Noble Gases and Evolution of the Atmosphere - Geol. 656

Geol. 656 Isotope Geochemistry

Lecture 26 Spring 2007

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NOBLE GASES AND EVOLUTION OF THE ATMOSPHERE

INTRODUCTION Just as variations in the isotopic composition of radiogenic incompatible elements provides some in-formation about the flux of incompatible elements from mantle to crust through time, variations in the isotopic composition of radiogenic atmophile elements provide information about the flux of these ele-ment from mantle to atmosphere through time. A number of radiogenic decay products are noble gases that are concentrated in the atmosphere. These include 40Ar and 4He, which are produced by beta decay of 40K and alpha decay of U and Th respectively, and 84K and 86Kr, 131Xe, 132Xe, 134Xe, and 136Xe produced by spontaneous fission of U and Th. In addition, 129Xe is the decay product of the extinct ra-dionuclide 129I (half life: 17 Ma) and other Xe isotopes were produced by fission of the extinct nuclide 244Pu (half life 82 Ma). Finally, 21Ne is ‘nucleogenic’, it can be produced by reaction between ‘fissogenic’ neutrons and magnesium as well as between alpha particles and 18O.

HE AND OTHER NOBLE GASES IN THE EARTH As usual, we need first to examine the available data set before attempting to draw any inferences. In this particular case, the data of interest consists the isotopic composition of atmospheric gases and gases from submarine-erupted basalts and some deep wells. When basalts are erupted subareally, the gaseous elements exsolve from the melt and are lost to the atmosphere. Solubility of volatile com-

pounds in a silicate melt is a strong function of pressure. When basalts are erupted under several kilometers of seawater, the solubility is such that at least some of the gases remain in the melt and are trapped in the quenched glassy rims of pillow basalts. Noble gases in the continen-tal crust are generally at low concentration and further-more, are dominated by ra-diogenic components. Thus the two main reservoirs of noble gases in the Earth are the atmosphere and the man-tle. Figure 26.1 summarizes the variations in He isotope ratios observed in MORB and OIB. He isotope data is fairly abundant because the atmosphere contains very little He, and therefore con-tamination is not usually an issue. Measurement of the

Figure 26.1. Comparison of 3He/4He analyses of 573 MORB and 759 OIB from the PetDB and GEOROC databases..



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isotopic composition of other atmophile elements is much more problematic and difficult due to (1) their pervasive presence in the atmosphere and seawater, (2) low concentrations in basalts, and (3) the loss upon eruption of lavas.

Helium Noble gases in the atmosphere have uniform isotope ratios, which are listed in Table 26.1, and they thus provide a good reference against which mantle values can be compared. While some workers ad-here to the usual convention of placing the radiogenic isotope in the numerator, most report the 3He/4He (hence the convention for He isotopes is to defy the convention). Most often, He isotope ratios are reported relative to the atmospheric value in the R/RA notation:

�

3He

4He

!

" #

$

% & R /RA

=

3He /

4He( )

sample

3He /

4He( )

atmosphere

26.1

In these units, crustal rocks generally have He isotope ratios in the range of 0.01 to 1 while mantle-derived rocks have values in the range of 5 to 40. Low values in the crust reflect degassing of He that occurred during their formation and the subsequent production of 4He by radioactive decay. Higher 3He/4He in mantle-derived rocks indicates that the mantle has not been entirely degassed and retains at least a part of its initial, or primordial, inventory of noble gases. He is unique in that it is the only ele-ment that is lost from the Earth in significant quantities. This is because it light enough that some frac-tion of He atoms reach escape velocity in the upper atmosphere (while H is lighter, almost all H in the atmosphere is present as H2O, which is too heavy to reach escape velocity)∗. The residence time of He in the atmosphere is not known exactly, but is estimated to be in the range of 106-107 yr. The isotopic composition of He in the atmosphere thus reflects the isotopic composition of He leaking from the solid Earth, and is therefore intermediate between the crust and mantle values. Figure 26.1 illustrates the isotopic composi-tion of He in MORB. There are several obser-vations: first, the ratio in MORB, and presuma-bly therefore the depleted upper mantle is higher than the atmospheric values, with a mean value in MORB of 8.8±2.5 and a median value of 8.1. Second, this value is quite uni-form in MORB. Most of the samples with R/RA > 10 come from parts of the ridge close to oce-anic islands and are thus likely influenced by mantle plumes. Figure 26.2 shows the isotopic composition of

∗ Creationist’s have claimed that He cannot escape from the Earth’s atmosphere because it does not reach escape velocity. Since 4He is steadily produced by α decay, 4He should steadily accumulate in the atmos-phere if it does not escape. The atmospheric abundance, they argue, therefore fixes the age of the Earth to be young (<40,000 yrs). The argument is flawed because thermal escape, sometimes called Jean’s escape, in which He is accelerated to escape velocity through thermal collisions, is the least important of 3 princi-pal He escape mechanisms. Most important appears to be the “polar wind” in which He is first ionized, then accelerated along magnetic field lines which allow flow outward at the poles. The third mechanism is acceleration by interaction with the solar wind. Partly as a consequence of this complexity, the exact flux out of the atmosphere remains somewhat uncertain, hence the uncertainty in atmospheric residence time.

