All?gre Claude J. Isotope Geology

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the two U^Pb systems can be exploited provided correction is made for the initial lead.

Combining the¢rsttwo equationsofthe previousparagraphsgives:

206

204



206

204



207

204



207

204



¼ 137:8

 1



 1ðÞ

206



207



;

206

and

207

being the radiogenicfractions of

206

Pband

207

Pb.

In a

206

Pb=

204

Pb;

207

Pb=

204



plot, if a su ite of cogenetic boxes becomes isotopically

homogenized, the representative points will cluster in a point, instead of a straight line in

the simple parent^daughter case (Figu re 3.21). The radioactive system will evolve

207

Pb/

204

207

Pb/

204

206

Pb/

204

T = initial age

= metamorphic age

metamorphic age

Isotopic ratios

of re-homogenization

M'2

Isochron T

Figure 3.21 Plot of

207

Pb–

204

Pb and

206

Pb–

204

Pb isotope evolution for a complex geological history.

(a) The system is assumed to have re-homogenized at

as a result of a secondary event; (b) the

evolution of three rocks (WR

,WR

, and WR

) whose minerals re-homogenized at

87 Poor systems

subsequently with di¡erent trajectories depending on the

238

204

Pb ratios. But if the

system remains closed, the cogenetic boxes will remain on a straight lin e (Figure 3.22).The

initial aget

of the system can be determined by measuring the slope of whole ro cks and t

canbe determined bymeasuringtheisochronofthe minerals.Asthis method involves mea-

suring lead isotope compositions on ly, with no need to measure U and Pb concentrations,

itis fareas ier to implementexperimentally. Itisvery widelyemployed.

Exercise

The Pb isotope composition and U and Pb contents of the Muntshe Tundra massif in

Russia’s Kola Peninsula have been determined (Manhe

., 1980) (Table 3.4).

Determine the Pb–Pb age. What can you say of the U–Pb or Th–Pb ages?

Answer

The Pb–Pb isotope age is 2.13 0.25 Ga. No age can be determined from the U–Pb isotope

plot. The Th–Pb isotope plot indicates an age of 2.09 0.28 Ga.

206

Pb/

204

207

Pb/

204

Sphene

Magnetite

Apatite

Leached whole rocks

1100 Ma

Plagioclase

Perthite

30 40

Figure 3.22 Mineral isochron (Pb–Pb) of the Essonville granite. Data after Tilton

.(1958).

Table 3.4 Lead isotope composition and uranium, thorium, and lead contents of the

Muntshe Tundra massif

Sample

206

Pb/

204

207

Pb/

204

208

Pb/

204

Pb Pb(ppm) U (ppm) Th(ppm)

232

Th/

204

1B 14. 70 1 4.88 35 .07 3 .63 0.0391 0.375 6.04

2B 1 4 .8 3 1 4.9 1 35.1 8 8.93 0. 031 8 0.928 6.11

3B 14.72 14.89 35.15 0.97 0.0 038 0.1194 7.2

4B 1 5.38 14.98 35.72 1.40 0.0413 0.299 12.2

5B 1 5 .84 1 5 .03 36.29 1 .02 0.0625 0.287 1 6.85

6B 15 .1 2 1 4.95 3 5.5 5 9.85 ^ 1.55 9.45

Source: After Manhe

set al.(1980).

88 Radiometric dating methods

3.3.5 The

230

Th–

238

U method and disequilibria of radioactive

chains

These are methods related to radioactive chains for periods younger than 300 000 years.

Radioactive equilibrium is assumed to have been destroyed as a result of some geological

phenomenon orother (volcanism, formationofa shell in the ocean, erosion). As seen in the

previou s chapter, the systemthentends to returnto equilibriu m. Letus dealwiththe case of

230

Th.The general equation iswritten:

230

Th ¼ l

230

lt

þ l

238

U1e

l



Noticing that

232

Th has a very long period which may be considered constant relative to

230

Th(Al le

gre, 1968), wecanwrite:

230

232

230

232



lt

238

232



1e

l



On a l

230

Th=l

232

Th; l

238

U=l

232



plot that is in activity

230

Th=

232

Th;

238

232



the cogenetic boxes lie attime zero (time when the radioactive equilibrium is destroyed) on

ahorizontal line andthen evolvealonga straightline whose slopeis 1e

l



This straight line cuts the¢rstbisector, which is thelocus ofpointsin secularequilibrium

(equiline); the point of intersection (equipoint) is a ¢xed point around which the isochron

pivots. Itcorrespondstotheoriginal [

230

Th/

232

Th]

value.This methodis used successfully

for young vol canicrocks (Figures3.23and 3.24).

