The Astrophysical Journal, 647:1506Y1516, 2006 August 20 # 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.
MASS-INDEPENDENT ISOTOPE FRACTIONATION OF MOLYBDENUM AND RUTHENIUM AND THE ORIGIN OF ISOTOPIC ANOMALIES IN MURCHISON Toshiyuki Fujii,1,2 Fre´de´ric Moynier,2 Philippe Telouk,2 and Francis Albare`de2 Received 2006 January 9; accepted 2006 April 22
ABSTRACT Dauphas et al.’s model for the nucleosynthetic origin of Mo and Ru anomalies in meteorites leaves the case of Murchison (CM2) unexplained. We explore the possibility that such a discrepancy is due to mass-independent effects controlled by nuclear field shift with, in particular, ‘‘staggering’’ between odd and even masses. We first demonstrate the existence of such mass-independent fractionation of Mo and Ru isotopes by chemical exchange of Mo and Ru between DC18C6 crown ether and aqueous solutions. Our results fit the nuclear field shift theory of Bigeleisen. We then review the correlation between the mean-square charge radius (which controls the nuclear field shift) and the isotopic anomalies found in an Allende CAI and in Murchison. Although Mo and Ru in the Allende CAI show a clear indication of nucleosynthetic components, the mass-independent anomalies observed in Murchison show a strong correlation with the nuclear charge distribution. We therefore argue that some isotopic anomalies observed in meteorites may be due to nuclear field shift rather than nucleosynthetic processes. Such effects are temperature dependent and may represent either genuine nebular processes or analytical artifacts. This new interpretation may help assess the existence of anomalies due to the extinct isotopes 97Tc and 98Tc. Subject headingg s: meteors, meteoroids — nuclear reactions, nucleosynthesis, abundances
1. INTRODUCTION
existence of the mass-independent effects predicted by the nuclear field shift effect (see references in Fujii et al. 2002) We argue elsewhere (Fujii et al. 2006) that the isotopic anomalies of alkaline earth elements ( Mg, Ca, Sr, and Ba) and transition metals ( Ti and Cr) found in the so-called fractionated and unknown nuclear effects (FUN ) refractory inclusions in the Allende CV3 chondrite show properties that closely follow their nuclear charge radii. The present work demonstrates that the Mo and Ru in the Murchison whole rock present very similar effects and therefore that an overall clarification is needed for the interpretation of isotopic anomalies in meteorites as reflecting either nucleosynthetic effects or non-mass-dependent fractionation. In the present work, we present experimental evidence of chemical mass-independent isotope fractionation for both Mo and Ru. Since chemical exchange methods using macrocyclic compounds (so-called crown ether) are effective at seeing large mass-independent isotope effects ( Fujii et al. 2002), we employed a solvent extraction technique with a crown ether of dicyclohexano-18-crown-6 (DC18C6). Then the nuclear field shift theory was applied to the actual isotopic anomalies found in Murchison. We show that the elucidation of nuclear field shift effects in meteorites is particularly relevant to the issue of 97Tc and 98 Tc extinct radioactivities.
