ionic Radius (nm)
Experiment C10, 1495°C ___,.~OFe'M ' ' ' ' ' ' '
'
10-4
Ionic Radius (nm)
101
\,
Tb Q
10-5
0.12
o\Ca
"', ~e, ST
: l
o= 10-3 10-4 10-5
0.06
0.08 0.1 0.12 Ionic Radius (nm)
0.14
10-6 0.06
0.08 0.1 0.12 Ionic Radius (nm)
0.14
Fig. 4. Graphs showing the partition coefficients calculated for each of the experiments plotted against ionic radius (in rim). These graphs show that the variation in trace-element partition coefficients is controlled by ionic radius and charge. The partition coefficients for the divalent ions and trivalent cations form two separate trends. The solid curves in each graph are the values predicted using Eqs. 9 and 12, using an octahedral bulk modulus for the olivine of 95.3 GPa for divalent cations. The curve for
P. Beattie I Chemical Geology 117 (1994) 57- 71
crystal by glass, indicating that fluorescence of the glass surrounding the crystals analysed was the dominant factor controlling the partition coefficients of the LREE, as suggested by McKay (1986). By contrast, the partition coefficients measured by McKay (1986) and Colson et al. (1988) using Mo guards to suppress glass fluorescence, and the SIMS analyses of isothermal experiments conducted by Kennedy et al. ( 1993 ) are in close agreement with the data of this study, confirming the accuracy of both the SIMS and EPMA analyses.
4. Energetics of trace-element substitution
4. I. Divalent cations The olivine/melt partition coefficients measured in each experiment are shown in Fig. 4. These graphs demonstrate that the variation in partition coefficients are controlled by the ionic radius and charge of the trace components, as was proposed by Onuma et al. ( 1968 ). The relationship between ionic radius and the value of the mineral/melt partition coefficient for the divalent cations indicates that the substitution mechanism of all these cations is similar to that of Mg, and partitioning therefore occurs by substitution of cations onto well-defined cationic sites in the crystal. If partitioning occurs by substitution onto lattice sites, the large incompatible cations will partition onto the M2 site in the crystal, as this is larger than the M 1 octahedra and the tetrahedral sites. The partitioning reaction may therefore be defined as:
MO L+ MgMgSiOO~ ~
65
( 1)
MgO L+ MgMSiOO~ where M is any divalent cation. The condition for equilibrium is therefore:
A H - TAS+ ( P - 1 )AV=
_Fa oa°' M ,O41
- R T I - / ~ i La M O a MgMgSiO,, _]
(2)
where R is the gas constant; and T is the temperature in kelvins. If it is assumed that the trace elements obey Henry's law in each phase, and that the degree of non-ideality in the two phases is similar then: a L o = X L o . TL aO¿
yOI .O1 M g M S i O 4 ~- i x M O * YM
1
(3) (4) (5)
which will be true unless the ratio of Henry's law constants for the two elements is different in the two phases, then: In ~'M.r~OI/L=In D°~ L + A G / R T
(6)
The terminology used here is that of Beattie et al. ( 1993): X ~ o . and 7~ are the molar fraction of component MO in phase a and its activity coefficient, respectively; and D~/5 is the molar partition coefficient for component MO substituting between phase a and a silicate melt L, and o~ L is defined as XMO./XMo. • Thus the mineral/melt partition coefficient of any divalent cation can be calculated from that for Mg if GMO and GM~O are known for each phase. Unfortunately, accurate calorimetric data
trivalent cations is calculated using a value for the heat capacity of AI,Si- ~exchange between tetrahedral sites in the olivine and glass of 55 J m o l - 1 K - ~and an olivine octahedral bulk modulus adjacent to AI tetrahedra of 180 GPa. The dashed line gives the partition coefficients calculated for an octahedral bulk modulus of 90 GPa for divalent cations. Ionic radii are for octahedral coordination and are taken from Shannon ( 1976 ). The error bars shown are one standard error of the partition coefficient, and are calculated by propagating the variance of crystal and melt analyses for each element, in most cases the symbol size is larger than one standard error of the partition coefficient.
66
P. Beattie / Chemical Geology 117 (1994) 57-71
for trace components in silicate minerals and melts are not available, and the fact that the structure of silicate melts is complex and poorly known precludes the calculation of these parameters ab initio. The approach followed here is therefore to model the enthalpies of the divalent oxide components using macroscopic strain theory. Following Nagasawa ( 1966 ), the strain energy of the anionic lattice associated with the substitution of a large cation into a site of given size is: U " = 6rrr30 "' siteKC
(7)
per atom, where .c2= e 2[1 .t. t (1 +a'~si'c) 1
~ o~,oc1 __
2(1_2~ -.~i~e) 3( 1 _ ~.si~)
e=rM/ro - 1
and U ~ is the strain energy for phase oe; ro is the radius of the unstrained site; rM is the ionic radius of the trace element; K msite and er~'s~'~ are the bulk modulus and Poisson's ratio, respectively, of the site in phase o~ into which large cations substitute. The radius of an unstrained cationic site (to) can be calculated to be 0.058 nm, assuming the condition of zero strain is that where the oxygen ions in an octahedron would just touch each other if they were rigid spheres of radius 0.14 nm. While the temperature dependence of the bulk modulus of the unit cell is known for the forsterite and fayalite, the measurement of the bulk modulus of the MO6 octahedron at supra-solidus temperatures requires structure refinement of high-pressure, high-temperature experiments. These data are not yet available due to the experimental difficulties involved. The octahedral bulk modulus at high temperatures must therefore be calculated from the compressibility of the unit cell. The bulk modulus of the MO6 octahedra in forsterite, fayalite and intermediate Fe-Mg-olivines (Hazen, 1976, 1977) are similar, though slightly smaller, than those of the host phase. Thus at 300 K the bulk modulus of forsterite ( 129
GPa; Isaak et al., 1989 ) is almost identical to that of the M2 MgO6 octahedron (130 GPa; Kudoh and Takeuchi, 1985). Furthermore, the compressibility of forsterite and fayalite (128 GPa: Graham et al., 1988) are almost identical. Thus the compressibility of pure forsterite will be a good approximation to that of the M2 octahedra of Fe-Mg-olivines such as those in this study. Isaak et al. (1989) also measured the elastic constants of forsterite at 1700 K, and found the isothermal bulk and shear moduli to be 95.3 and 61.32 GPa, respectively. Thus the Poisson's ratio and bulk modulus of the olivine M2 site are assumed to be 0.25 and 95.3, GPa respectively. The negligible shear modulus of silicate melts requires that the Poisson's ratio of the melt is 0.5: 0 c.s~e is therefore negligible. Thus if the difference in standard state free energy between different trace components is dominated by the differences in strain energy associated with their substitution into the mineral and melt lattices, then the molar partition coefficient for a divalent cation M ( D r . ) should be given by:
In
D Ol/L *
=In r~Ol/L *'* Mg*
6zrN~r3°O°l"°~tg°l'°c'(f2M RT
--~Mg)
(8)
where Na is Avogadro's number; and f2 is calculated using the ionic radii of Shannon (1976). The ratio of molar to weight partition coefficients (shown as F in Table 3 ) is identical for all elements for phases of any given composition. Partition coefficients by weight (D) should therefore be given by: In D ° u c = In ~.rlOI/LMg 6rcNA ro 3 RT 0 °l'°ctK°l'°cl (~QM - f2Mg)
(9)
where D °~/L is the weight partition coefficient for component MO. The fit to the experimental partition coefficients is excellent for most elements, as shown in Fig. 4. The value ofD°~/L can be calculated accurately from a knowledge of the composition of the melt phase and the equilibration tempera-
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
ture and pressure (Beattie et al., 1991; Beattie, 1993b). Thus the partition coefficients of the alkaline earths can be calculated accurately from the cationic radius, pressure, temperature and melt composition alone, given the bulk modulus and Poisson's ratio for the mineral phase. DOUL is accurately predicted using Eq. 9, but Mn D OI/L and F,--Co I O I / L are lower than the values predicted by about a factor of 2, even after correction for the presence of Fe 3+. These deviations may be caused by the large electronegativities or crystal field effects of these ions. The accurate fit to the alkaline-earth and Mn data is consistent with the zero octahedral site preference energy for these cations. The Ba partition coefficient may be dominated by the sputtering of peripheral glass, electron multiplier background or contamination during polishing, and should therefore be considered an upper limit. In most analyses, the difference between the calculated and measured values for the divalent cations other than Fe, Co and Ba is < 30% which is comparable to the standard errors of the measured partition coefficient and is clearly trivial compared with the five orders of magnitude difference between the partition coefficients for the alkaline earths. Hazen (1985) noted that polyhedral bulk moduli differ from the bulk moduli of the unit cell for phases that are not close packed, thus the octahedral bulk modulus may be slightly lower than that of olivine. The best fit to the partition coefficients for the alkaline earths is obtained if the value of the octahedral bulk modulus is reduced from 95.3 to 90 GPa. The values of the partition coefficients predicted for this bulk modulus are shown as a dashed line in the graphs of Fig. 4. 4.2. Trivalent cations
The partitioning of trivalent cations is not as straightforward as that of the divalent cations due to the requirement that local charge balance is maintained. Charge balance can be maintained by the generation of vacancies or interstitials, giving a substitution reaction of the form:
67
RO L5 + Mg2 SiO2~ ~ 1.5MgO L+ Mgo 5 l;~ 5RSiO ol where R is a trivalent cation; and V i s a vacancy. This substitution mechanism for trivalent cations has been proposed to explain the partitioning of Sc between olivines and melt in experiments in which the Sc content of the olivines was too high for charge balance to be maintained by A1 (Colson et al., 1989; Nielsen et al., 1992). The equilibrium constant for this reaction is proportional to the vacancy density in the crystalline phase, which must be equal to half the concentration of the trivalent cations. The difference between ZJR* r~O~/L and ~r~o~/u will therefore Mg* be dependent on the concentration of RO~5, and Henry's law will not be satisfied for trivalent cations. Similarly, if the substitution of the trivalent cation were balanced by the creation of an oxygen interstitial, ~-r.t~ O~/L would be dependent on the abundance of interstitials and again Henry's law would cease to be satisfied. However, in natural magmatic systems, olivines always have sufficient AI to charge balance all the other trivalent cations. The REE/A1 ratios of these experiments were chosen to reflect this condition and, as was shown earlier, no deviations from Henry's law are observed at the low concentrations oftrivalent ions in the olivines of this study. Thus the substitution mechanism of trivalent cations into the olivine lattice at these low concentrations cannot be charge balanced by the generation of vacancies or interstitials. As the concentrations oftrivalent trace elements during partial melting or crystallisation within the Earth are even lower than those of the experiments in this study, substitution mechanisms involving the generation of vacancies or interstitials are therefore unlikely to be applicable to natural magmatic systems. The maintenance of local charge balance must therefore be accomplished by a paired substitution of R,A1 for Mg,Si, as found for equilibria between clinopyroxene or orthopyroxene and melt on the basis of stoichiometric constraints (Lindstrom, 1976; Colson et al., 1989). Thus the substitution reaction is probably:
P, Beattie / Chemical Geology I 17 (1994) 5 7- 7I
68
RO ~s +A10 ~5 + Mg2 SiO ° ~ MgO L+ SiO } + MgRA10 4TM
( 11)
It is clear that if the substitution of trivalent cations is charge balanced by this mechanism, then D °~/L will be independent of X °~, but will vary with the activities of A1Oj.5 and SiO2 in each phase. Thus, if it is assumed that A1 is evenly distributed between the tetrahedral and octahedral sites, the trivalent partition coefficients will be given by: In D °'/L =In D°lg/L
" [ D°'I/L "~ ACp --,n~)--
6nNAr3°OOl'°clKOl°ct(~R -- 12Mg) RT
(12)
where ACp is the difference in heat capacity of A1 and Si tetrahedra in the olivine and melt phases. The A104 tetrahedra required locally to maintain charge balance are larger than SiO4 tetrahedra and tetrahedral sites in olivines are much less compressible than octahedral sites (Hazen, 1977). The bulk modulus of octahedra in unit cells containing A1 tetrahedra will therefore be greater than those of unit cells without A1 tetrahedra. Thus K °~'°~' will be greater for the trivalent cations than for the divalent ions. The observed partition coefficients can be modelled accurately using Eq. 12 if K °~°~t = 180 GPa for the trivalent cations. Similarly, zlCp is found to be 55 J mol-~ K -j. The fit to the trivalent partition coefficients using these values for the heat capacity and bulk modulus are shown in Fig. 4 for each experiment. The imperfect fit of the Cr partition coefficients may be a result of electronegativity or crystal field effects. The slight deviation from the calculated values for the very light REE (Ce and La ) reflects the difficulty of measuring partition coefficients lower than 2 . 1 0 - 5, and probably reflects the sputtering of very small amounts of glass during analysis of the crystals. The partition coefficients for the other trivalent cations are accurately predicted by Eq. 12. For most analyses the difference between the calculated and observed partition coefficients is < 20%.
Thus apart from those elements for which electronegativity or crystal field effects are important, the partition coefficients for all the diand trivalent cations studied are be accurately predicted by Eqs. 9 and 12. The calculation of the partition coefficients for these elements can be performed if the temperature and melt composition are known using the equations of Beattie et al. ( 1991 ) and Beattie (1993b) to calculate JtJMg nO~/L olivine bulk moduli and Poisson's ratio from the literature for the divalent cations, an octahedral bulk modulus of 180 GPa and an A1-Si exchange heat capacity of 55 J m o l - ~ K for trivalent cations. The accuracy with which these partition coefficients can be calculated indicates that the crystal chemistry and thermodynamics of partitioning of these elements between olivine and silicate melt is now well understood.
5. The nature of trace-element partitioning in magmatic systems The accuracy of Eqs. 9 and 12 has several important implications: ( 1 ) It clearly demonstrates that the variation in ionic radius and charge exerts the dominant control on the partitioning of incompatible elements, owing to the increased lattice strain associated with the substitution of large cations into small sites. The zero strain radius of the site (ro) is not that of the host cation (Mg), but is that for an octahedron whose oxygen atoms touch, and is therefore expected to be independent of the cation for which the trace elements substitute. (2) The accuracy of these equations suggests that the incompatible trivalent cations all partition onto the same sites in the crystalline phases as Cr does, and that all divalent cations substitute onto the same sites as Mg and Mn. The concentration of Mn and Cr in the olivines of this study are generally of the order of 1000 ppm. The number of defect sites in the olivines is unlikely to exceed 1-1000 ppm (Navrotsky, 1978 ), which indicates that the partitioning of Mn and Cr, and therefore of the other di- and trivalent cations, are not dominated by substitution into defect sites. Since the concentration of La in the olivine
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
is of the order of 0.1 ppm, then partitioning even at these low crystalline concentrations occurs by substitution onto M sites rather than defect sites in the crystals. This conclusion is in partial conflict with the electron paramagnetic data of Morris (1975) which suggest that Gd and Eu in olivine are not situated on lattice sites but form clusters at room temperatures. Morris noted, however, that substitution on lattice sites at higher temperatures could not be discounted. Furthermore, the samples analysed in that study were Al-free precluding an A1,Si-l charge balance mechanism, regardless of whether it might be energetically favourable compared with cluster formation. ( 3 ) The lack of major deviations from the predicted values implies that there are no large changes in substitution mechanism or deviations from Henry's law between the different dior trivalent cations studied, even at concentrations as low as 0.05 ppm. These low concentrations are comparable to those in the Earth's mantle, and Henry's law is therefore expected to be satisfied during mantle melting in accordance with the conclusions of Watson ( 1985 ). The lack of any deviations from Henry's law implies that the trivalent cations are charge balanced by an AI,Si-1 paired substitution rather than by the generation of vacancies or interstitials. The partition coefficients for trivalent cations may therefore be expected to be pressure dependent, as olivines in equilibrium with a given melt composition are progressively more AI rich as the pressure of equilibration increases (Agee and Walker, 1990). Work is now in progress to test this hypothesis. The partition coefficients for orthopyroxene-, clinopyroxene-, plagioclase-, biotite- and hornblende-melt pairs are also monotonic functions of ionic radius (Onuma et al., 1968; Jensen, 1973). Thus the systematics observed for olivine/melt partitioning are typical of partitioning between minerals and silicate melts, and it is reasonable to assume that trace-element partitioning between silicate crystals and melts generally occurs by substitution onto well-defined crystallographic sites. No deviations from Henry's law have been observed for trace elements in these
69
minerals, which all have higher A1 contents than olivine. The substitution oftrivalent cations into these minerals therefore probably also occurs via a coupled substitution of A1 for Si.
6. Conclusions The experimental and analytical procedure developed here is capable of ensuring a close approach to equilibrium and the accurate measurement of partition coefficients as low as 10-5. The olivine/melt partition coefficients determined by SIMS in this study agree well with the high-precision EPMA data o f M c K a y (1986) and Colson et al. (1988) for the less incompatible trace elements. Previous studies of olivine/melt partitioning using INAA or routine EPMA have given results for the most incompatible elements that appear to be dominated by the addition of between 0.3% and 1% of glass in the analysis of the olivines, and therefore give partition coefficients that are up to three orders of magnitude greater than those reported here. The excess energy required to expand the octahedral site in olivine and silicate melts can be calculated using bulk moduli consistent with values from the literature, and assuming that the local Poisson's ratio of the mineral and melt are 0.25 and 0.5, respectively. The partition coefficients for divalent cations can be accurately calculated from the value of this strain energy. The ability to calculate partition coefficients for divalent cations with a wide range of ionic radii demonstrates that the incompatible trace elements substitute onto the same site in the olivines as Mg, and are not sensitive to the presence of defects. The partition coefficients for Fe and Co are slightly anomalous compared to those for the alkaline earths; these anomalies may be caused by the anisotropic electron densities and high electronegativity of these cations. REE,Mg- ~ substitution is charge balanced by a coupled A1,Si- ~substitution rather than by the creation of vacancies or interstitials, as no deviations from Henry's law are observed. The variation between partition coefficients for the trivalent cations is independent of olivine and melt
70
P. Beattie / Chemical Geology l 17 (I 994) 57- 71
composition and can again be calculated from the energy associated with octahedral expansion. The value of the local bulk modulus for olivine is much greater for the trivalent cations than for the divalent cations, reflecting a local stiffening of the crystalline lattice near A104 tetrahedra. The substitution mechanism is identical for trivalent cations whose partition coefficients differ by up to five orders of magnitude. The partition coefficients for these trivalent cations may be pressure dependent, as the amount of tetrahedral AI increases with pressure. The partition coefficients between other silicate minerals and melts exhibit a similar dependence on ionic radius and charge, indicating that the substitution mechanisms for olivine may be typical of those for other silicate minerals. Thus the partitioning of di- and trivalent trace elements within the Earth is expected to occur by substitution onto well-defined crystallographic sites in the crystals, with charge balance maintained by A1,Si -~ substitution. Trace-element partitioning should therefore be amenable to thermodynamic modelling.
Acknowledgements Gordon Biggar, Mike Bickle and Godfrey Fitton are thanked for providing the rock powders used in this study. Facilities for the experimental and SIMS work was kindly provided by the University of Edinburgh with the invaluable help of Gordon Biggar, John Craven and Richard Hinton. Thomas Bleser, Stephen Reed and David Newling helped with the EPMA analyses. Thanks too to Francis Albar6de, Don Baker, James Brodie, Mike Drake, Steve Foley, Tony Irving, Dan McKenzie, David Palmer, Simon Redfern and an anonymous reviewer whose helpful comments greatly improved this manuscript. This is contribution number 3815 of the Department of Earth Sciences, Cambridge. This work was performed while the author was in receipt of NERC and Corpus Christi College, Cambridge research studentships and fellowships.
