Chemical fractionations in meteorites—I. Condensation of the elements

Geochimicn

et Cosmochimicn

Acta, 1967,

Vol. 31,pp.

1215 t? 1238. Pergamon

Press Ltd.

Printed

in Northern

Ireland

Chemical fractionations in meteorites-I. Condensation of the elements Enrico

(Received

Fermi

Institute

9 January

JOHN W. LARIMER for Nuclear Studies University Chicago, Illinois GO637

1967;

accepted

in revised

form

of Chicago,

3 April

1967)

Abstract-The condensation history of a cooling gas of cosmic composition is outlined. Two condensation sequences are derived: one for fast cooling, with the formation of pure elements and compounds and another one for slow cooling, with the formation of solid solutions. These sequences bear a striking resemblance to the depletion patterns observed in ordinary chondrites. The element,s Pb, Bi, In and Tl, which are most strongly depleted are among the last ones to condense, with condensation temperatures <5OO”K at a total pressure of 6.6 x 10m3 atm. A somewhat less strongly depleted group (Zn, Cd, Ag, and probably Te and Se) condense near 68O”K, also the temperature at which FeS forms according to the reaction Fe + H,S = FeS + H,. Finally, elements showing only moderate depletion (Sn, Ga, Ge, Au, and Cu) condense between 700°K and 1000°K. Manganese and the lighter alkalis (Na, K, and Rb), elements depleted in carbonaceous but not in ordinary chondrites, lie still higher in t,he sequence, between 1100” and 1300°K. It is proposed that the fractionation patterns observed in chondrites arose in the solar nebula during condensation and accretion. Subsequent heating in a meteorite parent body does not appear t,o have cffectcd any further fractionations, with the possible exception of the most volatile trace element,s, t,he noble gases and Hg.

THE SEPARATION of condensed planetary matter from its cosmic complement of volatiles was the most important cosmochemical fractionation process in the early solar system (SUESS, 1965). Meteorites and the inner planets are apparently deficient in volatiles while the outer planets appear to have retained a larger percentage of the more volatile constituents. UREY (1952a, 1952b, 1954) has examined this process in some detail, attempting to determine the temperature at which the gas-solid separation took place. Although the most volatile elements (H, C, N and 0) were clearly deficient in meteorites and the earth, the next most volatile group (Hg, Cd, As and Zn) did not seem markedly depleted. UREY pointed out that fractionations by volatility tended to be very sharp, usually resulting in complete retention or complete loss of the element in question. The retention of substantial amounts of Hg, Cd, As and Zn therefore suggested that the earth and meteorites accreted at low temperatures, less than 300°K. This conclusion was reached by UREY on the basis of the meteorite abundance data available at that time (GOLDSCHMIDT, 1937 ; NODDACK and NODDACK, 1934). With the advent of neutron activation analysis it became clear, however, that many trace elements thought to be undepleted were, in fact, fractionated. The tist major 1215 1

1210

JOENW.

LARIMER

fractionation was discovered by REED et al. (1959) who found that Pb, Bi and Tl were grossly under-abundant in ordinary chondrites, but were present in their predicted cosmic abundance in carbonaceous and enstatite chondrites. Other elements, including Hg, Cd and Zn, were soon discovered to be similarly fractionated. It now appears that nearly one-third of the elements are depleted in most chondrite classesrelative to either Type I carbonaceous chondrites, solar, or cosmic abundances (Fig. 1). Elements

q Fig. 1. “KormaJ relative to Type

“Normal”

depletion

depletion” I carbonaceous 0.001

depleted

in meteorrles

I ‘/’ a”

“Excess”

depletion

corresponds to a depletion by chondrites; “excess depletion”, (LARIMER and ANDEHS, 1967).

factors of to factors

0.5-0-I of O.l-

At first the excess depletion was linked to the chalcophile character of the elements involved (FISH, GOLES and ANDERS, 1960; UREY, 1966). However, as the list expanded to include siderophile, lithophile, and atmophile elements, it became obvious that the only property shared by all the depleted elements was volatility. ANDERS (1964, 1965) proposed a model based on the theory of WOOD (1963) in which he attempted to explain the fractionation in terms of two types of material: an undepleted fraction which separated from its cosmic complement of gas at low temperatures and a depleted fraction which separated at high temperatures. This model was able to account for the carbonaceous chondrites where all the fractionated trace elements appear to be depleted by a constant factor, and which also seem to consist of a mixture of high- and low-temperature minerals. However, it was difficult to extend the model to ordinary chondrites where the depletion factors for fractionated elements were variable. He was forced to propose an ad hoc hypothesis for the excess depletion of Cd, Hg and I; and called the even greater depletion of Pb, Bi, In and Tl, which were not thought to be outstandingly volatile, a “mystery”. To determine whether the fractionation occurred during the initial separation of gasesand solids in the solar nebula or during a subsequent heating event, a quantitative study of the condensation process is required. The basic approach to the problem will be similar to that of UnEY (1952a, 1952b, 1954) but updated with respect to meteoritic abundance data and models of the solar nebula.

Chemical

fractionations

in meteorites-I.

Condensations

of the elements

1217

CONDENSATION OF THE ELEMENTS Because of the large number of elements to be considered, I have attempted to treat the problem at successively higher levels of complexity. First, the condensation of individual elements from pure hydrogen is considered, neglecting the effect of other constituents in the cosmic gas. Possible density variations within the solar nebula are then discussed. Finally, a more complex situation is considered, in which the effect of compound and alloy formation is taken into account. Pure element For this part of the discussion each gaseous species will be assumed to be an ideal gas. By definition, in such a gas mixture the partial pressure of gaseous species E, p(E), is equal to the atomic fraction, N(E), times the total pressure.

P(E) = NV-W,

(1)

For simplicity, we may treat all elements heavier than hydrogen as monatomic in the vapor state. Then the atomic fraction of element E is simply the number of atoms. n(E), divided by the sum of all atomic and molecular gaseous species. i=k fl(E)

=

n(E)/izHnni

(2)

If the gas is of cosmic composition, the number of atoms of a particular element may be set equal to the cosmic abundance of the element: n(H,) = l/M(H), n(He) = A(He), n(Li) = A(Li), etc. Hydrogen would be by far the most abundant species and thus an approximate atomic fraction is given by N(E) N 2A(E)/A(H)

(3)

combining equations (1) and (3) we obtain P(E) = 2NWWV’,

(4)

This expression defines the partial pressure of a monatomic element in a cosmic gas. If the element exists largely in a diatomic form, the partial pressure is only half as great as given by equation (4). CAMERON'S (1963b) cosmic abundance data were used in the calculations, except for the following : 1. The mass region 105-127 and 2. The Zn-Kr region, where new data on Type I carbonaceous chondrites are available (AKAIWA, 1966; GREENLAND: 1965; REED and ALLEN, 1966). Vapor pressure curves for a number of depleted and undepleted elements are presented in Fig. 2. These data apply only to a pressure of 1 atm, but can be used over a wide range of pressures with little error.* Now it is possible to predict the temperatures of condensation. The partial pressure is calculated from the abundance data and equation (4) above. In the * The effect of variations in total pressure on the position of the curves can be shown to be trivial. The equation of interest is (d log PJdP, = B/RT, where 1’ is the molar volume of the solid or liquid (10-20 cm3) and R = 82 cm3 atm/‘K. At a low temperature (273°K). a maximum increase in log PE of -0.1% per atm is predict,ed.

