The condensation and fractionation of refractory lithophile elements

ICARUS 40, 446--454 (1979)

The Condensation and Fractionation of Refractory Lithophile Elements J O H N W. L A R I M E R Department of Geology and Center for Meteorite Studies, Arizona State University, Tempe, Arizona 85281 Received March 15, 1979; revised July 20, 1979 It has long been recognized that Cr, Mg, and Si are fractionated in chondritic material along with, but to a m u c h lesser extent than, a large group of more refractory elements. Reasoning that this might imply some unique distribution at the time of fractionation, the patterns have been reexamined. It now appears as if two distinct fractionation patterns can be resolved: one involving ordinary and enstatite chondrites and the other involving c a r b o n a c e o u s chondrites, the Earth, the Moon, and the eucrite parent body. Significantly, the two trends inevitably intersect at C 1 composition. Ordinary and enstatite chondrites appear to have evolved from C I composition via the removal of about 40 and 56% of a high-temperature condensate. A n o t h e r high-temperature condensate, with a distinctly different composition, appears to be enriched in the c a r b o n a c e o u s chondrites, the Moon, and possibly the Earth, but depleted in the eucrite parent body. The compositions of t h e s e two c o m p o n e n t s are constrained to fall on the appropriate mixing lines. T h e s e lines intersect the condensation path at two points, one where Mg2SiO4 h a s j u s t begun to c o n d e n s e ( - 2 0 % ) and a second where Mg2SiO4 was almost completely condensed ( - 9 0 % ) . This represents about an 80° temperature difference. But it is within this range that the largest fraction of planetary matter (Mg, Si, and Fe) condenses. Conceivably the relatively sudden appearance of large a m o u n t s of c o n d e n s e d material is in s o m e way related to the fractionation process, although the exact relationship cannot be specified.

1. I N T R O D U C T I O N

E v e r since the difference in Mg/Si ratios a m o n g chondrites was first noted (Urey, 1961) it has been regarded as a key to understanding genetic relationships. Each chondrite class has its own characteristic and narrow range of ratios which decrease in the order: c a r b o n a c e o u s > ordinary > enstatite. In retrospect, this variation in Mg/Si ratio must also be regarded as the first clear sign of a major fractionation event in the solar nebula. At first the observation lacked an interpretative f r a m e w o r k , which was only built up o v e r the next l0 years by careful petrographic and analytical work. In 1969, Ahrens et al. presented evidence that several other elements (A1, Ca, and Ti) were similarly fractionated. The list of such elements was expanded considerably by L a r i m e r and Anders (1970) who further pointed out that all the elements involved would be among the first to condense from a cooling solar gas. The signifi-

cance of these observations b e c a m e even m o r e apparent after the arrival of the AIlende meteorite and lunar rocks with their uniquely high concentrations of these same refractory elements. It now appears as if each b o d y in the solar system, for which sufficient chemical data exist, possesses a characteristic amount of refractory elements. An intuitively appealing argument can be made that the variations in refractory element content are the result of different admixtures of a c o m p o n e n t resembling the C a - A I inclusions found in AIlende (e.g., G a n a p a t h y and Anders, 1974; W a n k e et al., 1974a). These inclusions are highly enriched in refractory elements and consist of an aggregate of minerals predicted to be the initial condensates in the nebula (Grossman, 1972, 1973). But while the inclusions are enriched in most of the fractionated elements there are also some notable exceptions. The two elements Mg and Si, the first recognized to be fractionated, are depleted rather than en446

0019-1035/79/120446-09502.00/0 Copyright© 1979by AcademicPress, Inc. All rights of reproduction in any form reserved.

REFRACTORY LITHOPHILE ELEMENTS riched. In the first attempt to infer the composition and mineralogy of the fractionated component, before the Allende inclusions had been studied, Larimer and Anders (1970) concluded that it must contain appreciable olivine (MgzSiO4). This inference still seems valid and worth pursuing because it may provide some additional insights into the fractionation process. 2. A B U N D A N C E DATA

2.1. Chondrite Abundances

The fractionation patterns observed in chondritic meteorites provide a useful starting point. The data in Table I represent only a partial list of all the elements now known to fall into the general pattern; a complete list would include Ba, Nb, Ta, Th, etc. plus the remaining 11 rare earth elements (REE). The factors in the first two columns were obtained by first normalizing the concentration of each element in the three classes of meteorites (C1, ordinary, and enstatite) to Si and then dividing the ordinary and enstatite values by the C1 value. The virtually TABLE I REFRACTORY ELEMENT FRACTIONATION IN CHONDRITES; ABUNDANCES RELATIVE TO C1 CHONDRITES Element