Equiline

Isochron

238

232

Initial

230

Th/

232

at time t = 0 at time t = T

238

232

Initial

238

232

ratio

Figure 3.23 Principle of the (

230

Th–

232

Th,

238

U–

232

Th) dating method. The sub-systems are isotopically

homogeneous in thorium at time

¼0. They lie on a horizontal line representing isotopic equilibrium.

The system has evolved by isotopic decay of

238

U and

230

Th. It evolves along an isochronous straight line

whose slope gives the age. After about 10 periods the system is once more in radioactive equilibrium

deﬁned by the equiline. The initial isotopic ratio is given by the intersection with the equiline since this

point is ﬁxed because it is in equilibrium. After Alle

gre and Condomines (1976).

89 Poor systems

Exercise

Table 3.5 gives the concentrations and isotope ratios measured on an andesite rock of the

Irazu

volcano, Costa Rica (Alle

gre and Condomines, 1976). Calculate the age of the lava.

What was its initial

230

Th/

232

Th isotope ratio?

Answer

Age: 68 000 years; initial ratio in activity: 1.17.

The same method may be used for other isotopes of radioactive chains. Unfortunately

226

Ra has no stable isotope and barium is used for normalization. Similarly,

231

Pa has no

stable isotope, and niobium is used as the norm. These slight di⁄culties explain why the

230

Th^

238

Umethod is the most widelyused.

3.3.6 Extinct radioactivities

These are radioactive elements that were present when the Solar System ¢rst formed and

which havebeco me extinct since.We shall speakof theirorigin i n the nextchapter (see also

Wasserburg,1985).

1.5

0.5

0.5 1 1.5 2 2.5

Whole rock

Plagioclase

Hypersthene

Augite

t = 110 000 yr

16 000

238

232

230

Th/

232

Equiline

Magnetite

Figure 3.24 Isochron of minerals on a volcanic rock from lrazu

, Costa Rica. After Alle

gre and

Condomines (1976).

Table 3.5 Concentrations and isotope ratios measured on andesite rock of the Irazu

volcano, Costa Rica

Activity Activity

Sample CA12 U (ppm) Th (ppm) Th/U (

238

232

Th) (

230

Th/

232

Th)

Whole rock 5.83 16.4 2.80 1.07 1.13 0. 02

Magnetite 0.45 1 .34 2.98 1.01 1 . 08 0. 04

Plagioclase 0.30 0.73 2.43 1.22 1.16 0.05

Hypersthene 0.53 1.43 2.70 1.12 1.14 0.04

Glass 7.15 19.4 2.71 1.11 1.15 0.03

Apatite 1 4. 0 53 . 6 3. 83 0.78 0.98 0.04

Source: After Alle

gre and Condomines (1 976).

90 Radiometric dating methods

The case of

Al^

The aluminum isotope

Al is radioactive. It decays to

Mg with a half-life of 0.72 million

years. Imaginethat

Al is incorporated in a meteoriteattimet. Fromwhat wehave already

said ofextinctradioactivity, by notingthe initialmagnesium

Mg(i) and

Alincorporated

attimet

(t ), wecanwrite:

Mg ¼

MgðiÞþ



ðtÞ:

Ifthe stable andn on-radiogenic isotopes

Aland

Mg areintroducedas references:



iðÞþ

tðÞ

In a

Mg=

Mg,

Al=



plot,theslopeoftheisochronstraightlinegives





Now, weknowthat:



t¼0

lt

;

t ¼0 beingthe endofthenucleosyntheticprocess thatengendered

Al.

Ifwehavetwo meteorites(I) and(II) we canthereforewrite:



ðt

¼ e

lðt

t

Therefore, as in the case of iodin e ^xenon (see below), we can date the di¡erence in age of

formationoftwo meteorites(see Figure3.25).

Allende

chondrite

Feldspar

(CaAl

)

Feldspar

(CaAl

)

Melilite

(Ca

MgSi

+ Ca

SiO

)

Al/

Mg/

Spinel (MgAl

)

0.155

0.150

0.145

0.140

0 100 200

Figure 3.25 Plot of the

Mg–

Mg,

Al–

Mg isochron obtained for the Allende meteorite. After

Wasserburg (1985).

91 Poor systems

Thecaseof

129

As said, th is te chnique was p ioneered byReynolds (196 0). As show n in Section 2.4.2,

129

todayisthesumof(

129

Xe)

plus

129

Xe p roduced by the complete decay of

129

J. If we chos e

to refer to a non-radiogenic xenon isotope

130

Xe, introducing the stable iodine isotope

127

we can write:

129

130



total

129

130



129

130

129

130



129

127





127

130



As stated above, to measure

127

I, we resort to the n eutron activation method of analysis hit

uponbyJe¡rey and Reyno lds consisting intransforming

127

Iinto

128

Xe.

