All?gre Claude J. Isotope Geology

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repeated by the teams of B e rnard B ourdon in the Paris laboratory (Caro et al., 20 03) yield-

ing an excess of

142

Nd in the Isua rocks of Greenland dated 3.8 Ga, but of on ly þ10 to þ 15

ppm (Figure 6. 78). Notice thatthe p recision reported in the measurementof isotopic com-

positions is the extremelimitofwhatcurrenttechniques canachieve.

Dating ofthe same rocksby the convention al

147

Sm^

143

Nd metho d con¢rmed the ageof

3.8 Ma and yielded the initial

143

Nd/

144

Nd ratio expressed in "

CHUR

¼þ2. It is possible,

then, to reason in terms of a two-stage model.The ¢rst stage involves meteoritic material

from4.576GatoT

.Then, fromT

to 3.8 Ga, the primitive crust (or the pr imitive residual

mantle),T

being theageofterrestrial di¡erentiation.

To dothe calculation,wetake 4.576 Gaasthe origin, which is more convenientforextinct

radioactivities. Letus call thetwoisotopicratios of Nd  and .



143

Nd=

144

Nd; ¼

142

Nd=

144

Nd:

We note "

143

in10

4

and f

142

in10

6

as relativevalues against astandard:



143

143=144 Nd

sample

143=144 Nd

standard

 1



 10

143

143=144 Nd

sample

143=144 Nd

standard

 1



 10



147

144

;

142

(ppm)

x 100

Metasediments

Orthogneisses

Metabasalts

Amphibolite

enclave

Acasta

Barberton

Pitcairn (EM I)

Societys. (EM II)

MORBs

-5 0 5 10 15 20 25

Figure 6.78 Measurements of

142

Nd anomaly in the Isua rocks of Greenland. After Caro

. (2005).

349 The early history of the Earth

butis calculatedat 4.576 Ga and not atth e presenttime.

a ¼

146

147

at 4:576 Ga:

The two evolution equations are written as multi-stage model with  as thefractionation

factorbetweenthe chondritic episodeandth e primitiveEarth episode.

 ¼ 

þ 

1  e

l



þ 

l

 e

l



 ¼ 

þ 

a 1  e

l



þ 

l

 e

l



;



and  bei ng the i nitial isotopic ratios, l

and l

the two radioactive constants, and T

being thetime3.8 Ga calculate d since 4.576,thatis,T

¼0. 776 Ga.

This non-linear system of two equations with two unknowns  and T

can be solved gra-

phicallybyconstructing the two curves corresponding to thetwo equations with thevalues

measured for , 

, ,

, a,and

A fewvalues areneededfor the calculation.

143

Nd=

144

NdÞ

t¼0

¼ 0:506 677 48



present day

¼ð

147

Sm=

144

NdÞ

Bulk Earth

¼ 0:1966; or 

¼ 0:201 942 for 4:567 Ga

147

Sm=

144

SmÞ

present day

¼ 4:888 99; or 5:037 316 6 for 4:567 Ga

142

Nd=

144

Nd ¼ 1:141 838 2; or 1:141 478 8 for 4:567 Ga

146

Sm=

144

SmÞ

¼ 0:008:

From this it can be deduced that

146

Sm/

147

Sm ¼a ¼0.001588178 and therefore the param-

eter 

a ¼0.000320 719.

The curves  ¼f(T

) are therefore drawn for the pairs

147

Sm^

143

Nd and

146

Sm^

142

takingtwovaluesforobservations at3.8 Ga.

143

¼þ1:5 and þ 2f

142

¼ 15 and 10 ppm:

It can be s een that the two curves intersect between 4.46 and 4.35 Ga for (T

) (Figure 6. 79).

This is about the age determined for the di¡erentiation of the core and the atmosphere,

with  for the present day of 0.216.

