All?gre Claude J. Isotope Geology

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The idea underpinning the method is that, since

Ar di ¡uses readily, it has departed

from the most vulnerable crystallographic sites over the course of geological time but has

remained in the more res istant sites (Figure 3.11). Bystepwise heating, we drive outsucces-

sively the fractions of argon located in increasingly retentive sites, ¢nally getting it from

‘‘closed’’ sites. This m ethod bec ame particularly successful with lunar exploration. At the

time, the ages reported by Turne r concurred so well with those obtained by the Rb^Sr

method that the model was ‘‘established’’ in spectacular fashion. Subsequently it was

re¢ ned. First itwasrecall edthatthevarious mineralsdid notcloseatthe same temperature,

which is unsu rprising. Insteadoflooking for justthe‘‘true’’age, attempts were made to take

advantage of the di¡erences observed to determine the conditions under which the rock

had cooled by us ing the concept of closure age already mentioned. Later still, a laser was

used to degasspeci¢c sites ofthevarious minerals andin stages.

An analogous method was proposed for U^Xe dating but it is still little used for the time

being (Figure 3.12), which is probably a shame. It may be resurrected. It involves irradiating

thesampleandproducingvariousxenonisotopesby¢ssionof

235

U.Asthexenon-induced¢s-

sionspectrum isdi¡erentfrom the spontaneous¢ssionspectrumof

238

U, we can measurethe

136

Xe produc ed by natural ¢ssion and the uranium in the mineral.Then the age is cal culated

(Shukolyukovetal.,1974;Teitomaetal.,1975).

Direct

20 6

Pb^

207

Pb analysis

Thistechniqueis even more audacious although itstem s fromthesame principle as thepre-

vious one. It involves depositing the mineralunder analysis by the Pb^Pb method (zircon)

directly on theTIMS mass spectrometer ¢lament. It is h eated in stages and the Pb di¡uses

from the zirco n and ionizes and the

207

Pb/

206

Pb ratio given o¡ is measured (Figure 3.13).

This method, devised byKoztolanyi at N ancy in France in1965, was neglected for 20 years

Hornblende

Biotite

K - Feldspar

0 0.5 1.0

Release fraction of

K-Ar age (Ma)

780

820

860

900

940

980

1020

Figure 3.11 Examples of

Ar–

Ar age spectra for three minerals from a rock aged 1000 Ma, showing

sensitivity to the different minerals (from Berger and York, 1981).

77 Rich systems

before being taken up by Kober in 1986! It yields interesting and sometimes impressive

results, even ifall criteria ofconcordan ce or discordance are lost, preventing any reliability

checkas the concordiadiagram cannotb e used.

3.3 Poor systems and the radiometric isotopic

correlation diagram

Withpoor systems, the main problem is notjustthe question ofopennessbut alsothatofthe

initial presence, when the system closes, of a certain amount of radiogenic isotope. How

canthisbe evaluated?

1.0

0.5

2.0

1.5

500100

Percentage Xe degassed

t(Xe–Xe)

= 1.59 ± 0.12 Ga

t(Pb–U)

= 1.57 ± 0.05 Ga

Age (Ga)

Figure 3.12 Example of a spectrum of the

133

Xe–

136

Xe method imitated from

Ar–

Ar for a Rapakivi

granite from Finland. After Shukolyukov

.(1994).

0.40

0.35

0.30

3.6

3.7

3.8

3.9

4.0

4.1

4.2

1450

Evaporation temperature (°C)

207

Pb/

206

Age (Ma)

1500

Figure 3.13 The

207

Pb–

206

Pb spectrum obtained by thermo-ionization of lead. This spectrum is

obtained by progressively heating the ﬁlament after having deposited zircon on it. The example

shown is of detrital zircon from Australia, among the oldest recorded (Kober, 1986).

78 Radiometric dating methods

3.3.1 The

Rb–

Sr system

This method was proposed, after an initial attempt by AustraliansWilliam Compsto n and

Peter Je¡rey (1959), then at the Univers ity of Western Au stralia, by Lou is Nicolaysen

(1961) of South Africa’sWitwatersrand University for the

Rb^

Sr system, but it is more

generaland applies to allparent^daughtersystems.

Letus turnbacktothe fundamental

Rb^

Srdecayequation ina closed system:

SrðtÞ¼

Srð0Þþ

RbðtÞðe

 1Þ:

Let us divide memb er by member by

Sr, which is one of the stable Sr isotopes and whose

abundance is notdependenton radioactivityand is therefore constantover time.The equa-

tionbecomes:



ðe

 1Þ:

The mathematical operation of

Sr normalization by

Sr is not just a simple algebraic

man ipulation. It brings outthe strontium isotope ratios in the equation.This is the magni -

tude measuredbythe mass spectrometer.Now,wehaveseen thatisotope ratiosobeyprecise

laws, particularlythos e ofisotope exchange.