Ordinary chondrites

Enstatite chondrites

AI Ca Hf La Sc Sr Ti U Y Yb Zr

0.76 0.76 0.50 0.80 0.72 0.62 0.74 0.68 0.75 0.81 0.58

0.58 0.58 0.43 0.43 0.63 0.48 0.55 0.50 0.44 0.48 0.47

Cr Mg

0.85 0.90

0.77 0.74

Allende inclusions" 21 17 23 26 24 15 21 13 21 22 23 0.16 0.68

" W/inke et al. (1974b); the sources of the chondrite data can be found in Larimer and Anders (1970), updated for Al, Ca, Mg, and Ti (Ahrens et al., 1969).

447

constant factors obtained (except for Mg and Cr) indicate that the fractionated material, the component that was gained or lost to produce this pattern, contained all the elements in nearly cosmic proportions. The factors in the last column are obtained by simply dividing the m e a s u r e d concentration of the element in the inclusions by the concentration in C 1 chondrites. The constant enrichment factor of about 20 (excepting Mg and Cr) is significant, as has often been emphasized, because the predicted amount of the initial condensate in the nebula represents about 5% by mass o f the total condensate. On the other hand, it is now widely recognized that there are real variations in composition among the inclusions. We will return to this point later. The exceptions to the general pattern, Mg and Cr, differ in two ways. Compared to the remaining elements, they are fractionated to a lesser extent in chondrites (columns 2 and 3, Table I) and depleted rather than enriched in the Allende inclusions (column 3). Actually, a third element, Si, should also be included along with Mg and Cr. This would be apparent had we chosen to normalize to some o t h e r e l e m e n t , Mg, for e x a m p l e . These three elements thus display a pattern that is similar to the others, but much less extreme. Such behavior is suggestive of partial fractionation and may imply that these elements were somehow distributed differently at the time of fractionation. Turning now to the carbonaceous chondrites a somewhat different pattern is apparent (Table II). For element pairs, where both are quite refractory (Ca/A1, Ti/AI), the proportions in all carbonaceous chondrites are essentially constant. The same is true for the three elements Cr, Mg, and Si. H o w e v e r , the proportions of the latter three elements relative to any one o f the more refractory elements (e.g., A1) vary in a systematic manner. The fractionation pattern is in the direction of increasing AI (and all the more refractory elements), or decreasing Cr, Mg, and Si, in the order C1 > C2, C3(0) > C3(V). The most probable expla-

448

JOHN

W. L A R I M E R

T A B L E II REFRACTORY ELEMENT ERACTIONATION IN CARBONACEOUS CHONDR1TESa Element ratios

C1

CII

CO

CV

Ca/AI Ti/AI

0.75 0.033

0.73 0.032

0.75 0.033

0.73 0.030

Mg/Si Cr/Si

1.06 0.0128

1.06 0.0133

1.07 0.0130

1.05 0.0134

Mg/AI Si/AI Cr/AI

12.47 11.76 0.150

11.33 10.69 0.142

11.66 10.89 0.142

9.6 9.1 0.122

~' Data were obtained from Wiik (Mason, 1962), A h r e n s et al. (1969), which were assigned double weight after correction for Mg ( x 1.06), and Schmitt et al. (1972).

ble III). The uncertainties involved obviously are quite large. Rather than belabor this point it seems more worthwhile to establish the fractionation patterns from the chondrite data and simply explore the implications of the apparent compositions of these bodies. One salient feature in the rocks from the Earth, the Moon, and the EPB is that the most refractory elements (Ba, La, Th, U, etc.) always occur in nearly the same proportions. Evidently neither nebular not planetary processing has effected appreciable fractionation of these elements. This well-established pattern has obvious implications. 3. F R A C T I O N A T I O N P A T T E R N S

nation, first noted by Van Schmus and Hayes (1974), is a systematic enrichment of the refractory elements evidenced by the more numerous Ca-A1 inclusions in C3(V) chondrites.