The question is what does this age mean? The rocks analyzed by Caro et al.(20 03)

were mostly metamorphic and metasedimentary rocks. They interpreted the results

as being th e value of a primitive depleted mantle which was the complement of di¡eren-

tiation of the ¢rst continental crust. Given the nature of the rocks, it is not obvious that

th is was their origin. An alternative interpretation would be that these values are those

of a lunar-type primitive crust, that is, on e rich in plag ioclase. The residual mantle (not

found) would have a negative "

142

value. As thi ngs stand , both interpretations are possi-

ble. In addition Harrison et al. (2 005) using hafnium isotopes in old zircons claim the

existenc e of a very early crust. The pre cise age of this crust and its nature are still sub-

jects of debate.

350 Radiogenic isotope geochemistry

ISUA

CHONDRITES

0.196

100x ε

142

144

146

Sm /

144

-30

-20

-10

-3.5

1 2 3 4 5

4.5 Ga 4.4 Ga 4.3 Ga

6 7 8

μ = 0.216

μ = 0.11

4.576 Ga 4 Ga

K-1

Time relative to 4.576 (Ga)

4.46

μ = 0.216

present time

0.1

0.2

0.3

0.4

100 200 0 300 400 500 600

4.38

1.5

100 ε

147

146

Figure 6.79 (a) Age determination of differentiation of the primitive crust using the two Sm–Nd

systems. (b) Isua anomalies represented on the isochron diagram.

351 The early history of the Earth

Remark

More recently Boyet and Carlson (2005) have asserted that ordinary chondrites have a f

142

value of

–20 ppm compared with the Earth. Unfortunately, there are few C1 and C2 carbonaceous chon-

drites in their measurement sets and the dispersion is quite wide. What are the values for Bulk

Earth? It is best to wait a while, then, before incorporating these results into this textbook although

readers need to know of their existence and should follow the development of this chapter.

6.7.4 The

187

Re–

187

Os system and accretion–differentiation

chronology

Examination of the evolution of the

187

Os/

186

Os ratio of the Earth’s m antle showed us that

theRe/Oschemicalratioofthemantlewasveryclosetothe Re/Osratioofthe carbonaceous

chondrites. Now, this is a surprising result giventhat both Re and Os arehighlysiderophile

elements,thatis,theyenterli quidiron inpreference tosilicates.

Laboratory experiments for these elements give a partition coe⁄cient D ¼C

silicate

10

^10

. Most Re and Os therefore passes intothe iron core, as theyarein the iron

phase ofordinary chondrites and in the metallic iron of iron meteorites. But Re and Os do

nothave exactly thesame a⁄nity for iron: Os is more siderophilethan Re.We speakofafac-

torof10 to100betweenthem.

Letuslookatthiswitha simple model.Fromthe partitionequation oftrace elements:

mantle

¼ C

=F þ Dð1  FÞ

where Fis the prop ortionofthe mantle (between 0 and1).

Inthe caseof Re andOs,because D is verylarge, F << D (1 F), therefore:

mantle

¼ C

=Dð1  FÞ:

Accordingly, theratiobetween thetwoele mentsRe and Os iswritten:



mantle



Therefore:

ðRe=OsÞ

mantle

10ðRe=OsÞ:

Now,observation showsthat(Re/Os)

mantle

¼(Re/Os)

initial

How can this apparent contradiction be accounted for? By admitting that the accretion

p rocess continued after di¡erentiation of th e core and so contributed enough Re and Os,

incorporated i n the mantle (probablyby primarysubduction processes) for them to domi-

nate the Re an d Os balance of the present-day mantle. Let us try to put this in somewhat

morequantitativeterms. Letuswriteabalance equation:

mantle

meteorite

mantle

where C

is the concentration in osmium, M

mantle

the mass of the mantle, and m the

added mass. Now, C

mantle

¼3 ppb and C

chondrites

¼490 ppb. Hence m/M ¼0.6%. Less

352 Radiogenic isotope geochemistry

than 1% of the mass of the mantle was added after 4.4 Ga by the accretion processes.

This in dicates that accretion probably de creased very rapidly after 4 Ga, as the curve

of lu nar craters also indicates.

Exercise

(1) Given that

mantle

¼0.26 ppb and

chondrites

¼37 ppb, calculate the ratio (

(2) If we underestimate the abundance in the mantle by 100%, how is the result altered?