References Agee, C.M. and Walker, D., 1990. Aluminium partitioning between olivine and ultrabasic silicate liquid to 6 GPa. Contrib. Mineral. Petrol., 105: 243-254. Beattie, P.D., 1993a. On the occurrence of HenD,'s Law in experimental partitioning studies. Geochim. Cosmochim. Acta, 57: 47-55. Beattie, P.D.. 1993b. Olivine-melt and orthopyroxene-melt equilibria. Contrib. Mineral. Petrol., 115:103-111. Beattie, P.D., Ford, C.E. and Russell, D.G., 1991. Partition coefficients for olivine-melt and orthopyroxene-melt systems. Contrib. Mineral. Petrol., 109:212-224: see also erratum Contrib. Mineral. Petrol., 114:109. Beattie, P., Drake, M., Jones, J., Leeman, W., Longhi, J , McKay, G., Nielsen, R., Palme, H., Shaw, D., Takahashi, E. and Watson, E.B., 1993. Terminology for trace element partitioning. Geochim. Cosmochim. Acta, 57:1605-1606. Biggar, G.M., 1978. Wire hook supports for samples in atmospheric pressure quench experiments. Progr. Exp. Petrol., 4: 118-120. Bird, M.L., 1971. Distribution of trace elements in olivine and pyroxenes, an experimental study. Ph.D. Thesis, University of Missouri, Rolla, Mo. Bottazzi, P., Ottolini, L. and Vannucci, R , 1991. SIMS analysis of REE in natural minerals and glasses: an investigation of structural matrix effects on ion yields. 8th Int. Conf. Second. Ion Mass Spectrom., p.274 (abstract). Colson, R.O., McKay, G.A. and Taylor, L.A., 1988. Temperature and composition dependencies of trace element partitioning: Olivine/meh and low-Ca pyroxene/melt. Geochim. Cosmochim. Acta, 52: 539-553. Colson, R.O., McKay, G.A. and Taylor, L.A., 1989. Charge balancing or trivalent trace elements in olivine and lowCa pyroxene: a test using partitioning data. Geochim. Cosmochim. Acta, 53: 643-648. Deines, P., Nafziger, R.H., Ulmer, G.C. and Woerman, E., 1974. Temperature-oxygen fugacity tables for selected gas mixtures in the system C - H - O at one atmosphere total pressure. Bull. Earth Mineral. Sci. Exp. Stn., Pa. State Univ., Vol. 88, 129 pp. Graham, E.K., Schwab, J.A., Sopkin, S.M. and Takei, H., 1988. The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4. Phys. Chem. Mineral., 16: 186-194. Hazen, R.M., 1976. Effects of temperature and pressure on the crystal structure of forsterite. Am. Mineral., 61:12801293, Hazen, R.M., 1977. Effects of temperature and pressure on the crystal structure of ferromagnesian olivine. Am. Mineral., 62: 286-295. Hazen, R.M., 1985. Comparative crystal chemistry and the polyhedral approach. In: S.W. Kieffer and A. Navrotsky (Editors), Microscopic to Macroscopic. Mineral. Soc. Am., Rev. Mineral., 14: 317-346. Higuchi, H. and Nagasawa, H., 1969. Partition of trace elements between rock forming minerals and the host vol-
P. Beattie / Chemical Geology 117 (1994) 57- 71 canic rocks. Earth Planet. Sci. Lett., 7:281-287. Irving, A.J., 1978. A review of experimental studies of crystal/liquid trace element partitioning. Geochim. Cosmochim. Acta, 42: 743-770. Isaak, D.G., Anderson, O.L, Goto, T. and Suzuki, I., 1989. Elasticity of single-crystal forsterite measured to 1700 K. J. Geophys. Res., 94: 5895-5906. Jensen, B.B., 1973. Patterns of trace element partitioning. Geochim. Cosmochim. Acta, 37: 227-2242. Kennedy, A.K., Lofgren, G.E. and Wasserburg, G.J., 1993. An experimental study of trace element partitioning between olivine, orthopyroxene and melt in chondrules: equilibrium values and kinetic effects. Earth Planet. Sci. Lett., 115: 177-195. Killinc, A., Carmichael, I.S.E,, Rivers, M.L. and Sack, R.O., 1983. The ferric-ferrous ratio of natural silicate liquids equilibrated in air. Contrib. Mineral. Petrol., 83: 136-140. Kudoh, Y. and Takeuchi, Y., 1985. The crystal structure of Mg2SiO4 under high pressure up to 149 kb. Z. Kristallogr., 171: 291-302. Leeman. W.P., 1974. Petrology of basaltic lavas from the Snake River Plain, Idaho, and experimental determination of partitioning of divalent cations between olivine and basaltic liquids. Dissertation, University of Oregon, Corvallis, Oreg. Lindstrom, D.J., 1976. Experimental study of the partitioning of the transition metals between clinopyroxene and coexisting silicate liquids. Dissertation, University of Oregon, Corvallis, Oreg. Matsui, Y., Onuma, N., Nagasawa, H., Higuchi, H. and Banno, S., 1977. Crystal structure control in trace element partition between crystal and magma. Bull. Soc. Fr. Mindral. Cristallogr., 100:317-324. McKay, G.A., 1986. Crystal/liquid partitioning of REE in basaltic systems: Extreme fractionation of REE in olivine. Geochim. Cosmochim. Acta, 50: 69-79. McKay, G.A. and Weill, D.F., 1977. KREEP petrogenesis revisited. Proc. 8th Lunar Sci. Conf., pp. 2339-2355.
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Morris, R.V., 1975. Electron paramagnetic study of the site preferences of Gd 3+ and Eu 2+ in polycrystalline silicate and aluminate minerals. Geochim. Cosmochim. Acta. 39: 621-634. Nagasawa, H., 1966. Trace element partition coefficient in ionic crystals. Science, 152: 767-769. Navrotsky, A., 1978. Thermodynamics of element partitioning: ( 1 ) systematics of transition metals in crystalline and molten silicates and (2) defect chemistr? and the "Henry's Law problem". Geochim. Cosmochim. Acta, 48: 887902. Nielsen, R.L., Gallahan, W,E. and Newberger. F., 1992. Experimentally determined mineral-melt partition coefficients for Sc, Y and REE for olivine, orthopyroxene, pigeonite, magnetite and ilmenite. Contrib. Mineral. Petrol., 110: 488-499. Onuma, N., Higuchi, H., Wakita, H. and Nagasawa, H., 1968, Trace element partilion between two pyroxenes and the host lava. Earth Planet. Sci. Lett., 5: 47-51. Philpotts, J.A., 1978. The law of constant rejection. Geochim. Cosmochim. Acta, 42: 909-920. Schnetzler. C.C. and Philpotts, J.A., 1970. Partition coefficients of rare-earth elements between igneous matrix material and rock-forming mineral phenocryst, 11. Geochim. Cosmochim. Acta, 34: 331-340. Shannon, R.D., 1976. Revised effective ionic radii in oxides and fluorides. Acta Crystallogr., Sect. A, 32:751-767. Walker, D., Shibata, J. and DeLong, S.E., 1979. Abyssal tholeiites from the Oceanographer fracture zone. Contrib. Mineral. Petrol., 70:111-125. Watson, E.B., 1985. Henry's Law behaviour in simple systems and in magmas: criteria for discerning concentration-dependent partition coefficients in nature. Geochim. Cosmochim. Acta, 49: 917-923. Watson, E.B., Ben Othman, D., Luck, J.-M. and Hofmann, A,W., 1987. Partitioning of U, Pb, Cs, Yb, Hf, Re and Os between diopsidic pyroxene and haplobasaltic liquid. Chem. Geol., 62: 191-208.
ELSEVIER
Chemical Geology 117 (1994) 57-71
Systematics and energetics of trace-element partitioning between olivine and silicate melts: Implications for the nature of mineral/melt partitioning Paul Beattie Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK Received 29 October 1993; revision accepted 31 March 1994
Abstract
Olivines are structurally simple and provide an ideal phase with which to examine what controls the variation in partition coefficients between different elements. Electron probe analysis and secondary ion mass spectrometry have yielded high-precision in situ measurements of partition coefficients for alkaline earths, transition metals and rare-earth elements for olivine-glass pairs produced in experiments. Partition coefficients for these elements range from < 10 -s to > 1. The variation in divalent partition coefficients can be accurately modelled in terms of the strain energy associated with the expansion of the oxygen octahedra to accommodate a large cation, calculated using the olivine bulk modulus taken from the literature. No deviations from Henry's law are observed for trivalent cations between concentrations of 0.05 ppm to > 1%, thus local charge balance for the partitioning of trivalent cations into olivine is maintained by a coupled REE, Mg- '-A1,Si- i substitution rather than by the creation of vacancies or interstirials. The bulk modulus required to model the trivalent cations is much larger than that for the divalent cations and probably reflects the local decrease in compressibility of the oxygen lattice near sites where Si has been replaced by the larger AI ion. The ability to calculate the partition coefficients for these elements demonstrates that the substitution mechanism for the very incompatible cations is indistinguishable from that for Mg or Cr. and is now well understood. The partition coefficients between clinopyroxene, orthopyroxene, garnet or amphibole and silicate melts exhibit similar dependencies on ionic radius and charge. This similarity suggests that mineral/melt partitioning generally occurs by substitution onto crystallographic sites in crystalline phases and that the partitioning of trivalent cations is charge balanced by a coupled substitution of A1 for Si.
