All?gre Claude J. Isotope Geology

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and forgalena2:



 



 

137:8

 e



;

andthreeunknownquantities

, 

,andT

Holmes (1946) then hituponthe ideaofasortofstatisti calmethodand reasoned likethis:

suppose I give myself ages of the EarthT

¼2 Ga,3 Ga, and 4 Ga. If we replaceT

by these

values in the equations, we can calculate the two unknowns 

and 

on a case-by-case

basis (Figure 5.25). Sowe can plot an (

) diagram.This operation maybe repeated with

2.00

T = 3.33 Ga

= 11.22

3.00 4.00

206

Pb/

204

Time (Ga)

Solutions for

samples 18 and 25

Solutions for

samples 1 and 19

Figure 5.24 Measurements giving the age of galena by Holmes’s method.

2.00 2.50 3.00 3.50

Mode: 3.35 Ga

Solutions

with

anomalous

lead from

Joplin

Solutions

with

other

galenas

Mean

(without Joplin):

3.29 Ga

Mean:

3.20 Ga

4.00

200

160

120

Number of solutions

Time (Ga)

Figure 5.25 Age statistics determined by Holmes with his two-by-two galena method.

197 The age of the Earth

a second p airofgalena specimens, giving us a second curve, with athird pair, and so on.We

just haveto takethe mean ofthe intersectionsbetween the curves togetthe real pair (

)

and T

. Holmes came up with 3.4 Ga, an astonishing convergence with the date calculated

by G erling. Houtermans (1946) adopted much the same method, leading him to a result

closeto3 Ga.

Inthe195 0s,then,wehadan estimatefortheageoftheEarthofabout3.5 Ga.(Meanwhile

astronomershadrecalculatedHubble’s equationandfoundanageof4 Gafor theUniverse.)

In1950, advances in mass spectrometry meanttheisotopic composition oflead ofordin-

aryrockscouldbe measuredalthoughthis elementisonlyfoundintraces.In hisPh.D.thesis

at Chicago University, Clair Patterson (1953) ¢rst measured two m eteorites, an iron

meteorite (Canyon Diablo) and a basaltic meteorite (Nuevo Laredo) by the

206

Pb^

207

method (Figure 5.26). By joining up the two points in the (

206

Pb/

204

Pb,

207

Pb/

204

Pb) dia-

gram, he calculated an age of 4.55 Ga, which he claimed to be the age of pl anetary objects

(Patterson,1953,1956).

He then m easured a present-day volcanic rock from Hawaii, which supposedly repre-

sentedwhatwas assumedtobe thehomogeneous interiorofthe Earth, ¢ne sediments from

the Paci¢c, and a manganese nodule supposed to represent averages of rocks from the

Earth’s surface.These three rocks lay roughly on the straight line at 4.55 Ga. He attr ibuted

to the Earth the same age as the meteorites and asserted th is was the age at which the Solar

System formed.This is the age which now features in all the textbooks. It also determines

the initialvalues 

and 

These values have since been determined more precis ely as (

206

Pb/

204

Pb)

¼9.307,

(

207

Pb/

204

Pb)

¼10.294,and (

208

Pb/

204

Pb)

¼29.476.

Apartfrom thevalue oftheage ofthe Earthand thebenchmark itprovides for thehistory

ofgeological times, Patterson’s workhas an important consequence. It can be u sed to‘‘situ-

ate’’ the isotopic compositions of galena measured in geological formations relative to the

10 20 30 40 50

207

Pb/

204

206

Pb/

204

Nuevo Laredo meteorite

Canyon Diablo

meteorite

(sulfur)

Sea water

Recent

sediments

Hawaiian

basalt

Age 4.55 Ga

Figure 5.26 The age of the Earth as determined by Clair Patterson, 1953–6.

198 Uncertainties and results of radiometric dating

initial reference point (

, 

) and by the same tokento allow a series of calculations for the

ageoftheEarthfrom eachsampleofgalena.Weshallseewhatthisworkleadstoin Chapter 6.

Exercise

Calculate the age of the Earth from Casapalca and Yancey galena samples given by Nier in

Figure 5.24 and Table 5.7, assuming 

and 

to be the values known today and assuming

their age is about zero.

Answer

Casapalca

¼4.39 Ga and

Yancey

¼4.45 Ga.