Table 26.1. Atmospheric Noble Gas Isotope Ratios Isotope Ratio Value in the Atmosphere 3He/4He 1.39 × 10-6

4He/3He 7.19 × 105 21Ne/20Ne 0.00296 22Ne/20Ne 0.102 40Ar/36Ar 295.5 129Xe/130Xe 6.496 132Xe/130Xe 6.607 134Xe/130Xe 2.563 136Xe/130Xe 2.176



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He in basalts from a variety of mantle plumes plotted as a function of plume flux estimates of Davies (1988) and Sleep (1990). As may be seen, there is no obvious relationship between plume flux and He isotopic composition. He isotopic ratios in plumes vary widely, and can be both higher and lower than the MORB value, although most are higher.

The generally higher 3He/4He ratios in mantle plumes provide evidence that they are derived from a part of the mantle that has been less degassed that the mantle that gives rise to MORB. The latter is generally assumed to be the upper mantle or asthenosphere. Simple logic suggests that the deep mantle should have experience less melting and degassing than the upper man-tle (because melting and degassing can occur only near the surface). Hence, high He isotope ratios in plume-derived basalts is often cited as evidence that plumes come from the deep mantle. Once must be careful, however. Since the Earth is not a simple place, simple logic might be misleading. Low 3He/4He ratios in some plumes, such as Tristan and St. He-lena, could reflected the presence or predominance of material recycled from the Earth’s surface, such as oceanic crust, in these plumes. There is an inherent inconsistency between He and non-noble gas ra-diogenic isotope ratios in mantle-derived basalts. Overall, there is little correlation between He isotope ratios and other isotope ratios, such as 87Sr/86Sr, as is illustrated in Figure 26.3 (although correlations often exist within individual oceanic is-lands). Furthermore, the highest 3He/4He ratios are associated with intermediate 87Sr/86Sr, 143Nd/144Nd, and Pb isotope ratios (Figure 26.3). These high 3He/4He ratios suggest that this material has been substan-tially less degassed than material with lower 3He/4He ratios. On the other hand, isotope ratios such as 87Sr/86Sr associated with these high-

aa

MORB

MORB

Plume Flux (km3/y)

10

20

30

40

0 5 10 15

4He3He

(R/RA)

10

20

30

40

0 5 10 15

4He3He

(R/RA)

Pacific Hawaii(Loihi)

Societies

Marquesas

Cook-AustralsPitcairn

Juan FernandezCV

CanariesTristan/Gough

AtlanticIndian

Heard/Kerguelen

Reunion

Continental

Hawaii(Loihi)

Yellowstone

MarquesasCook-AustralsEaster

AfarSamoa

Azores

St. Helena

Bouvet

Iceland

Galapagos

ASP

(Davies, 1988)

(Sleep, 1990)

Figure 26.2. Helium isotope ratios in plume-derived ba-salts and MORB as a function of plume flux. There is no apparent relationship between plume flux and He isotope ratios. ASP = Amsterdam-St. Paul. Modified from Graham (2002).



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est 3He/4He ratios indicated these plumes consist of material that is incompatible element-depleted relative to primitive mantle. As yet, there is no model of mantle evolution that fully reconciles noble gas and non-noble gas isotope ratios.

Argon Recall that 40Ar is created by radioactive decay of 40K. Ar has two other isotopes, 36Ar, and 38Ar; the 38Ar/26Ar ratio in the atmospheric is 0.188. The initial solar system 40ar/36Ar is thought to be something like 10-3 to 10-4 (the ratio in the atmosphere of Venus is 1). Comparing this to the atmospheric ratio of 295.5 leads immediately to the conclusion that most of the Ar in the atmosphere is radiogenic. Fur-thermore, atmosphere Ar must owe its origin to degassing of the Earth’s interior (since there is no K in the atmosphere). Indeed, it is fairly easy to calculate that 40Ar must have been released from a substan-tial fraction of the solid Earth to account for its atmospheric abundance. The K content of the bulk sili-cate Earth is estimated at 250 ppm. Over the Earth’s history, this would produce about 140 x 1018 g 40Ar. The amount of 40Ar in the atmosphere is 66 x 1018 g. This amounts to 47% of all 40Ar produced in the Earth. Figure 26.4 shows a plot of 40Ar/36Ar vs. 3He/4He in some oceanic basalts. The 40Ar/36Ar ratio in MORB can be as high as 40,000 and ratios in OIB and related xenoliths can be as high as 10,000. In all these examples, 40Ar/36Ar is highly variable, due almost entirely to atmospheric contamination. In con-trast to He, Ar is very abundant in the atmosphere (concentration of 0.93%), so that small amounts of atmospheric contamination have a large effect on the 40Ar/36Ar measured in basalts. The He concentra-tion in the atmosphere is low enough that such small amounts of atmospheric concentration have little effect. In general, maximum 40Ar/36Ar ratios in MORB are higher than in OIB, even though MORB are systematically poor in K than OIB. While this could imply the time since degassing has been longer for

aa

0.703 0.704 0.705 0.706 0.70787Sr/86Sr

MaunaLoa

JuanFernandezM. Kea

Koolau

Loihi

St. HelenaAtlanticMORB Shimada

SmtTristanGough

Samoa

HeardCRB

Galápagos

African Xenoliths

Iceland

ReykjanesRidge4He

3He

(R/RA)

