Fractionation in the solar nebula, II. Condensation of Th, U, Pu, and Cm

Earth and Planetary Science Letters, 40 (1978) 63-70 © Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

63

[61

FRACTIONATION IN THE SOLAR NEBULA, II. CONDENSATION O F Th, U, Pu AND Cm WILLIAM V. BOYNTON Department o f Planetary Sciences and Lunar and Planetary Laboratory, University o f Arizona, Tucson, AZ 85721 {U.S.A.)

Received September 22, 1977 Revised version received March 16, 1978

Reasonable assumptions concerning activity coefficients allow the calculation of the relative volatility of the actinide elements under conditions expected during the early history of the solar system. Several of the light rare earths have volatilities similar to Pu and Cm and can be used as indicators of the degree of fractionation of these extinct elements. Uranium is considerably more volatile than either Pu or Cm, leading to fractionations of about a factor of 50 and 90 in the Pu/U and Cm/U ratio in the earliest condensates from the solar nebula. Ca,Al-rich inclusions from the Allende meteorite, including the coarse-grained inclusions, have a depletion of U relative to La of about a factor of three, suggesting that these inclusions may have been isolated from the nebular gas before condensation of U was complete. The inclusions, however, can be used to determine solar Pu/U and Cm/U ratios if the rare earth patterns are determined in addition to the other normal measurements.

1. Introduction Understanding the fractionation o f actinides is important for three reasons: (1) In order to study the time dependence o f r-process nucleosynthesis via 244Pu and 247Cm in meteorites or other solar system material, the material must have unfractionated actinide abundances or the degree o f fractionation must be known. (2) Determination o f relative ages via 244Pu-Xe, 244Pu-tracks, or 247Cm-U requires an estimate of the amount o f these nuclides initially present. (3) Fractionation o f the actinides may provide information about chemical processes occurring in the early history o f the solar system. Most workers have generally assumed that U can be used as an indicator for Pu, but recently it has been demonstrated that different minerals will accept different ratios o f Pu and U [1,2]. It is still thought, however, that Pu and U will not fractionate in early condensates from the solar nebula [3], but the theoretical arguments leading to this conclusion were based on the assumption that Pu and U formed ideal solid solutions with host phases. Because U and pre-

sumably Pu are incompatible elements, i.e. they are not readily accepted by most host phases, this assumption is not reasonable. A more general consideration o f the effect o f real solid solution formation will be considered in this work. This treatment will yield different results concerning fractionation. A reliable means o f measuring fractionation o f Pu as well as another extinct actinide, Cm, will also be proposed.

2. Discussion 2.1. Condensation o f actinides The condensation o f trace elements is somewhat more complicated than that o f major elements because of the effects o f non-ideal solid solution formation. The method o f Boynton [4] will be used to simplify these calculations b y considering ratios o f trace elements rather than absolute concentrations. As before, La will be used as the normalizing element. The condensation o f a trace element is governed b y two independent properties: the volatility o f the

64 element in its standard state (here taken as the pure oxide) and the ability o f the element to substitute in the host phase, as described b y an activity coefficient. The treatment will first consider the element to substitute to the same degree as La, i.e. ')'E - - 'YLa, where 7 is the activity coefficient. (Note that this not identical to the assumption o f ideality, which is 3'E = TEa = 1.0.) Later, more realistic activity coefficients will be considered. As in Boynton [4], a relative solid/gas distribution coefficient, D, can be calculated and is an excellent measure o f the relative volatility o f trace elements. The calculation assumes that the trace elements are condensing in solution in an oxide phase. This is quite reasonable for the actinides under most conditions, but in highly reduced environments (e.g. enstatite chondrites), sulfides or phosphides may be appropriate phases to consider. The distribution coefficient relates the ratio of the element to La in the solid to the ratio in the gas by:

(ElLa)solid = DE(ElLa)gas The solid/gas distribution coefficients are calculated from thermodynamic data in Ackermann and Chandrasekharaiah [5] ; all solid and gaseous species were considered. The results are given in Table 1. Where an element exists in more than one valence,

TABLE 1 Relative solid/gas distribution coefficients for actinides and rare earths at 1650 K assuming 3,(+3) = -r(+4) * E

DE(+3 valence)

DE(+4 valence)

DE(total)

Th U Pu Cm La Ce Pr Nd Sm Gd Er Lu

0.014 1.9 2.9 -=1.0 0.46 2.6 0.75 1.3 65 4300 32000

15000 9.5 2.4 0.018 -

15000 9.5 4.3 2.9 1.0 0.48 2.6 0. 75 1.3 65 4300 32000

* Rare earth distribution coefficients from Boynton [4] except Ce adjusted for CeO2 in the gas phase not considered in Boynton [4].

separate distribution coefficients are calculated using the pure oxide o f the same valence as the standard state. The sum will yield the distribution coefficient for the element in all its valence states. The uncertainties in the thermodynamic data are such that these D values are uncertain b y about a factor of two. If all these elements, in either valence state, have similar activity coefficients, then the data imply that Th is far less volatile (more refractory) than any of the other actinides. With this assumption, all but about 0.1% o f condensed U will be in the +4 valence, whereas Pu will be distributed about equally between its two valence states.

2.2. Activity coefficients It was noted [4] that there is considerable evidence from a large number of studies that the different rare earth elements (REE) are quite similar in geochemical properties. The differences that are observed are always smooth functions o f the ionic radii o f the REE. This allows reasonable estimates to be made o f relative activity coefficients for the trivalent REE. If the liquid from which a crystal grows has no preference for one REE over another, then the solid/liquid partition coefficients are inversely proportional to the relative activity coefficients in the solid. Because the chemistry o f trivalent actinides are similar to the REE, it is likely that the activity coefficient o f a trivalent actinide will be similar to that o f a REE o f similar size. In order to consider the condensation o f the actinides in detail, the ratio o f the activity coefficients of the actinides in the two valence states, 7(+4)/7(+3), is required. It is expected that 7(+4) will be larger than 7(+3) because most common host minerals cannot accept tetravelent ions as readily as trivalent ions. For example, Zr and Hf, although having ionic radii nearly identical to the common rock-forming element Mg [6], are incompatible elements; their charge does not allow them to substitute for Mg. The trivalent elements Sc and Cr, on the other hand, are readily incorporated into many host phases [7,8]. An example o f the degree by which a host phase can prefer trivalent over tetravalent ions can be made from the work o f Johnston [9], who measured the concentration ratio o f Ce÷4/Ce÷3 in Na2Si2Os glass as a function o f temperature. The activity ratio o f

65 i

TABLE 2 Activity coefficient ratios derived from concentration ratios [9] in Na2Si205 glass and calculated activity ratios T(K)

Ce+4/Ce + 3 concentration

1273 1358 1473 1573

2.80 2.14 1.70 1.51

7(+4)/7(+3 ) activity

26400 9050 2450 943

9400 4250 1430 620

t

i

50

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tO ito "---

ILl hi nA

20

o = B-32

white

X : calculated I0

5

Q.

E 0 {It

2

ILl

hi n"

ce+a/ce ÷3, calculated from thermodynamic data [ 10], allows the activity coefficient ratio, 7(+4)/7(+3), to be calculated directly. The results at different temperatures are given in Table 2. It can be seen that the ideal solution model is clearly inadequate;the activity coefficients differ by up to a factor of 10 4. Cerium is intermediate in size between U and Pu, and is therefore quite appropriate to use in estimating the ratio of activity coefficients for both U and Pu. The NazSi2Os system is clearly not applicable to nebular condensation. However, the above calculations suggest that the assumption of unit activity coefficients in nebular condensates [3] can yield errors of many orders of magnitude. Because the effect of nonideality can be so large, one should at least be cautious of ideal solution models unless it is demonstrated that ideality is a reasonable assumption.

