All?gre Claude J. Isotope Geology

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in the literature over a long period were h eavily contaminated and so too low. In 1985, the

author’s Paris team ¢nally managed to measure reliable

Ar/

Ar ratios for MORB by

using pillow lava glass, yielding

Ar/

Ar ¼30 000 (compared with the

Ar/

Ar ¼296

ratio of the atmosphere) (Sarda et al.,1985). From this, a mass balance for the Earth’s

could be esti mated (Alle

gre et al.,1996)(Figure6.44).The K content of the silicate Earth is

quitewellknown(250^280ppm).

Knowingthat

Kis1.16 10

4

oftotalK,wecancalculate

the total

Ar produc ed in 4.55 10

years: from140  10

gto15610

g, depending on the

valueuse dforK.Now,thetotalquantityofargonintheatmosphereis66 10

g.Ifweev aluate

Ar in the continental crust at a maximum of 4^10  10

g, there remains 60^86  10

gof

Ar, which is the missing argon inside the Earth.This means that for

Ar, the Earth is only

halfdegassed.

Thereislittle

Ar intheupper mantle.The£owof

Hefromtheoceanridges

is estimated at 1.1 10

moles yr

1

. Using the

He/

He and

He/

Ar ratios measured in

MORB, we ¢nd an

Ar £ux of 2 10

moles yr

1

. Ifwe acceptthatthe oceanic lithosphere is

entirely degassed when it passes through the ocean ridges by the fusion processes occurring

there, we can calculate the quantity of argon in the mantle if the mantle were homogeneous.

We ¢ n d 2.41.8 10

g,which doesnotmatchtheamountofmissingargon.

Where is the missing argon then? Experimental measure ments have shown that

neither argon nor potassium is soluble in iron even at h igh pressures. The refore the

argon is not stocked in the Earth’s core. That leaves just the lower mantle. Supposing, in

the standard model, an upper layer above 670 km convecting separately from the lower

Upper

mantle

Atmosphere

670 km

Continental

crust

Lower

mantle

Ar = 2.8–3.5 x 10

Ar = 4–10 x 10

Ar = 66 x 10

M = Mass

K = 1.7%

K = 40 ppm

Ar = 60–80 x 10

K = 220 ppm

Figure 6.44 The

Ar mass balance of the Earth. After Alle

gre

.(1996).

We know the terrestrial uranium value quite well as it is analogous to that of carbonaceous chondrites

(as is Nd which is also a refractory chemical element). Now, the K/U ratio, which is about constant on

Earth, is between 10 000 and 12 000. We can therefore deduce K.

This is not the case for

Ar, but

Ar was produced later by K decay. We shall see the explanation at the

end of this chapter.

289 Isotope geochemistry of rare gases

mantle: by the same cal culation as before we ¢nd that the upper mantle contains 2 10

g of argon. Therefore 60^86 10

gof

Ar is stored in the lower mantle. This model

therefore also supports the standard model with two layers which are degassed to di¡er-

ent extents.

In all, then, the three raregases c on¢rmth e two-layer stan dard mo del: a degassedupper

mantle an d a less-degassed (more primitive) lower mantle.This is an extremely important

con¢rmationbecause degassingofraregaseshasnothingtodowiththegeologicalphenom-

ena associated with di¡erentiation of the continental crust and which causes Rb/Sr, Sm/

Nd , and Lu/Hf fractionation. Yet both approaches l ead to the same outcome: a mantle

divided intotwolayers.

Twoimp ortantconsequencesfollowfrom thispatternofargon distributioni nthe mantle.

First, given the present-day distribution of roughly half of the total

Ar being found i n the

atmosphere and half in the lower mantle but none in the upper mantle, and assuming the

initial distributionwasuniform, theatmospheric

Ar is derivedfrom complete outgassing

of the upper mantle and one-third outgassing of the lower mantle. Since this calculation

conc erns

Ar, which has no p rim itive component, the observation relates to‘‘geological

outgassing’’from 4.4 Gatothe presentday.