Answer

(1) 0.7%.

(2) The ratio changes to 1.4%, which does not alter the conclusion in qualitative terms.

Ifweattempttomakea(provisional)reviewofthesestudiesoftheprimordialEarth,what

can we say today? First of all, a methodological point we shall return to i n quantitative

terms in the ¢nal chapter: extin ct forms of radioactiv ity do not record pr imordial p heno -

mena i n the same way as long - period forms of radioactivity. Th e former are sensitive to

short- term £uctuations, the latter on th e contrary average var iations out more over the

long term.

Together they give complementary views of primordial phenomena, each of which is

insu⁄cient in itself. This is the case for

Ar and

129

Xe for the atmosphere and for

206

Pb,

207

Pb, and

182

Hf for the core, and will be the case for any new form of extinct radioactivity

that mightbeused inthefuture.

Accretion is a process that lasted for quite some time after 4.4 Ga.The formation of the

coreis aphenomenonthatwaspreparedbydi¡erentiationof iron in planetesimalsanditself

occurred rather suddenly (perhaps in less than 100 or 1000 years) sometime between 4.4

and 4.35 Ga.Theatmospherewasproduce d byoutgassingofthe mantle. It¢rstformedvery

suddenly at 4.4 Ga and has been enriched throughout geological time through volc anic

eruptions.

And the continents? The interpretation of the

142

Nd anomalies is still a matter of debate,

but workers agree that if there was a primordial crust dating from the great di¡erentiation

of 4.4 Ga, that crust was destroyed and digested by the mantle, because we have no record

of tha t

142

Nd in rocks as old as 3.4 Ga.The existence of detrital zircons dated 4.3 to 4.4 Ga

seemto carryasimilar message. No continental rocks. Onlydetritalminerals. Allofth is sug-

gests that the primordial continental crust was ephemeral. Apart from this possible occur-

rence of a very primordial continental crust (perhaps a plagioclast crust like that on the

Moon) thegrowth curvesofcontinentsinthegeological and geo chemicalsense oftheterm is

what wehave established. Allofthis is roundedup in a su mmary ¢gure.The PAT (Patterson)

age isthe mythicalageof4.55 GadeterminedbyPatterson(Figure6.80) (see Chapter 5).

6.8 Conclusion

Like the remainder of this textbook, this chapter places more emphas is on methods of rea-

soning than on any would-be ¢rm and ¢nal results. However, it exposes results that s eem

either tobe robustor whichprobablyform a ¢rst approximationofreality.

353 Conclusion

The general method develop ed in this chapter isbased on the idea ofusing radiogenic iso-

topes as tracersofphenomena.Biologistsinjectradioactivetracerstounderstandthephysio-

logyofan animalbodyora cell; hydrologists or chemists use coloringagents to monitor £uid

movement. Like them, we too use tracers to study geologi cal phenomena.This method has

proved extraordinarilye¡ectivefordecipheringthestructureandphysiologyoftheplanet.

4.7 4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9 3.8

PAT age

Age (Ga)

METEORITES

Accretion

Condensation

Core

Atmosphere

Continents

Differentiation

of iron

Figure 6.80 Timescale of the different phenomena that occurred in the early Solar System and the different

phases of early formation and differentiation of the Earth from the isotope results. PAT age, Patterson age.

354 Radiogenic isotope geochemistry

Geological tracers have an original feature compared with other tracers in that they are

chronometers too.They move around with the motion of matter but keep a record of their

history, which is what makes them so valuable. In addition, they c an be used for exploring a

widetime range: notonlythe12billionyearsofthehistoryofthe Universeandthe 4.5billion

years of the Earth’s historybut also the details of planetogenesis some 4.5 billion years ago

or recent phenomenaofth e last millennia.

A second original feature is that the isotopic variations explored here are tiny, ranging

from1 0

3

to1 0

5

.Inotherwords,none ofthis wou ldb efeasiblewithoutth ei ncrediblypre -

ciseand sensitive technique ofmass spect rometry.