5.6.3 The modern approach

A ¢rst, probablysomewhatdisarming, observation is thatwith modernanalytical methods

(see Alle

gre et al., 1995) we cannot repeat Patterson’s measurements and ¢nd the same

result! The points that are supposed to representthe Earth do notl ie on the straightline for

meteoritesbutforma cloud.Moreover, the decayconstantsfor uranium havebeen changed

since, and so we would no longer ¢nd 4.55 G a with modern valu es. And yet, Patterson’s

result is about right (Ta t s u m o t o et al., 1973)! Unfortunately for him, the ver y concept of

the age ofthe Earth has changedandhasbecome much lesswellde¢ned than in his day.

First, it has been realized that the Earth’s historyhas been very complicated and that the

mo delsofevolution of lead involving just a single episode in a closed system do not apply to

any terrestrial reser voir. Al l ofthe systems ^ crust^mantle^ocean ^ are open systems that

exchange material with each other: there is absolutely no ground for applying the closed-

box model to reservoirs like the mantle or continental crust as Patterson did, even as a ¢rst

approximation(asweshall see i n Chapter 6).Then, withthe advances inplanetaryexplora-

tion and planetological models, it was realized that th e Earth had not been formed in an

instant but by a slow process (named accret ion) which probably lasted 100^150 Ma.We

come back to the question we rais ed at the begi nning of this chapter: for dating we need a

box that closes at a de¢nite given time. Ifwe date the Earth byany particular metho d, what

isthe meaningofthatage? Isitthetimethe coreformed,or the endofdegassingoftheatmo-

sphere? Isitthe age ofthesolid materialthat is its main component?

WeshallreturntothisprobleminChapter6.LetusbecontenttosaythattheEarth formed

over a period of 100 to 120 Ma and that the pro cess began 4.567 Ga ago! The concept of

Table 5.7 Samples of galena used by Nier in two-by-two determinations

206

Pb/

204

207

Pb/

204

Pb Age(Ma) Number

Casapalca( Peru) 18.83 15.6 25 1

Ivigtut(Greenland) 14.54 14.70 600 19

Yancey (North Carolina) 18.43 15.61 220 18

GreatBear Lake (Canada) 15.93 15.30 1330 25

SeeFigure5.24.

199 The age of the Earth

dating can be applied in s everal ways. Either we date the beginning an d end of accretion of

the Earth, or we d eterminean‘‘averageage’’offormation oftheEarthwith noprecis e mean-

ing.We can see that analy tical uncertainty is no longer an issue, but that it is ‘‘geological

u ncertainty’’ or even conceptual uncertainty that challenges the validity of the reference

mo deloutside ofwhichanyage is meaningless.This, then, is agood example ofthe di¡erent

meanings we can attribute touncertaintyofageological age measurement! For fun, we c an

end by noti cing that i f we represent the age of the earth in semi-logarithmi c coordinates

against the date of research into the subje ct (Figure 5.27), we obtain a straight line: this is

food for thought aboutthe meaningof correlations with no theoreticalsupport. (Perhap s a

sociologistorapsychologistcould drawconclusionsfrom this?)

5.7 The cosmic timescale

One of the great success stori es of radiometric dating is that it has been able to extend its

investigativepowerbeyondtheterrestrialdomain and¢xchronological markersforcosmic

evolution.

5.7.1 Meteorite ages

Meteorites are pieces of embryon ic planets dating from early times, which were sent hur-

tling o¡ into space after collisio ns and spent millions of years in interplanetary space

before falling toEarth.

Wehavesaidthat,asa¢rstapproximation,meteoritesareasoldastheformationoftheSolar

Systemandtheplanets(around 4.55 Ga),butwehavejustseenthatthisageispoorlyde¢ned.

Modern U^Pb methods applied to uranium-rich phases developed in Paris by Ge

rard

Manh e

s, Ch rista Go

pel, and the present author have yielded meteorite ages with a prec i-

sion ofabout 300 000 years, whilethe age is close to 4.55 Ga, giving arelativeuncertaintyof

3 10

/4.5 10

(60 ppm),whichcorrespondsto aprecisionof 60yearsforadateof1million

years! Using these U^Pb methods as our reference, we havebeen able to establish a precise

chr onology (Go

pel etal.,1994)(Figure5.28).

20001950190018501800

Age of the Earth (yr)

Year

Patterson

Holmes

Boltwood

Joly

Kelvin

Buffon

Thousand years

Million

years

Billion

years

Figure 5.27 Changes in the age attributed to the Earth as geological sciences have developed.