1. Introduction
The study of the nature of mineral/melt partitioning requires high-quality partitioning data for crystalline phases that are structurally simple: olivine-melt pairs were therefore chosen for this study. The olivine/melt partition coefficients for the compatible elements are fairly well
known (e.g., Bird, 1971; Leeman, 1974), largely as the result of electron-probe analyses of experimental mineral-melt pairs. However, electron probe microanalysis (EPMA) is not sufficiently sensitive to allow the measurement of partition coefficients for the very incompatible elements. It is these incompatible elements that are of most interest petrologically, as information on the na-
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58
P. Beattie / Chemical Geology 117 (1994) 5 7-71
ture of the melting process can be extracted most easily from the concentrations of elements whose bulk partition coefficients are of the same order as the melt fraction involved. Several studies have obtained mineral/melt partition coefficients for incompatible elements by analysing phenocryst-matrix pairs using more sensitive techniques such as instrumental neutron activation analysis (INAA) (e.g., Onuma et al., 1968; Higuchi and Nagasawa, 1969; Schnetzler and Philpotts, 1970; Matsui et al., 1977 ). This approach has the advantage that the concentration of the elements of interest is at natural levels. Unfortunately phase separation is never perfect, and this method may give apparent partition coefficients which are several orders of magnitude too high for the more incompatible elements, as will be shown later. Furthermore, phenocryst-matrix pairs provide no information on the pressure or temperature dependence of partitioning, and may be strongly affected by the presence of inclusions in the crystalline phase, and by incomplete equilibration between the crystal and melt. In order to avoid the problems associated with the analysis of phase separates, olivine-melt pairs were grown experimentally and analysed in situ by secondary ion mass spectrometry (SIMS) and EPMA. This combination of techniques allows the intensive and extensive parameters of crystallisation to be controlled and the analysis to be made with the required sensitivity and precision. Several authors (e.g., Onuma et al., 1968; Philpotts, 1978) have noted that partition coefficients for elements of a given valency vary smoothly with ionic radius. It is the purpose of this paper to model these variations and to explore their implications for the energetics and substitution mechanisms of trace-element partitioning between olivines and silicate melts.
2. Experimental methods If experimental data are to be used in modelling magmatic evolution, care should be taken to use partition coefficients measured from experiments in which the temperature and composi-
tion of the melt phase approximated that of the magma to be modelled, as the value of mineral/ melt partition coefficients are dependent on these factors (Irving, 1978; Beattie et al., 1991; Beattie, 1993b). Experiments were therefore performed at temperatures ranging from 1190 ° to 1500°C, and with melt compositions ranging from basalt to komatiite. I suggest that the partition coefficients measured in experiment B 7 be used for modelling fractional crystallisation of basalts, and that the data from experiment C10 should be used in models of partial melting. The samples used were natural or synthetic rock powders to which a mixture of oxides, carbonates and sulphates of di- and trivalent cations were added in proportions chosen to ensure that the concentrations of the elements of interest were above detection limits for SIMS in both the glass and crystalline phases. These samples were attached to Pt hooks following Biggar (1978). Iron loss to the Pt wire was minimised for all experiments other than C10 by mounting an aliquot of sample on each hook and allowing it to equilibrate with the wire for at least 24 hr at the run temperature, as suggested by Walker et al. (1979). The hook was then recovered and the experiment performed using a second aliquot of the same sample. The experiments were conducted at atmospheric pressure in vertical quench furnaces. The furnace temperatures were measured using PtPt87Rhl3 or Pt95Rhs-Pts0Rh2o thermocouples, calibrated against the melting points of gold and diopside. The oxygen fugacity of each run was maintained at about the Ni-NiO buffer by a CO2 and H2 mixture (Deines et al., 1974). Ideally, partition coefficients should be measured in reversed experiments to ensure that a close approach to equilibrium has been attained. Unfortunately, the diffusivities of the large trace elements of interest are far too low to allow crystals of a size sufficient for analysis to equilibrate with any other phase on experimental timescales. The experimental procedure was therefore chosen such that the crystals would grow from small nuclei during the experiment. As long as the crystal growth rate is small compared with the diffusion rate in the melt the crystal will grow
P. Beattie / Chemical Geology I 17 (I 994) 57- 71
59
Table 1 Run conditions of the partitioning experiments Experiment
Temperature
Duration
Fugacity
Composition
Products
B7 CI CIO CI1 F6 L2
1,250 1,400 1,495 1,495 1,450 1,190
336 336 24 24 284.5 720
- 7.1 -5.5 -4.7 -4.7 - 5.1 - 7.6
50/0.33 152 I52 152 KIA WY2
G1 +O1 GI+O1 GI+OI GI+OI GI+OI G I + O1 + Cpx
Run temperature (in ° C), duration (hours) and oxygen fugacity (log~o fo2 ) for the experiments. The experimental procedure was as described in the text, except for runs CIO and C l l which were isothermal. 50/0.33 is a synthetic sample largely CaOMgO-FeO-A1203-SiO2; 152 is a komatiite from the Belingwe greenstone belt; K1A is a kimberlite; and WY2 is an alkali basall from Wyoming, U.S.A.
in equilibrium with the melt, even if the effects of diffusion within the crystal are negligible. Large crystals can be readily grown if the sample is cooled from above its liquidus. On cooling, no crystals will grow until the melt is supercooled sufficiently for homogeneous nucleation to occur. All subsequent olivine precipitation occurs around these few nuclei. However, the rate of crystal growth may be rapid owing to the high degree of supersaturation required for homogeneous nucleation, often generating large, skeletal crystals. This technique has been avoided in this study, as the rate of crystal growth associated with this technique may be large compared to the low diffusivities of the large cations being studied. In this study samples were never taken above their liquidi, thus ensuring that many small nuclei exist for heterogeneous nucleation at all times. Large degrees of supersaturation and rapid crystal growth are thus avoided, allowing chemical equilibrium to be maintained during crystal growth. Unfortunately this procedure also precludes the growth of large crystals making analysis difficult and time consuming, but at least this procedure ensures that as close an approach to equilibrium as possible is attained. Preliminary experiments of identical run conditions to those of CI1 show that all phases other than olivine dissolve in the melt within the first 5 min, at which time the largest crystals are < 1% of an analysable size. After this time crystal growth continues slowly by Ostwald ripening. Thus almost all of the analysed material is precipitated in
equilibrium with a melt after all phases other than olivine have been dissolved. The procedure used to grow the crystals analysed in this study was to lower the samples into the hot spot of the furnace set 20°C above the run temperature. Preliminary experiments were conducted to check that the sample was never above its liquidus at this stage. The samples were held at this temperature for 24 hr and then cooled at 1 ° C h r - 1 for 20 hr to encourage the growth of large ( > 40 #m ), homogeneous crystals (Colson et al., 1988 ). Run durations were between 24 and 720 hr [which is an order of magnitude longer than the comparable experiments of McKay (1986)] to ensure equilibration. The charges were dropped from the hot spot into water to ensure a rapid quench: no evidence of quench crystallisation was observed in any of the samples. Run temperatures, oxygen fugacities and durations are shown in Table 1. All SIMS analyses were made with the Cam6ca ® ims-4f at the University of Edinburgh, using a beam of O - ions and counting positive secondary ions. The mounted samples were polished and gold-coated to prevent sample charging or sputtering from the periphery of the beam. The low concentrations of the elements analysed prevented the use of high mass resolution, and energy filtering (using a 77-V offset) was therefore used to reduce molecular interferences and matrix effects. Ions were sputtered using a 1.252-nA beam with a secondary accelerating voltage of 10.7-13.23 kV to minimise spot size and
60
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
Table 2 Olivine and glass compositions
Na20 MgO AlzO3 SiO2 K20 CaO Sc203 TiO2 Cr203 MnO FeO Fe203 Co SrO Y2O3 BaO La203 Ce203 Pr203 Sm203 Tb203 Ho203
Yb203
Experiment B 7
Experiment C1
Experiment CIO
Experiment CI 1
Experiment F6
Experimenl L2
glass
glass
glass
glass
glass
glass
0.44 8.58 14.02 48.44 1.33 1.70 0.10 0.06 0.05 0.08 15.75 1.15 0.00 0.59 0.2t 0.82 0,88 0.59 0.36 0.53 0.46 0.30 0.08
olivine
37.73 (1,683) 37.36 (638) (383) (603) (917) 0.09 23.09 (158) (0.4) (26.0) (0.0) (0.1) (0.1) (0.2) (2.9) (19.0) (35.3) (38.2)
n.d. 18.29 7.98 47.81 0.01 8.18 0.15 0.31 0.02 0.20 6.02 0.46 n.d. 0.72 0.28 n.d. 1.12 0,83 0.53 0.71 0.64 0.39 0.24
olivine
53.30 (822) 41.48 (1,571) (182) (28) (203) 0.15 5.86 n.d. (0.7) (15.3) n.d. (0.3) (0.3) (0.3) (2.4) (12.6) (19.2) (37.7)
n.d. 24.88 6.01 47.18 0.05 6.26 0.16 0.34 0.17 0.23 6.24 0.46 0.03 0.73 0.21 0.98 1.03 0,63 0.45 0.56 0.53 0.36 0.14
olivine
53.27 (764) 41.22 (901) (197) (317) (1,094) 0.14 4.08 (404) (1.0) (15,3) (0.2) (0.2) (0.3) (0.4) (3.5) (14.5) (22.9) (26,2)
n.d. 24.58 6.04 46.77 0.02 6.16 0.01 0.38 0.13 0.18 8.85 0.68 n.d. 0.15 0.05 0.24 0.22 0.16 n.d. 0.12 0.19 2.61 n.d.
olivine
51.85 (760) 40.89 (801) (10) (407) n.d. 0.08 5.80 n.d. (0.4) (3.7) (0.0) (0.0) (0.1) n.d. (0.7) (5.9) (181.2) n.d.
n.d. 21.46 5.85 47.67 0.03 6.42 0.18 0.38 0.03 0.25 7.84 0.61 0.03 0.72 0.25 1.03 1.08 0,88 0.50 0.59 0.57 0.39 0.17
olivine
52.07 (591) 40.64 (1,772) (242) (41) (314) 0.15 5.63 (329) (0.7) (17.2) (0,0) (0,1) (0,2) (0,4) (2,6) (15.5) (24.7) (32.4)
0.41 8.99 10.11 43.81 0.43 12.88 0,13 3.61 0.05 0.26 5.76 0.55 0.02 1.85 0.29 2.51 1.17 0.95 0.49 0.65 0.59 0.40 0.21
olivine
48.98 (2,245) 40.03 (3,799) (169) (491) (593) 0.28 8.29 (431) (0.7) (14.2) (0,1) (0.0) (0.1) (0.1) (1.6) (9.6) (19.1) (37.9)
Composition of olivines and glasses (in weight percent), as determined by electron probe. Data in parentheses are concentrations in parts per million (weight) calculated from the partition coefficients measured by SIMS.
counting times. Counting times at each mass varied from 5 s for major elements to > 600 s for low-abundance isotopes. The number of counts per second for each isotope was corrected for mass overlaps and normalised to that of 28Si. The partition coefficient for each element was calculated from these data as the ratio of oxide concentration in the crystal to that in the glass phase using the SiO2 content of each phase determined by EPMA. It was assumed that there is no difference in high-energy secondary ion yields between phases (Bottazzi et al., 1991 ). The sputtering of the glass around one crystal in experiments C1 and B 7 gave rise to anomalously high and constant partition coefficients for the very incompatible elements; these analyses were discarded. The Fe 2+ concentration in the melt phases were calculated from the total Fe content, oxy-
gen fugacity, run temperature and melt composition using the equation ofKillinc et al. ( 1983 ). All partition coefficients for Fe were calculated from the Fe2+O concentrations alone.
