Geol. 656 Isotope Geochemistry
Lecture 26
Spring 2007
NOBLE GASES AND EVOLUTION OF THE
ATMOSPHERE
INTRODUCTION
Just as variations in the isotopic composition of radiogenic incompatible elements provides some information 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 element 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 radionuclide 129I (half life: 17 Ma) and other Xe isotopes were produced by fission of the extinct nuclide
244
Pu (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 compounds 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 continental crust are generally at low
concentration and furthermore, are dominated by radiogenic components. Thus
the two main reservoirs of
noble gases in the Earth are
the atmosphere and the mantle. 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 con3
4
Figure 26.1. Comparison of He/ He analyses of 573 MORB and 759
tamination is not usually an
OIB from the PetDB and GEOROC databases..
issue. Measurement of the
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Lecture 26
Spring 2007
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 adhere to the usual convention of placing the radiogenic isotope in the numerator, most report the
3
He/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:
! 3 He $
( 3 He /4 He)sample
= 3
#4 &
4
" He % R / R A ( He / He) atmosphere
26.1
In these units, crustal rocks generally have He isotope ratios in the range of 0.01 to 1 while mantlederived 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
3
He/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 element that is lost from the Earth in significant quantities. This is because it light enough that some fraction of He atoms reach escape velocity in the upper atmosphere (while H is lighter, almost all H in the
atmosphere is present as H2 O, 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 composition of He in MORB. There are several obserTable 26.1. Atmospheric Noble Gas Isotope Ratios
vations: first, the ratio in MORB, and presumaIsotope Ratio
Value in the Atmosphere
bly therefore the depleted upper mantle is
3
He/4He
1.39 × 10-6
higher than the atmospheric values, with a
4
3
He/ He
7.19 × 105
mean value in MORB of 8.8±2.5 and a median
21
20
Ne/ Ne
0.00296
value of 8.1. Second, this value is quite uni22
Ne/20Ne
0.102
form in MORB. Most of the samples with R/RA
40
Ar/36Ar
295.5
> 10 come from parts of the ridge close to oce129
Xe/130Xe
6.496
anic islands and are thus likely influenced by
132
Xe/130Xe
6.607
mantle plumes.
134
Xe/130Xe
2.563
Figure 26.2 shows the isotopic composition of
136
Xe/130Xe
2.176
∗
Creationist’s have claimed that He cannot escape from the Earth’s atmosphere because it does not reach
escape velocity. Since 4 He is steadily produced by α decay, 4He should steadily accumulate in the atmosphere 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 principal 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.
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Lecture 26
Spring 2007
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
40
evidence that they are derived from
Pacific
Hawaii
a part of the mantle that has been
Atlantic
(Loihi)
less degassed that the mantle that
gives rise to MORB. The latter is
30
Indian
generally assumed to be the upper
Continental
mantle or asthenosphere. Simple
3He
logic suggests that the deep mantle
4He
20 Heard/Kerguelen Societies
should have experience less melting
Juan
Fernandez
and degassing than the upper man(R/RA)
CV
Reunion Cooktle (because melting and degassing
can occur only near the surface).
Australs
Pitcairn
10 Canaries
Hence, high He isotope ratios in
MORB
plume-derived basalts is often cited
Tristan/
Marquesas (Davies, 1988)
as evidence that plumes come from
Gough
the deep mantle. Once must be
however. Since the Earth is
0
5
10
15 careful,
not a simple place, simple logic
might be misleading.
Low 3He/4He ratios in some
Iceland
plumes, such as Tristan and St. He40
lena, could reflected the presence or
Hawaii
predominance of material recycled
(Loihi)
from the Earth’s surface, such as
30
Galapagos
oceanic crust, in these plumes.
There is an inherent inconsistency
between
He and non-noble gas ra3 He
Samoa
diogenic isotope ratios in mantle4He
20
Afar
derived basalts. Overall, there is
(R/RA) ASP Yellowstone
little correlation between He isotope
ratios and other isotope ratios, such
Bouvet
Easter
as 87Sr/86Sr, as is illustrated in Figure
Azores Cook-Australs
10
26.3 (although correlations often
MORB
exist within individual oceanic isMarquesas
St. Helena
lands). Furthermore, the highest
(Sleep, 1990)
3
He/4He ratios are associated with
0
5
10
15 intermediate 87Sr/86Sr, 143Nd/144Nd,
and Pb isotope ratios (Figure 26.3).