30

20

10

Figure 26.3. Relationship between 3He/4He and 87Sr/86Sr in mantle materials. CRB = Columbia River Basalts. From Graham (2002).



183 3/29/07

MORB than for OIB, it is more often interpreted as implying the MORB source has been more thor-oughly degassed than the OIB source(s). This more thorough degassing results in more complete loss of 36Ar, hence radioactive decay lead to higher 40Ar/36Ar ratios in such thoroughly degassed systems. This explanation is also consistent with the generally higher 3He/4He observed in OIB than MORB.

Neon Neon isotopes in oceanic basalts are shown in Figure 26.5, and again, Ne isotope ratios are distinct from the atmospheric ratio. This might at first seem perplexing, since there are no radioactive nu-clides decaying to any of the Ne isotopes (20Ne, 21Ne, and 22Ne). However, 21Ne can be produced by several nuclear reactions, such as 18O (α,n) 21Ne or 24Mg (n,α) 21Ne (the α and n coming from α decay and fission). Hence 21Ne is “nucle-ogenic”. These reactions produced significant variations in the 21Ne/22Ne ratio in the mantle since 21Ne is a very rare nuclide (0.26% of Ne), and the abundance of Ne in

Figure 26.5 Ne isotope variations in oceanic basalts and related rocks. From Graham (2002).

Figure 26.4. 3He/4He vs. 40Ar/36Ar in MORB, OIB, and some related xeno-liths. Variation in 40Ar/36Ar is due largely to atmospheric contamination – hence interest centers on the maximum values. From Graham (2002).



184 3/29/07

the mantle is very low. In the atmosphere, Ne is much more abundance and these reactions are uncommon, so there is no significant variation in 21Ne/22Ne. The variation in 20Ne/22Ne is more difficult to account for. Sarda et al (1988) have suggested the following scenario (illustrated in Figure 26.6) to account for these variations. They note that the atmosphere has Ne isotope ratios that differ from those of the Sun. They suggest Ne was largely lost from any early primitive terrestrial atmosphere, and extensive mass fractionation oc-curred during this processes (driving the 20Ne/22Ne and 21Ne/22Ne down along a line with slope = 2 in Figure 26.6). The Ne in the mantle at that time, however, did not suffer this fractiona-tion and retained “solar" Ne isotopic composi-tion. Over time, 21Ne was produced in the man-tle by the reactions mentioned above, driving the mantle isotope ratio horizontally to the right in Figure 26.6. (It is also possible to produce 20Ne by these same reactions with different targets, but because 20Ne is so much more abundant, the af-fect on the 20Ne/22Ne ratio would be insignificant.) OIB, in their model, are derived from a less de-gassed reservoir in which the nucleogenic component of 21Ne is less significant, and they are not shifted as far away from the “solar” value. The concentration of Ne in the atmosphere is fairly high (18 ppm), so contamination of the basalts by atmospheric gases, during, before, or after eruption then shifts values of individual MORB and OIB toward the atmospheric composition along lines labeled mixing. (In contrast to Figure 24.4, the denominators of both the ordinate and abscissa are the same, so mixing lines are straight.)

Xenon As was the case with He, Ne, and Ar, Xe from the Earth’s interior is also isotopically distinct from atmospheric Xe. This is illustrated in Figure 26.7 for the same sample set. 136Xe is ‘fissogenic’, being produced by fission of 238U and now-extinct 244Pu. The higher 136Xe/130Xe measured in oceanic basalts compared to the atmosphere is just what we expect, since 238U is present in the Earth’s interior, but not in the atmosphere. 129X is the product of decay of now-extinct 129I, as we saw in an earlier lecture. Since the half-life of 129Xe is only 16 Ma, the difference between the atmospheric and mantle 129Xe/130Xe ratio must have been established very early in Earth’s history, within at most the first 160 Ma. This provides an important constraint on evolution of the Earth’s atmosphere, as we shall see in the next section. The linear correlation in Figure 27.7 suggests that most basalts have suffered some degree of con-tamination with air , as was the case with Ne and Ar. So once again, it is the maximum values that are most interesting. The is no guarantee that even the maximum values have not been influenced by con-tamination, so these must be regarded as the “minimum” values for the mantle sources of these basalts. Maximum values are greater in MORB than in OIB and related xenoliths, which again suggested the MORB source has been more thoroughly degassed.