2.3. Use of nebular condensates to infer activity coefficient ratios A more direct means of inferring the activity coefficient ratios in early nebular condensates is to consider the evidence contained in the condensates themselves. In Fig. 1 is a typical REE abundance pattern (group II [11]) calculated for a nebular condensate. The values are calculated using solid/gas distribution coefficients from Boynton [4] and assuming an increase in activity coefficients of a factor of nine (esentially the inverse of the solid/liquid partition coefficients for perovskite [12]). These relative activity coefficients are used because perovskite has been predicted to be one of the earliest condensates [13] and it can readily accept the REE. The activity coefficients are consistent with the known preference of

I

0.5

LO

I Ce

l Pr

I Nd

REE

l Sm

Ionic

I I EuGd

I Tb

I I DyHo

I I I Er TmYb

I Lu

Radius

Fig. 1. Rare earth elements in a group II aggregate from the AUende meteorite [26]. Calculated values are based on the volatilities of the REE [4] ; Eu and Yb are not calculated because their abundance is determined by a later event that occurred when this inclusion was isolated from the gas. The calculated values agree quite well with observed values, suggesting that the abundance pattern was determined by the volatilities of the REE during a solid/gas fractionation event. The volatility of other refractory elements, relative to the REE, can be estimated from their abundance in group II aggregates.

perovskite for light REE [ 12,14]. The calculated REE pattern in Fig. 1 is not the pattern of the initial condensate; rather, it is the complementary pattern of the gas phase after an earlier, more refractory material formed and was isolated from the gas [4]. The least volatile REE, Lu, is the least abundant; REE of greater volatility are more abundant. Because the abundances of the REE agree quite well with calculated volatilities, the group II aggregates will be used to relate the volatility of Th to those of the REE. Table 1 shows that if all activity coefficients are equal, Th should be slightly more volatile than Lu. The assumed Lu activity coefficient in perovskite, however, lowers the effective Lu solid/gas distribution coefficient to 3600. Therefore, if the activity coefficient of Th were the same as that of La, Th (D = 15000) should be considerably less volatile than

66

TABLE 3 60 40

Relative solid/gas distribution coefficients of actinides at 1650 K assuming 3,(+4)/3,(+3) = 500 E

DE(+3 valence)

DE(+4 valence)

DE(total )

Th U Pu Cm

0.014 1.9 2.9

30 0.019 0.005 -

30 0.033 1.9 2.9

20 10 o

8

6

E 2 I 0.8

Fig. 2. A portion of the REE patterns and Th in group II aggregates from Allende [23]. Thorium is present at the same relative abundance as Gd, suggesting similar volatilities of these two elements. The ideal solid solution model, which does not apply here, would predict Th to be much less volatile than Gd and hence far less abundant than observed. In order for the volatility of Th to equal that of Gd, the activity coefficient ratio 3,(+4)/3,(+3) must equal 500.

Lu and should be even more strongly depeleted than Lu in the group II aggregates. Fig. 2. presents portions o f the REE patterns o f all group II aggregates in which b o t h Th and REE data are available [23]. In every case, Th is depleted, relative to La, to about the same level as Gd, suggesting that Th is more volatile than Lu and that DTh ~ DGd. From Table 1, DGd = 65, b u t since the activity coefficient o f Gd may be larger than that o f La b y about a factor or 2 or 3, the effective DGd is reduced to approximately 30. In order for the effective DTh to equal 30, the activity coefficient ratio 7(Th ÷4)/ "y(La÷a), must equal 500. Admittedly, this number is a highly uncertain estimate o f the activity coefficient ratio, but it is certainly better than the value o f unity assumed b y Ganapathy and Grossman [3].