JOHN W. LARIMER

1218

cosmic gas, an element will begin to condense when its vapor pressure equals its partial pressure calculated from equation (4). Table 1 lists the elements according to their predicted condensation temperatures. Significantly the strongly depleted elements such as In, Pb, Bi, Tl, Zn, Cd and Hg are found at the bottom of the table. Thus, even a highly simplified approach to the problem has given a significant, correlation between volatility and depletion. Temperature 400

500

25

20

600

;“K) 730

SOC

15 (I/T1 I IO4 1-K)

Fig. 2. Vapor pressures of depleted elements, plus Fe, Changes in slope due to phase transitions are masked

9,30

IO00

‘5438’

IO

Ni and V (BREWER, on a diagram of this

2:::

5

1946). scale.

The condensation temperatures given in Table 1 would be valid if the elements did not react to form compounds or alloys. This possibility may appear remote in view of the complexity of the chemical system being considered. However, the formation of compounds and alloys will be dependent, at least in part, on the kinetics of reaction and the rate of diffusion. Thus, in a rapidly cooling system, alloy and compound formation may be hindered by incomplete equilibration. This factor would be particularly critical for those elements condensing at low temperatures. A more quantitative discussion of diffusion rates will be presented in the section on alloy formation. Pressure effects Two models of the solar nebula were discussed by CAMERON (1962) corresponding to convective and radiative equilibrium, with total masses of 4 M, and 2 &I@ respectively. The following values indicate the predicted range of pressures. The differences in total pressure will affect the partial pressure of the elements, and therefore, the condensation temperatures. It should be noted that the pressure is

Chemical

fractionations

in meteorite,s-I.

Condensations

of the elements

Planet

Orbital Radius (a.u.)

4M,

2M,

Mercury Earth Asteroids

0.387 1.000 2.8

0.9 0.1 1 x IO-2

-17 -0.6 6.6 x 1O-3

Table

1. Condensation

PT = 1 atm Element Fe V Ni CU

SC

Mn Ge Au Ga Sn 4 In Pb Bi Sb2 Tl ye2 2% 82 se2 Cd Hg I2

*

Pressure

temperatures

1219

(atm)

of the pure elements P, = 6.6 x 1O-3 atm

Tcmp 1790 1760 1690 1260 1250 1195 1150 1100 1015 940 880 765 655 620 590 540 517 503 489 416 356 196 185

“K

Element Fe V Ni SC CU Ge

Au Mn Ga Sn 4 In Pb Bi Sb2

Tl

Te, Zn 82 Se2 Cd Hg I*

* Elements in italics form compounds which their respective condensation temperatures.

Temp

“K

1620 1500 1440 1090 1045 980 970 920 880 806 780 670 570 530 515 475 460 430 400 375 318 181 169 significantly

alter

independent of temperature (CAMERON, 1962). In a later paper, CAMERON (1963s) presented an alternative formula for the pressure distribution in the nebula, which allows for the existence of a central condensation. Here the pressure is a function of the initial density of the interstellar cloud. With reasonable values for the density ( 103-lo4 atom/cm3) pressures of 10-4-10-2 atm are obtained for the center of the asteroid belt. I have therefore used 6.6 x 1O-3 atm as a representative figure. In general, the relative position of the elements should be independent of pressure, except for elements whose vapor pressure curves cross.

JOEN 11'.

19*7(-JIti

CONDENSATION

hRIJfER

0~ COMPOUNDS

Method of calculation Determining the condensation temperature of compounds is basically the same problem encountered in the case of the elements, i.c. finding the temperature at which the partial pressure of the compound in the atmosphere equals its vapor However, there is an additional complication in that it becomes necessary pressure. to determine the distribution of a particular element between various possible gaseous species. For example, Si will be distributed among such gaseous compounds as SiO, SiS, SiH,, Si,. and SiO,. LORD (1965) has discussed certain aspects of the distribution problem and the method may be briefly summarized. Consider the reaction X(g) + Y(g) = XY(g)

(5)

for which we may obtain an equilibrium constant *? K:,,, the ratio of the activities, ai, of the products to those of the reactants. Since we will be dealing with pressures in the range 1 > pi > 0 we can safely assume that ai N pi for all constituents in the gas phase. Thus, the equilibrium consta,nt is reduced to a ra#tio of partial pressures Ii, The equilibrium equation

= p(XY)/p(X)

* p(Y)

(6)

constants are calculated from the well known thermodynamic AG”

=

-RT

In K,

(7)

where AG” is t,he standard free energy change for the reaction. From this equation, we note that AG” and also Ii, is a function of temperature only. Therefore changes in total pressure at consta,nt temperature will affect the rat,io of partial pressure in such a manner that K, remains constant. The ,&ate of a system at equilibrium is physically determined by fixing the massesof the components and any two intensive properties such as temperature and pressure. We set up a series of simultaneous equations of two types: 1. Those expressing the state of equilibrium, such as equation (6) above and 2. Those expressing conservation of mass. An example of the second type for the case of Si may be set up as : n(Si) = ?L(SiO) -t n(SiS) f n(SiHJ + n,(SiO,) -I- ,n(Si,) + n(Si) (8) In an exact treatment, all conceivable species must be included. At equilibrium the number of independent equilibria (equations of the first type) equals the number of gaseous species minus the number of components. The unknowns are the masses of the various gaseous species which when calculated can be used to obtain the partial pressure of each species Pi = n&P, (9) However, a rigorous solution to this problem is not required in the present study because we are only concerned with the major species of each element. Instead, we * The sources of data used in calculating the equilibrium constant,s arc given in the appendix. Also, the magnitudes of t,he uncert.ainties are discussed there.

Chemical

fractionations

in meteorites-I.

Condensations

of the elements

1221

approach the problem by using a method of successive approximations, and obtain values which are accurate to within a few per cent of the actual partial pressures. This in turn leads to a vanishingly small error in condensation temperature. It turns out that for almost all elements, there are relatively few gaseous species whose abundance is greater than 1% of the total elemental abundance. We begin by considering the most abundant species. Thus for the reaction 2H = H, the equilibrium

(10)

constant is calculated at 2000°K K, = p(H2)/p2(H2) = 10s‘6

(11)

Bt lower temperatures, the value of K, is found to be even larger, and therefore our earlier assumption that H, is by far the most abundant hydrogen species has been justified. Proceeding to the next most abundant elements, 0 and C, we assume that H,O and CO are the major 0 containing species. This assumption is checked when the abundances of the other species are calculated. For example, LORD (1965) has shown that p(Si0) N 3% of the p(H,O) and must also be considered in the distribution of 0. Returning now to the determination of condensation temperatures, consider the two reactions (178) X(g) + Y(g) = XYlg) AG’,O X(g) + Y(g) = XY(s)

(1%)

AG,’

The activity of the solid phase, XY(s), may be set equal to unity under the condition that it is in its standard state, a pure compound. Then the vapor pressure, p’(XY), of compound XY may be found at any temperature according to log prST = -(AG,”

- AG,“)/2.303

RT

(13)

The condensation temperature of XY is the temperature at which the pressure of XY from equation (12a) equals the vapor pressure calculated from equation (13). The solution may be obtained by plotting the curves on a p(X)-T diagram and determining the point of intersection, or the equations may be solved for T. A problem frequently encountered is that data from which to calculate free energies of the vapor phase (equations of the type 12a) are not available. WOOD (1963) has discussed an alternative means of deriving condensation temperatures for cases such as these. Consider the reaction 2Mg(g) + SiO(g) + 3H,O(g) = Mg,SiO,(s)