Figure 26.6. Model for the variation of Ne isotope ratios in the Earth. The atmospheric ratios de-crease relative to solar values along a mass-dependent fractionation line during loss of Ne from early atmosphere. 21Ne is produced in the mantle by (α, n) and (n,α) reactions. Variations observed in MORB and OIB represent mixing be-tween this ‘degassed mantle’ Ne and atmospheric Ne as a result of contamination during eruption.



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MODELING ATMOSPHERIC EVOLUTION We should begin our discussion of atmospheric evolution by making the assumption, as we have for the crust, that the Earth was initially a homogeneous body. After separation of the core, we were left with a homogeneous silicate portion of the Earth with the composition of ‘primitive mantle’. Our working model will assume that the atmosphere, like the crust, was created from the mantle. We shall refer to the process that created the atmosphere as degassing or outgassing. We know that the magma-tism continues to outgas the mantle today. Quite possibly this is the main process by which the atmos-phere (and hydrosphere) was created. However, much of the discussion below is independent of the precise mechanism of outgassing. We shall be concerned primarily with the degree and rate of out-gassing. We should also note that this is not the only possible mechanism by which the atmosphere was produced. One alternative hypothesis that has been suggested is production of the atmosphere by accretion to the Earth of volatile-rich bodies such as comets after formation of the Earth. (However, al-though their C and N isotope ratios are similar to terrestrial (and solar) values, comets appear to have D/H ratios that are about twice the ratio in the Earth (and meteorites). This would seem to be some-thing of an obstacle to the oceans-from-comets theory.) Each of the nuclides mentioned above provides a different perspective on the evolution of the Earth's atmosphere. Obviously, 129Xe variations could only be produced very early in Earth's history (within ~10 × 16 = 160 Ma of nucleosynthesis, after that time the parent, 129I, had completely decayed). That variations in the 129Xe/130Xe ratio are observed suggests (1) the Earth formed shortly (within 160 Ma) af-

Figure 26.7. Xe isotopes in oceanic basalts are related xenoliths. There are far fewer data for Xe than for the other noble gases because the concentrations are exceedingly low and the measurements are extraordinarily difficult. From Graham (2002).



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ter a nucleosynthetic event, and (2) a substantial fractionation of I from Xe must have occurred early in Earth's history. So 129Xe variations pro-vide clues to the early degassing history of the Earth. Helium is unique because the Earth is an open system with respect to He. 4He is continu-ally created, while 3He, for all practical pur-poses†, is not, hence He should give us a perspec-tive on the present degassing rate. The U-fissogenic Xe isotopes and Ar are daughters of long-lived nuclides and should integrate the en-tire degassing history of the Earth. Lets take a hypothetical Earth box model of the Earth (Figure 26.8). It has the three reservoirs we have discussed before, continental crust (denoted C), depleted and outgassed upper mantle (denoted D), and undegassed and undepleted lower mantle, or virgin mantle (V). But for the atmophile elements we need to include some additional reservoirs: the atmosphere (denoted A), and, since allowing for the possibility that some part of the mantle has been outgassed but not depleted, an outgassed, but undepleted, or virgin, mantle (VO). The atmosphere has sub-stantial concentrations of the noble gases, but no significant amounts of the parent isotopes such as U and K; the continental crust has substantial concentrations of U and K but no significant amounts of the noble gases, the depleted and outgassed upper mantle is relatively poor in both the incompatible par-ents and the noble gas daughters, though the exact concentrations of both are unknown. Together, res-ervoirs D and VO constitute the outgassed mantle, which we denote by the subscript O. We will use the subscript T to denote the total system. We can write a number of mass balance equations of the sort we introduced in Lecture 18 or used for Nd in Lecture 20. Note that mass balance equations for intensive parameters* written for the bulk sil-icate Earth will also hold for bulk silicate Earth less the undegassed, undepleted, lower mantle, e.g., the mean concentration of Ar above the dashed line in Figure 26.8 must be the same as the concentration of Ar below the dashed line. We begin by determining the relative amount of Ar in the various boxes. We have already noted the assumption that the amount of 36Ar in the crust is negligible. We define the present degree of outgassing, d, as the ratio of the mass of 36Ar in the atmosphere to the mass of 36Ar in the atmosphere plus the outgassed mantle. In other words, d is the fraction of Ar in the atmosphere relative to the total amount of Ar above the dashed line.

d =

36Ar

A

36Ar

O+

36Ar

A

26.2

We assume the mass of 36Ar in the continental crust is negligible. In this case, the isotopic budget for reservoirs A and O may be written as (40Ar/36Ar)Τ = d(40Ar/36Ar)A + (1 – d)(40Ar/36Ar)O 26.3

† There is a very small amount of nucleogenic production of 3He, such that the 3He/4He produced in the Earth should have a R/RA ratio of around 0.01. * Intensive parameters are those which are independent of the mass of the system, such as concentration, isotope ratios, temperature, etc. Extensive parameters, such as mass, heat content, amount of an element or isotope, depend on the total mass of the system.

aaa

atmosphere

V

VO

D

continental crust

degassed

undegassed

depleted

undepleted

upper mantle

lower mantle

mantle

mantle

C

Figure 26.8. Box model of the volatile inventory of the Earth (from Allégre et al., 1986).