127

I ¼ k

128

Xe;

where k is a proportionality factor relative to the activation analysis.This ¢nally yields the

dating equation:

129

130



total

129

130



129

127



128

130



In practice, the meteorite is irradiated and then degassed in stages (in a combination

betweenthe

Ar^

Arand isochron m ethods).The isotope compositionofXeis measured

ateachstep and aplotmade of

129

Xe/

130

Xe as afunction of

128

Xe/

130

Xe.

The slope of the straight line is equal to (

129

127

I) at the time the meteorite formed.The

ordinate to the origin is equal to (

129

Xe/

130

Xe)

at the time the meteorite formed

(Figure3.26).

By taking a g iven meteorite as a reference (the Bju

rbole meteorite) the various

‘‘ages’’ of di¡erent meteorites c an be calculated step by step. This was done by the team

atBerkeleyunderthesupervisionofJohnReynolds(Hohenbergetal.,1967)

(Figure 3.26).

The isochron plot therefore works in th e same way as for the othe r pairs. In just the same

way, similar plotscanbe constructed:

;



;

182

184

;

180

184



; etc:;

forotherextinct radioactivities:

Mn^

Cr,

182

Hf^

182

W, e t c .

Exercise

Table 3.6 gives the

182

Hf–

182

W experimental results for three meteorites. Plot the iso-

chrons. What are the relative ages of the three meteorites given that the reference for the

formation of the Solar System is

182

Hf/

180

Hf ¼2.5  10

4

Answer

The relative ages in respect of the initial reference are 5 Ma, 3 Ma, and 3 Ma. Estimate the

errors for yourself.

92 Radiometric dating methods

Shallowater

chondrite

129

Xe*/

128

Xe*

129

Xe*/

130

Xe*

128

130

Xe*

200

250

100 150

15 20 30 40

200

150

100

1,2

1,5

1000

1500 2000

Temperature (°C)

150

100

Figure 3.26 Dating by (I–Xe) on the Shallowater meteorite. (a) Isochron representation; (b) step

degassing. After Hohenberg

.(1998).

Table 3.6 Studies of three meteorites

Hf(ppb)W(ppb)(

180

Hf/

184

W)atomic

182

184

Fore st V al e

M-L 3 .61 647 0.006 58 0.86471 6 16

M-B-L 14.8 758 0.023 0 0.86469 0 50

M-B-2 63.0 642 0.1 15 7 0.864737 17

M-R 204 588 0.408 7 0.86480033

WR 172 178 1.14 0.8 64945 43

NM 176 114 1.82 0.8650 49 29

Sainte-Marg uerite

M-L 156 761 0.241 0.864751 24

M-B* 9.81 754 0.015 4 0.864700 41

M-R 77.6 1523 0.060 1 0.86477828

WR 141 166 1.01 0.864888 31

R ichardton

M-B-1* 56.2 46 0 0.14 4 0.864681 44

M-B-2 53 .2 582 0.108 0. 864680 31

NM 87 . 1 41 .2 2.49 0.8651 10 43

Source: After Lee and Halliday (2000).

93 Poor systems

3.3.7 Conditions of use of the isochron diagram

The essential criter ion for using the isotopic correlation diagram and th e iso chron con-

struction is thattheexperimentalpoints shouldbe align ed.Otherwise oneofthe conditions

forapplyingthe modelisnolonger metandnostraightline canbeplotte dtomakeanage cal-

culation.When th e data points form a cloud, this criterion is easy enough to apply. But in

p ractice, where eachpoint is a¡ected by experimentalerror, the alignmentis imperfect and

it is no simple matter to decide whether or not there is a straightline.We shall come backto

th is issue when discussing uncertainties.

When dealing with minerals, whether in rocks or in meteorites, there is a phenomenon

one mustbewaryofand which is related toisotopic exchange. Rich minerals (typicallybio-

tite and muscovite for

Rb/

Sr and zircon or apatite for U^Pb systems) tend to lose their

radiogenic isotopes as those isotopes have been introduced ‘‘indirectly’’ through

radioactivity.

Butwhere dothese radiogenic isotopesgowhentheymigrate?

The places where they might be accommodated are the usual crystallographic sites of

their chemical element, that is, generally in ‘‘poor minerals’’ (apatite and sphene for

Rb/

Sr an d feldspar for U^Pb).Thus

Sr will migrate from biotite to apatite (and even

more ea silyas often apatite is included in biotite). Similarly

206

Pbwill migratefrom zircon

tofeldspar(andagainthereareoften zircon inclusions in feldspar).