2.4. Consequence of non-ideal solid solution formation Assuming that the tetravalent actinides are similar to Th ÷4 and the trivalent actinides are similar to La÷3,

the value o f the ratio "),(Th+4)/'y(La +3) = 500 will be used for the more general ratio ~'(+4)/7(+3) (Effects o f differing size are probably small [factor o f two?] relative to the uncertainty o f this ratio.). Using this value, a new set o f preferred solid/gas distribution coefficients are calculated in Table 3. The change in activity coefficient ratio has no effect on Cm which has no significant stability as Cm +4, but the stability o f Pu ÷4 is reduced to insignificant levels. For U, the change makes b o t h valences about equally stable. The important effect is that U was calculated to be slightly less volatile than Pu before considering the effects o f non-ideal solid solution formation, but considerably more volatile after this consideration. Although the ratio 7(+4)/7(+3) = 500 is high uncertain, the volatility o f Pu relative to La is essentially independent o f the ratio, providing the ratio is greater than about five (which is nearly certainly the case, considering arguments in the two previous subsections). This is because the total Pu distribution coefficient is determined b y the sum o f Pu ÷a and Pu ÷4 ; as long as 7(+4)/7(+3) is greater than 5, the amount o f Pu ÷4 is insignificant. * The observed correlation o f light REE and Pu in Angra dos Reis [ 15,16] and the large difference between Pu and either Th or U cllnopyroxene/liquid partition coefficients [2] support the existence o f Pu dominantly in the +3 state even in systems much more oxidizing than the solar nebula. Thus, the D ~ o f 1.9 should be a quite reasonable estimate o f the relative volatility o f Pu. In the case o f U, the relative volatility cannot be considered well-known, because o f its strong depen* Note that this enhanced stability of Pu ÷a is not peculiar to the process of nebular condensation but is a function of oxygen fugacity, temperature and 3"(+4)/3'(+3) for the host mineral. For example, at 1450 K and with lunar oxygen fucacity [171, Pu+a/Pu +4 = 7.0 if 3,(+4)/'/(+3) = 500.

67 dence on 7(+4)/7(+3). This is particularly so when one recognizes that the ratio is a function o f temperature and the presence of different host phases. Fortunately, U is not an extinct element; its concentration can easily be measured in the laboratory, making the uncertainty in these calculations less important.

Grain Size Fine

,IS-] , J I

2. 6. Uranium depletion in high-temperature condensates One means to test this model is to examine U abundances in Ca,Al-rich inclusions in the Allende meteorite. These inclusions are widely held to be samples of early solar system condensates [ 1 8 - 2 0 ] or residues from a partial vaporization event [21,22]. The solid/gas distribution coefficients (Table 3) are calculated at 1650 K, the approximate temperature of perovskite condensation [ 13] and may not be appropriate to the temperature at which the inclusions were isolated from the gas. Distribution coefficients at 1450 K, suggested as an approximate temperature for isolation of the coarse-grained inclusions from the gas [23], are not appreciably different from the 1650 K values. Assuming 7(+4)/7(+3) = 500, the values are D T h = 42, D u = 0.011, D v u = 0.92, and Dcm = 1.6. The tendency is for U to become even more volatile than the other actinides at lower temperatures. Fig. 3 shows histograms of La/U ratios and Th/U ratios (normalized to CI chondrites) from Allende inclusions. In nearly every example, U is depleted

~

~

-

0.6 0.8 1 2 4 Th/U (relative to CI chondrites)

2.5. A ctinide fractionations It thus seems likely that large actinide fractionations are possible during condensation. Although we do not know the required activity coefficient ratios very accurately, it would be most unlikely that the actinides would have identical volatilities. Whether or not these fractionations are ever observed depends on tile temperature at which the sample becomes isolated from the gas. If the sample equilibrates with the gas down to sufficiently low temperatures such that U, the most volatile actinide, has fully condensed, the record of which element condensed first is lost. However, if the sample is removed from the gas at a temperature at which U is only partially condensed, U will be less abundant than either Th, Pu or Cm.