2.2. Planetary Abundances Some further clues on the fractionation event can be obtained from estimates of the bulk composition of other bodies in the solar system. Two approaches for estimating bulk compositions have been developed recently. In one, sometimes referred to as the "cosmochemical" approach, the concentrations of a few elements coupled with several key ratios are used to estimate the proportions of various components in the body (e.g., see Ganapathy and Anders, 1974; W~inke et al., 1974a). In these models the refractory elements are assumed to be concentrated in one component and the Mg-silicates in another. Since part of this study is to evaluate this assumption, these models will temporarily be tabled. In the second, the "geochemical" approach, the bulk composition is estimated from elemental abundances, elemental ratios, and petrologic and geophysical data. The method has been applied to the Earth, the Moon, and the eucrite parent body (Ta-

The data from chondritic material and the Moon can be used to summarize the overall pattern (Fig. 1). Here, I have chosen to normalize the data to AI, rather than the conventional Si. Past attempts to disentangle the fractionation pattern have been frustrated because every important lithophile element appears to have been involved. The problems with using Si for normalization have already become apparent in the preceding discussion. Aluminum seems to be a TABLE II| ELEMENTAL ABUNDANCES IN THE EARTH, THE MOON, AND THE EUCRITE PARENT BODY (EPB) Element A1 (%) Ca (%) Cr (ppm) L a (ppm) Mg (%) Sc (ppm) Si (%) Ti (ppm) U (ppm)

Earth" 1.10 ± 0.8 1.2 ± 0.8 ? 0.3 ± 0.31 15.8 7.6 ± 3 14.7 640 ± 400 12 ± 6

Moon ~

EPB"

4.3 4.3 1330 (6650) 1.1 18.7 20 20.6 1800 60

1.35 1.32 ? 0.35 16.9 6 19.31 570 20

" Larimer (1971) except for Mg and Si which are from Green and Ringwood (1963), pyrolite III. o Taylor and Jakes (1974). c Consolmagno and Drake (1977) plus the a s s u m p tion that e l e m e n t / A l = cosmic for Sc, Ti, and U.

REFRACTORY LITHOPHILE ELEMENTS 10i

i

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+

449

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i

C3V C30CI 0

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i

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Mg

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10-4

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~o

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SILICON/ALUMINUM

FIG. 1. Most refractory lithophile elements are present in the s a m e proportions (horizontal lines) in a variety of planetary materials. Three notable exceptions are Cr, Mg, and Si; the extent of fractionation o f the first two is indicated by the marked deviation from horizontal lines while the variations in Si/AI ratio can be read along the abscissa.

much better choice. It is the most refractory of the m o d e r a t e l y abundant elements ( G r o s s m a n and L a t i m e r , 1974) and since all refractory elements a p p e a r to behave coherently, the fractionation o f A1 can be used to tag that o f all the others. M o r e o v e r , its relatively large a b u n d a n c e enhances analytical accuracy. Relative to A1, all of the most refractory elements (Ca, Sc, La, etc.) are unfractionated in planetary material, as evidenced by the horizontal lines ( = constant ratios) in Fig. 1. In m a r k e d contrast, Mg and Cr clearly are fractionated relative to Al in the various groups of chondrites, the Moon, and the Allende inclusions. The data are plotted against the Si/AI ratio merely to generate a large spread. H a d we chosen to plot the data against Mg/A1 ratios, the spread would not be as great and a Si/A1 line, with virtually the same orientation, would a p p e a r at the top of the diagram in

place of the M g / A I line. All other features would remain unchanged.

3.1. AI, Mg, Si Fractionation To further elucidate the relationships among these three elements, the data are presented in a s o m e w h a t unconventional m a n n e r in Fig. 2. On such element (or isotopic) ratio diagrams, straight lines can be considered " m i x i n g lines." When a series of points defines a straight line, each point can plausibly be assumed to represent a mixture of two c o m p o n e n t s falling at the end of the lines. In some cases, this being a probable example, a straight line might evolve via the removal of a c o m p o n e n t falling on an extension of the mixing line. By treating the data in this m a n n e r two distinct fractionation trends are resolved. One is defined by the ordinary and enstatite chondrites and a second by the carbona-

450 2~

JOHN W. LARIMER I

I

Il

I

/

I FRACTIONATION]

I

to the Allende inclusions. [The lunar value is somewhat uncertain. Taylor and Jakes (1974) obtained their Cr value from the well-defined C r / V ratio and assuming V was not refractory, which it evidently is (W~inke et al., 1974b). Accordingly, I have taken the liberty of increasing the estimated Cr content by a factor of 5 (the upper limit in Table III, and on Fig. 3).]