Letus nowconsider a se riesofcogeneticboxes (assumedtobe inthermodynamic equili-

brium). As a result of isotopic equilibration, theyhavethe same initial

Sr=

SrÞ



isotope

ratio and the same age. In an

Sr=

Sr;

Rb=



plottheyare aligned on a straightline

ofslope (e

1)andofordin ateattheorigin of

Sr=



.This straightlineis an isochron,

which is the locus of boxes of the same age (Figure 3.14). If we w ish to break down the way

the system evolves over time, we can say that at time t ¼0, the points representing all the

boxes lie on a horizontal line, each box being characterized by its own

Rb/

Sr ratio but

with the same strontium isotope ratios.Then eachboxevolves along a diagonal ofslope 1

with þd

Sr=dt ¼d

Rb=dt. The straight line rotates around the ¢xed point

Sr=



. Its slope is constantly (e

1).

Remark

The inverse problem is interesting, of course. Let us take the example of a series of minerals (or

total rocks) which are assumed to be cogenetic (minerals from the same rock, or rock from the

same massif). The

Sr/

Sr and

Rb/

Sr isotope ratios of each of them are measured. If the

representative points lie in a straight line, the slope of the straight line is equal to (e

1) and

the age of the system of boxes can be calculated.

Exercise

Annie Michard measured the Mont-Louis, granite, Milhas, and Que

rigut in the Pyre

Orientales (France) (Table 3.2). Draw the isochron graph and calculate the age of the series

of granite rocks of the Que

rigut and the initial ratio (Michard and Alle

gre, 1979).

Answer

79 Poor systems

We calculate the

Rb/

Sr ratios. The experimental points are plotted on the

Sr=

Sr;

Rb=

SrðÞgraphs not shown here. The straight line through the points ‘‘yields’’

an age of

¼271 10 Ma, with an

Sr=

ðÞ

initial

ratio ¼0.710 0.005.

This method, often calledthe is ochron method,isoneofthepillarsofradiochronology.It

b oth dispenseswiththe assumption (acceptedfor rich system s) thatthe

Sr(0) is negligible

or constant and so allows poor systems to be used and tests the closed system hypothesis

by alignment or n on-alignment of the measurements made on the di¡erent boxes. If Rb

1 2 3 4 5 6 7

Rb/

Sr/

slope –1

isochron at time

α = tan

–1

λτ

–1

⌠

0.760

0.700

1 2 3 4

Rb/

Sr/

isochron at time

1 Ga

Figure 3.14 Principle of the

Rb–

Sr isochron method. At time

¼0 the points have the same

strontium isotope ratio and different

Rb/

Sr ratios. They therefore all lie on a horizontal line

corresponding to (

Sr/

Sr)(

). After time

, the points are aligned on a straight line of slope

1) 

. In practice, in real graphs, the straight lines of evolution do not have a slope of 1

because the

Rb/

Sr ratio varies little and the

Sr/

Sr ratio varies greatly, given the chosen scales.

The evolution vectors are very steep.

80 Radiometric dating methods

and Sr have m igrated di¡erentially, then the representative points of the various boxes will

not remain aligned. In thefavorable case, this method can be used to measure anage (t)and

to determine the initial

Sr/

Sr ratio, which we will se e late r to be important. Measuri ng

an age therefore involves measuring the Sr isotopic ratio, measuring Rb and Sr concentra-

tions for eachboxandthis isforaseries ofcogeneticboxes.

3.3.2 Two-stage models

Im agine we have a series of cogenetic boxes evolving in a closed system. All the systems

are therefore aligned on an isochronous straight line. Suppose that at t

a su dden event

occurs which re-homogenizestheboxesisotopically.This eventmaybe metamorphism, for

example. The sub-systems will exchange their atoms and become isotopically homoge-

neous.The representative points oftheboxes then lie on a horizontal line whose ordinate at

the origin iswritten

Sr=



m; t

with m, t

signifyingthe meanvalue att

.Thentheboxes

evolve radiogenically until the present time in a closed system. The alignment observed

between thepoints representing theboxes has a slope of e

1



and an ordinateatthe ori-

ginof

Sr=



m; t

Let us explain our model a little to m ake it realistic.We consider the cogenetic boxes

are both whole rocks and minerals. Metamorphism occurs at time t

which re-homo-

genizes the minerals isotopically around the value of the whole ro ck, but it is not

intense enough to re-homogenize the whole rocks at the scale of the entire massif

(Figure 3.1 5).