200 Uncertainties and results of radiometric dating

Theresultsobtainedwiththeotherchronomete rsbasedon

Rb^

Sr,

146

Sm^

143

Nd,and

187

Re ^

187

Os long-period radioactivity are in general agreement w ith U^Pb ages but they

are far less accurate. Results obtained using extinct radioactivity (

129

Xe,

Al^

Mg,

182

Hf^

182

Mn^

Cr)all indicateages close tothose ofthe reference meteorite, con¢rm-

ingthegreat ageofalltheseobjects. However, whenever wetry tousetheextraordinarytem-

poral powerofresolution ofthese extinct forms ofradioactivity, their relative ages and ages

relative to the U^Pb clock, substantial inconsistency is observe d. The age di¡erence

between two objects (meteorites, minerals) is p ositive with U^Pb, negative with Mn^Cr

and Al^Mg, and positive but di¡erent with I^Xe, or the c ontrary. Between two other

objects, the di¡erences ob ey some other rationale, and so on. This raises two questions.

Where does thisanarchycomefro m?Whatdothe‘‘apparentages’’obtained mean?

Observation of meteorite structures an d textures using the techniques of petrology has

revealed that most meteorites are brecciated and impacted. Chondrites, which are the

most ‘‘primitive’’ meteorites, are composed of spherical chon drules, evidence of transition

through a molten state, surrounded bya matrixcontaining manylow-temperature minerals.

The overall impressionisone ofverycomplex relations among minerals.

Dating using

Ar^

Ar methods by Grenville Tu rner s ince 1968 has revealed highly

complicated outgassing patterns and ages of generally less than 4.56 Ga.

Rb^

Sr ages

obtained onthe mineralsalsoshow the systemdid not remain closed.When alignments can

beobtained from the isochron diagramtheyyieldapparentages ofless than4.56 Ga.

All this evidence suggests that meteorites were subjected to many complex dis ruptive

phenomena (metamorphism, impacts, reactions w ith £uids, etc.) during the evolution of

the solar nebula. It waslong thoughtthatdi¡erentiated meteorites (basaltic or iron m eteor-

ites) had formed much later. In fact, the use of the

182

Hf^

182

Wmethod has shown thattheir

207

Pb/

206

ages (Ga)

Achondrites

Phosphates

ordinary

chondrites

Allende CAIs

4.50 4.55

[

Δt (Ma)

556

65 5 5

6564

Figure 5.28 The chronological scale of meteorites after Go

pel

.(1994) and Alle

gre

.(1995). CAIs,

calcium–aluminum inclusions.

201 The cosmic timescale

di¡erentiation, that is their fusion in small bodies, was alsoveryold, dating from 3 to 4 mil -

lion years after the Allende meteorite (Lee an d Halliday, 2000). It must therefore be con-

cluded that most of the ages obtained on meteorites are disrupted by secondary

phenomenathatoccurred rightatthebegin ningofthe Solar System.

Inthe currentstateofknowledge,wecansaythattheoldestobjectsarethe calcium- andalu-

minum-rich, white inclusions in Allende. They are aged 4.567 0.0003 Ga (Alle

gre et al.,

1995). Chondr ites and di¡erentiated iron meteorites formed in the 2 millionyears (probably

forless) that followed. Basaltic achondrites formed in the ¢rst 4 (maybe ¢rst 2) millionyears.

These objectswerethensubjectedover50to100millionyearstoi mpacts,heating,andchemi-

cal reactions with £uids. All these phenomena brought about chemical and mineralogical

changes in these objects making the primitiveness oftheir dating extremelydoubtful, notjust

in terms ofthe ¢gures obtained but alsoin terms ofwhat the date means. Here is an example

ofuncertainty thatisnotanalyticaland is mathematicallydi⁄cultto quantify.

EXAMPLE

Meteorites

Meteorites are rocks that fall from the sky (see Wood, 1968; Wasson, 1984; Hutchinson,

2004). Although they have been known since ancient times, their scientiﬁc value came to be

understood less than a century ago. They are pieces of small planetary bodies gravitating for

the most part in the asteroid belt between Mars and Jupiter. They are produced by impacts

between these bodies and then move through interplanetary space before falling to Earth.

During their travels, they are irradiated by galactic cosmic rays, as we have seen. This means

they can be identiﬁed positively because they contain radioactive isotopes that are speciﬁc to

such irradiation. They are of huge interest because the material dates from the time the Solar

System and the planets formed. All meteorites are aged about 4.56 Ga. The chemical composi-

tion of some of them, the carbonaceous chondrites, is similar to that of the solar photosphere.

Meteorites are classiﬁed into two main categories: chondrites and differentiated meteorites

(Table 5.8).