+ 3H,(g)

(lia)

Here we note that the product, Mg,SiO,, occurs as a solid phase. We can thus set its activity equal to unity and write the equilibrium constant Jk = p3(H2)/p2(Mg)p(SiO)p3(H,0) Now recalling that from our previous assumptions I)~ N [n,/n(H2)]PT write equation (14b) as K, N n6(H2)/n2(Mg)n(SiO)n3(H20)P3T

(14b) we may re(15)

JOHN W. LARIMER

1222

Thus, equation 15 may be plotted on a P,-T diagram and the condensation temperature readily established at any P,. It is difficult to predict how the condensation of one compond quantitatively affects that of another. The temperatures calculated by the above methods merely determine the point of initial condensate. As the temperature drops, the composition of the gas phase will be continually changing as material is removed. Coupled to this problem are the relative stabilities of the various compounds at lower temperatures. If a reaction path is available a reaction may occur which releases one element back into the gas phase while others are being condensed. Throughout the calculations each compound has been treated as if it were independent of all others. For example, in the case of Mg, Al and Si each compound is considered to condense from a gas of cosmic composition. However, for In a more detailed treatment is presented. We are now ready to determine the condensation temperatures of the various types of compounds.

Suljides Let us begin by assuming that essentially all of the sulfur is present as H,S. The cosmic sulfur to hydrogen ratio (6 x 105/1.6 x lOlo; CAMERON, 1963) corresponds to an H,S/H, ratio of lo- 4 43. This factor will be somewhat smaller at high temperatures (> 1300°K) due to the presence of other stable gaseous compounds. LORD (1965) has shown that at 2000°K the amount of H,S will be lowered by a factor of ~2 ; however, over the temperature range in which sulfide compounds condense or form (500-1500°K) the change is much smaller and can safely be ignored. Because of the large number of elements to be considered, it would be extremely useful if we could quickly determine which ones are likely to condense as sulfides. Obviously, for an element to condense as a sulfide, the sulfide must be stable relative to the pure element in a gas of cosmic composition. Such a test can be made by constructing a diagram such as Fig. 3. Here we are considering only the relative stabilities of solid or liquid metal relative to solid or liquid sulfide. Therefore, with the exception of the cosmic H&/H, ratio, cosmic abundances do not enter into the construction of this diagram. As was noted previously, AG” is a function of temperature only; therefore on this diagram the relationship AG” vs. T is plotted for reactions such as M(s) + S,(g) = MS(s) AC,” (16) making sure that the equations are always balanced so as to include one mole of Sz. Now, if both solid or liquid metal and metal sulfide are in their standard states [a(M) = a(MS) = l]* the vertical axis is also a plot of the right side of the equation AC,’ = This

assumption

greatly

(17)

simplified the construction of the diagram. As was noted by if AG” is calculated from heat capacity data, the resulting curve may be represented by a straight line between phase changes in the metal or sulfides. Although this may seem fortuitous, the explanation is straightforward. With temperature change, variations in AS” and AH” caused by changes in the heat capacity of the reactants and products affect AG” in a compensatory manner.

RICHARDSON and

also

2.303RT log ps,

JEFFES (1948),

Chemical

fraction&ions

Plotting the H&/H, reaction

in meteorites-I.

Condensations

addition

1223

ratios is merely a graphic means of adding equation (16) to the 2H,S = 2H, + S,

After

of the elements

of equation (16) 0

,

,

,

and (18) ,

II

AG,“

the H,S/H, I1

,I

1,

/

(18)

ratio may be considered a L , ,’

(

I&-

G”

=: .ii! .H B

-3-

-* oc

IO

8 I” 10-t

3; I”

. \ IOi

IO”,

400

600

800

1000 Temperoture

1200

1400

1600

lSO(

“K

Fig. 3. Free energy of formation of metal sulfides. All equations are balanced to include 1 mol of S,. The sulfurization potential in an atmosphere of known H,S/H, ratio can be obtained by drawing a straight line between the ratio on the right hand axis and the point marked H on the left. The cosmic H&l/H, ratio is shown as a dotted line. In a cosmic gas, formation of sulfides becomes possible below this line.

driving force for reaction (16). rearranging equation ( 18).

2.303RT

The position of the ratio plots may be derived by

log ps, = AG,’ + 2.303RT

log (pH$)2/p2(H2)

(19)

Note that the resulting plot has the same dimensions as equation (18). Figure 3 is interpreted in the following manner. At all temperatures to the right of a particular reaction line, the element does not form a sulfur compound, but exists in its stable elemental form: gas, liquid, or solid. If just the cosmic H,S/H,

1224

JOHN VI'. LARIMER

ratio is considered, the point of intersection of the H,S/H, line with a reaction line is the temperature at which the sulfur compound of the element becomes stable in an atmosphere of cosmic composition. Other ratios are given on the right-hand ordinate. Three elements, Cd, Zn and Mn, are unique in that they form stable sulfides at high temperatures, much higher than the condensation temperatures of the pure elements. Of the other elements, In is a borderline case, sulfide forming at ~700°K and metal condensing at 750-650°K, while the remaining elements would condense as metals. Therefore, for Cd, Zn and Mn it is more realistic to consider condensation of sulfides rather than metals (see Table 2). The behavior of In is actually more complex than Fig. 3 indicates. The compound In,S has been found to be a stable gaseous species in a hydrogen-rich atmosphere (MILLER, 1963). Thus, in contrast to the Cd, Zn and Mn sulfide systems in which compound formation raises the condensation temperatures, compound formation in the In-S system lowers the condensation temperature. From the data of MILLER (1963) the equilibrium constant for the reactions : In(g) + H,S = I@(g)

+ H,

(4

and In&(g)

= InS(s) + In(g)

(b)

can be calculated as a function of temperature. An apparent condensation temperature of In (292-247’K) may then be determined in the manner described above. But sulfur will condense primarily as FeS startling at 6SO”K. Below this temperature the sulfur potential in the atmosphere will be controlled by the 2Fe + S, = 2FeS reaction. The removal of sulfur from the atmosphere will thus decrease the H&!/H, ratio below the cosmic value. This will tend to drive reaction (a) to the left, resulting in a higher condensation temperature for In(400-360’K). Unfortunately, for several depleted elements thermodyamic data are unknown or incomplete. These include Se, Te and I, whose actual condensation temperatures will be somewhat higher than those of the pure elements. Oxides In Fig. 4 a number of metal-oxide reactions have been plotted as a function of AG” vs. T. The cosmic H,O/H, ratio of 1O-2’74is shown as a dotted line. Again, Zn and Mn form stable oxides well above the predicted condensation temperature of the respective elements. However, Cd0 and all the remaining trace element oxides do not become stable until the temperature has dropped well below the condensation point of the element (Hg, Ag, Au, Bi, Cu, Sn, Ge, Ga, In, Pb and Tl were tested). We will reserve discussion of the remaining lines on Fig. 4, and the problem of whether Zn and Mn condense as oxides or sulfides until after the effects of silicon have been considered. Silicates At high temperatures (> 1500”K), most of the Si will be present as SiO in an atmosphere of cosmic composition. LORD (1965) has shown that SiS is also present in fairly large amounts. The abundance of SiS is large enough to lower the partial pressure of Si by a factor of two below the value based on SiO alone. [p(SiO) =

Chemical

Table

fraction&ions

in meteorites-I.