/

2(

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1-= S._j

Cl COSMIC /\//Z~ EucrdePro.Body

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4. D I S C U S S I O N

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V~ 0,i ~ :-'iMgA[~2(Sp)

~AIIeade 5

10

Mg/A[

15

20

25

FIG. 2. Two distinctly different fractionation trends are revealed on element ratio diagrams. The two trends intersect at CI compositions. One trend is defined by the ordinary and enstatite chondrite data, the other by the eucrite parent body (EPB), C2, CO, and CV chondrites, the Moon, and possibly the Earth (not plotted, but with large uncertainties it falls near the C 0 - C 2 points). The two trends intersect the condensation path at two different points during the condensation of Mg2SiO4. Most Ca-A1 inclusions have compositions that fall above the C 1 - C 2 - C O - C V fractionation trend (see inset), implying that the fractionated component must contain appreciable Mg2SiO4 ( - 2 0 % of the total Mg2SiOD in addition to all the more refractory elements.

ceous (CO, CII, and CV) chondrites, the Moon, the eucrite parent body, and perhaps the Allende inclusions. The two trends intercept at the C 1, or cosmic, composition point. This pattern was not anticipated but it obviously is satisfying.

Now that the two fractionation trends have been disentangled it becomes possible to consider the fractionation processes themselves in a more quantitative framework. There are several key areas that can be approached with considerable confidence: (1) The composition o f the fractionated components can be constrained which in turn permits some constraints to be placed on the (2) extent of fractionation and (3) the conditions under which it took place. 0.25- -

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~E

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Mg-cr 0,20_

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/ Ordnor, 0.10-

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005/ALtende

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3.2. Al, Cr, Mg Fractionation On a similar diagram for Cr/AI vs Mg/A1 (Fig. 3) a nearly identical pattern, including two distinctly resolved fractionation trends, is apparent. Neither trend is as well defined, owing to less numerous and somewhat more uncertain data. Carbonaceous chondrites (other than C1) tend to fall above a line drawn through C 1 and the origin. This may suggest that the mixing line passes through a component with a Cr/A1 ratio considerably above the low value common

5

10

Mg/At

15

20

25

FIG. 3. On an element ratio plot similar to Fig. 2 but substituting Cr for Si, a nearly identical pattern is resolved. Evidently the fractionation behavior of Cr is closely linked to that of Mg and Si, suggesting that most of the Cr is associated with MgzSiO4. The C 1 C 2 - C O - C V trend appears to fall distinctly above the line passing through C1 composition and the origin. This indicates that the Cr/AI ratios in the hightemperature component were larger than observed in Ca-A1 inclusions.

REFRACTORY LITHOPHILE ELEMENTS

4.1. Condensation Sequence The patterns are most readily explained in terms of a nebular process involving the fractionation of dust, perhaps via settling or accretion, relative to the coexisting gas. The predicted composition of the dust that would be in equilibrium with a solar gas has been superimposed on Fig. 2. For the elements of interest here, the condensation sequence is: A1 (as A1203), Ti, Ca and Si (as CaTiO.~ and Ca,,AlzSiOT), Mg (as MgA1204 and CaMgSi206), and finally the bulk of the Mg and Si (in a 2 : 1 ratio as Mg.,SiO4 and in a 1 : l ratio as MgSiO3). In the absence of any fractionation, the initial gas o f solar (or C1) composition would yield dust with the same composition. The temperature range is pressure dependent; for definitiveness let us assume Pt = 10-4 atm. At this pressure A120.~ begins to condense at about 1660°K, CaMgSi206 appears at about 1370°K, MgzSiO4 at 1355°K, and MgSiO.~ at 1275°K. Condensation of AI, Mg, and Si is complete at about 1150°K. Note that the length of the lines on Fig. 2 has no relationship to the temperature interval. The initial condensate (A1203) appears at 1660° and CaMgSi.206 at 1370 °, nearly a 300 ° drop. But the Mg2SiO4 line, representing the condensation of a large amount of material, begins at 1355°K and ends at 1275°K, only an 80° drop. Evidently it is within this 80° drop, as Mg2SiO4 condenses, where the fractionation takes place. Unfortunately, the condensation of Cr is not well understood. Grossman and Olsen (1974), noting that some metal grains from C2 chondrites contain appreciable Cr, suggested that a significant quantity o f Cr might condense as metal. H o w e v e r , Kelly and Larimer (1977), noting that Cr tends to behave like a fractionated lithophile element, which is apparent in the data presented here, suggested that Cr may be stable at high temperatures as an oxide or silicate. Large enrichments of Cr in olivines from carbonaceous chondrites have now been

451

found to support this latter suggestion (Larimer, unpublished data).