Dauphas et al. (2002) and Yin et al. (2002) reported molybdenum isotopic anomalies in bulk undifferentiated and differentiated meteorites, which was the first time that isotopic anomalies were found on the scale of a meteorite hand-specimen. More recently, Chen et al. (2003) and Papanastassiou et al. (2004) identified ruthenium isotopic anomalies in meteorites. Dauphas et al. (2004) used theoretical production ratios in stars to show that Mo and Ru isotopic anomalies correlate as predicted by nucleosynthetic models and concluded that such a correlation demonstrates the nucleosynthetic origin of the isotopic anomalies. The predicted correlation, however, fails for one sample, the Murchison CM3 chondrite, and the present manuscript suggests a new mechanism to account for this particular discrepancy. This mechanism solicits non-mass-dependent isotopic fractionation processes, which Bigeleisen (1996a) ascribed to the finite size of the nucleus. The conventional theory (Bigeleisen & Mayer 1947; Urey 1947) holds that mass-dependent fractionation arises as a quantum mechanical effect due to different zero-point vibrational energies for different isotopes (Bigeleisen 1996a). Bigeleisen, however, pointed out that the spatial distribution of protons in the nucleus obeys symmetry requirements and therefore impacts the charge distribution interacting with electronic shells. It is well established that nuclear charge radii do not vary smoothly with the number of neutrons characterizing the different isotopes of a same element (King 1984). The ensuing shift of the nuclear field imparts a mass-independent character to the distribution of minimum vibrational potential curves of the different isotopomers ( Bigeleisen 1996a) and therefore to mass fractionation among coexisting species. A number of experiments mostly involving solvent extraction and liquid chromatography confirmed the
2. EXPERIMENTAL Dicyclohexano-18-crown-6 ( DC18C6, over 97% purity) and 1,2-dichloroethane (over 99.8% purity) are products of Fluka Chemie GmbH. Hydrochloric acid and nitric acid (Merck KGaA) of analytical grade were purified by distillation. 2.1. Molybdenum Molybdenyl dichloride ( MoO2Cl2) of analytical grade was purchased from Sigma-Aldrich and dissolved in HCl to produce 0.1 M Mo( VI ) solutions at various strengths of HCl normalities. The organic phase was 0.1 M DC18C6 in 1,2-dichloroethane. Five ml of aqueous solution and 5 ml of organic solution were
1
Research Reactor Institute, Kyoto University, 2-1010 Asashiro Nishi, Kumatori, Sennan Osaka 590-0494, Japan;
[email protected]. 2 Laboratoire de Sciences de la Terre, UMR 5570 CNRS, Ecole Normale Supe´rieure de Lyon, 46 Allee d’Italie, 69364 Lyon Cedex 7, France.
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ISOTOPE FRACTIONATION OF Mo AND Ru TABLE 1 Configuration of the Faraday Collectors for the Mo Data Acquisition Collectors Mo
L5
Isotope..................
92
IC2
L4
IC1
L3
IC0
94
L2
L1
95
mixed in a glass vial and then sealed and stirred with a magnetic bar for 30 minutes, which is sufficient to achieve extraction equilibrium. The two phases were then separated by centrifugation (2000 rpm, 1 minute). An aliquot of the supernatant aqueous solution was taken for concentration determination. Temperature during the procedures was maintained at 295 0:5 K. The Mo concentrations in the equilibrated aqueous phase were analyzed by quadrupole inductively coupled plasma mass spectrometry ( ICP-MS) using a Thermo Elemental X7 instrument. Molybdenum was subsequently purified from leftover traces of organic materials left by the DC18C6 solution on a 100 l column of anion-exchange resin (AG1-X8, 200Y400 mesh). Molybdenum was fixed on the resin in a 1 M HCl medium, rinsed with the same solution, and then eluted with 2M HNO3. A solution containing 200 ppb Mo in 0.05 M HNO3 was prepared for mass-spectrometric analysis. Isotopic ratios of Mo in all samples were analyzed with the MC-ICP-MS Nu plasma 500 HR coupled with a desolvating nebulizer Nu DSN-100. The 15 Faraday cups were positioned to collect masses 92, 94, 95, 96, 97, 98, and 100 (Table 1). Forty ratios, in two blocks of 20 ratios each, were measured for each sample with an integration time of 10 s per scan. The instrumental mass bias was controlled by bracketing each sample with the unprocessed Mo solution. We checked that potential isobaric interferences with Zr at masses 94 and 96 and with Ru at masses 96, 98, and 100 were below the detection limit of the mass spectrometer. The isotopic ratios are reported as deviations of the measured values in parts per 10,000 (" units) from those of the unprocessed solution. 