Second,the( primitive)

Ar concentration is about200 times higher in thelower mantle

than in the upper m antle.Therefore the outgassing ofthe lower mantle has tobe suchthat it

travels through the upper mantle as a transient. Otherwise it would contaminate the upper

mantle.

Exercise

Just as we calculated the age of the continental crust we can calculate the mean age of the

atmosphere using argon isotopes. Given that the mass of the mantle is about 4  10

g, the

potassium content is 250 ppm with

K ¼1.16  10

4

total

; the mass of

Ar in the atmo-

sphere is 66  10

g and we can estimate the

Ar ratio of the Earth from

(

Ar/

Ar)

atmosphere

¼296. In addition we assume

Ar is degassed by 90–100%. Calculate

the age of the atmosphere.

Answer

We write the equation



atmosphere



Earth

 e

atm



We obtain

¼3.3 Ga. So the indication from argon is that the atmosphere formed much

earlier than the mean age of the continents. But this is not the end of the story!

6.4.4 Isotope geochemistry of xenon

Xenon has nine isotopes, of masses124, 126,128,129,130,131,132,134, and136. On Earth,

variations inabundancerelatedtoradioactive decayareoftwotypes: extinctforms ofradio -

activityand spontaneous fusion of

238

U.To these mustbe added the exceptional ¢ssion pro-

cess induced by

235

U in the Oklo nuclear reactor. Xenon-130 is taken as the reference

290 Radiogenic isotope geochemistry

isotope because it does not derive from any of these processes. Hence we can speak of

129

Xe/

130

Xe,

131

Xe/

130

Xe,

132

Xe/

130

Xe, and

136

Xe/

130

Xe ratios.

The¢rstoftheseratiosvariesbecau se

129

Xeisthedecayproductof

129

I,whichisanextinct

form of radioactivity (Reynolds,196 0).We saw in Chapter 3 how this form of radioactivity

was exploited for determining age di¡erences among meteorites. Now, this ratio varies on

Earth and is an essentialdatum.

The

131^136

Xe/

130

Xe ratios var y too, but the situation h e re is more c omplex as

their variation s may be attributed to extinct spontaneous ¢ss ion from

244

Pu or to

very-long-period spontaneous ¢ssion of

238

U. These isotope ratios were measured in

primitive carbonaceous meteorites, in the atmosphere, and also in rocks from the

Earth’s mantle. That is, like helium, neon, and argon, xenon too is found in the g lassy

margins of MORBs.

It has long been known that xenon isotope compositions in th e Earth’s atmosphere are

di¡erent from those i n carbonaceous chondrites, proving that the Earth’s atmosphere

formed after the carbonaceous chondrites did, because the isotopes in the denominators

oftheisotope ratiosaremoreabundantintheatmospherethanin carbonaceous chondrites.

Astheyareofradiogenic origin, theyare demonstrably younger.

The second important discovery, made byTho mas Staudach er and the present author

(1982), is that the

129

Xe/

130

Xe isotope ratios and the

132

Xe/

130

Xe isotope ratios (to choose

justone ¢ssiogenic ratio) of MORBs are greater than those ofthe atmosphere.They vary in

acorrelated manner (Figure6.45).

By contrast, the isotope ratios of what corresponds to OIBs, whether in Hawaii or in

Iceland, are only marginally greater than those of the atmosphere. For the

129

Xe/

130

ratio, this is unambiguous. It is proof of the intense

129

I activity in the upper mantle early in

the Earth’shistory.

The situation is mo re complex for

131^136

Xe/

130

Xe isotope ratiosbe cause their variations

stem either from extinct ¢ssion of

244

Pu or from long-period

238

U ¢ssion (Kuroda,1980).

The verydi⁄cult workof distinguishing between the e¡ect ofeach has led to acceptance of

thefollowingapproximation:



in MORBs, the excess of

131^136

Xe compared with the atmosphere (normed to

130

Xe) is

mostlydueto

244

Pu;



ingranites,onthe contrary, itis

238

U¢ssionthatis responsiblefor the essentialvariations.