]

Intermediate

r--I Coarse

-<

0.6 0.8 I

2 4 6 8 10 L a / U (relative to CI chondrites]

20

140

Fig. 3. Histogram of La/U and Th/U from Ca, Al-rich inclusions from Allende [24,25,27-30], values for CI nor-

malization from Palme et al. [29], Chen and Tilton [31], and Schmitt et al. [32]. Uranium is clearly depleted relative to La or Th, suggesting that it is sufficiently volatile that it failed to condense fully before the inclusions were isolated from the gas. This U depletion is not predicted from ideal solid solution model calculations [3]. Plutonium and Cm are predicted to be enriched relative to U to the same extent as La.

relative to either La or Th. Except for a few finegrained inclusions with severe La/U fractionations, the La/U data form a quite tight cluster with a mean U depletion o f about a factor of three. Fewer data are available for Th/U ratios, but a depletion o f U relative to Th is indicated here also. (Additional Th/U data [24,25] confirm this, but the data were not plotted to avoid counting any inclusion twice.) The data provide strong support for the theoretical condensation calculations o f this work. The data do not support the conclusions o f Ganapathy and Grossman [3] that U was not fractionated from other refractories in coarse-grained Allende inclusions. They cited their own unpublished data showing no U depletion in support o f their ideal solution calculations; apparently either sampling bias or systematic errors in the analyses is involved in this discrepancy. Even considering only the coarse-grained inclusions in Fig. 3, the U abundance is depleted by a factor o f 2.8 with a log-normal distribution. 2. 7. Use o flight rare earths to measure Pu and Cm fractionations Lugmair and Marti [15] observed that Pu correlated with Nd in mineral separates from the Angra dos Reis meteorite and suggested the use o f Nd as an

68

+4 Actinide

® @ @ ®

+3 Actinide +3 Rare Earth I

104

i

I

I

@ ®

® @ ®®

I

h

I

1.02 1.00 0.98 Ionic Radius (/~]

® I

I

I

0.96

Fig. 4. Ionic radii of REE and actinides [6]; trivalent elements in VI coordination, tetravalent elements in VIII coordination. Both the size and volatility of Pr are such that it is a good indicator of Pu and Cm in gas/solid and igneous fractionations.

indicator of Pu during igneous fractionation. This work offers a thermodynamic basis for their observation. From Table 3, in which realistic activity coefficients are considered, Pu is found to be in the trivalent state and will therefore behave like a trivalent REE of comparable size. If Pu oxides had formed ideal solutions in these minerals, significant amounts of tetravalent Pu would be present and the observed Pu-Nd correlation would not have been expected. The sizes of the actinides and REE (Fig. 4) suggest that for igneous fractionations, Pr or Ce might be a slightly better indicator of Pu than Nd. Either Nd or Sm would be a good indicator of Cm. The light REE have the additional characteristic of being good indicators of Pu and Cm during nebular fractionations as well. Each of the light REE except Ce have solid/ gas distribution coefficients (Tables 1 and 3) within a factor of four of Pu and Cm. Probably the best single element for estimating either Pu or Cm fractionations is Pr, which is nearly identical to Pu and Cm in both its ionic radius and its solid/gas distribution coefficient. Because both nebular (solid/gas) and igneous (solid/ liquid) partitioning can fractionate the actinides, it may not be reliable to use a single element, even one as well-suited as Pr. Because the REE offer a unique means to distinguish between nebular and igneous fractionations, a better means of estimating the extent of fractionation is to determine the complete REE pattern as well as Th and U in a sample of interest. If the REE are fractionated as a smooth function of size with no anomalies except at Eu, then one may conclude that only igneous fractionations are important. The sample can then be assumed to have nearly solar ratios ofPu, Cm and light REE. In cases where the