2.2. Ruthenium Hydrated ruthenium trichloride (over 99.98% purity, SigmaAldrich) was dissolved in HCl to produce 0.07 M Ru(III) solutions at various HCl strengths. One ml aliquots of aqueous solution were mixed with 7 mL organic solution in glass vials. The other details of the extraction procedure follow those described for Mo. Potential traces of organic materials left after equilibration with the DC18C6 solution were eliminated by running the Ru extract on an anion-exchange resin. Ruthenium was fixed on the resin in 2 M HCl media, washed with the same solution, and then collected in 8 M HNO3. Samples and standards are run on the mass spectrometer as a 70 ppb solution in 0.2 M HNO3. The 15 Faraday cups were positioned to collect the masses 96, 97, 98, 99, 100, 101, 102, and 104 (Table 2). The measurement protocol was the same as that used for Mo. We checked that potential interferences with Pd at masses 102 and 104 were below de-
Ax
H1
H2
96
H3
H4
97
H5
98
H6 100
tection limits. Mass 97 was measured to correct possible isobaric interferences with Mo at masses 96, 98, and 100, but the intensity ratio of the 97/104 ion beams remainedT105. Because of the small abundances of 96Ru and 98Ru (5.54% and 1.86%, respectively), these isotopes were not used for discussing the chemical isotope fractionation in our experiments. 3. RESULTS The organic phase/aqueous phase distribution ratios (D) of the extraction experiments are shown in Figure 1. For Mo, the D values increase monotonically with [HCl], whereas for Ru they pass through a maximum. The decrease at strong HCl molarities may be attributable to the formation of the RuCl 4 complex. We define the isotope separation factor as 0
m; m 0
¼
(½ m M =½ m M )org 0
(½ m M=½ m M )aq
;
of light and heavy0 isotopes, rewhere m 0 and m indicate masses 0 spectively. The quantities0 ([ m M ]/[ mM ])org and ([ m M ]/[ mM ])aq are the isotope ratios of m M (M ¼ Mo or Ru) relative to mM found in the organic and aqueous phases, respectively (m ¼ 100 for Mo and 104 for Ru). The isotope enrichment factor " is defined as "m;m 0 ¼ ( m;m 0 1)10;000:
4. DISCUSSION The present results first demonstrate unexpectedly strong mass-dependent fractionation for rather heavy elements. Such effects have previously been observed for Mo in sea water and
Collectors L5
Ru isotope ............ Mo isotope ...........
96
IC2
L4
IC1
L3 98
97
IC0
ð2Þ
The isotope enrichment factors between the organic and the aqueous phases are shown in " units in Figures 2 and 3 and Tables 3 and 4 as a function of mass and HCl molarity. Substantial (>0.2") deviation from the linearity indicates mass-independent isotope fractionation. For Mo, mass-independent fractionation only appears at low HCl molarity, whereas the overall mass-independent fractionation of Ru becomes more prominent at strong HCl molarity. Both the magnitudes of " and the strength of massindependent fractionation are greater for Ru than for Mo. The even atomic mass isotopes show mostly mass-dependent fractionation, whereas the odd atomic mass isotopes show a breakdown of the mass-dependent law.
TABLE 2 Configuration of the Faraday Collectors for the Ru Data Acquisition
Element
ð1Þ
L2 99
L1
Ax 100
H1
H2 101
H3
H4 102
H5
H6 104
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Fig. 1.—Distribution ratios of Mo and Ru as D ¼ ½M org /½M aq in which [M ] stands for the molarity and ½M org ¼ ½M init ½M aq , with init = initial and org = organic phase (DC18C6 in 1,2-dichloroethane, aq = aqueous HCl solution).