Analysis of MORBs plotted on the (

129

Xe/

130

Xe,

132

Xe/

130

Xe) diagram (Figure 6.45)shows

thereis an excellentcorrelationpassing throughthe atmosphericvalue.

To derive the most information possible from this observation we concentrate here on

129

Xe from the mantle. The value observed in MORBs is

129

Xe/

130

Xe ¼7.65. T h e valu e

found in OIBs (Hawaii, Iceland, the Gala

pagos Islands) is 7 at most. The atmospheric

value is 6.5.These values con¢ rm the di¡erencebetween the MORB and OIBreservoirs. As

with neon, helium, andargon, the MORBreservoir (upper mantle)is more radiogenicthan

the OIB reservoir.

There is coherence then. Exceptthatthe di¡erencehere can onlyhave been established

in the early history of the Earth, since

129

Xe came from the decay of

129

I, which is extinct

radioactivity.The MORB and OIB reservoirs must have separated in the ¢rst150 mill ion

years of the Earth’s history and not have been merged since. Exchanges of the MORB

291 Isotope geochemistry of rare gases

reservoir both with the atmosphere and with the OIB reservoir have been limited for 4.3

billionyears.

We shall return to other repercussions for the age of the early E arth, but it is already

apparent that the ages we are dealing with here are much older than the ‘‘ag e of the

atmo sphere’’ calcu lated from a simple mass balance equation fo r the

K

system.

6.4.5 Coherence in rare gas geochemistry

We have seen that the use of four rare gases yielded coherent and co mplem entary results

when taken independently (Alle

gre et al., 1983c). It is natural and essential to see whether

analyses on the same samples yield coherent results too.Two graphs give the correlations

obtained between all the rare gases in MORBs and in OIBs (Figure 6.46) obtained by

Moreira etal.(1998).

For all rare gases (helium is not shown here because it is not contaminated by th e atmo-

sphere) we can distinguish two separate reservoirs with distinctive isotopic signatures.

Notice, though, that the essential thing about these correlations is the mi xing that occurs

air

136

Xe/

130

129

Xe/

130

Source

mantle

7.80

7.60

7.40

7.20

7.00

6.80

6.60

6.40

6.20

2.202.00 2.30 2.40 2.50 2.60

Figure 6.45 Correlation diagram of xenon isotope ratios in MORB. The

129

Xe/

130

Xe ratios are evidence

of extinct

129

I radioactivity. The

136

Xe/

130

Xe ratios are mostly from extinct

244

Pu ﬁssion and are coupled

with spontaneous long-term

238

U ﬁssion. The variations are due to mixing with atmospheric air either

in nature or in the laboratory during measurement.

292 Radiogenic isotope geochemistry

betweenthegasintheoriginalrockandth eair, whichinvariablycontamin atesthemeasure-

mentto some degree and makes raregasgeochemistrysoverydi⁄cult. In all cases MORBs

aremore radiogenicthanOIBs.

Exercise

Isotope ratios measured in the same glassy margin of a MORB are

Ne/

Ne ¼0.055,

Ne/

Ne ¼11.8,

Ar/

Ar ¼18 000, and

129

Xe/

130

Xe ¼7.2. Can you estimate the isotopic

compositions of the source, correcting for atmospheric contamination?

Answer

Yes, assuming contamination is identical for all rare gases. We take the value of neon as

the reference: 12.5 (or 13.5) and given the values of the isotope ratio of the atmosphere,

the other ratios can be computed. The answers are dependent on the chosen reference for

neon.

Exercise

Why do we not adopt the same reasoning for helium and neon as we used for argon by

computing the budget between the atmosphere, upper mantle, and lower mantle?

Answer

Because the atmosphere is not closed for helium and so the extent of outgassing is unknown.

The situation is even worse for neon. The atmosphere has a very different

Ne/

Ne isotopic

composition from the mantle. In other words, the present-day atmospheric content cannot be

considered as the product of mantle outgassing.