3. Results
The composition of each phase (as measured by EPMA) and the olivine/melt partition coefficients calculated from the SIMS data are shown in Tables 2 and 3. These data are presented in weight percent, as this is the basis on which partition coefficients are generally used in petrogenetic models. The partition coefficients can be converted to molar partition coefficients by multiplying them by the factor F shown in Table 3. The standard errors of the partition coefficients are calculated by propagating the variances of the
P. Beattie / Chemical Geology 117 (1994) 57- 71
61
Table 3 Olivine/melt partition coefficients B7
CI
CIO
MgO 4.44(0.04) AI?O3 1.20(0.13)-10 -2 SiO2 0.77 CaO 3.75(0.12).10 -2 Sc203 0.38(0.01) Cr203 1.85(0.13) MnO 1.07(0.02) Fe(total ) 1.55(0.03) FeO 1.44(0.02) Co 3.56(0.05) SrO 7.17(0.46)-10 -5 Y203 1.25(0.06)'10 -2 BaO 4.09(0.71)'10 -6 ka203 1.20(0.24)-10 -5 Ce203 2.42(0.40)'10 -5 PrzO 3 6.05(1.61).10 -5 Sm203 5.49(0.55)-10 -4 Tb203 4.15(0.43)-10 -3 Ho203 1.18(0.12).10 -2 Yb203 4.69(0.39).10-'-
3.23(0.21) 1.03(0.09)-10 2 0.87 1.92(0.28).10 -2 0.12(0.01) 1.02(0.14) 0.61(0.08) 0.58(0.06) 0.54(0.06) 1.50(0.01 ) 1.03(0.23)-10 -4 5.45(0.35)'10 -3 3 . 2 5 ( I . 1 5 ) ' 1 0 -s 2.67(0.54).10 -5 3.57(1.03).10 -5 5.57(1.37).10 -~ 3.33(0.60)'10 -4 1.97(0.26).10 -3 4.93(0.57).10 -3 1.57(0.23)-10 -2
2.17(0.02) 1.27(0.19).10-2 0.87
2.10(0.01) 1.96(0.03) 1.26(0.11).10 2 1.01(0.03).10 2 0.87 0.85 2.76(0.03).10 2 0.12(0.00) 0.15(0.00) 0.13(0.00) 0.63(0.04) 0.94(0.01) 1.13(0.17) 0.52(0.02) 0.50(0.02) 0.56(0.02) 0.53(0.02) 0.51(0.01) 0.57(0.02) 0.49(0.02) 0.48(0.01 ) 0.53(0.02) 1.18(0.03) 1.10(0.04) 1.29(0.05) 1.38(0.11).10 4 2 . 5 6 ( 0 . 7 5 ) . ! 0 - 4 9.13(2.93).10-5 7.19(0.31).10 3 7.54(0.40).10-3 6.77(0.31).10-3 2.30(0.15)-10 -5 n.d. 1.39(0.46)-10 -6 2.18(1.26).10 -5 2.16(2.63).10 -5 6.69(1.17).10 6 4.51(1.06).10 s 7.61(1.90).10 5 2.63(0.13).10-5 8.45(4.32)-10 -5 6.80(4.94).10 -5 7.19(0.36).10 -5 6.36(0.23)-10 .4 6.33(3.36)'10 -4 4.35(0.64)-10 -4 2.75(0.12).10 -3 3.09(0.44)-10 -3 2.72(0.16)-10 -3 6.43(0.24).10 -3 6.94(0.55).10 -3 6.27(0.35).10 3 1.88(0.11).10 -2 2.12(0.33)-10 -2 1.87(0.15).10 2
3.75(0.35) 2.22(1.06).10-2 0.91 2.95(0.71).10-2 0.13(0.01)
n F
5 0.85
3 0,84
2 0.83
3 0.90
CII
3 0.84
F6
3 0.85
L2
0.82(0.10) 0.90(0.12) 0.82(0.11 ) 2.24((1.28) 3.94(0.65).10-5 4.94(0.15).10-3 2.09(1.98).10 ~ 3.77(0.12).10-6 1.02(0.13).10-5 2.61(0.32)-10 -5 2.44(0.35)'10 -4 1.63(0.08).10 3 4.72(0.15)-10 3 1.84(0.09).10 2
Data in parentheses are one standard error of the partition coefficient, calculated by propagation of the variance of crystal and glass concentrations. Electron probe was used to measure D °~/L for all experiments and n* J Ot/L for experiments B 7, C 10 and C l 1: Mg all other partition coefficients were measured using SIMS. n is the number of cD'stals analysed for each experiment: F is the ratio of molar to weight partition coefficients and is identical for all elements.
concentration of each component in each phase, as this source of error is much larger than that associated with counting statistics. EPMA traverses across the crystals demonstrate that a close approach to equilibrium has been attained, at least for the major elements. More than one hundred analyses were made of the olivines in experiment CIO, which had the shortest equilibration time (24 hr), giving a Mg number of 0.900_+ 0.0013. Thus the analytical error of the electron probe is greater than one standard error of the variation in crystal composition. Thus no significant disequilibrium is observed in the major-element compositions of the crystals. The homogeneity of the trace-element concentrations in the olivines cannot be checked by EPMA due to their low concentrations (0.1-100 ppm). The degree of trace-element equilibration in these experiments can be assessed only by ex-
amining the variability of analyses of different crystals in a given experiment. The partition coefficients calculated from five different crystal-glass pairs in experiment C1 are shown in Fig. 1. The standard errors of the concentrations measured for the five different crystals are < + 20% of the average concentrations for all but the most incompatible trace elements, where peripheral sputtering of glass may become significant. Similar small variations in compositions within a single experiment is seen in many partitioning experiments (e.g., Watson et al., 1987). It is clear from Fig. 1 that the small variation in concentrations of the different crystals is negligible compared to the difference between the partition coefficients of the different elements studied, which varies by more than five orders of magnitude. The lack of large variations in the calculated
62
P. Beattie / Chemical Geology 117 (1994) 57- 71
Five Olivine/Glass Pairs Experiment CI, 1400°C
each of the other experiments, owing to the long analysis time and high cost of SIMS. The lack of variation between the different crystal-glass pairs of experiment C1 demonstrates that each crystal-glass pair gives an accurate measurement of the equilibrium partition coefficient; the measurement of three crystal-glass pairs for each experiment is therefore sufficient to allow the value of the partition coefficients to be determined with adequate precision.
1 01
Mg
'
"
'
1 0° 10-1
E
.=o
Sc'~
~ ,
Ca
10-2 10-3 10 -4 i 10-5 10-6 0.06
Smpr ~
~
a
Ce La
3.1. Henry's law 0.08 0.1 0.12 Ionic Radius (nm)
0.14
Fig. 1. Graph showing the partition coefficients calculated from the analyses of five olivine-meltpairs in experiment C 1 plotted against ionic radius (in nm). The partition coefficients are calculated on a weight percent basis. Separate trends are shown for the divalent and trivalent cations. There is little variation in the partition coefficients for any given element between the different crystal-glass pairs. It is therefore clear that a close approximation to equilibrium has been attained. The low partition coefficients for Ba and the LREE demonstrates that the effects of contamination of crystals during polishing and sputtering of peripheral glass during analysis changes the measured partition coefficients by <3.10 -5"
partition coefficients between the different crystal-glass pairs demonstrates that a close approach to equilibrium has been obtained in these experiments, even for the low-diffusivity trace elements. This conclusion is supported by the similarity of the partition coefficients for experiments F6 and CIO, despite a difference in equilibration times of more than an order of magnitude (284.5 and 24 hr, respectively). Partition coefficients for the very incompatible elements are difficult to measure, due to the contamination of the crystals during polishing of the sample, the finite background of the electron multiplier and the sputtering of small amounts glass around the periphery of the beam. The partition coefficients for all elements will be equally increased by these effects. The upper limit for the errors introduced by these effects is therefore equal to the lower of nOl/L and is JL"Ba and nOl/L .tJLa therefore < 3" 10- 5 in all the experiments. Only three olivine-glass pairs were analysed in
Experiment C l l was performed to test the validity of Henry's law in olivine-melt systems. The Ho concentration in sample C l l is approximately six times higher than that in CIO and the concentration of all other trace elements is lower by about a factor of 4; the Y / H o ratio in the olNines differs by a factor of 20. As can be seen from Table 3 and Fig. 2, the partition coefficients for each element are identical in the two experiments to within two standard errors, and vary by less than one standard error for all elements other than Ce. Thus no deviations from Henry's law are observed for elements whose concentration in the olivines range from 0.05 to 180 ppm, even though heterovalent substitutions are required for these trivalent cations. Henry's law will be violated if the dominant partitioning mechanism changes with concentration. No definitive proof exists in the literature for deviations from Henry's law at concentrations of < 1% for trace elements which substitute for another cation of the same valency (Beattie, 1993a). Deviations from Henry's law are therefore most likely to be observed in the partition coefficient systematics of the trivalent cations, as the trivalent cations must substitute for either Mg or Si in olivines.