Table 3.2 Mont-Louis, Milhas, and Que

rigut granites

[

Sr/

Sr] Rb (ppm) Sr (ppm)

Mont-Lo uis sample nu mbers:

4 B1 0.721 1 57 181

4 B2 0.719 146 20 0

Mi l has sample nu mbers:

V90 0.723 150 146

V92 0.717 164 302

Que

rigutsamplenu mbers:

A 0.7 14 105 241

B0.719189214

C0.723161135

A4 0. 720 1 60 1 53

X0.7205155170

Q 1 0.742 202 88

Q2 0. 743 257 90

Q3 0. 746 245 74

Ap1 0.780 192 32

Ap2 0.875 257 18

81 Poor systems

The

Sr=

Sr;

Rb=



graph shows two types of straight line: the straight line

f or w hole r ock of slope e

1



and the straight lines of the minerals of slope e

1



This method is illustrated with the historical example of the Baltimore gneiss of the

UnitedStates(Figure 3.16.b) studiedby thegroupatthe Carnegie Institutionof Washington.

2 3 4 5 6

⌠

isotopic

re-homogenization

isochron at time

2 3 4 5

isochron

τ'

τ = 0

τ = τ'

Rb/

Sr/

⌠

Apatite

K-Felspar

Whole rock

Muscovite

Biotite

Plag.

isochron

τ'

Figure 3.15 Isotopic re-homogenization of minerals at time

. Top: the re-homogenization event.

Bottom: the evolution of the system after

. WR, whole rock. After Lanphere

.(1964).

B''

Rb/

Sr/

τ'

isochron

whole rock

0,80

0,78

0,76

0,74

0,72

21 43

1050 Ma

287 Ma

294 Ma

6 75

Rb/

Sr/

0,80

0,75

0,70

2 4 6

Figure 3.16 Example of two types of isochron. (a) The whole-rock isochron indicates the initial age, that

of the minerals dates the age of the disruptive event; (b) classic example of Baltimore gneiss with the

whole-rock isochron and the mineral isochrons. WR, whole rock; B, biotite; KF, potassium feldspar; P,

phosphate. After Wetherill

.(1968).

82 Radiometric dating methods

3.3.3 Extension of the isochron graph to other radiochronometers

The method initially developed for

Rb^

Sr was extended to other chronometers with

spe ci¢c features for each, particularly di¡erent sensitivities to disruptive phenomena.

Withoutth is isochron method, the

147

Sm^

143

Nd and

176

Lu ^

176

Hf methods would not have

cometolight, astheyhaveno richsystems.

The case of

147

Sm^

144

This method was i ntroduced by Notsu et al.(1973)anddevelopedbyLugmai r and Marti

(1977).Thebas ic dating equation iswritten:

143

144

143

144



147

143



147

t l

147

¼ 6:54  10

12

1

The stable reference isotope is

144

Nd.This method has the advantage of being applicable

to ultrabasic and basic rocks, which cannot be readily dated by

Rb^

Sr, and to gran ites

(Figure 3.1 7).With regard to minerals, garnet and pyroxene are useful since geochemical

fractionationbetween Sm and Nd, although slight,is relatively constantacross the petrolo-

gicalspectrum.

Exercise

Calculate the initial

143

Nd/

144

Nd ratio of a rock of which we know the age (2 Ga), the

present-day

143

Nd/

144

Nd ratio (0.512 556) and whose neodymium and samarium contents

are 36 and 10.4 ppm respectively. What do you think the error is if samarium and neody-

mium are measured to the nearest 3%, the isotope ratio to 1.10

5

and age to 10%?

Answer

143

Nd/

144

Nd ¼0.510 31 Absolute error ¼0.000 35.

0.513

0.512

0.511

0.10 0.15 0.20

Basic

rocks

Intermediate

rocks

Acidic gneiss

147

Sm/

144

Age = 2920 Ma

143

Nd /

144

Lewisian

gneiss

(Scotland)

Figure 3.17 Example of a

147

Sm–

143

Nd isochron on rocks of the Lewisian Complex of Scotland. After

Hamilton

.(1979).

83 Poor systems

Thecaseof

176

Lu^

176

Inth is casewetakethe

17 7

Hf isotope as thestable reference.

176

177

176

177



176

177



lt l

176

¼ 1:94  10

1

This method, introduced by John Patchett and Mitsunobu Tatsumoto (1980) working at

the U.S. Geological Survey in Denver was long neglected because of analytical di⁄culties

in measuringhafnium.Ithasbeen increasinglyusedwiththeadventofICPMS(Figure3.18).