natural minerals (Anbar 2004) but have not so far been reported for Ru, an element chemically similar to Fe. In addition, the results show unsuspected non-mass-dependent fractionation for both elements. We contend that these are produced by the nuclear field shift effect (Bigeleisen 1996a). If nuclei could be considered as electric point charges, the curve describing the intermolecular potential between each isotope of a same element and a particular molecule or ligand would be unique. The zero-point energy would largely control mass fractionation between species, and mass fractionation would vary linearly with mass number, or approximately so. In contrast, when the charges in the nucleus are distributed over a finite volume, changes in the nucleus configuration affect the intermolecular potentials, in particular, the zero-point energies, from one isotope to another and therefore give rise to mass-independent isotope fractionation. We now show how such effects can be accounted for by an extension of the standard massdependent theory of the Bigeleisen-Mayer equation ( Bigeleisen & Mayer 1947). Bigeleisen (1996a) shows that the isotope fractionation factor in the presence of the field effect can be expressed as ln ¼
2 hc 1 h 1 1 fs A þ B; kT 24 2kT m0 m
ð3Þ 0
where m 0 and m indicate the masses of the light and heavy isotopes, respectively. The expression fs is the field shift and is proportional to the isotopic difference in nuclear charge radius hr 2i
Fig. 2.—Enrichment factors for molybdenum isotopes.0 The ([ m Mo]/ 0 [100Mo])org ratios were determined from ([ m Mo]/[100Mo])init , ([ m Mo]/[100Mo])aq, and DMo (see Fig. 1 for symbol key). The dotted line shows the mass-dependent line drawn by using the data of the even atomic mass isotopes.
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( King 1984). The quantity T is the temperature; k and h are the Boltzmann and Planck constants, respectively; c is the velocity of light; and A and B are adjustable constants. The field shift effect was introduced to explain the uranium isotopic anomalies found in a liquid chromatography redox experiment. Besides uranium, isotopic anomalies have been found for transition metals, alkaline earth elements, and rare earth elements in their redox reactions and /or ligand exchange reactions (see references in Fujii et al. 2002). The variability of nuclear spins from one isotope to another has also been considered to be an extra cause of massindependent isotope fractionation (Fujii et al. 2001; Knyazev et al. 1999). Yet, Bigeleisen (1996a) concluded that this effect could safely be neglected with respect to the field shift effect, at least in the case of uranium. The hr 2i values are shown for the different isotopes of Mo and Ru in Figure 4. These mass-independent patterns are similar to our experimental results shown in Figures 2 and 3, which suggests that the mass-independent isotope fractionations of Mo and Ru result from the nuclear field shift effect. We fitted the theoretical " values for both Mo and Ru by adjusting parameters A and B to the experimental isotopic variations. The fitting results are shown in Figure 5, and the analytical data are shown in Table 5. These results indicate that the observations are correctly explained by Bigeleisen’s theory of non-mass-dependent fractionation. The tunability of the parameters A and B strongly depends on the precision and accuracy of the measured "-values. However, B is mostly controlled by vibrational isotope effects ( Bigeleisen & Mayer 1947; Urey 1947) and can therefore be estimated with confidence from the reduced partition functions (Bigeleisen & Mayer 1947) of the coexisting isotopomers, i.e., using spectroscopic data and ab initio quantum mechanical calculations. Since our experiments demonstrate the existence of massindependent fractionation, we tried to identify natural systems with similar features, and the most obvious observations to reanalyze in the light of Bigeleisen’s theory are the isotopic data of Mo and Ru in meteorites. The potential systems in which nonmass-dependent fractionation is taking place are essentially the same as those allowing regular mass-dependent effects: coexisting vapor and solid during condensation or vaporization, and coexisting aqueous fluids and minerals during metamorphism on planetary bodies. It is common usage in geochemistry to normalize isotopic variations to a standard value for an isotope ratio. Under a constant temperature, equation (3) can be simplified as ( Fujii et al. 2006)
2
"m; mi0 ¼ 10;000 hr im1 ; mi
0
Fig. 3.—Enrichment factors0 for ruthenium isotopes. The ([ m Ru]/[104Ru])org 0 ratios were determined from ([ m Ru]/[104Ru]) init , ([ m Ru]/[104Ru]) aq , and DRu (see Fig. 1 for symbol key). The dotted lines show the mass-dependent line drawn by using the data of the even atomic mass isotopes. The data on 100Ru were corrected for 100Mo isobaric interferences, and the resulting error is negligible. Similar corrections were applied to masses 96 and 98, but reproducibility on "96/104 and "98/104 was inadequate to demonstrate the presence of mass-independent isotope fractionation. Nuclear field shift effects on Ru were therefore assessed without taking the 96Ru and 98Ru isotopes into account.