Table 5.8 Summary classiﬁcation of meteorites

Chondrites

They are formed by the

agglomeration of small

sphe res ofsilicates(chon-

dru les)inamaterialcom-

posedofsmallminerals

Carbonaceous Theycontain nometal.Theirchemical

comp osition is similar to that of the

solar photosphere.

Ordinary These are the most numerous. They

areformed from a mixture of metallic

iron minerals and sil icate minerals.

Their composition is close to a mix-

ture of peridotites and of metallic

iron.

Enstatite All th e iron is in the form of FeS or

metallic Fe.

Di¡erentiated meteorites

Basaltic achondrites

(eucrites)

These are basalts analogous to terres-

trial basalts.

Mesosiderite and pal-

lasite (ir on and rock)

Large pieces of metallic iron asso-

ciatedwithpieces ofsilicates.

Iron meteorites Alloyofm etallic iron and nickel.

202 Uncertainties and results of radiometric dating

The chondrites are the more common. They contain small spheres known as chondrules and

their chemical composition is roughly similar to that of the whole Earth. They contain silicates

but also scattered metallic iron minerals. The distribution of iron forms a subdivision into

enstatite chondrites, ordinary chondrites,andcarbonaceous chondrites.Inenstatite chondrites

(E) all of the iron is in the form of metal or iron sulﬁde FeS. In ordinary chondrites, the iron is

divided between metal sulﬁde and silicates. Some have high (H) and others low (L) iron

contents. Carbonaceous chondrites (C) have no metallic or sulﬁdic iron and all their iron is in

the silicates and oxides.

A further classiﬁcation is superimposed on the mineralogical–chemical one, based on the

extent of metamorphism of the chondrites. Chondrites were subjected to reheating after the

formation of the bodies from which they derived. This heating wrought more or less intense

mineralogical changes in all of the chondrites, except for the carbonaceous ones, thus causing

varying degrees of metamorphism. This metamorphism is rated on a scale from 1 to 6. So we

speak of H(3), L(5), or E(3) chondrites, etc.

Differentiated meteorites are the relicts of liquid–solid separation phenomena that

occurred within small planetary bodies upon their formation. Some of them are basalts

(eucrites), others are enormous blocks of metallic iron whose textures show they were

initially molten (iron meteorites). Yet others are made up of an assemblage of massive

metallic iron and of silicates such as olivine and pyroxene (pallasites and mesosiderites).

These structures are indicative of the differentiation of the metal cores of the small

protoplanets.

As can be seen, the distribution of iron between metal and silicate is fundamental in

meteorite classiﬁcation. This must be related to the case of the Earth, where iron is mostly

present in the core in metallic form and less present in the mantle where it is scattered among

the silicates olivine and pyroxene. Most meteorites come from the asteroid belt between

Mars and Jupiter, but some have quite different origins. They are pieces of planets broken off

by impacts. Some are known to come from the Moon and it is thought others come from Mars

(Figure 5.29).

Collision

0.3 Ga4.56 Ga

Accretion Fragmentation

Figure 5.29 History of a meteorite.

203 The cosmic timescale

Meteorites can be studied by using radiochronometers with long half-lives, by c os-

mogenic isotopes, and by extinct radioactivity. They are prize items for radiometric

dating.

5.7.2 The history of the Moon

Moon rocks (seeTaylor,1982) brought backby the American Apollo and Soviet Luna m is-

sions have also been dated by various geochronolog ical methods. Here very brie£yare the

main¢ndings.

There is an ultrabasic lunar rock aged 4.50 Ga (the oldest evidence ofthe Moon) but that

apart,the Moon is composedoftwogeological entities:

(1) thehighlandswhere the domi nantrock is anorthosite (calcium plagioclase) withan age

range of 4.3^4.0 Ga;

(2) the maria, which are large depressions formed by gigantic impacts and are made up

of basalts ranging in ag e from 3.7 Ga (Sea of Fecun dity) to 3.2 Ga (Sea of

Tran qu i l l ity).

Since that date it seems there has been no internal geological activity on the Moon.The

mo stimportantinformation derived fromthese studies isprobably thataboutthe number

of i mpact craters, which varies with time, decre asing markedly bet ween 4.3 and 3.2 Ga.