2. Condensnt.ion

temperatures

P, = 1 atm [‘ompound

or element

MgAl,O 4 CaTiO, AI,SiO, Ca$iO, CaAl,Si,O, CaSiO, Fe CaMgSi,Os KAlSi,O, Ni MgSiO, EGO, Mg,SiO, SaAlSi,O, lMnSi03 NasSiO, K,SiO, Ml-& CU Ge Au Ga Sn Zn,SiO, & ZnS FeS Pb CdS Bi PbCl, Tl In Fe304 H,O Hg

Condensations

of compounds

of the elements

and elements

P, = 6.6 x 10B3 atm T( “K) 2050 2010 1920 1900 1900 1860 1790 1770 1720 1690 1670* 1650 1620* 1550 1410 1350 1320 1300 1260 1150 1100 1015 940 930 880 790 680 655 625 620 570 540 400 400 260 196

Compound

or rlrment

CaTiO, W+%O, Al,SiO, C’aAl,Si,Os Fe Ca,SiOp CaSiO, CaMgSi,O, KAISi,O, MgSiO, SiO, Ni Mg,SiO, XaAlSi,O, MnSiO, MnS Sa,SiO, K&i0 3 cu Ge Au Ga Zn$iO, Sn 4 ZnS Fe8 Pb C’CIS PbCI, Bi Tl Fe304 In HZ.0 Hg

T(“K) 1740 1680 1650 1620 1620 1600 1680 1560 1470 1470 1450 1440 1420 1320 1240 1160 1160 1120 1090 970 920 880 820 806 788 730 680 570 570 536 530 475 400 360 210 181

* The condensation temperatures for MgSiO, and Mg,SiO, will vary depending on which set of data is used. There is an apparent error in the calculat.ed free energy values for MgSiO,, which, in effect, decreases its stabilit,y (LNXIMER, 1966). If the data from the JAXAF Tables are used, the condensation temperatures of Mg,SiO, and MgSiO, are reversed. Data from KELLEY (1960) are more consistent with experimental data and therefore were used in the present calculations.

1226

1226

JOHN

W.

LARIINER

20JH2

R&J-

-

,’

,MnO’

A-”

, /’

.Y _-’ ,,’ -200

’ 400

’

1 600

’

800

1000

Temperature

1200

1400

,600

OK

Fig. 4. Free energy of formation of metal oxides. All equations are balanced to include one mol of 0,. The oxidation potential in an atmosphere of known H,O/H, ratio can be obtained by drawing a straight line between the ratio on the right hand asis and the point marked H on the left. The cosmic H,O/H, ratio is shown as a dott.ed Iine. In a cosmic gas, formation of oxides is possible only below this line. Curves for ordinary and enst,atite ohondrites are shown for an Fe+2 of 15-30 mole % and -cl mole ‘4 respectively (LARIMER, 1966). Material of this composition is in equilibrium wit.h the cosmic H,O/H, ratio at 800 and 1300°K. The curve for enstatite chondrites is only an upper limit; the lower limit would be the Si + Oc = SiO, curve.

BA(Si)/A(H)]. Th’is effect has been neglected here ; if it were included the predicted condensation temperatures would be lowered by ~10-20°K. The condensation temperatures for the silicates are given in Table 3. Calciumand magnesium-rich pyroxenes and olivines would be the first silicates to condense, followed by SiO, ; provided, of course that the Si/Mg atomic ratio* is greater than unity. Subsequently, MnSiO, will condense, followed by Na,SiO, and K,SiO,, and at considerably lower temperatures, Zn,SiO,. Condensation temperatures for FeSiO, and Fe,SiO, may also be calculated. However, both of these compounds would condense at temperatures below the condensation point of pure Fe. Therefore, the equations depicting formation of iron * The Si/Mg ratio is close to unity in both the sun and meteorites. is based on carbonaceous chondrites in which Si/Mg -0.95; however, vary among the subclasses of chondrites. The solar ratio appears MILLER and ALLER (1960)].

CAMERON'S (1963) this to be

ratio -1.3

is known

value to

[GOLDBERG,

Chemical

silicates

fraction&ions

must involve 2Fe(s)

Condensations

solid iron ( < 1825’K)

+ 2MgSiOJs)

2Fe(s)

in meteorites-I.

+ SiO,(s)

of the

elements

1227

and should be written:

+ 2H,O(g)

= Fe,SiO,(s)

+ Mg,SiO,(s)

+ 2H,O(g)

= Fe,SiO,(s)

+ 2H,

+ 2H,

Because both olivine and pyroxene form Mg-Fe solid solutions, these reactions take place over a considerable temperature range. The reactions would begin with the formation of Mg,SiO, or MgSiO,, at which time the Fe2+ content would be quite small (~0.1 mol %). If the reaction kept pace with the cooling rate and sufficient amounts of the reactants were available, all the Fe would be converted to Fe,SiO, at 550°K (see Fig. 4). For Mn and Zn, silicate condensation precedes element, oxide or sulfide condensation. Prior to assuming that these elements would condense as silicates, we must check the relative stabilities of the silicates and sulfides in an atmosphere of cosmic composition. We therefore compute equilibrium constants over the temperature range of interest for reactions such as: H,S + MSiO, = MS + SiO, + H,O First, we assume that the activities of the solids are unity, and substituting the cosmic H,O/H,S ratio ( 10-1’68) we determine the direction in which the reaction will proceed. For the assumption that the activities are unity, it turns out that the metal sulfides are stable relative to the silicates. However, the atomic fraction of Mn and Zn m1O-2 and 1O-3 that of Fe or Mg, the dominant sulfide or silicate cations. The condensation point of MgSiO, is much higher than that of FeS, and therefore Mn and Zn would tend to form solid solutions in the silicates at high temperatures. Mn should be almost exclusively contained in the silicates, although, as discussed below, some may occur in solid solution as an Mn-Fe alloy. The point at which Zn,SiO, begins to condense (900-800’K) is not much higher than the threshold for condensation of ZnS (790’K) or formation of FeS (630°K). In an unequilibrated, rapidly cooling system both Zn and Mn could conceivably form sulfides. Of the alkali silicates, data are available on only the K and Na compounds. Condensation temperatures for these are given in Table 2. It is difficult to predict the amount of Si which will be available to these elements. The Mg silicates condense at higher temperatures than do the alkalis, and because the Mg/Si ratio is approximately unity, very little Si should be available. However, the cosmic ratios of Na/Si (= 10-1’3s) and K/Si ( = 10-“‘53) are small, and plagioclase compounds (NaAlSi,O,) could form. It is also possible that Na and K would enter solution as pyroxene molecules (Na,SiO,) with the previously condensed MgSiO,. Condensation temperatures for both types of molecules are given in Table 2.* * STILES et al. (1964) havo reported experiments in which K, Rb and Cs were vaporized from meteoritic material. The maximum loss of Cs occurred at -llSO”K, Rb at -1225°K and K at 1225°K and 1325°K. It is difficult to relate these vaporization data to condensation temperatures in the nebula. However, for K, where a comparison is possible, condensation temperatures of 1450”-1100°K are predicted here which agree fairly well with the values obtained by SMALES et 01.