Exercise

The question of metamorphism related to the subduction of the Himalayas is an important

one for geologists. One way of determining this age is to use eclogite (that is, basalt

metamorphosed at high pressure) whose mineral composition is sodium pyroxene termed

omphacite and pyrope garnets.

The occurrence of garnet and pyroxene makes lutetium–hafnium dating easier. Table 3.3

gives the results obtained on eclogite rock from Ladakh. Calculate the age of metamorph-

ism (formation of eclogite) (De Sigoyer

., 2000).

Answer

55 Ma.

Thecaseof

187

Re ^

187

This method was introduced by Hirtet al.(1963)anddevelopedbyLuck et al.(1980). The

referenceisotopebeing

186

Os and more recently

188

Os,we canwrite:

187

186

187

186



187

186



187

t l

187

¼ 1:62  10

11

1

This method is potentially importantbut, although meaningful on meteorites (Luck et al.,

1980), it is di⁄cultto applybecause the systemdoes notseem to remain closed, particularly

0.2820

0.2816

0.2812

0.2808

0.2804

0.010 0.020

3.58 ± 0.22 Ma

176

Lu/

177

Amitsoq

gneiss

176

Hf/

177

Figure 3.18 The lutetium–hafnium isochron of the Amitsoq gneiss. After Blichert-Toft

.(1999).

84 Radiometric dating methods

for molybdenite, although containing a large amount of Re, nor for basalt, with a very

high Re/Os ratio. Even so the present authorobtained isoch rons includingone for Deccan

basalt (Figure3.19).

The case of u raniu m^thoriu m^lead

Ta k i n g

204

Pb as the reference isotope,the dating equations arewritten:

206

204

206

204



238

204



1



207

204

207

204



235

204



1



208

204

208

204



232

204



1



Table 3.3 Dating of eclogite rock from Ladakh

Lu (ppm) Hf (ppm) Lu/Hf

176

Hf/

177

Whole rock 0.3630 3.5991 0.1009 0.282996 0.01431 0

Garnet 0.7324 3. 0907 0 .2370 0.283012 0.033630

Pyroxene 0.0302 3.0727 0.0098 0.28977 0.001400

Source: Afterde Sigoyeretal.(2000).

500 1000 1500 2000

187

Re/

188

187

Re/

188

Deccan

basalts

(India)

T = 65.6 ± 0.3 Ma

Figure 3.19 The rhenium–osmium isochron of the Deccan Traps. After Alle

gre

.(1999).

85 Poor systems

These methods have undoubtedly been insu⁄ciently us ed (Figure 3.20) although they

are very powerful as they have an internal concordance criterion (chemically identical

p arent and daughter is otopes) guaranteeing their reliability. They should combine the

advantag es of the iso chron and concordia methods. Unfortunately this is not yet the

case.

Exercise

Given that the

238

204

Pb ratio of granite varies from 2 to 30 and that the Th/U ratios vary

from 1 to 10, calculate the deviation in the

206

Pb/

204

Pb,

207

Pb/

204

Pb, and

208

Pb/

204

Pb ratios

for granites of 1, 2, and 3 Ga.

In calculating the

206

Pb/

204

Pb,

207

Pb/

204

Pb, and

208

Pb/

204

Pb ratios of the granite, it is

assumed that this granite derives from evolution of a reservoir with ratios

238

204

Pb ¼7

and Th/U ¼4, having evolved for 4.5 Ga. The initial ratios of these reservoirs are

206

Pb/

204

Pb ¼9.30,

207

Pb/

204

Pb ¼10.29, and

208

Pb/

204

Pb ¼29.47.

Answer

(

206

Pb/

204

Pb) ¼15.534–29.998, (

207

Pb/

204

Pb) ¼14.44–16.18, and (

208

Pb/

204

Pb) ¼

35.14–79.69.

3.3.4 The lead–lead method

We have come across the

206

Pb/

207

Pb method when the two isotopes were of purely radio-

genic origin. Minerals or rocks generally contain some initial lead.The speci¢c feature of

1100 Ma

1050 Ma

Plagioclase

Perthite

Apatite

Sphene

Magnetite

Leached

whole rock

Leached

whole rock

Unleached whole rock

238

204

206

Pb/

204

207

Pb/

234

0.20

235

204

0.40 0.60 0.80 1.00 1.20

100 150 200

Plagioclase

Figure 3.20 Isochrons of lead–uranium minerals of the Essonville granite. After Tilton

.(1958).

86 Radiometric dating methods