light REE are highly fractionated by igneous processes, the abundance of Pu and Cm may have to be interpolated between the appropriate REE on the basis of size. The various actinide ratios (e.g. Pu/U), relative to solar ratios, can then be determined from the Th and U abundances in the sample and measured values of solar (chondritic) Th/REE and U/REE ratios. If, however, the REE pattern shows anomalies at elements other than Eu, e.g. Yb or Tm, one may conclude that nebular processes are important and that the solid/gas distribution coefficients should be used to estimate fractionations of light REE from Pu and Cm. Even though the solid/gas distribution coefficients have uncertainties on the order of a factor of two, their fractionation relative to the light REE can often be estimated with greater precision. In cases where the light REE are not significantly fractionated from each other and are enriched to an extent greater than or equal to the other REE, then Pu and Cm will not be significantly fractionated from the light REE. This is because Pu, Cm and the light REE will be nearly totally condensed in the sample; the few percent of the elements remaining behind in the gas phase are of little consequence. (The highly fractionated REE pattern in Fig. 1, as well those in most other Ca, Al-rich inclusions from Allende [12], satisfy these criteria.) In cases where the light REE are depleted and fractionated from each other, as expected for very early condensates [4], Pu and Cm can only be estimated to within a factor of about two with present thermodynamic data.

2.8. Estimation of solar abundance of Pu and On from Allende inclusions Ganapathy and Grossmann [3] proposed an experiment to measure the solar 244pu/238U ratio, in which samples of ten Ca, Al-rich inclusions would be mixed together and analyzed as one sample for U and fissiogenic Xe. Because U may be depleted relative to Pu, this experiment can yield an incorrect result. If, however, the observed 244pu/238U ratio is normalized to the U/light REE ratio (relative to solar), the experiment should yield the solar 244pu/23suratio, provided the full REE pattern satisfies the criteria above. It is preferable not to mix the inclusions before analysis, since analyzing individual inclusions allows

69 the hypothesis of unfractionated light REE/Pu ratios to be tested. The extinct nuclide 247Cm (tl/2 = 1.5 × 107 years) decays to 235U. An enrichment in the Cm/U ratio in a sample should manifest itself as an increase in 23Su/ 23Su ratio. A determination o f the REE pattern, U concentration, and 2asU/2aaU ratio in an inclusion with enriched light REE/U will permit a determination o f the 247Cm/238U ratio at the time o f Cm condensation. Because the daughter product is not a rare gas, this chronometer is not subject to later outgassing events and should preserve a true record o f the 247Cm/238U ratio. The importance o f the 247Cm chronometer has been discussed b y Blake and Schramm [26].

3. Summary and conclusions (1) For incompatible elements such as the actinides, the assumption of ideal solid solution o f pure oxides [3] is shown to be unreasonable during condensation from the solar nebula. (2) It is likely that the activity coefficient o f the actinides in the +4 valence is much larger than in the +3 valence, making Pu ÷3 the most stable Pu species in early nebula condensates. (3) Two extinct actinides, Pu and Cm, are sufficiently similar to the light REE in b o t h volatility and in their ability to substitute in host phases that the extent o f their fractionation can be determined from REE fractionation patterns. (4) Uranium is considerably more volatile than Pu under nebular conditions, suggesting that large Pu/U fractionations are possible during condensation. (5) The mean depletion o f U relative to La o f about a factor o f 2.8 in coarse-grained Ca,M-rich inclusions from Allende suggests the method proposed by Ganapathy and Grossmann [3] is unsuitable for estimating the solar Pu/U ratio. The Pu/U ratio can, however, be estimated from the inclusions if the REE pattern is determined in addition to U and fissiogenic Xe. (6) Large Cm/U fractionations are also expected in the Allende inclusions, suggesting that variations in 235U/238Uratios may be observed, allowing the determination o f the 247Cm/2aaU ratio at the time o f Cm condensation.

Acknowledgements The author is grateful to S.R. Taylor, H. Palme and F. Podosek for permission to cite their unpublished data. Helpful comments from A. Navrotsky and anonymous reviewers are also appreciated. This was was supported in part b y NASA grant NSG-7335.

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