Lastly, andthis is nottheleastadvantage, wehaveahigh numberofisotopic tracers(more

than 40).Thus extremely vari ed problems can be addressed with the same techniques an d

the same metho ds.There is no doubtthatthe futurewill see more detailedstudiesofthevar-

ious fundamental phenomena (ocean ridges, subduction) and of the primordial Earth

usingthesamemethodology.

Problems

1 We consider the following geological history of a granite. Some 1500 Ma ago a volcanic–

detrital sediment formed by mixing in the proportions of 1/3 and 2/3. The volcanic

sediment has a

Sr/

Sr ratio of 0.703, and the Sr and Rb concentrations are 300 ppm and

10 ppm, respectively. For the detrital sediment, the

Sr/

Sr ratio ¼0.720 and the Sr and

Rb concentrations are 100 ppm and 100 ppm, respectively. The sediment is changed into

rock and sinks progressively over 500 Ma. At that time, caught up in orogenic convulsions,

it undergoes anatexis, which gives rise to a granite by partial melting. The Rb/Sr ratio of

the melt is (Rb/Sr)

melt

¼3(Rb/Sr)

sediment

. The granite then evolves over 1 Ga.

(i) Show the isotope history of the granite on a graph.

(ii) Calculate the initial and present-day

Sr/

Sr ratios of the granite.

2 In some cases, workers ascribe an important role to the metal core to modify classical

conclusions about the mantle.

(i) We assume the core contains potassium in a concentration of about 100 ppm. How does

that affect the

Ar balance as it has been envisaged? Calculate the mass of

Ar in the

core and the lower mantle.

(ii) Core–mantle reactions are also evoked to explain the lead isotope compositions of OIB. Take

the

238

204

Pb ratios for the current  value of the Earth of 1; the ratio of the primordial

mantle is 7 and that of the core is 0. Calculate the lead concentration in the core, given that

the total lead concentration of the core–lower mantle system is

¼0.696 ppm and that

in the lower mantle, after initial differentiation of the core,

¼0.1611.

(iii) Suppose that after initial differentiation, the core continues to deplete the lower mantle

of lead. Schematically, let us accept that 20% of the lead disappears (increasing the



mantle

value) and that the phenomenon can be modeled by a two-stage process involving

an extraction episode followed by an episode with no extraction, the age of the change in

regime being 3 Ga. Calculate the

206

Pb/

204

Pb and

207

Pb/

204

Pb ratios of the lower mantle.

Locate them relative to the 4.5 Ga geochron.

(iv) Do the same calculation with

diff

¼4 Ga.

(v) Can you draw any geochemical conclusions from these calculations?

355 Problems

3 The Canadian Dick Armstrong (1981) proposed a new model of continent growth. This problem

looks more closely at his idea. Armstrong supposed that all of the continental crust differentiated

say 4.5 Ga ago (like the core and most of the atmosphere) but that since then, during each

mountain-building episode, part of the continent is reinjected into the mantle (as sediment or as

detachment from the lithosphere) and that symmetrically an identical piece of continent is

formed at the expense of the mantle.

In this model, the  of the mantle and continental crust remain constant. It is supposed there

were four periods of exchange: at 3.5 Ga, 2.5 Ga, 1.5 Ga, and at the present day. It is assumed

that at present a quarter of the continental crust is swallowed up and regenerated.

(i) Calculate and draw the two (, t) curves of evolution for average continental crust and for

the supposedly isolated upper mantle.

(ii) Calculate and draw the statistical age diagrams for

143

Nd/

144

Nd represented in (

Sr/

Sr,

147

Sm/

144

Nd ¼

Rb/

Sr ¼

. The subscripts c, m, and 0 represent the

continent, mantle, and Earth, respectively. We note

143

Nd/

144

Nd ¼

Sr/

Sr ¼

4.4 Ga, the starting point of the calculation.

So:



¼ 0:506 677; 

¼ 0:6989



¼ 0:11; 

¼ 0:25



¼ 1; 

¼ 0:05:

(iii) What do you conclude?