1228

JOHN W. LARIMER

Chlorides FeS will become stable in the cooling gas at 680°K. Below this temperature exposed iron surfaces will be coated with sulfur which will effectively remove an abundant nucleation site for siderophile* elements remaining in the gas phase. Elements which are only partly condensed, or have yet to begin condensation include Pb, Bi, In and Tl. Therefore, for these elements it is worthwhile to consider the possibility of compound formation with other relatively abundant elements. A study of these elements in the presence of H and Cl in the cosmic ratio indicates that Pb will react to form PbCl,f at 610°K which will then condense at 570-525°K. The other three elements do not form stable chlorides until the temperature drops well below that predicted for t4heir condensation (see Table 2). ALLOY

FORMATION

For those elements which remain siderophile at temperatures higher than their condensation temperatures the possibility of alloy formation with metallic iron must be considered. In such an alloy, the trace element would comprise an atomic fraction of only 10-3-10-7. At such small concentrations, the solute may be considered to obey Henry’s Law and the actual vapor pressure of a trace element, p’(E), may be calcula.ted according to p’(E) = kiVp”(E) (20) where N is the mol fraction and p”(E) is the vapor pressure of the pure element. If some fraction, cc, of a trace element of cosmic abundance A, dissolves in a major phase of cosmic abundance M the mole fraction equals aA(E)/M. The vapor pressure over the trace element in solution is: (31)

P’(E) = ~[~~E)/~IP”(E) The gas phase now contains only a fraction, partial pressure is reduced to

1 - cc, of the trace element and its (22)

p’(E) = 1 - a[2A(E)/A(H)]P,

The temperature at which p’(E) from equation (21) and (22) are equal may again be found by determining the point of intersection on a diagram such as Fig. 2. Unfortunately values for k are not available for any of the systems we are considering. I have therefore set k = 1 assuming, in effect, that the solution is ideal. We shall return to this point later on. Let us set a = 0.10, corresponding to significant but not complete condensation. The vapor pressure curves as drawn in Fig. 2 will then be displaced downward by 4-S orders of magnitude according to equation (21) [A(E)/M = 10-3-10-7]. Predicted temperatures at which 0.10 of each element will have condensed are given in Table 3. In general, the elements retain their positions, but the condensation temperatures are higher. Moveover, the transition from complete volatilization to complete condensation is no longer sharp, but occurs over a temperature range of several hundred degrees. * As used here, siderophile will mean the tendency substrate in favor of sulfide, silicate or oxide surface. t PbCl, is also stable relative to FeCI, below 670°K.

of a metal

to condense

on a metallic

Chemical

fraction&ions

in meteorites-;-I.

Condensations

of the elements

1229

Now we must consider the effect of our assumption that the solution is ideal with E = 1. Some qualitative trends can be predicted from thermodynamic principles and experimentally determined phase diagrams. Systems tending toward immiscibility will have k > 1, while those tending toward compound formation will have k < 1. From binary phase diagrams (HANSEN, 1958; ELLIOTT, 1965) we find that Au ancl Cu are only slightly soluble in Fe at low temperatures, and Ag, Bi, Cd, Hg, Pb Table

3. Temperat,ures P,

Elrment,*

Ad?l Cl1 SC

Gc Ga Snt Au 4s In

=

for 10% condensation solution with iron

1 atm

P,

Temp. 2220 2010 1870 1850 1680 1640 1550 1275 1110

“K

of elements

= 6.6 x 1W3 atm

Element CL1 w Ge &In Ga Au Sn 4z In

PD

985

Pb

Bi Z?l

865 820 775 527 290

Bi Tl Zn

Tl Cd Hg

in solid

Cd

Hg

Temp.

“K

1770 1540 1460 1430 1315 1310 1170 1070 945 805 722 650 640 440 241

* Elements in italics may form compounds other than metallic alloys. t Iron condenses at 1790” and 1620”K, at P, = 1 atm and 6.6 x 10m3 atm, respectively, and may therefore incorporate a significant amount (> 10 ‘A) of those elements which lie above Sn and Sc, respectively.

and Tl are nearly insoluble. Hence, for these elements k should be greater than unity, which implies that their condensation temperatures would be lower than those given in Table 3. For the last six elements, it would seem that k would be quite large so that their true condensation temperatures may lie close to the value for the pure element. Conversely, Ga, Ge and Zn form intermetallic compounds with Fe, so that k < 1. Thus, their condensation temperatures are apt to be higher than those given in Table 3. Other important qualifications must be attached to the temperatures given in Table 3. Strickly speaking they are upper limits, valid only for the case where M is equal to the cosmic abundance of iron. In reality, M will always be lower for the following reasons. First, not all the iron will be present 89’ metal, and M would be reduced accordingly. A second, and more important reason is that equilibration throughout the metal phase will not necessarily be complete as has been assumed in the above discussion. If an iron particle exposed to a cosmic gas cooled quite rapidly, only the outer surface may have approached equilibrium. Diffusion throughout the

JOHN W. LARIMER

1230

particle would not occur on a short time scale, and with the interior of the grain not participating in the equilibration M would be reduced drastically. Qualitatively, the effects of limited diffusion should be most pronounced for the elements at the bottom of the condensation sequence. To assessthe magnitude of this effect, one must know the cooling rate, as well as grain size and diffusion coefficients. It would be of interest then to estimate the cooling rate of the solar nebula. Table

Diffusing

metal

Ag Au Bi Ga Ge Ni Pb Sn

4. Activation

energy

Activation (kcal/gm

for

energy atm) *

Fusion

of trace

A&iv&ion energy (cm*/sec) *

1 x 10-l

50

55 40 55 2 Got 60 40 45

1 x 10-s 1 1 x 10-l

-1

1 x lo-‘? >: 10-l

1 3 7 10-Z

elements

into

iron

Temperature

range

(“W 500-1000

500-l 300 500-1000 soo-1500 1000-1500 1000-1500 500-l 000 500-l 200

in italics have been estimated, the remainder are calculated from JOST(1952). t Based on the fact that Ge is distribut,ed in a manner similar to Xi in t,he taenite and kamacite phases at the Butler iron meteorite (GOLDSTEIN,19GG). * Values

An approximate formula for the radiative cooling of the nebula after its collapse has been given by CAMERON (1962). The cooling process may have been retarded by solar heating if the protosun had already reached its high-luminosity, fully convective stage (HAYASHI, 1961; EZER and CAMERON; 1965). If this effect is neglected, the nebula would cool from a high initial temperature to a temperature T in t yr: t = 1.4’7 x lo4 us/T3

(23)

where crsis the surface density at the base of the nebular disk (2-3 x lo5 gin/cm3 at 2.8 a.u., CAMERON, 1962). Thus a temperature of 1OOO”I~is reached in a few years and 200°K in a few centuries. The diffusion distance of the various elements into iron grains can be determined from the known activation energies or diffusion coefficients of the various elements into iron. Diffusion data were obtained or were estimated on the basis of diffusion theory (JOST, 1952; NACHTRIEB, 1966); and are given in Table 4. The diffusion distance, 2, is estimated from z2 = 2Dt where D is the diffusion coefficient and t the time. This equation applies to isothermal diffusion, but cau be adapted to diffusion at falling temperatures. For this purpose, the actual time spent in the interval T, - T, is replaced by an equivalent time t,, at T, (ARMSTRONG, 1958):

teq =

R( ToI ~

SQ

(24)

Here, R is the gas constant, T, is the temperature at which cooling commences, Q is the activation energy, and S is the cooling rate (dT/dt) obtained by differentiating equation 23. ARMSTRONG'Sequation was specifically derived for a linear cooling rate ; therefore, the equation was integrated numerically at 100’ intervals and the curves smoothed. This leads to a l-5% error in the activation energy curves drawn on Fig. 5.