187 3/29/07

where the subscript T stands for total, or bulk Earth. Equation 26.3 says the total 40Ar/36Ar ratio above the dashed line is the average of the two reservoirs, weighted by the proportion of 36Ar in each. Rear-ranging equation 26.3 yields:

d =( 40

Ar / 36Ar)

O– ( 40

Ar / 36Ar)

T

( 40Ar / 36

Ar)O

– ( 40Ar / 36

Ar)A

26.4

We define a second value of d, d' by using (40Ar/36Ar)D instead of (40Ar/36Ar)O in 26.4:

d ' =( 40

Ar / 36Ar)

D– ( 40

Ar / 36Ar)

T

( 40Ar / 36

Ar)D

– ( 40Ar / 36

Ar)A

26.5

where D stands for for depleted mantle. Since the K concentration in D is less than in VO (by definition: D is depleted, VO is not), (40Ar/36Ar)D ≤ (40Ar/36Ar)O and d' ≤ d. Assuming (40Ar/36Ar)D = 40,000 (maximum value in undegassed MORB), (40Ar/36Ar)A = 295.5 (atmos-pheric), and taking the maximum value in Loihi seamount as representative of (40Ar/36Ar)V = (40Ar/36Ar)T = 10,000, we can calculate the lower limit for d as:

d > d ' =40,000 !10,000

40,000 ! 295.5

Our first conclusion then is that the depleted mantle has lost 75.5% of its 36Ar inventory. If the Loihi source has also experienced gas loss, then the gas loss of the MORB source would be even greater. The initial ratio of 40Ar/36Ar of the Earth can be estimated in various ways, most of which suggest a value less than or equal to 10-2. 40Ar has been produced steadily throughout geologic time by decay of 40K, and the 40Ar/36Ar has consequently increased. Because of the time-integrating character of ra-diogenic isotopes ratios, they should allow us to estimate the rates at which outgassing has occurred. To understand this, imagine a choice between 2 extremely simple models of atmospheric evolution. To make the case as simple as possible, imagine an Earth with only two reservoirs: the atmosphere and a degassed mantle. In the first model, the atmosphere is produced by degassing of the mantle yesterday. In this case, the degassed mantle and the atmosphere should have identical 40Ar/36Ar ratios. In model two, the atmosphere is produced when the Earth forms 4.55 Ga ago, and the atmosphere and mantle have remained as closed systems ever since. In this case, the 40Ar/36Ar ratio of the atmosphere should be very close to the initial value (since 40K/36Ar of the atmosphere is 0, the 40Ar/36Ar would not change with time). The 40Ar/36Ar ratio in the mantle in this model would be very high, the exact value depend-ing on the degree of outgassing and the 40K/36Ar ratio of the mantle. The available data are not in ac-cord with either of these simple models: the 40Ar/36Ar ratios of the mantle and atmosphere are clearly not equal, so degassing did not occur as a single recent burp. On the other hand, the atmospheric ratio is greater than the initial ratio, so it could not have been a closed system. Therefore we must consider more complex models. Any model of atmospheric evolution of He, Ar or fissogenic Xe is bound to be rather complex, be-cause it must take account of 1.) transport of gas from mantle to atmosphere, 2.) growth of the radio-genic isotopes in the mantle, and 3.) transport of the parent isotopes, K, U, and Th, to the crust. These sorts of models turn out to be rather complex indeed, and we do not have time to consider them in de-tail. However, the situation for 129Xe is somewhat simpler. Because of the short-half life of the parent, 129I, we can neglect transport of 129I from mantle to crust. This is equivalent to assuming no permanent crust formed within the first 160 Ma of Earth history, which is not an unreasonable assumption. Let's then consider a simple model of evolution of 129Xe/130Xe ratio in the mantle and atmosphere. What we ultimately want to understand is the rate at which the mantle was degassed. Our first task is to determine the form of the equation describing the degassing history of the mantle. We assume that degassing rate is some function of time. We must also know how degassing occurs.



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Today it occurs in association with volcanism at mid-ocean ridges, which is in turn related to mantle convection. The main driving force for all tectonic activity involving the mantle is heat, mainly heat produced by radioactive decay. We can suppose that tectonic activity, such as volcanism and mantle convection, that causes outgassing of the mantle has decreased with time as heat production has de-creased, i.e., exponentially according to the radioactive decay equation. Therefore, we chose an equa-tion to describe the outgassing rate having an exponential form:

J0e!"t 26.6

where J0 is the initial flux (integrated over the Earth's entire surface) and β is a rate constant analogous to the decay constant in the radioactive growth equation. If β is 0, then the degassing rate has been constant and equal to the initial rate, J0. A very large value of β corresponds to a single burp early cata-strophic degassing. J should depend on the amount of the nuclide in the mantle (since we expect that the more of the nuclide in the mantle, the higher the flux out of the mantle), so for 130Xe: J0 = κ130Xe0 26.7 where κ is a constant. The rate of change of the amount of the non-radiogenic nuclide 130Xe in the man-tle is then given by:

d(130Xe

m,t)

dt= !" 130

Xem,0

e!#t 26.8

where 130Xem,t is the amount of 130Xe in the mantle at time t, and 130Xem,0 is the initial amount of xenon in the mantle. The minus sign indicates the flux is from mantle to atmosphere. The change is the amount of 130Xe in the atmosphere is then just the opposite:

d(130Xe

a,t)

dt=! 130

Xem,0

e"#t 26.9

Integration of equations 26.8 and 26.9 yields:

130Xe

m,t=! 130

Xem,0

1+!"

e#"t #1( )

$

%&

'

() 26.10

130Xe

a,t=!"

130Xe

m,01# e

#"t$% &' 26.11

Now if β is very large (implying catastrophic early degassing), in particular, if 1/β << 4.55 Ga, then the exponential term approximates to 0 for t= 4.55 Ga, and equation 26.11 can be rearranged as:

!

"#

130Xe

a

130Xe

m,0

26.12

So for early catastrophic degassing, the κ/β ratio is equal to the ratio of the 130Xe content of the at-mosphere to the initial 130Xe content of the mantle, i.e., the fraction of the 130Xe outgassed. For a radiogenic isotope, such as 129Xe, we have the added complexity that it is being produced si-multaneously with the outgassing process. The rate of change of the amount of 129Xe in the mantle is then equal to the rate at which it is lost (degassed) plus the rate at which it is produced. We can write this as:

d(129Xe

m,t)

dt= !

129Xe

130Xe

"

#$%

&'m,t

( 130Xe

m,0e!)t

+ * 129I

m,t 26.13



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We assume that 129I is not lost from the mantle, so

129Im,t

=129I0e!"t 26.14

and

d(129Xe

m,t)

dt= !

129Xe

130Xe

"

#$%

&'m,t

( 130Xe

m,0e!)t

+ * 129I

0e!*t 26.15

We assume that atmosphere does not, and never did, contain significant amounts of iodine, so the rate of change of 129Xe in the atmosphere is simply:

d(129Xe

a,t)

dt=

129Xe

130Xe

!

"#$

%&m,t

' 130Xe

m,0e()t 26.16

We now want to consider how the 129Xe/130Xe ratio has evolved with time. For the mantle:

d(129Xe / 130

Xe)m,t

dt=!

129I

m,t

130Xe

m,t

26.17

substituting equations 26.14 and 26.10 for the right side denominator and numerator respectively:

d(129Xe / 130

Xe)m,t

dt=

!129I

0e"!t

130Xe

01+# / $(e"$t "1)%& '(

26.18

For the atmosphere:

d(129Xe / 130

Xe)a,t

dt=

!e"#t

(e"!t "1)

129Xe

130Xe

$

%&'

()m,t

"129

Xe

130Xe

$

%&'

()a,t

*+,

-,

./,

0, 26.19

Integrating these equations from 0 to T = 4.55 Ga yields the following rather messy equations:

(129Xe / 130

Xe)m,T

0

=

129Xe

130Xe

!

"#$

%&0

+'129

I0

130Xe

0,m

e('t

1+) / *(e(*t (1)0

T0

+ dt 26.20

(129Xe / 130

Xe)a,T

0

=

129Xe

130Xe

!

"#$

%&0

+

'129I

0

130Xe

0,m

e()* e

('t

1++ / )(e()t (1)0

T0,

0

-0

, dtd*

(e(T

0t (1) / )

26.21

Both these equations have the form 129Xe/130Xe = initial + radiogenic; the radiogenic component is the last term in both cases. We define the ratio of the radiogenic component in the 129Xe/130Xe ratio (i.e., in our usual notation 129Xe*/130Xe) of the mantle and atmosphere as R:

R =

129Xe *

130Xe

!

"#$

%&m,T

129Xe *

130Xe

!

"#$

%&a,T

=

129Xe

130Xe

!

"#$

%&m,T

'129

Xe

130Xe

!

"#$

%&0

129Xe

130Xe

!

"#$

%&a,T

'129

Xe

130Xe

!

"#$

%&0

(

)

**

+

**

,

-

**

.