Despitetheseintrinsic di⁄cultieswiththelightraregases,we can estimatethe di¡erences

in concentrations between the upper and lower mantle for non-radiogenic isotopes by

using m easuredisotope ratios:

(

Ne/

Ne) x 10

air

um um

Ne/

0.03 0.04 0.05 0.06

(

Ar/

Ar) x 10

air

1 23

(

129

Xe/

130

Xe) x 10

2σ

air

Iceland

6.5 77.58

MORB

Figure 6.46 Correlation diagram of various rare gas isotope ratios related to radioactivity with the

Ne/

Ne ratio. The diagrams can be used to correct for atmospheric contamination. On one side is the

slope for MORBs and the other the result of the study on Iceland by Trieloff

.(1998), supposedly

representing the lower mantle. lm, lower mantle; um, upper mantle.

293 Isotope geochemistry of rare gases

He=

HeÞ

¼ð

He=

HeÞ

initial

þðU

HeÞ

ðtÞ

He=

HeÞ

¼ð

He=

HeÞ

initial

þðU=

HeÞ

ðtÞ

whereum andlmaretheupperandlowermantle, f

(t)andf

(t)theexpressions ofradioac-

tivedecay, and Uthe uran ium concentration.

Bytakingthe ratiosbetweenthe twoexpression s:







initial







initial



ðtÞ

weobtain (

He/

He)

initial

6000andU

4.

Ifwe take the mean age of the lower mantle tobe 4.5 10

years and less than1 10

years

for th e upper mantle,

ðtÞ18:58 and f

ðtÞ2:12:

 360:

Thisyields similarratios toargon and neon.

The di¡erence in concentration between the lower and the upper mantle is such that a

piece ofcontaminated lower mantle can onlydisplay upper-mantlevalu es if mixed in min-

ute proportions.Therefore, if the OIBs were from the lower mantle exclusively, the isotopic

composition of the rare gases they contain would be uniform (except in the unlikely case

of the lower mantle being highly heterogeneous). Since OIB composition is not uniform

(see Figure 6.38 for He), it must be concluded that OIBs are a mixture of lower and upper

mantle, but withonlysmall proportionsofmaterialfrom the lower mantle.

6.5 Isotope geology of lead

As seen when discussing geochronology, three of the isotopes of lead are produced by the

¢nal decay of radioactive chains:

206

Pb by

238

207

Pb by

235

U, an d

208

Pb by

232

Th.

Assuming the chains are i n secular equilibrium (given the length of geological time), we

can suppose that Uand Th de cay directly to the Pb isotopes (see Chapters 2 and 3). Just as

with Sr and Nd, we can try to ¢nd out whether the lead isotope ratios vary in basalts and

granites and so seek con¢rmation of the models developed with the threesome Rb^Sr,

Sm^Nd, and Lu^Hfandwiththe raregases.

In fact, the advantage with lead isotopes is that the results are naturally correlated since

the two decay schemes are chemically similar and it is only the decay constantthat di¡ers.

294 Radiogenic isotope geochemistry

It should also be reme mbered that as the Pb isotope ratios have the same denominator

(

204

Pb),mixturesarealwaysshownbystraightlines on thevariousplots.

6.5.1 The (Pb–Pb) isotope diagram or Holmes–Houtermans

diagram

One oftheuniqueadvantagesw ithuranium^leadsystemsis thatitis apriori easy to calcu-

late theo retical models to act a s references for the experimental data involvi ng on ly iso-

tope compositions that are more robustthan the parent^daughter ratios (se e Rus sell and

Farqu har, 1960). Let us see how a model Earth would behave i f it di¡ere ntiate d into two

envelopes, say, from the beginning of the Earth’s history if the two envelopes (continental

crust and mantle) evolved ever since as closed systems. As usual (

238

204

Pb)

today

is writ-

ten 

.Then

¼14 and 

¼ 8. It is assume d that the initial value of lead isotope com-

position is given by the analysis of sul¢des from iron meteorites which, as they do not

contain any uranium, record the isotope composition of the ¢rst instants of the Solar

System.