Chemical

frectionations

in meteorite-I.

Condensations

of the elements

1231

In Fig. 5, condensation efficiency is shown as a function of grain size. For simplicity, let us consider all grains as spherical, of radius r. At 1300”K, lOOo/o of the Ni and 25% of the Ge will have condensed on the initial iron grains, provided the grains are no larger than r = 10e2 cm. Larger grains would equilibrate only to a

Diffusion in

Iron

Cooling

1200

of

Trace

Groins of Cosmic

Element Ge 0.15

During

-

Gas

-

IIOOComplete 1000

Diffusion

-

Diffusion

Distance

(cm)

Fig. 5. Diffusional distance of trace elements in iron as a function of temperature. The cooling rate is that predicted for radiative cooling of the solar nebula (equation 23). The numbers indicate the fraction aondensed at each temperature under equilibrium conditions; the abscissa then gives the marimum grain radius for which equilibration is possible. If the actual grain radius were larger, only the surface region of the grains would equilibrate, and the fraction condensed would be smaller than the equilibrium value. All remaining elements will presumably be bracketed by the two curves for activation energies (Q) of 60 and 40 Kcal/mole.

depth of 10-z cm and would hence contain smaller amounts of Ni and Ge. For Sn, the situation is more favorable in spite of its higher volatility. At 1300°K only 1% of the Sn will condense, but the grains may be as large as O-3 cm before equilibrium breaks down. The elements Pb and Bi represent an interesting case. Owing to their high volatility, the temperature must drop to 800°K before l/10 of the Pb or l/100 of the Bi can condense. At these low temperatures diffusion is sluggish and only grains of r I 10m2 2

1232

JOHN W. LARIMER

However, as indicated above, these elements are almost cm could equilibrate. completely insoluble in Fe. Thus, if the value of k for these elements was close to lo3 rather than 1, which is perhaps more reasonable in view of the extreme tendency toward immiscibility (HUSEN, 1958), the temperature would be close to 600°K. In this case, diffusion would be even further restricted; only grains of r ~2 10F4 cm could be equilibrated. In the above discussion on alloy formation, all elements which remain siderophile at low temperatures were considered to form alloys with iron. However, the formation of FeS at 680°K will prevent such alloy formation below this temperature owing to the surface coating of sulfur. Siderophile elements still remaining in the gas phase will be forced to condense as pure elements or, to form other compounds such as PbCl,. If the protosun had already reached its fully convective, high luminosity stage by the time condensation began in the solar nebula, the cooling times below 850°K would be lengthened by 2-3 orders of magnitude (LARIMER and ANDERS, 1967). The diffusion distances in Fig. 5 would then be shifted upward by factors of 10-30. Therefore, the above discussion can only be considered illustrative at present. However, the important point to be gained is that the composition of the condensed and gaseous phases will be a function of the cooling rate. CONDENSATION

HISTORY

We can now construct a condensation sequence for a cosmic gas. Two limiting casesmay be distinguished. If the cooling rate is rapid, diffusion and alloy formation will be negligible, so that only pure elements and compounds will condense. If the cooling rate is slow, diffusional equilibrium will be maintained, and the condensate will consist of alloys and other solid solutions. These two cases are illustrated in Fig. 6(a) and (b). Both figures show the fraction of the element condensed as a function of temperature with the curves labeled according to the predicted phase in which an element would be found. The shaded curves indicate the temperature regions at which major phases condense or become stable. Each of the shaded curves is of special significance in the condensation sequence. The shaded region which lies at 1350-1450°K indicates condensation of Mg and Si as MgSiO, and Mg,SiO,. These compounds, together with the previously condensed Fe are the first major condensates to form in the cooling nebula. A second shaded curve at llOO--1300°K indicates the temperature at which the alkali metals would condense. Thus, material which is deficient in the alkali metals may be considered to have ceased reaction with the gas phase at or above these temperatures. Mn, as MnS and MnSiO,, is only slightly less volatile than the alkalis and should follow their behavior in any condensation or volatilization process. Below 680°K the surface of the iron grains will become coated with FeS and further alloy formation of siderophile elements will be hindered. Thus, elements which do not condense until the temperature has dropped below 68O”K, and which do not form stable sulfides, will compete with sulfur for any of the residual free iron surfaces. Significantly these elements include In, Bi, Pb and Tl, all of which are strongly depleted in ordinary chondrites. We shall now examine the correlation between condensation temperature and trace element depletion (Fig. 7). For the ordinary chondrites, there is a general

Chemical

fraction&ions

in meteorites-I.

Condensations

of the elements

1233

correlation between volatility and depletion factor for the “strongly depleted” elements : Ag, Zn, Cd, Pb, Bi, In and Tl. However, for Type II and III carbonaceous chondrites, there is no apparent correlation; nor is there a correlation for the “normal” elements in ordinary chondrites. These elements are depleted by constant factors regardless of volatility.

FAST COOLING

SLOW

400

600

000

COOLING

1000 Temperature

1200

1400

1600

1000

(OKI

Fig. 6. Condensation of the elements as a function of temperature and cooling rate. a. Fast cooling; successive layers of pure elements or compounds condense on grain surfaces with little or no diffusion into the grain interior. Condensation range for each element is quite narrow. b. Slow cooling: newly condensed elements diffuse into the grain interior forming solid solutions. Activity in the condensed phase is lowered, leading to higher condensation temperatures and broader condensation ranges.

At tist sight one might be tempted to attribute this uniform depletion to reheating or incomplete condensation under conditions where the elements are partially volatile. But according to Fig. 6, there is no one temperature at which two or more elements are depleted by the same factor. It seems necessary to assume that these meteorites are a mixture of two types of material: an undepleted fraction containing all the elements and a depleted fraction containing none. This is, of course, the same conclusion reached by ANDERS (1964) using less quantitative arguments. Bor the case of the ordinary chondrites, the same argument applies to the “normal elements: Cu, Ga, Ge and Sn in Fig. 7. Again a two-component origin seems to be required. However, the excess depletion of the strongly depleted elements must now be explained. In terms of the two-component model these elements either were inefficiently collected by the undepleted fraction, or were lost in a heating episode. This latter possibility can be ruled out. It requires that there be a single temperature in Fig. 6 at which the observed depletion pattern could develop. For example, there

JOHX W. L.UEIMER

1234

should be a temperature at which Ag is depleted factor of 10-a. Actually the temperatures indicated 1100°K and 10-3 Tl at 700°K. Additional evidence reheating model is presented in the following paper

5 2

o,ol

_ I

Correlation Abundance

Between of Trace

Volatility Elements

Corbonoceous Type 0 Corbonoceous Type 0 Ordinory Chondrites l

ifi 6 z2

by a factor of O-1 and Tl by a are widely divergent: 0.1 Ag at which is not in accord with the (LARIMER and ANDERS, 1967).

and II III

2

1400

1200 Condensotion

1000 Temperoture

800

600

400

(OKI

Fig. 7. Type II and III carbonaceouschondrites show a constant degree of depletion for elements of widely differing condensation temperature. Ordinary chondrites show a similar trend for the least volatile elements (Cu, Ge, Ga) but not for the remaining ones which become progressively more deploted with decreasing condensation temperature.