m2 ðmi m1 Þ 2 hr im1 ; m2 a; mi ðm2 m1 Þ
ð4Þ
where m1 and m2 are the masses of the isotopes used for normalization (e.g., m1 ¼ 96 and m2 ¼ 98 for Mo, and m1 ¼ 101 and m2 ¼ 99 for Ru) and a is an adjustable parameter. As shown in Figure 4, the mean-square charge radius hr 2i of an odd atomic mass number isotope (with odd number neutrons) is smaller than the value expected from adjacent even atomic mass number isotopes (with even number neutrons). This phenomenon is well known as the odd-even staggering and found for all multiisotopic elements ( King 1984). A correlation of the isotope fractionation " with hr 2i should therefore be taken as indicating a strong nuclear field shift effect. Distinctive isotopic anomalies of Mo have been reported for a number of differentiated and bulk primitive meteorites (Dauphas et al. 2002; Yin et al. 2002). Figure 6 shows these results, which are the largest isotopic variations reported for two carbonaceous
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TABLE 3 Isotope Enrichment Factors of Mo Conc. HCl (M )
Number of Measurements
5.4.......................................... 6.5.......................................... 8.7.......................................... 12.0........................................
5 2a 5 5
"100,94 (104)
"100,92 (104) 3.3 7.0 7.7 15.8
0.7 0.7 0.3 0.5
2.3 4.9 5.7 11.5
"100,95 (104) 0.3 0.5 0.2 0.5
2.4 4.4 4.7 9.7
0.2 0.2 0.2 0.2
"100,96 (104) 1.9 3.3 3.7 7.6
0.3 0.3 0.2 0.1
"100,97 (104) 1.6 2.3 2.8 5.5
0.1 0.2 0.2 0.2
"100,98 (104) 1.1 1.9 1.8 3.8
0.1 0.2 0.2 0.2
Note.—Errors are 2 of uncertainties (see Appendix for the error evaluation). a Because of fewer measurements, the error evaluation of this sample could not be performed. For each " 100, m 0 , the maximum error was selected from other experimental conditions.
chondrites, Allende (CV3) and Murchison (CM2). The 100/98 ratio is much higher for the r nucleosynthetic component (1.6) than for the s-component (0.002) (Arlandini et al. 1999), which justifies the selection of masses 96 (a pure s nuclide) and 98 for normalization. The nuclear field shift theory therefore accounts for isotopic abundances at mass 92 and 95 (in addition to 96 and 98) but still leaves positive anomalies at masses 94 and, particularly, at mass 100. As discussed by Yin et al. (2002) and Dauphas et al. (2002), these anomalies reveal the presence of a p-process component at mass 94 and an r-process component at mass 100, the most abundant r-process Mo isotope. As for mass 97, taking the nuclear field shift effect into account makes the anomaly negative (Figs. 6c and 6d ) instead of positive as previously found (Dauphas et al. 2002; Yin et al. 2002). It has been suggested that the 97Mo anomaly may attest to the presence of live 97Tc (T1/2 ¼ 3:8 Myr) when the last Tc/Mo fractionation took place. Early iron segregation in the iron meteorite parent bodies is already strongly supported by Hf-W evidence ( Horan et al. 1998; Kleine et al. 2004; Quitte´ & Birck 2004), and the short half-life of Tc would make the case for a short differentiation timescale even more compelling. Technetium geochemical properties are, however, poorly known, and the most closely resembling element seems to be Re ( Dauphas et al. 2002; Greenwood & Earnshaw 1984, p. 1600; Yin et al. 2002). Experimental evidence shows a strong dependence of Mo ( Righter et al. 1997) and other siderophile elements’ metal/ silicate partition coefficients (Chabot et al. 2004) on the sulfur content of the system. Likewise, Re abundances in iron meteorites vary by more than 2 orders of magnitude ( Horan et al. 1998; Smoliar et al. 1996), with group IAB-IIICD being fairly poor in Re, which may signal variable S concentrations in the planetary mantle.