Bynoting:

 ¼

206

204

;

 ¼

207

204

; l

238

¼ l

; l

235

¼ l

;¼

238

204

;

and given that

238

235



today

¼ 137:8, the equations for the evolution ofthe four suppo-

sedlyclosedsystems up toth e presentcanbe written:



þ 

 1







137:8

 1



;

where the subscript (cc) stands for continental crust. Similarly, for the mantle (m) we can

write:



þ 

 1







137:8

 1



whereT

istheageofthe Earth.The initialratios

¼9.307 an d 

¼10.294 havebeen deter-

mined exactly by various analyses of iron meteorites and carbonaceous chondrites

(Tatsumoto et al., 1973).

Remark

Look back at Chapter 2 for how to reach these equations from the laws of radioactivity. Reread the

exercise on the Rb/Sr ratio at the beginning of this chapter to calculate  from chemical composi-

tions of uranium and lead.

We have already mentioned the Pb–Pb method when discussing the age of the Earth. We shall review it

more fully here. It might then be useful to reread the part of Chapter 5 about the age of the Earth.

295 Isotope geology of lead

These equationsaretheparametric equationsoftwocurves,theleading parameterbeing,

that is the ratio (

238

204

Pb)

today

. Notice that these are the same equations as for the Rb^Sr

orSm^Ndsystems,exceptthat,inviewofthevaluesofthe decayconstants,thelinearapprox-

imation is no longer valid. Let us represent them as a fu nction of time (calculate them

from the formula  ¼ 

þ  e

 e



. It will be observed that the form of variation

with time is very di¡erent for the

206

Pb/

204

Pb ra tio and the

207

Pb/

204

Pb ra tio. The la t ter

increasesveryrapidlyat¢rstandthen much moreslowly. Itis almostan extinctformofradio-

activity. The

206

Pb/

204

Pb ratio increases much more steadily, but not linearly. Once again,

this is because of the di¡erence between the decay constants.The isotope evolution referred

toin correlationdiagrams canalsoberepresented:(

206

Pb/

204

Pb,

207

Pb/

204

Pb)(Figure6.47c).

Notice ¢rst that the three curves are concave downwards but to di¡erent degrees.This is

because ofthe di¡erentdecay constants. Letus try to de¢ne th e isochrons (geometric locus

ofpointsofthe same age) in Figure 6.47c.We can do thisgraphicallyby taking, for example,

p oints for 3 b illion, 2 billion, and1billionyearsand for the presentti me in the three systems

de¢ne d above ( let us take the 

and 

values u sed for calculating the age of the Ear th in

Chapter 5).We observe that each de¢nes a straight line, with the whole determining an

arrayofstraightlines convergingtowards (

, 

) (dashedin Figure 6.47).

Letustry todemonstratethis mathematically.ForagivenageT,whatisthe equationofthe

geometric locus of representative points independentlyof  ? From the equations giving 

and 

, we cantherefore eliminate 

by writing:



ðTÞ



ðTÞ

137:8

 e



HereT

is common at4.55 10

years(or4.50  10

years), and Tis ¢xed. The equationthe re-

foretakes theform:

y  y

x  x

¼ C:

This is the equation of a straight line through the point (x

, y

), that is the original isotope

compositions.We ¢nd the result ofour nume rical construction.This array of straight lines

therefore calibrates the diagram in ages. These straight lines are the geometri c locus of

p ointsofthe same age andareknown as isoch rons.

We thereforehave an (, ) plot formed bya series of curves cutbyan arrayofconverging

straight lines. The point of convergence is (

, 

), the initial composition of the Earth

(Figure6.47c).This isknown as theHolmes^Houte rmans (H^H)diagram.

If we assume the Earth is made up of concentric envelopes isolated from each other and

having evolved as closed systems since the ‘‘beginning,’’ then the initial ratios of any

geologicalobject (mineral,rock, massif) (

,

) plotted on the diagram show the age ofthe

object andthe  ofthesystem inwhich ithasbeen since the‘‘beginning.’’