As these craters result from the impact of celestial‘‘thunderbolts,’’ which after impact are

captured and accreted by the Moon, it is inferred thatthe phenomenon of lunar accretion

(and by extension accretion of the other planets) declinedvery rapidly in the earlyd ays of

the Solar System (Figure 5.30).This provides an indirect indication about the process of

Age (Ga)

Impact crater density

(relative to Sea of Tranquillity)

Flux of constant

bombardment

half-life

= 3

x 10

4321

0.1

half-life

= 8 x 10

Figure 5.30 Density of impact craters on the Moon versus age as measured by the Apollo missions. The

reference curve indicates what the density would be if the meteorite ﬂux were constant. The half-lives

measure the speed of decline of these meteorite straight lines.

A lunar rock dated to 2.8 Ga was found in November 2004, but the context of its formation is not well

understood.

204 Uncertainties and results of radiometric dating

formation of the Earth by the successive, progressive build-up of ever larger planetary

bodies.

Toillustratehowthe Moon is situated inthe developmentofplanetaryobjects,Figure 5.31

shows the abundance ofro cks withtheirages in three di¡erentplanetaryenvironments. No

long speeches are nee d to expl ain the value of comparative planetology for constructing a

histor yofplanetary formation.

5.7.3 Pre-solar cosmochronology

The chemical eleme nts were synthesized in the stars (see Ho hen ber g,1969;Wa s s e r b u r g

et al., 2006). This is the process of nucleosynthes is already discussed. The heaviest

chemical elements form in massive stars only and in particular during spectacular

explosionskn ownas supernovae.Theidea arose ofdatingthetimeofformation ofthe che-

mi cal elements by explosive nucleosynthesis.This dating system

isbasedontheabun-

dance of heavy radioactive elements and even more so on the abundance ratio of two

radioactive isotopes with di¡erent decay periods. Let us take the classic example of the

from

Mars

from

the

Moon

highlands

Kodaïdal

2.0 3.0 4.0

4.5

Earth

Moon

Meteorites

Age (Ga)

5.01.0

3.0 4.0

4.5

5.01.0 2.0

3.0 4.0

4.5

5.01.0 2.0

}

sea

}

Figure 5.31 Histograms of radiometric ages measured on three types of planetary object: Earth, Moon,

and meteorites. This illustrates how the dating of rock can be used for comparative planetology.

TwoimportantreferencesareHohenberg(1969)andWasserburgetal.(2006).SeealsoClayton(1968).

205 The cosmic timescale

isotopic ratio of

238

Uand

235

U, both of which have long decay periods (one being much

longer than the other, though).The historyof these two isotopes can be broken down into

two episodes:

(1) thetimebetweentheBigBangandtheformationofthe SolarSystem during whichthese

isotopesweresynthesizedin supernovaty pestars;

(2) the period since the formation of the Solar System during which these isotopes have

been incorporated into rockyobjects (meteorites or planets), after their nuclear synth-

esisofstellarorigin hadended,andtheyhavethen decayedoverthese4.55 Gabynatural

radioactivity.

If we are to build a quantitative scenario of explosive nucleosynthesis, we must ¢rst go

back 4.55 Ga, just before the Solar System formed, and calculate the

235

238

U isotope

ratioatthattime.

Exercise

Given that the

235

238

U ratio is now 1/137.8, calculate the ratio 4.55  10

years ago.

Answer

Uranium-255 decays by the law:

235

U ¼ð

235

UÞ

4:55Ga

l

. Uranium-238 decays by the law:

238

U ¼ð

238

UÞ

4:55Ga

l

. Therefore:

235

238



present

235

238



4:55 Ga

l

with

¼0.98485  10

1

and

¼0.155 129  10

1

.Therefore:(

235

238

4.55Ga

¼0.31.

This is what we shall havetoreproduce in the chronological scenario of nucleosynthesis.

Weshall examinetwo extremescenarios, whichwillserve as refe rences and onthatbasiswe

shall discuss the construction ofa moreplausiblescenario.

The d i¡erent s c e nario s of u ranium n ucle osynt hesi s

In the sudden nucleosynthe sis model, we assume that all the uranium in the Universe

formed shortlyafter the BigBangin averyshortperiodoftimewhenacon siderablenumber

ofsupernovae existed, synthes izing theheavy che mical elements in theirexplosions. In this

scenario, the remainderofcosmic timeafter theBig Bang witnessedon ly the decayofuran-

iumbyradioactivity. We c an write:

235

238



4:55 Ga

235

238



l

where t is the timebetween the Big Bang andtheformationofthe Solar System.

The question is, of course, howdo we ¢nd the

235

238

Uratio atthe time of nucleosynth-

esis, just after the supernova explosion? This production ratio is not well known.

FromD.D.Clayton(1968).

206 Uncertainties and results of radiometric dating