4 The residence time of oceanic lithosphere in the primitive upper mantle is 1 Ga. It can be

assumed that when it goes through the mid-ocean ridge, the corresponding 70 km of mantle is

entirely degassed. The

He in the upper mantle is the sum of two terms. The radiogenic part,

formed

in situ

over 1 Ga, and the part from the lower mantle at the same time as

He during

the same period. This second part will be ignored.

(i) Calculate the quantity of

He accumulated in 1 Ga in the upper mantle, knowing that

U ¼5 ppb and Th/U ¼2.5.

(ii) Given that degassing of

He from the ocean ridges is 1  10

moles yr

1

and that

(

He/

He) ¼10

, calculate the residence time of

He in the upper mantle. What do you

conclude about the processes involved?

5 We consider the continental crust–depleted mantle system, as in Section 6.3.

(i) We wish to calculate the best

143

Nd/

144

Nd and

147

Sm/

144

Nd ratios for the continental

crust ( )

, primitive mantle ( )

, and residual mantle ( )

We note the isotope ratios 

and the

147

Sm/

144

Nd ratio ¼

Sm/Nd

We give:



¼ 0:512 62  0:000 01



¼ 0:513 15 0:000 01:

From which 

is between 0.511 and 0.5120.



Sm=Nd

¼ 0:197  0:01



Sm=Nd

¼ 0:11  0:01:

From which 

Sm/Nd

is between 0.227 and 0.280.

356 Radiogenic isotope geochemistry

Calculate the factor

where

is the mass of the continental crust and

the mass of the primitive mantle, which

differentiated by extraction of the continental crust.

Calculate the model age of differentiation of the continental crust.

(ii) We also give the values for the

Sr/

Sr ratio noted 

and 

Rb/Sr

for

Rb/

Sr:



¼ 0:7047;

¼ 0:7020;

¼ variable



¼ 0:3  0:5;

Rb=Sr

¼ 0:09;

Rb=Sr



Rb=Sr

¼ 0:

Given that

¼1.5, calculate

, 

, the strontium model age, and 

Rb/Sr

357 Problems

CHAPTER SEVEN

Stable isotope geochemistry

When de¢ning the properties of isotopes we invariably say that the isotopes of an element

have the same chemical properties, because theyhave the same electron shell, but di¡erent

physicalp roperties,becausetheyhave di¡erentmasses.However, ifthebehaviorofisotopes

of any chemical element is scrutinized very closely, small di¡erences are noticeable: in the

course of a chemical reaction as in the course of a physic al process, isotope ratios vary and

isotopic fractionation occurs. Such fractionation is very small, a few tenths or hundredths

of1%, and is only well marked for the light elements, let us say those whose atomic mass is

lessthan40. However,thankstothe extremeprecisionofmodernmeasurementtechniques,

values can be measured for almost all of the chemical elements, even if they are extremely

small for theheavyones.

When we spoke of isotope geochemistry in the ¢rst part of this book, we voluntarily

o mitted such phenomena and concentrated on isotopevariations related to radioactivity,

which are preponderant. We now need to look into the subtle physical and chemical

fractionation of stabl e isotopes, the use of which is extremely important in the earth

sciences.

7.1 Identifying natural isotopic fractionation

of light elements

The systematic study of the isotopic composition of light elements in the various naturally

o ccurring compounds brings out variations wh ich seem to comply with a purely naturalis-

tic logic. These variations in isotope composition are extremely slight, and are generally

expressedinaspeci¢ cunit, th e d un it.

d ¼

sample isotope ratio  standard isotope ratio

standard isotope ratio



 10

Ultimately,d isarelativedeviationfromastandard,expressedasthenumberofpartsper mil

(ø). Isotope ratios are expressedwiththeheavier isotope inthenumerator.

If d is positivethenthe sampleisricher in theheavy isotopethanthestandard.If d is nega-

tive then the sample is poorer in the heavy isotope than the standard.The term s ‘‘rich’’and

‘‘poor’’are understood as relative to the isotope in the nume ratorof the isotope ratio in the

formula above: by convention it is always the heavy isotope.Thus we speakof the

D/H,

C ratio, etc. The standard is chosen for convenience and may be naturally