We explain in a similar way the Ru isotopic pattern observed in carbonaceous chondrites (Papanastassiou et al. 2004). Figure 6 shows the observed isotopic variations and the calculated values (normalized to m1 ¼ 101 and m2 ¼ 99 for Ru) for both Allende and Murchison. The original choice of odd nuclides (particularly prone to nuclear shift effects) for normalization is unfortunate. The isotopic abundances observed for Allende do not come anywhere near the pattern predicted by the nuclear shift effect ( Figs. 7a and 7c): excesses are conspicuous at masses 96 and 98, and, in particular, at masses 102 and 104, which reveal a strong r-process component. In contrast, the agreement for Murchison with our predicted values is, in general, excellent. A possible exception is an excess of 98Ru, which, especially for Allende, may reveal the presence of live 98Tc (T1/2 ¼ 4:2 Myr). The abundance of 98Ru is, however, very small (1.86%), and,
TABLE 4 Isotope Enrichment Factors of Ru Conc. HCl (M )
Number of Measurements
"104,99 [104]
"104,100a (104)
"104,101 (104)
"104,102 (104)
6.6.................. 7.7.................. 8.2.................. 8.8.................. 9.8..................
3 3 3 3 3
13.8 16.0 13.6 8.5 2.8
12.4 13.9 14.5 8.9 4.3
8.8 9.7 9.4 5.5 2.2
5.9 6.9 6.9 4.0 1.9
Note.—Errors of 2 uncertainties are less than 0.1 " unit (see Appendix for the error evaluation). a Isotopic interference of 100Mo on 100Ru was corrected by the following correlation: I100Ru I100Ru þ100Mo I97Mo I100Mo ¼ : I99Ru I99Ru I99Ru I97Mo
Fig. 4.—Changes in nuclear radii for Mo and Ru isotopes. The hr 2i values were calculated from literature rms charge radii in fermis (1015 m) (Angeli 2004).
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Fig. 5.—Isotope enrichment factors for Mo and Ru in crown ether DC18C6 extraction experiments. For Mo in 5.4 M HCl, the calculated "-values (using eq. [3]) are identical to the experimental results within error. For Ru, the calculated points fit well with the experimental results. The fit can be appreciated by the correlation coefficients (R 2): 0.990 (6.6 M HCl), 0.995 (7.7 M HCl), 0.949 (8.2 M HCl), 0.962 (8.8 M HCl), and 0.800 (9.8 M HCl). A representative result for the 8.8 M HCl system is shown.