Thus it appears that the “strongly depleted” elements must have been inefficiently collected by the low-temperature, undepleted fraction which comprises ~25% of ordinary chondrites. Three factors may have contributed to tho excess depletion of these elements during condensation and accretion. 1. An accretion temperature of 500-600°K for the ordinary chondrites. This alone would ensure incomplete condensation, particularly if the condensation temperatures of these elements are depressed due to insolubility. 2. Pre-emption of metahic nucleation sites by FeS, which would begin to form below 680°K. 3. Incomplete diffusion to grain interiors. The first factor, accretion temperatures, is examined in detail in the companion paper (LBRIMER and ANDPRS, 1967). The other two factors, FeS-formation prior to condensation of the highly depleted elements, and the effects of sluggish diffusion rates, have been discussed above. Neither effect has been considered previously to have played a role in the condensation process, although both are obviously important. The formation of FeS at 680°K affects only those elements which condense at still lower temperatures.

chemical

fiactionations

in meteorites-I.

Condensations

of the elements

1235

Incomplete diffusion coupled with variations in grain size may have played an important role for all the more volatile trace elements. As was discussed, the smaller grains will have the opportunity to equilibrate throughout, whereas the larger grains will retain unequilibrated interiors. One element, Hg, which is moderately depleted in ordinary chondrites presents a paradox in any fractionation process (REED and JOVANOVIC, 1967). As a pure element Hg is extremely volatile and would not condense until the temperature drops to 200”K-180°K. Of course, there is the possibility that Hg may form some unknown, relatively non-volatile compound which would raise its condensation temperature. But the volatile nature of Hg also suggests that it would be a relatively mobile element. Therefore, Hg and elements which are even more volatile, such as the noble gases, may have been redistributed in a closed system (FISH and GOLES, 1962; LARIMER and ANDERS, 1967). It should be pointed out that the relatively high abundance of Hg is a paradox to any model on chemical fractionation, not only the present one. For example if the observed depletions are assumed to have taken place during heating and degassing, in either the meteorite parent body of the nebula, the system would have to be open in order to lose Pb, Bi, In and Tl plus a certain fraction of the even less volatile elements, and yet somehow remain closed to Hg. Whatever the solution to the Hg paradox, it now appears that the extreme depletion of Pb, Bi, In and Tl is related to their volatility. In the companion paper, we have reviewed the abundance data and have attempted to interpret them in terms of the volatility data presented here. It appears that fractionation during condensation of the solar nebula provides the most consistent explanation of the evidence (LARLMER and ANDERS, 1967). Acknowledgements-I am grateful to Dr. E. AXDERS for any helpful suggestions and for Dr. P. W. GAST offered a number of constructive criticisms, critically reading the manuscript. which helped to clarify several sections of the paper. The work was supported by the National Aeronautics and Space Administration Grant No. NsG-366 and the U.S. Atomic Energy Commission, Contract AT(ll-l)-382.

REFERENCES AKAIWA

H. (1966) Abundances of selenium, tellurium and iridium in meteorites. J. Geophye. 71, 1919-1923. ANDERS E. (1964) Origin, age and composition of meteorites. &pace Sci. Rev. 3, 683-714. ANDERS E. (1965) Chemical fractionations in meteorites. Meteotitika 28, 17-26. (In Russian). English version published as NASA Contractor Report, CR-299. ARMSTRONG H. L. (1958) On solid state diffusion with a linearly varying temperature. Trans. Met. Sot. AIME, 212, 450-451. BREWER L. (1946) Vapor pressure of the elemonts. Report for the Manhattan Project MDDC438C. CANERON A. G. W. (1962) The formation of the sun and planets. Icurua 1, 13-69. CAMERON A. G. W. (1963) Formation of the solar nebula. Icarus 1, 339-342. CAMXRON A. G. W. (196313) Nuclear astrophysics. Lecture notes from a course given at Yale University, unpublished. COUGEIN J. P. (1954) Contributions to the data on theoretical metallurgy, &XII: Heats and free energies of formation of inorganic oxides. U.S. BUP. Mines Bull. 542. ELLIOTT R. P. (1965) Constitution of Bina?y A&ye, Firat Supplement. McGraw Hill. EZER D. and CAIKIZRON A. G. W. (1965) A study of solar evolution. Can. J. Plays. 43,1497-1517. Res.

1236 FISH

JOHN

W.

LARIMER

R. A. and GOLES G. G. (1962) Ambient xenon: a key to the history of meteorites. i~a~we 27-31. FISH R. A., GOLES G. G. and ANDERS E. (1960) The rooord in the meteorites, III: On the development of meteorites in asteroidal bodies. Astrophys. J. 132, 243-258. GOLDBERG L., MUELLER E. A. and ALLER L. H. (1960) The abundances of the elements in the solar atmosphere. Astrophys. J., Suppl. Series 5, l-138. GOLDSCHMX~T V. M. (1937) Geoohemisohe Verteilungsgesetze der Element0 IX. Skr. Norske vid-akad. Oslo, I, iMath.-Nat. Kl. 4. GOLDSTEW J. I. (1966) Butler, Missouri: an unusual iron meteorite. Science 153, 975-976. GREENLAND L. (1965) The abundances of selenium, tellurium, silver, palladium, cadmium and zinc in chondritic meteorites. Geochim. Cosntochi?n. Acta 31, 849-860. HANSEN M. (1955) Constitution of Binary Alloys. McGraw-Hill. HAYASHI C. (1961) Stellar evolution in early phases of gravitational contraction. Publ. -4stron. Sot. Japan 13, 450-452. JANAF TILES (1960 and later) Joint Army, Navy, Air Force Tables of Thermochemical Data. Compiled by Dow Chemical Company, Thermal Laboratory, Midland, Mich. JOST W. (1952) Diffwion. Academic Press. KELLEY K. K. (1960) Contributions to data on theoretical metallurgy, XIII: High-temperature heat-content, heat-capacity, and entropy data for the elements and inorganic compounds. U.S. Bur. Mii,tea Bull. 584. KWASCHEX~SKI 0. and EVANS E. LL. (1955) Metallwgical Tll.e~lflocllen,ist~~. Pergamon Press. LARIMER J. W. (1966) The petrology of chondritic motcorites in tho light of experimental studies. Ph.D. dissertation, Lehigh University. LARIMER J. W. and ANDEnS E. (1967) Chemical fractionation in meteorites II. Abundance patterns and their interpretation. Geochina. Cosv~ochi~n~+ Acta, 31, 1239-1270. LORD H. C. III. (1965) Molecular equilibria and condensation in a solar nebula and cool stellar atmospheres. Icarus 4, 279-288. PER A. R. (1963) The vapor pressures of indium sulfides as functions of composition and temperature. Univ. of Calif. Rad. Lab. Rep. UCRL-10857. NACHT~IEB N. H. (1966) Personal communication. NODDACG I. and KODDaCK W. (1934) Die geochemischen Verteilungskocff~zienten der Elemante. Suensk Kemisk Tidskrift 46, 173-200. REED G. W. and ALLEN R. 0. (1966) Halogens in chondrites. GeoclLim. Cosn~ochina. Acta 30, 7794300. REED G. W. and JOVANOVIC S. (1967) Hg in chondrites. J. Geophys. Rw. 72, 2219-2228. REED G. W., KIGOSHI K. and TURKEVICH A. L. (1960) Determination of concentrations of heavy elements in meteorites by neutron activation analysis. Geochivn. Cosv,ochin,. Acta 20, 122-140. RICHARDSON F. D. and JEFFES J. H. E. (1948) The thermodynamics of substances of interest in iron and steel making from 0°C to 24OO”C, I: Oxides. J. Iron Steel Inst. 130, 261-270. RICHARDSON F. D. and JEFFES J. H. E. (1952) The thermodynamics of substances of interest in iron and steel making, III: Sulphides. J. Iron Steel Inst. 171, 165-175. ROSENQTTST T. (1954) A thermodynamic study of the iron, cobalt and nickel sulfides. J. Iron Steel Inst. 174, 37-57. ROSSINI F. D. et al. (1952, and Supplements of 1965, 1966) Selected values of chemical thermodynamic properties. Nat. BUT. Stds. Circular 500. SMALES A. A., HUGHES T. C., MAPPER D., MCINNIS C. A. S. and WEBSTEI~ R. K. (1964) The determination of rubidium and caesium in stony meteorites by neutron activation analysis and by mass spectrometry. Geochina. Cosmochim. Acta 28, 209-234. SUESS H. E. (1965) Chemical evidence bearing on the origin of the solar system. Ann. Rev. As&on. Astrophys. 3, 217-234. UREY H. C. (1952a) The Planets. Yale University Press. UREY H. C. (1952b) Chemical fractionation in the meteorites and the abundance of the elements. Geochina. Cosmochim. Acta 2, 269-282. UREY H. C. (1954) On the dissipation of gas and volatilized elements from protoplanets. Astrophys. J. Supp. No. 6, 1, 147-173.