Plume Flux (km3/y)
These high 3 He/4He ratios suggest
that this material has been substanFigure 26.2. Helium isotope ratios in plume-derived batially less degassed than material
salts and MORB as a function of plume flux. There is no
with lower 3He/4He ratios. On the
apparent relationship between plume flux and He isotope
other hand, isotope ratios such as
ratios. ASP = Amsterdam-St. Paul. Modified from Graham
87
Sr/86Sr associated with these high(2002).
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Lecture 26
Spring 2007
Iceland
Loihi
30
3He
4He
(R/RA)
Reykjanes
20 Ridge
10
Galápagos
Mauna
Loa
Juan
Fernandez
M. Kea
Koolau
CRB
Samoa
Heard
Atlantic
MORB St. Helena
0.703
Shimada
Smt
0.704
0.705
87Sr/86 Sr
87
African Xenoliths
Tristan
Gough
0.706
0.707
86
Figure 26.3. Relationship between 3He/4He and Sr/ Sr in mantle materials. CRB = Columbia River
Basalts. From Graham (2002).
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
Ar/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. Furthermore, 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 substantial fraction of the solid Earth to account for its atmospheric abundance. The K content of the bulk silicate 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. 3 He/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 contrast 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 concentration 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
38
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Lecture 26
Spring 2007
Figure 26.4. 3He/4He vs. 40Ar/36Ar in MORB, OIB, and some related xenoliths. Variation in 40Ar/36Ar is due largely to atmospheric contamination –
hence interest centers on the maximum values. From Graham (2002).
MORB than for OIB, it is more often interpreted as implying the MORB source has been more thoroughly 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 nuclides decaying to any of the Ne
isotopes (20Ne, 21Ne, and 22Ne).
However, 21Ne can be produced by
several nuclear reactions, such as
18
O (α,n) 21Ne or 24Mg (n,α) 21Ne
(the α and n coming from α decay
and fission). Hence 21Ne is “nucleogenic”. These reactions produced
significant
variations in
the
21
Ne/22Ne ratio in the mantle since
21
Ne 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).
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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
21
Ne/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 occurred during this processes (driving the
20
Figure 26.6. Model for the variation of Ne isotope
Ne/22Ne and 21Ne/22Ne down along a line with
ratios in the Earth. The atmospheric ratios deslope = 2 in Figure 26.6). The Ne in the mantle at
crease relative to solar values along a massthat time, however, did not suffer this fractionadependent fractionation line during loss of Ne
tion and retained “solar" Ne isotopic composi21
from early atmosphere. 21Ne is produced in the
tion. Over time, Ne was produced in the manmantle by (α, n) and (n,α) reactions. Variations
tle by the reactions mentioned above, driving the
observed in MORB and OIB represent mixing bemantle isotope ratio horizontally to the right in
20
tween this ‘degassed mantle’ Ne and atmospheric
Figure 26.6. (It is also possible to produce Ne by
Ne as a result of contamination during eruption.
these same reactions with different targets, but
20
because Ne is so much more abundant, the affect on the 20Ne/22Ne ratio would be insignificant.) OIB, in their model, are derived from a less degassed 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 contamination 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 contamination, 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.
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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).
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 magmatism continues to outgas the mantle today. Quite possibly this is the main process by which the atmosphere (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 outgassing. 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, although 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 something 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-
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Lecture 26
Spring 2007
ter a nucleosynthetic event, and (2) a substantial
atmosphere
fractionation of I from Xe must have occurred
129
early in Earth's history. So Xe variations procontinental crust
vide clues to the early degassing history of the
Earth. Helium is unique because the Earth is an
C
open system with respect to He. 4He is continudepleted
ally created, while 3He, for all practical purdegassed
upper mantle
D
mantle
poses†, is not, hence He should give us a perspecVO
tive on the present degassing rate. The Ufissogenic Xe isotopes and Ar are daughters of
long-lived nuclides and should integrate the enundepleted
undegassed
V
tire degassing history of the Earth.
mantle
lower mantle
Lets take a hypothetical Earth box model of the
Earth (Figure 26.8). It has the three reservoirs we
Figure 26.8. Box model of the volatile inventory of
have discussed before, continental crust (denoted
the Earth (from Allégre et al., 1986).