**

26.22



190 3/29/07

This is the ratio of the last terms on the right in equations 26.20 and 26.21. We can see that these terms are functions of β, and κ/β only (the 129I/130Xe0 terms, terms for the initial 129I/130Xe of the Earth, which are also unknown, cancel). Staudacher and Allègre (1982) took the approach of solving for R through numerical integration using various values of β and κ/β. The results are plotted in figure 26.9, which shows R as a function of β with curves drawn for various values of κ/β. R can be independently esti-mated from the present 129Xe/130Xe ratios of the at-mosphere and degassed mantle if we can estimate the initial ratio (equation 26.22). Staudacher and Allègre estimated the initial 129Xe/130Xe as 6.34 from the solar wind value (the Sun would have had a very low (129I/130Xe)0 ratio because, unlike the Earth, it did not loose Xe relative to I when it formed; as a result, the present solar ratio should be similar to the initial terrestrial ratio). The atmospheric value is 6.48 and the mantle value is estimated from the highest 129Xe/130Xe observed, which was 7.09 when the paper was written. R is then estimated as:

R =7.09 ! 6.34

6.48 ! 6.34

"#$

%&'= 5.4

(Using the present observed maximum 129Xe/130Xe of ~7.5 yields a value of 8.3.) Recall that the ratio κ/β approximates to the fraction of 130Xe outgassed from the mantle. This can be independently esti-mated as about 0.5-0.6 (i.e., the mantle has lost 50-60% of its xenon). In Figure 26.9 the value of β corre-sponding to R= 5.4 and κ/β = 0.5 is about 10-7 yr-1 (R of 8 yields a value of β of about 2 x 10-7 yr-1). This value of β corresponding to releasing about 1/2 the 130Xe now in the atmosphere in about 7 million years (the factor of 2 higher β implies a factor of e (2.71) more rapid degassing). In other words, it im-plies a rather rapid early degassing. Notice that, at least in a qualitative sense, this result is very robust. Even if R were as low as 1.5 or as high as 100, if the fraction of xenon outgassed is anywhere between 20% and 100%, we still find a value of β between 10-8 and 10-6 yr-1, implying early catastrophic de-gassing. This sort of early catastrophic degassing is difficult to reconcile with the amount of radiogenic 40Ar observed in the atmosphere, which seems to require some later degassing (i.e., after some of the 40K had decayed to produce 40Ar). Therefore, Allègre et al. (1986) have proposed a more complex degassing function of the form:

J = J

0(1! b)e!"t

+ be!# t{ } 26.23

where b and γ are additional constants, with the value of γ being much shorter than that of β. Allègre et al. suggested appropriate values for b, β, and γ are 10-3, 3 × 10-7yr-1, and 2 × 10-9yr-1 respectively. This equation produces degassing fluxes through time as shown in Figure 26.10: an initial 'big burp' fol-lowed by slowly decreasing less intense degassing. We can interpret the 'big burp' as being a result of extensive melting of the mantle which may have occurred as a result heating due to release of gravita-tional energy during accretion (including as a result of a giant impact) and perhaps from decay of 26Al, which may have been abundant in the early Earth, if it formed early enough, as well. Subsequent, less intense degassing would result from volcanism, such as mid-ocean ridge volcanism today. Equation

aaa

1000

100

10

110-9

R

β

0.20.60.80.90.950.990.9991.0

κβ

10-8 10-7 10-6 10-5

Figure 26.9 Ratio of 129Xe*/130Xe in the mantle to 129Xe*/130Xe in the atmosphere as a function of β, the degassing rate constant and κ/β, the fraction of xenon degassed from the mantle.



191 3/29/07

26.23 still retains an early catastrophic term. Note that 129Xe would be insensitive to the second term in 26.23 because it all the 129I decays very early when the equation is still dominated by the first term. A number of workers have produced atmospheric evo-lution models and they differ from the Allègre et al. model we have discussed here in various details (e.g., Damon and Kulp, 1958, Ozima and Alexander, 1976, Hart, et al., 1985). However, they are generally consistent in concluding that there was an early phase of rapid degassing and subsequent slower degassing.

How much of the mantle has been degassed? A number of workers have considered this question, and, for the most part, they agree that about half the mantle has been degassed, although some workers have recently sug-gested the figure is much more than this. Some very simple assumptions and arguments lead to this conclusion, so let’s consider them briefly. Ar is the third most abundant element in the atmosphere. Its 40Ar/36Ar ratio, 295.5. Since the solar system initial 40Ar/36Ar ratio is < 1, essentially all the 40Ar has been pro-duced is radiogenic. There are 1.65 × 1018 moles of 40Ar in the atmosphere. From this, we can calculate how much of the solid Earth has been degassed if total amount of 40Ar by de-cay of 40K in the Earth. This can be calculated from equation 5.3:

40Ar* =

!e

!

40K(e!t

"1) (5.3)

provided we know the 40K content of the Earth. Unfortu-nately, K is not a refractory lithophile element (while litho-phile, it is moderately volatile), so its concentration in the Earth cannot be simply calculated from chondritic abun-dances. However, the ratio of K to U in the Earth appears to be reasonably uniform in all major reservoirs (Paul et al., 2002), with K/U = 10,000-12,700. The U content of the bulk silicate Earth appears to be in the range of 18 to 22.5 ppb. Combining these, we find that K concentration of the bulk silicate Earth is 180-285 ppm. Over geological time, we can compute that this would result in the production of 2.52-3.9 × 1018 moles of 40Ar. Comparing this value with the amount in the atmosphere, we find that 42 to 65% of the 40Ar produced over Earth’s history is now in the atmosphere. There are other views on this. For example, Albarede (1998) and Davies (1999) suggest much lower K/U ratios for the Earth and con-sequently calculate a much higher fraction of degassing. However, the evidence for low K/U ratio in the Earth is slim at best.