at least for Murchison, the error bar renders this anomaly insignificant. In addition, 98Tc is shielded, and, as pointed by Becker & Walker (2003), the fractionation of the Re/Ru ratio (a proxy for Tc/Ru) in carbonaceous chondrites is 500 C) in which mass-dependent fractionation becomes negligible. We therefore suggest that a wealth of information on high-temperature processes is hidden in mass-independent fractionation effects. The interaction of magnetic moments of nuclei with the magnetic moments of electrons (spin-orbit coupling) influences the rate of chemical reactions, but its influence on equilibrium property seems to be rather small (Turro 1983). This kinetic magnetic (nuclear spin) isotope effect is observed as a hyperfine structure of nuclear magnetic resonance (NMR) spectra and has been investigated especially in reactions producing or destroying radicals ( Turro 1983). The nuclear spin effect in equilibrium and kinetic systems is, however, a second-order mass-independent isotope effect, which we intend to explore in more detail in the near future. Even without it, however, the field shift model presented in this work reproduces the observed isotopic anomalies reasonably well. 5. CONCLUSION The existence of mass-independent fractionation of Mo and Ru isotopes has been demonstrated by chemical exchange experiments using DC18C6. These results are explained by the nuclear field shift theory of Bigeleisen (1996a). The correlation between the mean-square charge radius and the isotopic anomalies found in Allende and Murchison were investigated. Although Allende shows a clear indication of nucleosynthetic components, the mass-independent anomalies of Mo and Ru observed in Murchison show a strong correlation with the nuclear charge distribution. We therefore argue that some isotopic anomalies observed in meteorites may be due to nuclear field shift rather than nucleosynthetic processes. This new interpretation may help assess the existence of anomalies due to the extinct isotopes 97 Tc and 98Tc.
TABLE 5 Contributions of Mass Effect and Field Shift to the Isotope Enrichment Factors of Mo and Ru
Isotope Pair
"100, m (104)
fs100, ma (104)
m/mm 0 b (104)
Field Shift Effect (104)
Mass Effect (104)
Field Shift Effect+Mass Effect (104)
2 hc 1 h A ¼ 5:104, B ¼ 1:717 kT 24 2kT
Molybdenum, ½HCl ¼ 5:4 M, 100-92 .............................. 100-94 .............................. 100-95 .............................. 100-96 .............................. 100-97 .............................. 100-98 ..............................
3.3 2.3 2.4 1.9 1.6 1.1
1 0.725 0.649 0.478 0.450 0.287
5.10 3.70 3.31 2.44 2.30 1.46
1 0.733 0.605 0.479 0.355 0.234
1.72 1.26 1.04 0.82 0.61 0.40
3.4 2.4 2.3 1.6 1.7 1.1
Ruthenium, ½HCl ¼ 8:8 M, 104-99 .............................. 104-100 ............................ 104-101 ............................ 104-102 ............................ a b c d
8.5c 8.9c 5.5c 4.0c
1d 0.751d 0.646d 0.379d
2 hc 1 h A ¼ 12:62, B ¼ 22:18 kT 24 2kT 12.62 9.48 8.15 4.79
1 0.792 0.588 0.388
22.18 17.57 13.04 8.61
9.6 8.1 4.9 3.8
Relative value of hr 2i (Angeli 2004) was set as fs for calculation. The unit of fs (wavenumber) is contained in the scaling factor A. Relative value of m/mm 0 . These values are "104, m. These values are fs104, m.
Fig. 6.—Isotopic variations of Mo in the carbonaceous chondrites Allende (CV3) and Murchison (CM2) (Dauphas et al. 2002; Yin et al. 2002). The "92 values are not available in Yin et al. (2002). Panels (a) and (b) show the results after normalization to the reference 96Mo/ 98Mo ratio. Panels (c) and (d ) show the residual anomalies after correction of the nuclear field shift effect. The nuclear field shift theory accounts for the isotopic abundances at masses 92 and 95 (in addition to 96 and 98).
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Fig. 7.—Isotopic variations of Ru in Allende CAI and Murchison (Papanastassiou et al. 2004). Because of the poor fit for the Allende CAI, the fit to the hr 2i values was only constrained by 99Ru, 100Ru, and 101Ru. Panels (a) and (b) show the results after normalization to the reference 99Ru/101Ru ratio. Panels (c) and (d ) show the residual anomalies after correction of the nuclear field shift effect.