3.2. Comparison with previous data There have been several studies in the past that have attempted to measure the mineral/melt partition coefficients for incompatible elements in olivine or orthopyroxene. Olivine/melt partition coefficients were measured by Schnetzler
P. Beattie / Chemical Geology l 17 (1994) 57- 71 Olivine/meh Partition Coefficients
Experiments C10 and C11 1495°C 1 0 .2
I
.,~
[
"5 ° 10-3
L
.......
'
........
~ Y'
°°
.
.
.
.
.
Ho .
.
.
63
1
o
{'I1:~
0°
10-1 10-2
oSm •
©
L) ©
i
10-5 [ 0.01
0[,3.0
....... , 0.1 1 10 1 O0 Concentration in Olivine (ppm)
O
10-3
e~
10 -4
Sm~
i
i
1000
Fig. 2. If trivalent cations were charge balanced by the creation of vacancies or interstitials then the partition coefficient would cease to be independent of the concentration of the trace components. Thus deviations from Henry's law are more likely for heterovalent than for homovalent substitutions. Here the measured partition coefficients for the trivalent cations are plotted against the concentration of these elements in the olivines. Despite changes in Y / H o ratios of almost a factor of 20 there are no significant differences in the partition coefficients of any of these elements between experiments C 10 and C I 1 ( hollow and solid symbols, respectively ). Inspection of Table 3 demonstrates that partition coefficients for the two experiments differ by less than two standard errors for all the elements analysed, and by less than one standard error for all elements other than Ce. Thus no deviations from Henry's law are observed in these experiments, even for heterovalent substitutions. Error bars represent one standard error of the partition coefficients.
and Philpotts (1970) and Matsui et al. (1977) using INAA; by McKay and Weill (1977), McKay (1986) and Colson et al. (1988) using EPMA; and by Kennedy et al. (1993) using SIMS. Fig. 3 shows the olivine/melt partition coefficients for trivalent cations taken from the literature together with the data from experiment CI which is representative of the data from this study. The different studies all found similar values of the partition coefficients for the heavy rareearth elements (HREE) and yet the values of the light rare-earth elements (LREE) partition coefficients vary by up to three orders of magnitude. The INAA data and the EPMA data of McKay and Weill (1977) all show concave-upward trends on Fig. 3, indicating that the large parti-
i
Pr 10-5 0.06
0.07
0.08 0.09 Ionic Radius (nm)
! 0.1
0.11
Fig. 3. Graph of partition coefficients for trivalent cations against ionic radius allowing comparison of the olivine-melt data of this study (solid circles= experiment C 1) with data from the literature: hollow circles are the data of McKay ( 1986 ) and Colson et al. (1988) (experiment 115b ); hollow squares are the EPMA data of McKay and Weill ( 1977 ); hollow triangles are the data of Matsui et al. ( 1977 ); and hollow diamonds the data of Schnetzler and Philpotts (1970). The dashed lines shows the apparent partition coefficients that would be obtained if 0.3% or 1% of glass were incorporated in the material analysed as crystal. The correspondance between these lines and the LREE partition coefficients measured by INAA or routine EPMA suggests that imperfect isolation of the crystalline phase can give rise to partition coefficients that are in error by more than two orders of magnitude.
tion coefficients for the LREE may be a reflection of a small amount of glass being analysed during the analysis of the crystal, as proposed by McKay (1986). The dashed lines in Fig. 3 are the apparent partition coefficients that would be produced if the crystal analyses of experiment C1 were contaminated by 1% and 0.3% glass fluorescence. The excellent correspondence between these lines and the partition coefficients measured by INAA suggests that the high apparent partition coefficients of the LREE may be due to the incorporation of glass in the crystalline material analysed. Spurious partition coefficients of the order of 10 -2 may be produced even for perfectly incompatible cations because of imperfect phase separation. The EPMA data of McKay and Weill (1977) can also be modelled by a 1% contamination of
64
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
Experiment B7, 1250°C.
Experiment C1, 1400°C
1 01
1 0~ 1
0°
1
.
Sc
10-1
S c ~ ' ~ , ,
10-2
y Ho
O 10-3 c~ t0 .4
Ca ", ~,
i
Ce
10-6 0.06
0.08
'
Cr
Co '
T
" % ~'-.,..
10-1
Sm~
10 5
00
',
0.1
Yb~
g 10-2 L~ r~ 10-3 o
v,\.o
0.14
Ced' ~
10-6 0.06
0.08
100
' '
Tb
1 0~
' ~
5 10-1 i 10-2 L) 10-3
x
10 .4
't Sr
Pr~,c e
~"S
1o-
\.,,
0.06
. . . . 0.08
0.1
\,.
0.12
"; Ba~ 1
"i 0.14
10 -4 10 .5 ~ 1 0.6 ~(d) 0.06
Ionic Radius (nm) Experiment F6, 1450°C
101
'
Mg CO'Fe
10-1
10 -2 [
t-, 0
0.14
~.
! 10-41
~_
'
!
~ La ,,
Sr
\, \',
l . I
\°a I
0.08 0.1 0.12 Ionic Radius (nm)
0.14
1 01 0°
~.
10-1
Ho "%,~a
10-2
Sm S%L~
~
Experiment L2, 1190°C
1
{J
0.12
10°
e., o
"5
0.1
Experiment C11, 1495°C
5
lO
~ , , Ba,
Ionic Radius (nm)
Experiment C10, 1495°C ___,.~OFe'M ' ' ' ' ' ' '
'
10-4
Ionic Radius (nm)
101
\,
Tb Q
10-5
0.12
o\Ca
"', ~e, ST
: l
o= 10-3 10-4 10-5
0.06
0.08 0.1 0.12 Ionic Radius (nm)
0.14
10-6 0.06
0.08 0.1 0.12 Ionic Radius (nm)
0.14
Fig. 4. Graphs showing the partition coefficients calculated for each of the experiments plotted against ionic radius (in rim). These graphs show that the variation in trace-element partition coefficients is controlled by ionic radius and charge. The partition coefficients for the divalent ions and trivalent cations form two separate trends. The solid curves in each graph are the values predicted using Eqs. 9 and 12, using an octahedral bulk modulus for the olivine of 95.3 GPa for divalent cations. The curve for
P. Beattie I Chemical Geology 117 (1994) 57- 71
crystal by glass, indicating that fluorescence of the glass surrounding the crystals analysed was the dominant factor controlling the partition coefficients of the LREE, as suggested by McKay (1986). By contrast, the partition coefficients measured by McKay (1986) and Colson et al. (1988) using Mo guards to suppress glass fluorescence, and the SIMS analyses of isothermal experiments conducted by Kennedy et al. ( 1993 ) are in close agreement with the data of this study, confirming the accuracy of both the SIMS and EPMA analyses.
4. Energetics of trace-element substitution
4. I. Divalent cations The olivine/melt partition coefficients measured in each experiment are shown in Fig. 4. These graphs demonstrate that the variation in partition coefficients are controlled by the ionic radius and charge of the trace components, as was proposed by Onuma et al. ( 1968 ). The relationship between ionic radius and the value of the mineral/melt partition coefficient for the divalent cations indicates that the substitution mechanism of all these cations is similar to that of Mg, and partitioning therefore occurs by substitution of cations onto well-defined cationic sites in the crystal. If partitioning occurs by substitution onto lattice sites, the large incompatible cations will partition onto the M2 site in the crystal, as this is larger than the M 1 octahedra and the tetrahedral sites. The partitioning reaction may therefore be defined as:
MO L+ MgMgSiOO~ ~
65
( 1)
MgO L+ MgMSiOO~ where M is any divalent cation. The condition for equilibrium is therefore:
A H - TAS+ ( P - 1 )AV=
_Fa oa°' M ,O41
- R T I - / ~ i La M O a MgMgSiO,, _]
(2)
where R is the gas constant; and T is the temperature in kelvins. If it is assumed that the trace elements obey Henry's law in each phase, and that the degree of non-ideality in the two phases is similar then: a L o = X L o . TL aO¿
yOI .O1 M g M S i O 4 ~- i x M O * YM
1
(3) (4) (5)
which will be true unless the ratio of Henry's law constants for the two elements is different in the two phases, then: In ~'M.r~OI/L=In D°~ L + A G / R T
(6)
The terminology used here is that of Beattie et al. ( 1993): X ~ o . and 7~ are the molar fraction of component MO in phase a and its activity coefficient, respectively; and D~/5 is the molar partition coefficient for component MO substituting between phase a and a silicate melt L, and o~ L is defined as XMO./XMo. • Thus the mineral/melt partition coefficient of any divalent cation can be calculated from that for Mg if GMO and GM~O are known for each phase. Unfortunately, accurate calorimetric data
trivalent cations is calculated using a value for the heat capacity of AI,Si- ~exchange between tetrahedral sites in the olivine and glass of 55 J m o l - 1 K - ~and an olivine octahedral bulk modulus adjacent to AI tetrahedra of 180 GPa. The dashed line gives the partition coefficients calculated for an octahedral bulk modulus of 90 GPa for divalent cations. Ionic radii are for octahedral coordination and are taken from Shannon ( 1976 ). The error bars shown are one standard error of the partition coefficient, and are calculated by propagating the variance of crystal and melt analyses for each element, in most cases the symbol size is larger than one standard error of the partition coefficient.