aaa

10

1010

108

106

2

1

0

4

23

1

2

1

10 30Ma

30Ma

10 40Ma

4 3 2 1 0

age (Ga)

4 3 2 1 0

4 3 2 1 0

4 3 2 1 0

36Arfluxg/a

radiogenicgas

1010

108

107

106

4He1020

fluxg/a

5

0.51

0.1

40Ar1010

fluxg/a

129Xe105

fluxg/a

4

2

3

1

Figure 26.6. Fluxes of noble gases to the atmosphere as a function of time based on equation 26.22 and the val-ues of b, β, and γ given in the text.



192 3/29/07

An interesting question is where is the rest of it? Since the continental crust is rich in K, one might wonder how much 40Ar is there. Estimates of the K content of the crust range from 0.9 to 2.2%. We saw earlier that the mean age of the crust is about 2 Ga. Assuming complete retention of radiogenic Ar, we calculate that the crust would contain 0.12 to 0.29 × 1018 mol. Roughly speaking, only about 3 to 10 per-cent of the missing Ar is the crust; the rest must be in the mantle. One might ask how it is that the mantle can remain so distinct in its isotopic composition of at-mophile elements if surface material is continually recycled to the mantle in subduction zones. The an-swer seems to be that the subducting slab is thoroughly degassed (about 98%) in the early stages of subduction (Staudacher and Allègre, 1988). This probably occurs through a combination of ‘dewater-ing’ of sediments as they are initially compressed in the trench, and dehydration (which we should more accurately call devolatilization, particularly in this context) during the first 100 km of descent.

References and Suggestions for Further Reading: Albarede, F., Time-dependent models of U-Th-He and K-Ar evolution and the layering of mantle con-

vection, Chem. Geol., 145:413-430, 1998. Allègre, C. J., A. W. Hofmann and R. K. O'Nions, Constraints on the evolution of Earth's mantle from

rare gas systematics, Nature, 303:762-766, 1996. Allègre, C. J., T. Staudacher, and P. Sarda, Rare gas systematics: formation of the atmosphere, evolution

and structure of the Earth's mantle, Earth. Planet. Sci. Lett., 81, 127-150, 1986. Damon, P. E., and J. L. Kulp, Inert gases and the evolution of the atmosphere, Geochim. Cosmochim. Acta,

13, 280- , 1958. Davies, G. F. , 1988. Ocean bathymetry and mantle convection, 1, large-scale flow and hotspots, J. Geo-

phys. Res., 93:10467-10480. Davies, G. F., Geophysically constrained mantle mass flows and the 40Ar budget: a degassed lower

mantle?, Earth Planet. Sci. Lett., 166:149-162, 1999. Farley, K. A. and H. Craig. 1992. Atmospheric argon contamination of oceanic island basalt olivine

phenocrysts. Geochim. Cosmochim. Acta. 58: 2519-2526. Farley, K. A. and R. J. Poreda. 1993. Mantle neon and atmospheric contamination. Earth Planet. Sci. Lett.

114: 325-339. Farley, K. A., J. H. Natland and H. Craig. 1992. Binary mixing of enriched and undegassed (primitive ?)

mantle components (He, Sr, Nd, Pb) in Samoan lavas. Earth Planet. Sci. Lett. 111: 183-199. Graham, D., Noble gas isotope geochemistry of mid-ocean ridge and oceanic island basalts: characteri-

zation of mantle source reservoirs, in D. Porcelli, et al. (ed.), Noble Gases in Geochemistry and Cosmo-chemistry, 247-218, 2002.

Hart, R., L. Hogan, and J. Dymond, The closed-system approximation for evolution of argon and he-lium in the mantle, crust and atmosphere, Chem. Geol., 52, 45-73, 1985.

Ozima, M., Noble gas state in the mantle, Rev. Geophys., 32:405-426, 1994. Ozima, M. and E. C. Alexander, Rare gas fractionation patterns in terrestrial samples and the Earth at-

mosphere evolution model, Rev. Geophys. Space Phys., 14, 386- , 1976. Paul, D., W. M. White and D. L. Turcotte, Modelling the Pb isotopic composition of the Earth, Phil Trans

R Soc Lond. A, 360:2433-2474, 2002. Sleep, N. H., 1990. Hotspots and Mantle Plumes: some phenomenology, J. Geophys. Res., 95:6715-6736. Staudacher, T. and C. J. Allègre, Recycling of oceanic crust and sediments: the noble gas subduction

barrier, Earth. Planet. Sci. Lett., 89, 173-183, 1988. Staudacher, T. and C. J. Allègre, Terrestrial xenology, Earth. Planet. Sci. Lett., 60, 389-406, 1982.

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Noble Gases and Evolution of the Atmosphere - Geol. 656