196,

(8)

or

Table

0”:: 7.0 ;:; 10.0 o-1

9, 9 2; 9: 9 ;:i 9: 29

1*

0.1 1.0

+t ;:;

0.1 0.1

;:;

8::

-, 2 9, Q

i:: 9, Q et

8:: 1-o

0.1

9::

f:i

;:: 0.1 3.0

10.0 8::

0.1

8:: 0.1 3.0

Estimated error (kcal)

-. 2 3: 2: 2

1* 1* 9,‘;

292

s: 29 9, Q

Source of data

(s)

Mn (4 Mn (1) Mn (Id

MgSiO, (s) MgFeSi,O, (s) MgFeSi,O, (s)

Mg (4 Mg (1) W M MgA’,O, (4 Mg,SiO, b)

K (4 K (1) K (g) K,SiO, (s) KAISi,OB (8)

Inii) In8 w Ins (s)

In (1)

In (4

or

of thermodynamic

H k) H, k) 2: ($ Hb k) Hg (1) Hg M HgS(8)

GaO

Ga.(5) Ga 0) Ga k)

Compound element

6. Sources

data

used

i:!

-,

2

x 9: 9 9; 9 8: 8:

0”:: 0.1

;:; 10.0 6.0 6.0

0”::

0.1

;:: 7.0 10.0

kx 9: 9 9, 9 9::

0.1

;:;

8::

o-1

8:;

0.1

2

-,

9. 9

ix16$

-, 2

6-i

ii::

8:;

0”::.

0.1

0”:: 3.0

9, Q 4t 1* If 1+ 1* 1*

0.1

error

(8)

or

(8)

ZnS (8) Zn,SiO,

zn(4 Zn (1) zn M ZnO (8)

TlS (s)

T’ (4 1’1(1) T’ k)

Si (8) Si (1) Si (9) SiO (5) SiO, (8)

s,(g)

PbCI,

R I;;’ Pb k) PbS (s)

Ni (s) Ni (1) Ni Cd Ni,% (4

(s)

Na (4 Ne (1) Na k) Ne,SiO, (s) NaAlSi,Os (s)

MnSiO,

Mno (8) Mns (8)

Compound element

in calculations

Estimated (kcal)

s: 29

Source of data

Q

4t 6-l 9, Q

Q,Q

9::

Q Q,9

ii:: 9,

1* 1* 1* 1* 1*

1’

-, 2 3: it 1*

:;

1* 1*

9. Q 11**

1*

9:;

9,

if

Source date

of

0.1 o-1 0.1 1.0 1.0 3.0

;:: 0.1 2.0

;:;

0.1 0.1 0.1

0.3

2:; 2.0

8::

;:;

0.1 0.1

1E

8::

0.1

1.0 1-o 6.0

Estimated Ikcal)

error

two sources are given, the ilrst is for AH”,,,, the second is for SO,,,. The C, values for these compounds or elements were all obtained from KJSLLEY (1960). l Aff” obtained directly from tables. ** AQ” caIculated from date. ree energy is calculated from a function such as AQ’” = f(T). $ Experimental data were used to calculate Acf”. Refer!snFces 1. JXNAF TABLES (1960 and later). 4. COUCJHLIN (1964). 7. ROSENQUIST (1964). 10. &LLER (1963). 2. KUBASCHEWSEI and EVANS (1968). 6. RICHARDSON and JEFFES (1948). 8. LARII\~R (1966). 11. Lonn (1966). 3. KELLEY (1960). 6. RICEABDSON and JEFEES (1962). 9. ROSSIXI et al. (1962 and later).

Where

Fe304 (5)

FeS (s) F&l, (s)

Fe (4 Fe (1) Fe (6)

cu cu(4 (1) cuk) cu*s(4

:: I;; Cd (g) CdS (s)

ca (4 ca (1) ca (9) CaTiO, (s) Ca,SiO, (9) CaSiO, (9) CeAl$i,O, (8) CaMgSi,O, (s)

Bi (8) Bi (1) Bi (9) BG% (4

Al,SiO,

Al (6) Al (1) Al (id

Compound element

1238 UREY H. C. (1966) Chemical A&r. Sot. 131, 199-223. \$'OOD J. A. (1963) On the

JOHX evidence origin

IV.

relative

of chondrules

LARIMER

to the and

origin

of

chondrites.

the

solar Icarus

system.

Mon.

.i\-ot.

Roy.

2, 152-180.

APPENDIX The sources of data from which AG,” values were calculated are listed in Table 5. These values were obtained (a) directly from JAX4.F Tables; (b) by calculating AG,’ from AH:,,, Si,, and C,; (c) by calculating AG,” from experimental data; or (d) from a function such 8s AG,” = -A + BT - CT2 . . . Whenever possible, I have used method (d) instead of (b). Column (3) of Table 5 lists the maximum error in AG,’ up to the temperature at which t,he compound would form or condense. These errors, in turn, can be used to estimate errors in condensation temperature. An error of &5 kcal in AG,” at 1000°K leads to an error of approsimately f 1.0 in the value K,, corresponding to E change by a factor of 10 in the ratio of partial pressures. Thus, for the simple systems in which just two gases are involved, the error in pressure is about an order of magnitude, which in general leads to an error in condensation temperature of about &-IO-20°K (see Fig. 2). In the more complicated systems, where a number of gaseous compounds react to form a condensed compotmd, the error is in general somewhat larger. However, the increased error in AG” is offset by a steep dependence of condensation temperature on pressure. In the example ofMg,Si04, discussedabove, condensation temperature varies as PTs, so that even a substantial error in AG” does not greatly affect condensation temperature. It seems that the error in condensation temperature will generally be well within f30”K for all elements and compounds considered here. We must also consider the effect of a change in the relative elemental abundances. A drastic change in the H/O, H/S or C/O ratios would seriously affect many of our results, But the cosmic abundances of these elements are generally known to a factor of 3 or better. Gross changes in our results would be expected only if these elements had been chemically fractionated from each other, a possibility considered rather unlikely in the light of present knowledge,