4.2. Compositional Relations The fact that the fractionation trends intersect at C I composition adds further justification to its use as the starting composition. Another equally important inference to be drawn from the data is that the two fractionations each involved a second component which contained the elements in definite and fixed proportions. These inferences are further supported by statistical analysis of the data, where a least-squares regression indicates two well-defined correlation lines which pass within lo- of C1 composition (Kerridge, 1979). Evidently the second component in each case contained all the most refractory lithophile elements in their solar proportions plus specific amounts of Mg, Si, and Cr. Thus if the only condensate in the nebula once consisted of an inhomogeneous mixture of interstellar dust, with elemental as well as isotopic anomalies, and CaAl-rich objects with the spectrum of compositions observed, this material must have been efficiently blended to produce two uniquely fixed compositions. A suitable model is one in which the fractionations occur at some specific P - T condition, where all the elements which had condensed were fractionated relative to those which remained in the gas. Perhaps the process involved nothing more than condensed dust settling to the midplane of the nebula, which would leave some regions depleted and others enriched in refractory elements (Larimer and Anders, 1970). Other, more contrived mechanisms can certainly be imagined but each must satisfy the compositional constraints .of very specific compositions. In order to satisfy these constraints the two fractionated components must fall somewhere along the two mixing lines. Let us begin with the ordinary-enstatite line first. In principle, the composition of both groups of chondrites could be produced by

452

JOHN W. LARIMER

either adding to or subtracting from material with C 1 composition. H o w e v e r , if material were to be added it would have to possess Mg/A1 and Si/A1 ratios greater than those o b s e r v e d in estatite chondrites. N o such material is known nor is there any plausible m e c h a n i s m to produce such material. On the other hand, the initial condensation products in the solar nebula would have low element A1 ratios because AI is a m o n g the first elements to condense. A suitable composition is the one defined by the intersection of the condensation path with the fractionation trend (Fig. 2). An early attempt to infer the composition of the fractionated material involved finding the appropriate amounts of Mg2SiO4, AI2Oz, CaO, etc. required to bring the ordinary chondrite element/Si ratios up to the C I values ( L a r i m e r and Anders, 1970). This estimate involved calculating the small difference between two large numbers. G r o s s m a n (1972) noted that the composition c o m p u t e d in this way would n e v e r be matched in any equilibrium condensation sequence. This discrepancy has now been resolved, simply by treating the data differently. A suitable composition for the fractionated c o m p o n e n t required to account for the second trend, that involving the C-chondrites, Moon, and EPB, would app e a r to be the C a - A I inclusions from A1lende. H o w e v e r , before hastily accepting this seemingly satisfactory proposition an important piece of data must be evaluated. F r o m Table II, it is clear that the Mg/Si ratio in all c a r b o n a c e o u s chondrites is virtually the same, 1.06 +__ 0.03. If this ratio is to be kept constant then the c o m p o n e n t added to or subtracted from C1 material must have the same Mg/Si ratio, i.e., 1.06 _ 0.03. The initial condensates in the nebula are predicted to have M g / S i ratios > 1, a prediction borne out by the o b s e r v e d composition o f a large n u m b e r of Ca-A1 inclusions (e.g., see McSween, 1977, and the inset in Fig. 2). The appropriate Mg/Si ratio (> 1) is only obtained after a modest amount

(<20%) of the Mg2SiO4 has condensed. Evidently the fractionation event occurred near the beginning of the t e m p e r a t u r e interval where MgzSiO4 condenses, while in the case of the ordinary and enstatite chondrites it occurred after a large fraction of Mg2SiO4 had condensed.