66
P. Beattie / Chemical Geology 117 (1994) 57-71
for trace components in silicate minerals and melts are not available, and the fact that the structure of silicate melts is complex and poorly known precludes the calculation of these parameters ab initio. The approach followed here is therefore to model the enthalpies of the divalent oxide components using macroscopic strain theory. Following Nagasawa ( 1966 ), the strain energy of the anionic lattice associated with the substitution of a large cation into a site of given size is: U " = 6rrr30 "' siteKC
(7)
per atom, where .c2= e 2[1 .t. t (1 +a'~si'c) 1
~ o~,oc1 __
2(1_2~ -.~i~e) 3( 1 _ ~.si~)
e=rM/ro - 1
and U ~ is the strain energy for phase oe; ro is the radius of the unstrained site; rM is the ionic radius of the trace element; K msite and er~'s~'~ are the bulk modulus and Poisson's ratio, respectively, of the site in phase o~ into which large cations substitute. The radius of an unstrained cationic site (to) can be calculated to be 0.058 nm, assuming the condition of zero strain is that where the oxygen ions in an octahedron would just touch each other if they were rigid spheres of radius 0.14 nm. While the temperature dependence of the bulk modulus of the unit cell is known for the forsterite and fayalite, the measurement of the bulk modulus of the MO6 octahedron at supra-solidus temperatures requires structure refinement of high-pressure, high-temperature experiments. These data are not yet available due to the experimental difficulties involved. The octahedral bulk modulus at high temperatures must therefore be calculated from the compressibility of the unit cell. The bulk modulus of the MO6 octahedra in forsterite, fayalite and intermediate Fe-Mg-olivines (Hazen, 1976, 1977) are similar, though slightly smaller, than those of the host phase. Thus at 300 K the bulk modulus of forsterite ( 129
GPa; Isaak et al., 1989 ) is almost identical to that of the M2 MgO6 octahedron (130 GPa; Kudoh and Takeuchi, 1985). Furthermore, the compressibility of forsterite and fayalite (128 GPa: Graham et al., 1988) are almost identical. Thus the compressibility of pure forsterite will be a good approximation to that of the M2 octahedra of Fe-Mg-olivines such as those in this study. Isaak et al. (1989) also measured the elastic constants of forsterite at 1700 K, and found the isothermal bulk and shear moduli to be 95.3 and 61.32 GPa, respectively. Thus the Poisson's ratio and bulk modulus of the olivine M2 site are assumed to be 0.25 and 95.3, GPa respectively. The negligible shear modulus of silicate melts requires that the Poisson's ratio of the melt is 0.5: 0 c.s~e is therefore negligible. Thus if the difference in standard state free energy between different trace components is dominated by the differences in strain energy associated with their substitution into the mineral and melt lattices, then the molar partition coefficient for a divalent cation M ( D r . ) should be given by:
In
D Ol/L *
=In r~Ol/L *'* Mg*
6zrN~r3°O°l"°~tg°l'°c'(f2M RT
--~Mg)
(8)
where Na is Avogadro's number; and f2 is calculated using the ionic radii of Shannon (1976). The ratio of molar to weight partition coefficients (shown as F in Table 3 ) is identical for all elements for phases of any given composition. Partition coefficients by weight (D) should therefore be given by: In D ° u c = In ~.rlOI/LMg 6rcNA ro 3 RT 0 °l'°ctK°l'°cl (~QM - f2Mg)
(9)
where D °~/L is the weight partition coefficient for component MO. The fit to the experimental partition coefficients is excellent for most elements, as shown in Fig. 4. The value ofD°~/L can be calculated accurately from a knowledge of the composition of the melt phase and the equilibration tempera-
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
ture and pressure (Beattie et al., 1991; Beattie, 1993b). Thus the partition coefficients of the alkaline earths can be calculated accurately from the cationic radius, pressure, temperature and melt composition alone, given the bulk modulus and Poisson's ratio for the mineral phase. DOUL is accurately predicted using Eq. 9, but Mn D OI/L and F,--Co I O I / L are lower than the values predicted by about a factor of 2, even after correction for the presence of Fe 3+. These deviations may be caused by the large electronegativities or crystal field effects of these ions. The accurate fit to the alkaline-earth and Mn data is consistent with the zero octahedral site preference energy for these cations. The Ba partition coefficient may be dominated by the sputtering of peripheral glass, electron multiplier background or contamination during polishing, and should therefore be considered an upper limit. In most analyses, the difference between the calculated and measured values for the divalent cations other than Fe, Co and Ba is < 30% which is comparable to the standard errors of the measured partition coefficient and is clearly trivial compared with the five orders of magnitude difference between the partition coefficients for the alkaline earths. Hazen (1985) noted that polyhedral bulk moduli differ from the bulk moduli of the unit cell for phases that are not close packed, thus the octahedral bulk modulus may be slightly lower than that of olivine. The best fit to the partition coefficients for the alkaline earths is obtained if the value of the octahedral bulk modulus is reduced from 95.3 to 90 GPa. The values of the partition coefficients predicted for this bulk modulus are shown as a dashed line in the graphs of Fig. 4. 4.2. Trivalent cations
The partitioning of trivalent cations is not as straightforward as that of the divalent cations due to the requirement that local charge balance is maintained. Charge balance can be maintained by the generation of vacancies or interstitials, giving a substitution reaction of the form:
67
RO L5 + Mg2 SiO2~ ~ 1.5MgO L+ Mgo 5 l;~ 5RSiO ol where R is a trivalent cation; and V i s a vacancy. This substitution mechanism for trivalent cations has been proposed to explain the partitioning of Sc between olivines and melt in experiments in which the Sc content of the olivines was too high for charge balance to be maintained by A1 (Colson et al., 1989; Nielsen et al., 1992). The equilibrium constant for this reaction is proportional to the vacancy density in the crystalline phase, which must be equal to half the concentration of the trivalent cations. The difference between ZJR* r~O~/L and ~r~o~/u will therefore Mg* be dependent on the concentration of RO~5, and Henry's law will not be satisfied for trivalent cations. Similarly, if the substitution of the trivalent cation were balanced by the creation of an oxygen interstitial, ~-r.t~ O~/L would be dependent on the abundance of interstitials and again Henry's law would cease to be satisfied. However, in natural magmatic systems, olivines always have sufficient AI to charge balance all the other trivalent cations. The REE/A1 ratios of these experiments were chosen to reflect this condition and, as was shown earlier, no deviations from Henry's law are observed at the low concentrations oftrivalent ions in the olivines of this study. Thus the substitution mechanism of trivalent cations into the olivine lattice at these low concentrations cannot be charge balanced by the generation of vacancies or interstitials. As the concentrations oftrivalent trace elements during partial melting or crystallisation within the Earth are even lower than those of the experiments in this study, substitution mechanisms involving the generation of vacancies or interstitials are therefore unlikely to be applicable to natural magmatic systems. The maintenance of local charge balance must therefore be accomplished by a paired substitution of R,A1 for Mg,Si, as found for equilibria between clinopyroxene or orthopyroxene and melt on the basis of stoichiometric constraints (Lindstrom, 1976; Colson et al., 1989). Thus the substitution reaction is probably:
P, Beattie / Chemical Geology I 17 (1994) 5 7- 7I
68
RO ~s +A10 ~5 + Mg2 SiO ° ~ MgO L+ SiO } + MgRA10 4TM
( 11)
It is clear that if the substitution of trivalent cations is charge balanced by this mechanism, then D °~/L will be independent of X °~, but will vary with the activities of A1Oj.5 and SiO2 in each phase. Thus, if it is assumed that A1 is evenly distributed between the tetrahedral and octahedral sites, the trivalent partition coefficients will be given by: In D °'/L =In D°lg/L
" [ D°'I/L "~ ACp --,n~)--
6nNAr3°OOl'°clKOl°ct(~R -- 12Mg) RT
(12)
where ACp is the difference in heat capacity of A1 and Si tetrahedra in the olivine and melt phases. The A104 tetrahedra required locally to maintain charge balance are larger than SiO4 tetrahedra and tetrahedral sites in olivines are much less compressible than octahedral sites (Hazen, 1977). The bulk modulus of octahedra in unit cells containing A1 tetrahedra will therefore be greater than those of unit cells without A1 tetrahedra. Thus K °~'°~' will be greater for the trivalent cations than for the divalent ions. The observed partition coefficients can be modelled accurately using Eq. 12 if K °~°~t = 180 GPa for the trivalent cations. Similarly, zlCp is found to be 55 J mol-~ K -j. The fit to the trivalent partition coefficients using these values for the heat capacity and bulk modulus are shown in Fig. 4 for each experiment. The imperfect fit of the Cr partition coefficients may be a result of electronegativity or crystal field effects. The slight deviation from the calculated values for the very light REE (Ce and La ) reflects the difficulty of measuring partition coefficients lower than 2 . 1 0 - 5, and probably reflects the sputtering of very small amounts of glass during analysis of the crystals. The partition coefficients for the other trivalent cations are accurately predicted by Eq. 12. For most analyses the difference between the calculated and observed partition coefficients is < 20%.
Thus apart from those elements for which electronegativity or crystal field effects are important, the partition coefficients for all the diand trivalent cations studied are be accurately predicted by Eqs. 9 and 12. The calculation of the partition coefficients for these elements can be performed if the temperature and melt composition are known using the equations of Beattie et al. ( 1991 ) and Beattie (1993b) to calculate JtJMg nO~/L olivine bulk moduli and Poisson's ratio from the literature for the divalent cations, an octahedral bulk modulus of 180 GPa and an A1-Si exchange heat capacity of 55 J m o l - ~ K for trivalent cations. The accuracy with which these partition coefficients can be calculated indicates that the crystal chemistry and thermodynamics of partitioning of these elements between olivine and silicate melt is now well understood.