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 substantial 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 parents and the noble gas daughters, though the exact concentrations of both are unknown. Together, reservoirs 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 silicate 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.
36
d=
36
ArA
ArO + 36 ArA
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 3 He, such that the 3 He/4He produced in the Earth should
have a R/R A 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.
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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. Rearranging equation 26.3 yields:
d=
( 40 Ar /
36
Ar)O – ( 40 Ar /
36
Ar)T
( 40 Ar /
36
Ar)O – ( 40 Ar /
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 /
40
( Ar /
36
36
Ar) D – ( 40 Ar /
40
Ar) D – ( Ar /
36
Ar)T
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 (atmospheric), 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
40
K, and the 40Ar/36Ar has consequently increased. Because of the time-integrating character of radiogenic 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 depending on the degree of outgassing and the 40K/36Ar ratio of the mantle. The available data are not in accord 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, because it must take account of 1.) transport of gas from mantle to atmosphere, 2.) growth of the radiogenic 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 detail. However, the situation for 129Xe is somewhat simpler. Because of the short-half life of the parent,
129
I, 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 decreased, i.e., exponentially according to the radioactive decay equation. Therefore, we chose an equation to describe the outgassing rate having an exponential form:
J 0 e! " 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 catastrophic 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
tle is then given by:
d(130 Xem,t )
dt
= !" 130 Xem,0 e! # t
130
Xe in the man-
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(130 Xea,t )
dt
= ! 130 Xem,0 e" # t
26.9
Integration of equations 26.8 and 26.9 yields:
130
$ !
'
Xem,t = ! 130 Xem,0 &1 + e# " t # 1 )
% "
(
(
130
Xea,t =
)
! 130
Xem,0 $%1 # e# " t &'
"
26.10
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:
!
#
"
130
130
Xea
Xem,0
26.12
So for early catastrophic degassing, the κ /β ratio is equal to the ratio of the 130Xe content of the atmosphere 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 simultaneously 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(129 Xem,t )
dt
" 129 Xe %
= ! $ 130 ' ( 130 Xem,0 e! ) t + * 129 I m,t
# Xe & m,t
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We assume that 129I is not lost from the mantle, so
I 0 e! "t
26.14
" 129 Xe %
= ! $ 130 ' ( 130 Xem,0 e! ) t + * 129 I 0 e! *t
# Xe & m,t
26.15
129
d(129 Xem,t )
and
dt
I m,t =
129
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(129 Xea,t )
dt
! 129 Xe $
= # 130 & ' 130 Xem,0 e( ) t
" Xe % m,t
26.16
We now want to consider how the 129Xe/130Xe ratio has evolved with time. For the mantle:
d(129 Xe / 130 Xe) m,t
dt
=
! 129 I m,t
130
26.17
Xem,t
substituting equations 26.14 and 26.10 for the right side denominator and numerator respectively:
d(129 Xe / 130 Xe) m,t
dt
=
! 129 I 0 e" !t
130
26.18
Xe0 %&1 + # / $ (e" $ t " 1) '(
For the atmosphere:
d(129 Xe / 130 Xe) a,t
dt
$ 129 Xe ' .,
! e" #t *,$ 129 Xe '
= " !t
"
+
/
(e " 1) ,&% 130 Xe )( m,t &% 130 Xe )( a,t ,
0
26.19
Integrating these equations from 0 to T = 4.55 Ga yields the following rather messy equations:
T
129
(
Xe /
130
Xe) m,T
0
! 129 Xe $
' 129 I 0 0
e( 't
= # 130 & + 130
dt
Xe0,m +0 1 + ) / * (e( * t ( 1)
" Xe % 0
! 129 Xe $
(129 Xe / 130 Xe) a,T = # 130 & +
0
" Xe % 0
' 129 I 0
130
Xe0,m
-0
( )*
,e ,
T0
0
0
(e
e( 't
dtd*
1 + + / ) (e( ) t ( 1)
(T0 t
( 1) / )
26.20
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=
! 129 Xe * $
#" 130 Xe &%
!