Muchuse was mad e ofthis diagram in the earlydays of isotope geochemistry for extract-

ing informationfrom Pbisotopemeasurementsongalena.Galenacrystalswiththeformula

After the two scientists, the Scotsman Arthur Holmes and the Russo-Swiss Fritz Houtermans , who

developed it independently in 1946 (see Holmes, 1946; Houtermans, 1946).

296 Radiogenic isotope geochemistry

PbS contain neither uranium nor thorium and so the lead isotope measurement corre-

sponds to initial isotope ratios at the time they formed. Unfortu nately it is often di⁄cult to

determine the absolute age of galena directly with precision and very often we must settle

for an age of the geological setting.When working with galena, it c an be seen that very few

galenacrystalslieontheisochrons correspondingtotheirsupposedages,meaningthatgen-

erally the idea of evolution in the closed system of envelopes that have been isolated since

βo

αo

6 = μ

8 = μ

α =

206

Pb/

204

9 = μ

10 = μ

12 = μ

14 = μ

T = 0 Ga

T = 1 Ga

= 2 Ga

= 3 Ga

= 4 Ga

12 14 16 18 20 22 24

β =

207

Pb/

204

μ = 14

μ = 8

3 2 1

18.79

18.56

18.11

16.89

15.65

13.62

12.19

13.35

14.07

14.76

15.02

15.12

= 14

μ = 8

Time (Ga)Time (Ga)

3 2 1

10.48

12.62

14.16

16.026

17.29

23.29

21.07

18.34

15.13

11.39

Figure 6.47 Evolution of

206

Pb/

204

Pb and

207

Pb/

204

Pb ratios as a function of time for two  values

( ¼14 and  ¼8). (a, b) Notice that the

206

Pb/

204

Pb variation is very progressive while the

207

Pb/

204

ratio varies very little after 2 Ga. (c) Plot of  versus :

206

Pb/

204

Pb ¼,

207

Pb/

204

Pb ¼ for the previous

two  values (and some other values of ). Time is present here in parametric form. We distinguish the

geometric locus of points evolving over time with the same  (growth curves) from the geometric locus

of points of the same age having evolved with different  values (isochrons) (dashed lines).

297 Isotope geology of lead

the beginnings of the Earth does not correspond to geological reality. Nowadays, that does

not surp rise us after all that has been said about the evolution of the crust^mantle system

and its complexity.These results simply con¢r m this complexity, but in1950 this was a real

dis covery.

In practice, galena crystals have H^H model ages that are either older or you nger than

their geological ages. Some even have ‘‘model ages’’ in th e future. Lead with H^H model

ages that are older than the actual age are known in geochemical jargon as B-type lead

(after Bleiberg mine in Austria) while those with model ages younger than th e real age are

k nown as J-type lead (after Joplin mine in Missouri).T hese ages were ¢rst interpreted by

JohannesGeissof Bernein1954, byassuming atwo-stage geological history witha change

238

204

Pb ¼

ratios (Figure6.48).

The equationsofatwo-stagemodel arewritten:

 ¼ 

þ 

 e



þ 

 1



 ¼ 



137:8

 e





137:8

 1



When 

>

the model age is younger (J-type).When 

<

the model age is older (B-

type). Everything then comes down to constructing a gr id analogous to the H^H diagram

with a growth curve and isochron, but making the system start from a certain timeT

with

initialratios(T

)and(T

) (Figure6.48).

12 14 16 18 20

Geochron

Secondary isochron

Figure 6.48 Diagram of (, ) explaining how J-type or B-type lead is produced with a two-stage history

and change of . The ﬁrst stage is evolution from

in the same reservoir with 

. Two new

reservoirs are formed at

. One has a  value greater than 

and another a  value less than 

. The

ﬁrst yields J-type lead, the second B-type lead.

Nier was already alert to this, which is probably why he did not want to calculate an ‘‘age of the Earth.’’

298 Radiogenic isotope geochemistry