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Fig. 8.—Isotopic variations of Mo in carbonaceous chondrites. The values of "92Mo was estimated from reported "100Ru (Papanastassiou et al. 2004) by using Dauphas et al. (2004, Fig. 3)’s model. The "-values for other Mo isotopes were estimated in a similar way (Dauphas et al. 2004, Fig. 1). Panels (a) and (b) show the results after normalization to the reference 96Mo/ 98Mo ratio. Panels (c) and (d ) show the residual anomalies after correction of the nuclear field shift effect. The model works reasonably well for Allende. Some very large misfits for Murchison between predicted and observed values indicate that Mo isotopic anomalies in this meteorite are not of nucleosynthetic origin.
ISOTOPE FRACTIONATION OF Mo AND Ru This work was supported by the scientist exchange program of the Japan Society for the Promotion of Science. The authors thank Chantal Douchet for help in the clean lab and Janne Blichert-Toft for careful English editing. T. F. thanks Takafumi Hirata for his kind
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encouragements toward this collaborative research. F. M. thanks Nicolas Dauphas for his valuable comments on the nucleosynthesis model for Mo and Ru isotopes. The authors thank two anonymous reviewers for very useful suggestions on the manuscript.
APPENDIX ERROR EVALUATION Mass-independent isotope effects are determined as a deviation from the mass-dependent law. We therefore have to accurately assess the deviation with respect to the experimental error. The errors on " are mainly due to mass spectrometry. In the case of replicate measurements, mass-dependent fractionation may vary substantially from one run to another, but the isotopic compositions remain strongly correlated, which calls for a detailed analysis of the correlation structure. The relevant measure of error (or standard error, since it is the mean value that is being assessed) is measured by the conditional variance. For convenience, we discuss the procedure on the population variance, but the sample variances or the standard errors could be handled in a similar way. Let us, for example, consider the error on "1, when "2, : : : , "n are known. For "1, "2, : : : , "n, the covariance matrix, , is 0 B B ¼B B @
12
12
: : : 1n
1
21 .. .
22 .. .
: : : 2n .. .. . .
C C C; C A
n1
n2
:::
ð5Þ
n2
where i2 stands for the variance of "i and ij for the covariance between "i and "j. The matrix can be split into four parts such as 11 12 ; ¼ 21 22 where 11 ¼ 12 ; 12 ¼ ð12 : : : 1n Þ; 0
21
1 21 B . C C ¼B @ .. A; n1
0
22
22 B . ¼B @ .. n2
1 : : : 2n .. C .. C . A: . : : : n2
The conditional variance ˜ 21 of "1 when "2, : : : , "n are known, is ˜ 21 ¼ 12 21 1 22 12 :
ð6Þ
Our listed errors represent twice the standard error determined by this procedure. Taking the correlation structure into account normally reduces the errors by a factor of 3, or even more. If the inverse matrix 221 cannot be calculated (e.g., because of missing data), the covariance matrix is scaled down by reducing the number of "’s used for the calculation. REFERENCES Anbar, A. D. 2004, in Reviews in Mineralogy 55, Geochemistry of NonBigeleisen, J. 1996a, J. Am. Chem. Soc., 118, 3676 Traditional Stable Isotopes, ed. C. M. Johnson, B. L. Beard, & F. Albare`de ———. 1996b, Proc. Natl. Acad. Sci., 93, 9393 ( Washington: Mineral. Soc. America), 429 Bigeleisen, J., & Mayer, M. G. 1947, J. Chem. Phys., 15, 261 Angeli, I. 2004, At. Data Nucl. Data Tables, 87, 185 Chabot, N. L., Campbell, A. J., & Humayun, M. 2004, Lunar Planet. Sci. Arlandini, C., Ka¨peler, F., Wisshak, K., Gallino, R., Lugaro, M., Busso, M., & Conf., 35, 1008 Straniero, O. 1999, ApJ, 525, 886 Chen, J. H., Papanastassiou, D. A., & Wasserburg, G. J. 2003, Lunar Planet. Becker, H., & Walker, R. J. 2003, Chem. Geol., 196, 43 Sci. Conf., 34, 1789
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