In the isochron diagram, the data point of the recipient mineral will move verti cally

sometimes greatly and so move o¡ th e isoch ron, and sometimes little and so will tend tobe

indistinct.

Caution is required, then, with these ‘‘poor,’’ purely radiogenic minerals close to the

y-axis. One mightthinkthey could be used to determine the initial isotopic ratio (

Sr/

206

Pb/

204

Pb) accurately, as often they are more radiogenic than it is! This is the way the

donor^acceptor pair works. Failure to allow for it has led to errors, particularly when dat-

ing meteorites.

3.4 Mixing and alternative interpretations

3.4.1 Mixing

Using the two methods just expos ed (concordia and isochron) it is possible to determine

the age of th e formation of a cogenetic rocky system and also to obtain some infor-

mation aboutits complex geologic al history.These are valuable methods therefore for any-

onewantingtostudy thegeological historyofcontinents, an often complex history made of

superpositions of geological events. But the interpretations we have d evelope d are not

unique !

Whenwe obtain astraightline inthe

Sr=

Sr;

Rb=



plot, we mayconsider itnot

as an is ochron but as a straight line of mixing (Alle

gre and Dars,196 6) (Figure 3.27). The

same is true of the

206



238

207

Pb=

235



concordia diagram.

Lettherebe two reservoirs,1and 2, with distinct

Sr/

Srand

Rb/

Sr ratios.The mix

ofthe tworeservoirs iswritten:

94 Radiometric dating methods



mixture



SrðÞ









By noting x ¼



=½



and R ¼

Sr=

Sr,weobtain:

mixture

¼ R

x þ R

ð1  xÞ:

Ifa samemixing equation iswrittenwith the‘‘chemical’’ratior ¼

Rb/

Sr, weget:

mixture

¼ r

x þ r

ð1  xÞ:

We can eliminatexbetween thetwoprecedingequations,hence:

mixture

R

mixture

r

R

r

In an (R, r) plotthis is the equation ofa straightli ne th rough the coordin ates (R

, r

)and(R

) andwhose slope, equaltoðR

 R

Þ=ðr

 r

Þ, isunrelateda priorito lt. Notethatthese

arethe same equationsas for isotope di lution.

Exercise

Calculate the apparent age of an alignment on a

Rb=

Sr;

Sr=

SrðÞplot which actually

results from mixing of a limestone component for which

Rb/

Sr ¼0.001 and

Sr/

Sr ¼0.708 and a schist component for which

Rb/

Sr ¼1 and

Sr/

Sr ¼0.720.

Answer

857 Ma.

206

Sr/

238

mixing

207

Pb/

235

Sr/

mixing

reserv oir 2

reserv oir 1

Rb/

α = "f alse" age

Figure 3.27 Mixing straight lines. (a) The mixing line in the (

Sr/

Sr,

Rb/

Sr) plot. It represents the

straight line homogenized by the mixture in variable proportions between reservoir 1 and reservoir 2.

(b) A mixing straight line in the concordia diagram between two populations of zircon of ages

and

95 Mixing and alternative interpretations

EXAMPLE

The Sidobre granite

The Sidobre granite of the Montagne Noire in the south of the Massif Central (France) near

Castres is intruded in schists transformed by contact into hornfels (Figure 3.28). It contains

schist enclaves but also ‘‘basic’’ enclaves. This granite is composed of two imbricated facies:

one is light (and richer in SiO

) and the other dark. The latter has a high ‘‘basic’’ enclave

content.

Analyses of the light facies, dark facies of a ‘‘basic’’ enclave, and hornfels deﬁne a straight

line whose slope corresponds to 400 Ma. The analysis of biotites gives about 300 Ma.

A subsequent analysis of whole rock from the same massif gives 285 Ma.

The interpretation is that the straight line at 400 Ma is a straight line of mixing between the

enclosing rock and the basic magma which penetrated and cannibalized the enclosing rock.

There are more complex cases where the mixture occurs among several components. In

principle they do not give a single straight line but in some circumstances they may mimic a

pseudo-straight line.

Exercise

(1) At time

¼1 Ga, an ultra-basic magma mixes with the enclosing granite. The

ultrabasic magma has isotopic ratios

147

Sm/

144

Nd ¼0.35 and

143

Nd/

144

Nd ¼0.511 25.

0.730

Enclaves

0.720

2 4356 7 8 9

0.714

0.710

Dark

facies

Light

facies

Hornfels

Rb/

Sidobre granite

(Tarn, France)

300 Ma

Biotites

400 Ma

Sr/

Figure 3.28 The Sidobre granite. The age of emplacement is 300 Ma. The apparent age due to mixing is

400 Ma (from Alle

gre and Dars, 1966).

96 Radiometric dating methods