5. The nature of trace-element partitioning in magmatic systems The accuracy of Eqs. 9 and 12 has several important implications: ( 1 ) It clearly demonstrates that the variation in ionic radius and charge exerts the dominant control on the partitioning of incompatible elements, owing to the increased lattice strain associated with the substitution of large cations into small sites. The zero strain radius of the site (ro) is not that of the host cation (Mg), but is that for an octahedron whose oxygen atoms touch, and is therefore expected to be independent of the cation for which the trace elements substitute. (2) The accuracy of these equations suggests that the incompatible trivalent cations all partition onto the same sites in the crystalline phases as Cr does, and that all divalent cations substitute onto the same sites as Mg and Mn. The concentration of Mn and Cr in the olivines of this study are generally of the order of 1000 ppm. The number of defect sites in the olivines is unlikely to exceed 1-1000 ppm (Navrotsky, 1978 ), which indicates that the partitioning of Mn and Cr, and therefore of the other di- and trivalent cations, are not dominated by substitution into defect sites. Since the concentration of La in the olivine
P. Beattie / Chemical Geology 117 (1994) 5 7- 71
is of the order of 0.1 ppm, then partitioning even at these low crystalline concentrations occurs by substitution onto M sites rather than defect sites in the crystals. This conclusion is in partial conflict with the electron paramagnetic data of Morris (1975) which suggest that Gd and Eu in olivine are not situated on lattice sites but form clusters at room temperatures. Morris noted, however, that substitution on lattice sites at higher temperatures could not be discounted. Furthermore, the samples analysed in that study were Al-free precluding an A1,Si-l charge balance mechanism, regardless of whether it might be energetically favourable compared with cluster formation. ( 3 ) The lack of major deviations from the predicted values implies that there are no large changes in substitution mechanism or deviations from Henry's law between the different dior trivalent cations studied, even at concentrations as low as 0.05 ppm. These low concentrations are comparable to those in the Earth's mantle, and Henry's law is therefore expected to be satisfied during mantle melting in accordance with the conclusions of Watson ( 1985 ). The lack of any deviations from Henry's law implies that the trivalent cations are charge balanced by an AI,Si-1 paired substitution rather than by the generation of vacancies or interstitials. The partition coefficients for trivalent cations may therefore be expected to be pressure dependent, as olivines in equilibrium with a given melt composition are progressively more AI rich as the pressure of equilibration increases (Agee and Walker, 1990). Work is now in progress to test this hypothesis. The partition coefficients for orthopyroxene-, clinopyroxene-, plagioclase-, biotite- and hornblende-melt pairs are also monotonic functions of ionic radius (Onuma et al., 1968; Jensen, 1973). Thus the systematics observed for olivine/melt partitioning are typical of partitioning between minerals and silicate melts, and it is reasonable to assume that trace-element partitioning between silicate crystals and melts generally occurs by substitution onto well-defined crystallographic sites. No deviations from Henry's law have been observed for trace elements in these
69
minerals, which all have higher A1 contents than olivine. The substitution oftrivalent cations into these minerals therefore probably also occurs via a coupled substitution of A1 for Si.
6. Conclusions The experimental and analytical procedure developed here is capable of ensuring a close approach to equilibrium and the accurate measurement of partition coefficients as low as 10-5. The olivine/melt partition coefficients determined by SIMS in this study agree well with the high-precision EPMA data o f M c K a y (1986) and Colson et al. (1988) for the less incompatible trace elements. Previous studies of olivine/melt partitioning using INAA or routine EPMA have given results for the most incompatible elements that appear to be dominated by the addition of between 0.3% and 1% of glass in the analysis of the olivines, and therefore give partition coefficients that are up to three orders of magnitude greater than those reported here. The excess energy required to expand the octahedral site in olivine and silicate melts can be calculated using bulk moduli consistent with values from the literature, and assuming that the local Poisson's ratio of the mineral and melt are 0.25 and 0.5, respectively. The partition coefficients for divalent cations can be accurately calculated from the value of this strain energy. The ability to calculate partition coefficients for divalent cations with a wide range of ionic radii demonstrates that the incompatible trace elements substitute onto the same site in the olivines as Mg, and are not sensitive to the presence of defects. The partition coefficients for Fe and Co are slightly anomalous compared to those for the alkaline earths; these anomalies may be caused by the anisotropic electron densities and high electronegativity of these cations. REE,Mg- ~ substitution is charge balanced by a coupled A1,Si- ~substitution rather than by the creation of vacancies or interstitials, as no deviations from Henry's law are observed. The variation between partition coefficients for the trivalent cations is independent of olivine and melt
70
P. Beattie / Chemical Geology l 17 (I 994) 57- 71
composition and can again be calculated from the energy associated with octahedral expansion. The value of the local bulk modulus for olivine is much greater for the trivalent cations than for the divalent cations, reflecting a local stiffening of the crystalline lattice near A104 tetrahedra. The substitution mechanism is identical for trivalent cations whose partition coefficients differ by up to five orders of magnitude. The partition coefficients for these trivalent cations may be pressure dependent, as the amount of tetrahedral AI increases with pressure. The partition coefficients between other silicate minerals and melts exhibit a similar dependence on ionic radius and charge, indicating that the substitution mechanisms for olivine may be typical of those for other silicate minerals. Thus the partitioning of di- and trivalent trace elements within the Earth is expected to occur by substitution onto well-defined crystallographic sites in the crystals, with charge balance maintained by A1,Si -~ substitution. Trace-element partitioning should therefore be amenable to thermodynamic modelling.
Acknowledgements Gordon Biggar, Mike Bickle and Godfrey Fitton are thanked for providing the rock powders used in this study. Facilities for the experimental and SIMS work was kindly provided by the University of Edinburgh with the invaluable help of Gordon Biggar, John Craven and Richard Hinton. Thomas Bleser, Stephen Reed and David Newling helped with the EPMA analyses. Thanks too to Francis Albar6de, Don Baker, James Brodie, Mike Drake, Steve Foley, Tony Irving, Dan McKenzie, David Palmer, Simon Redfern and an anonymous reviewer whose helpful comments greatly improved this manuscript. This is contribution number 3815 of the Department of Earth Sciences, Cambridge. This work was performed while the author was in receipt of NERC and Corpus Christi College, Cambridge research studentships and fellowships.
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P. Beattie / Chemical Geology 117 (1994) 57- 71 canic rocks. Earth Planet. Sci. Lett., 7:281-287. Irving, A.J., 1978. A review of experimental studies of crystal/liquid trace element partitioning. Geochim. Cosmochim. Acta, 42: 743-770. Isaak, D.G., Anderson, O.L, Goto, T. and Suzuki, I., 1989. Elasticity of single-crystal forsterite measured to 1700 K. J. Geophys. Res., 94: 5895-5906. Jensen, B.B., 1973. Patterns of trace element partitioning. Geochim. Cosmochim. Acta, 37: 227-2242. Kennedy, A.K., Lofgren, G.E. and Wasserburg, G.J., 1993. An experimental study of trace element partitioning between olivine, orthopyroxene and melt in chondrules: equilibrium values and kinetic effects. Earth Planet. Sci. Lett., 115: 177-195. Killinc, A., Carmichael, I.S.E,, Rivers, M.L. and Sack, R.O., 1983. The ferric-ferrous ratio of natural silicate liquids equilibrated in air. Contrib. Mineral. Petrol., 83: 136-140. Kudoh, Y. and Takeuchi, Y., 1985. The crystal structure of Mg2SiO4 under high pressure up to 149 kb. Z. Kristallogr., 171: 291-302. Leeman. W.P., 1974. Petrology of basaltic lavas from the Snake River Plain, Idaho, and experimental determination of partitioning of divalent cations between olivine and basaltic liquids. Dissertation, University of Oregon, Corvallis, Oreg. Lindstrom, D.J., 1976. Experimental study of the partitioning of the transition metals between clinopyroxene and coexisting silicate liquids. Dissertation, University of Oregon, Corvallis, Oreg. Matsui, Y., Onuma, N., Nagasawa, H., Higuchi, H. and Banno, S., 1977. Crystal structure control in trace element partition between crystal and magma. Bull. Soc. Fr. Mindral. Cristallogr., 100:317-324. McKay, G.A., 1986. Crystal/liquid partitioning of REE in basaltic systems: Extreme fractionation of REE in olivine. Geochim. Cosmochim. Acta, 50: 69-79. McKay, G.A. and Weill, D.F., 1977. KREEP petrogenesis revisited. Proc. 8th Lunar Sci. Conf., pp. 2339-2355.
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Morris, R.V., 1975. Electron paramagnetic study of the site preferences of Gd 3+ and Eu 2+ in polycrystalline silicate and aluminate minerals. Geochim. Cosmochim. Acta. 39: 621-634. Nagasawa, H., 1966. Trace element partition coefficient in ionic crystals. Science, 152: 767-769. Navrotsky, A., 1978. Thermodynamics of element partitioning: ( 1 ) systematics of transition metals in crystalline and molten silicates and (2) defect chemistr? and the "Henry's Law problem". Geochim. Cosmochim. Acta, 48: 887902. Nielsen, R.L., Gallahan, W,E. and Newberger. F., 1992. Experimentally determined mineral-melt partition coefficients for Sc, Y and REE for olivine, orthopyroxene, pigeonite, magnetite and ilmenite. Contrib. Mineral. Petrol., 110: 488-499. Onuma, N., Higuchi, H., Wakita, H. and Nagasawa, H., 1968, Trace element partilion between two pyroxenes and the host lava. Earth Planet. Sci. Lett., 5: 47-51. Philpotts, J.A., 1978. The law of constant rejection. Geochim. Cosmochim. Acta, 42: 909-920. Schnetzler. C.C. and Philpotts, J.A., 1970. Partition coefficients of rare-earth elements between igneous matrix material and rock-forming mineral phenocryst, 11. Geochim. Cosmochim. Acta, 34: 331-340. Shannon, R.D., 1976. Revised effective ionic radii in oxides and fluorides. Acta Crystallogr., Sect. A, 32:751-767. Walker, D., Shibata, J. and DeLong, S.E., 1979. Abyssal tholeiites from the Oceanographer fracture zone. Contrib. Mineral. Petrol., 70:111-125. Watson, E.B., 1985. Henry's Law behaviour in simple systems and in magmas: criteria for discerning concentration-dependent partition coefficients in nature. Geochim. Cosmochim. Acta, 49: 917-923. Watson, E.B., Ben Othman, D., Luck, J.-M. and Hofmann, A,W., 1987. Partitioning of U, Pb, Cs, Yb, Hf, Re and Os between diopsidic pyroxene and haplobasaltic liquid. Chem. Geol., 62: 191-208.