#"
m,T
Xe * $
130
Xe &% a,T
129
( ! 129 Xe $
! 129 Xe $ ,
'
* # 130 &
# 130 & *
* " Xe % m,T " Xe % 0 *
= ) 129
129
* ! Xe $ ' ! Xe $ *
#" 130 Xe &% *
* #" 130 Xe &%
a,T
0 .
+
189
26.22
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Geol. 656 Isotope Geochemistry
Lecture 26
Spring 2007
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
R
0.999
numerical integration using various values of β and
1.0
0.99
1000
κ/β. The results are plotted in figure 26.9, which
κ
0.95
β
shows R as a function of β with curves drawn for
0.9
various values of κ/β. R can be independently esti0.8
0.6
mated from the present 129Xe/130Xe ratios of the at100
0.2
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
10
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
1
is 6.48 and the mantle value is estimated from the
10-7
10 -6
10-5
10 -9
10-8
highest 129Xe/130Xe observed, which was 7.09 when
β
the paper was written. R is then estimated as:
Figure 26.9 Ratio of 129Xe*/130Xe in the mantle to
129
" 7.09 ! 6.34 %
Xe*/130Xe in the atmosphere as a function of β,
R=#
=
5.4
&
the degassing rate constant and κ/β, the fraction
$ 6.48 ! 6.34 '
of xenon degassed from the mantle.
(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 estimated 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 corresponding 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 implies 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 degassing.
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' followed 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 gravitational 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
190
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Geol. 656 Isotope Geochemistry
Lecture 26
Spring 2007
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 evolution 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 suggested 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
40
Ar/36Ar ratio is < 1, essentially all the 40Ar has been produced 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 decay of 40K in the Earth. This can be calculated from equation
5.3:
40
Ar* =
!e
!
40
K(e!t " 1)
(5.3)
1010
1010
107
108
106
36Ar
108
flux
g/a 106
10 Ma 30
5
4
3
2
4
3
2
1
0
1
0
4He
1020
1
flux 0.5
g/a 0.1
4
40Ar
1010
4
3
2
1
3
flux 2
g/a 1
10
4
3
2
Ma
1
30
0
provided we know the 40K content of the Earth. Unfortu2
2
radiogenic
129Xe
nately, K is not a refractory lithophile element (while lithogas
phile, it is moderately volatile), so its concentration in the
105
Earth cannot be simply calculated from chondritic abun1
flux 1
dances. However, the ratio of K to U in the Earth appears to
g/a
be reasonably uniform in all major reservoirs (Paul et al.,
10 40
Ma
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.
0 4
3
2
1
0
Combining these, we find that K concentration of the bulk
silicate Earth is 180-285 ppm. Over geological time, we can
age (Ga)
compute that this would result in the production of 2.52-3.9 ×
Figure 26.6. Fluxes of noble gases to
1018 moles of 40Ar. Comparing this value with the amount in
the atmosphere as a function of time
40
the atmosphere, we find that 42 to 65% of the Ar produced
based on equation 26.22 and the valover Earth’s history is now in the atmosphere. There are
ues of b, β, and γ given in the text.
other views on this. For example, Albarede (1998) and Davies
(1999) suggest much lower K/U ratios for the Earth and consequently calculate a much higher fraction of degassing. However, the evidence for low K/U ratio in
the Earth is slim at best.
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Geol. 656 Isotope Geochemistry
Lecture 26
Spring 2007
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 percent 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 atmophile elements if surface material is continually recycled to the mantle in subduction zones. The answer 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 ‘dewatering’ 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 convection, 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. Geophys. 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: characterization of mantle source reservoirs, in D. Porcelli, et al. (ed.), Noble Gases in Geochemistry and Cosmochemistry, 247-218, 2002.
Hart, R., L. Hogan, and J. Dymond, The closed-system approximation for evolution of argon and helium 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 atmosphere 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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