4.3. Extent of Fractionation The amount of material gained or lost during the fractionation event can easily be c o m p u t e d if the composition of the two c o m p o n e n t s and that of the final product are known. Consider the case of the ordinary and enstatite chondrites. L e t ct = fraction of material lost. A series of equations may then be written: A1cl - orAl Hwc = A1°~d'L'),

(1)

Mg cl - otMg HTc = Mg °rd(E),

(2)

etc., where the superscripts C1, H T C , and Ord(E) indicate the molar concentration of each element in C1 chondrites, the hight e m p e r a t u r e component, and ordinary (or enstatite) chondrites. Assuming all the Al is condensed at the time o f fractionation (A1c~ = A1HTC), Eq. (1) can be divided by Eq. (2) and solved for a: MgCl - (Mg/A1)ora(E). AI cl a = Mg.T c _ (Mg/A1)O~d(e) " Ale1. (3) The results are: a = 0.42 (A1, Ca, Ti, etc.), aMg = 0.36, and asi = 0.24 for ordinary chondrites and a = 0.56 (A1, etc.), aMg = 0.48, and asi = 0.32 for enstatite chondrites. This represents a significant quantity of material, nearly half of the initial condensate. An obvious implication is that the fractionation process, w h a t e v e r its nature, was extraordinarily efficient. Another potentially important inference is that since half the AI was lost, including any live 26A1, this might explain why the ordinary and enstatite chondrite parent bodies did not completely melt.

REFRACTORY LITHOPHILE ELEMENTS 4.4. Fractionation Conditions

The fact that Mg2SiO4 was involved in both fractionations, but only partially, constrains the conditions at the time of fractionation to the temperature interval over which olivine condensed. This may suggest some causal relationship. Since MgzSiO4 is a major condensate, involving the two most abundant condensable elements, its condensation would greatly enhance the dust content of the nebula. At the same time the heat of reaction is quite large (125 kcal/mol) and would have to be dissipated before the nebula could continue cooling. This may have prolonged the time spent in this temperature interval which in turn may have allowed accretion to produce larger particles that could be segregated gravitationally. Finally, in the most plausible pressure range for the nebula, metallic Fe begins to condense during the condensation of Mg2SiO4 (e.g., see Grossman, 1972). The appearance of appreciable quantities (Cameron and Pine, 1973) of metal could have added to the dust concentration a n d /o r influenced the cooling rate. At present all of these possibilities are intriguing but highly speculative. In any case, several of the most important chemical and physical processes in the nebula apparently took place within a rather narrow temperature range. 5. C O N C L U D I N G R E M A R K S

While there remain many key unanswered questions surrounding the mechanism of this high-temperature fractionation process, it is clear that the nebula not only passed through a high-temperature stage but that it left its imprint on a variety of planetary materials. The fact that two fractionation trends can be resolved is both perplexing and satisfying. It tends to set the ordinary and enstatite chondrites apart from all other samples of planetary matter. The significance of this is not yet clear. Conversely, the second fractionation trend which involves a broader spectrum of mate-

453

rials indirectly provides further support for continuing to apply the "cosmochemical" approach to estimating planetary compositions. Most planetary material evidently contains a component very similar in composition to the Ca-A1 inclusions, plus a little bit of Mg2SiO4. Kerridge (1979) has concluded, from a similar study of these and other elements, that the patterns observed indicate that equilibrium could not have obtained at the time of fractionations. The argument is that the metallic FeNi should condense at about the same temperature as Mg2SiO4 and should therefore be fractionated along the refractory lithophile elements. While the argument is persuasive, several points should be kept in mind before accepting the conclusion. First, there are uncertainties in both the thermodynamic and cosmic abundance data, which taken together lead to uncertainties of up to 30° or so in the predicted condensation temperatures (Grossman and Latimer, 1974). Since we are concerned here with the 80° interval in which Mg2SiO4 is predicted to condense, there is clearly some uncertainty as to whether FeNi will condense simultaneously with Mg2SiO4, or would only begin condensing toward the end of the interval. Second, in most carbonaceous and unequilibrated ordinary chondrites large olivine masses (sometimes chondrules, but not always) usually contain little metallic FiNi. Whether or not this implies different condensation temperatures is not clear; but it does indicate that the silicates and metal usually were physically separate. Other than this difference in interpretation the conclusions reached by Kerridge are essentially the same as those reached here, the most important of these being that planetary material passed through a hightemperature shape while still dispersed as dust in the early solar system. ACKNOWLEDGMENTS This work was supported in part by N A S A Grant NSG-7040. The paper was written while the author

454

J O H N W. L A R I M E R

was a visiting professor at the California Institute of Technology, and the support of that institution is gratefully acknowledged. REFERENCES

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