All?gre Claude J. Isotope Geology

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Theneodymium mod el ageand itsgeological applications

The fact that Sm/N d fractionation is almost ze ro in geological surface processes after

extraction fromthe mantle means a model age canbe attributedto any neodymium isotope

measurement of a material belonging to the crust. In an ideal scenario, this is the age at

whichthematerial(oritsprecursors)wasextractedfromthe Earth’s mantletobeginits‘‘con-

tinental geological life.’’ This is the idea hit upon by Mal col m McCul l och and Jerry

Wa s s e r b u r g oftheCaliforniaInstituteofTechnologyin1978.Nosuchmodel agecanbecal-

culated for Rb^Sr as the Rb/Sr ratio varies considerably during the surface history

(although we shall see in Chapter 7 that it can still be used for l imestone). As will be seen, it

ispossibletouse Lu^Hf in a similar mannerbecause lutetium and hafnium arealsoalmost

insolubleinwater.

To calculate this model age (which we have already come across in calculating present-

day balances of the crust^mantle system), let us consider the straight line of isotope

evolution of the closed mantle (Figure 6.31 ). Imagine that a piece of continental crust

separated from the mantle at time T

, and has evolved since with constant 

Sm/Nd

growth. This straight line of evolution intersects the time axis at 

.Howcanwe

calculate timeT

in retur n?

Let us call the two parameters of evolution of the primitive mantle 

and 

, the two

parameters for the segmentofcontinental crust 

and 

Sm/Nd

, and the common isotope

ratio corresponding toT

we call I.

Age provinces

23 1 0

Age (Ga)

Formation of continental

crust at expense of mantle

4 23 1 0

Geological age

Model age

2 1 0

Figure 6.30 Data and results of the exercise. Top: starting data. Left: proportions of continents

determined by mapping age provinces. Right: proportions of continents as a function of extraction

from mantle. (Data corresponding to the two tables.) Bottom: what becomes of the various materials

extracted from the mantle, then the model ages as a function of geological age.

269 The continental crust–mantle system

We then havethetwoequations:



¼ I þ l

Sm=Nd



¼ I þ l

Sm=Nd

Byeliminating I, we get:



 



Sm=Nd

 

Sm=Nd

For the continentalcrust,

Sm/Nd

¼0.11and for theprimitivemantle 

Sm/Nd

¼0. 1 96.

But 

Sm/Nd



Sm/Nd

¼0. 11 0. 196 ¼0.086 is constant. Recalling the de¢nition of

"(0):

0ðÞ¼



 



 10

weobtain:

4

" 0ðÞ

6:54  10

12

 0:086

¼0:091 " 0ðÞ:

Ifwe want an approximation of T

in Ga, wehave about T

¼0.09 "(0), which is handy

for switching from"(0) toT

. (Itis almost "(0) divi ded by10 with a changeofsign!)

Naturally, ifthe crustal material contains a little ofthe original mantle material, the Sm/

Nd ratio is slightly higher than 0.11an d 

is also a littlelargerand the previous formula is

notstrictlyapplic able. Butitprovides a ¢rst approximation.

Time

Model age

143

Nd/

144

sample

Evolution of

primitive

mantle

Figure 6.31 Principle of model age calculation. Start from the sample. Draw a straight line of slope 0.11

cutting the straight line of mantle evolution at

, corresponding to the model age

270 Radiogenic isotope geochemistry

Exercise

We have a sediment of mixed origin: 90% is from continental crust with an average

"(0) ¼25; 10% is from the ancient mantle with "(0) ¼þ5. The Sm/Nd ratio of the

continental crust is 0.11 and that of the mantle is 0.21. It is taken that the two components

have the same Nd concentration.

(1) Calculate (0) of the sediment and its conventional model age.

(2) Calculate the model age using the Sm/Nd ratio measured on the sediment itself.

(3) Compare these ages with the model age of continental crust.

Answer

(1) 2 Ga.

(2) 2.26 Ga.

(3) 2.27 Ga.

By using the effective Sm/Nd age of the sediment, the dilution effect is ‘‘corrected’’ and we

get the age of differentiation of the continental fraction.

Exercise

If a shale is found with "(0) ¼20, what is its model age?

Answer

¼1.82 Ga.

Exercise

Supposing we apply the same formalism to Lu–Hf, given that (

176

Lu/

177

Hf)

¼0.02 and

(

176

Lu/

177

Hf)

¼0.036, calculate the model age of a schist whose "

(0) ¼25.

Answer

If "

Sch

(0) ¼25 

Sch

¼("(0)10

4

þ1) 

¼0.282 24



Sch

 



Sch

 

¼ 2:3Ga:

Neodymium model agesofgranites overgeological time

Dalila Ben Othman and the present author measured the initial isotope ratios of gran-

ites (major constituents of continental crust of varied ages) for the ¢rst time in 1979

(Alle

gre and Ben Othman, 1980; Ben Othman et al., 1984). The Nd model age is plotted

against geological age (Figure 6.32). If all the granites were derive d from the mantle,

the points would lie on a straight line of slop e 1. Now, this is generally so for ancient

granites ( Mont d’Or granite of Zimbabwe is a spectacular excep tion) while for more

recent granites, their model age i s much older th an their ‘‘geological age.’’ This con-

¢rms the idea of recycling wh ich increases with time. Let us try to be even more

speci ¢c.

271 The continental crust–mantle system

Geneticcartography ofcontinents

We have spoken of geological maps showing the di¡erent tectonic provinces which are

assembled to form the continents and we have given an overall explanation of these maps.

D on DePaol o (1981a,1981b) and hisgroup attheUniversityofCaliforniaatBerkeley under-

tooka similarapp roach (FarmerandDePaolo,1983;BennettandDePaolo,1987),consider-

ing the model ages of Nd only, that is, by trying to eliminate contin ental recycling. He and

his team studied two cases from the western United States: thatof Colorado andthe neigh -

b oring states where the age of emplacement of granites is1.8 Ga and the west of the region

(Rocky Mountains) wherethegraniteintrusions are of Tertiary age (Figure 6.33).

In the Colorado province, there is a central part formed 1.8 Ga ago an d which di¡eren-

tiated from the mantle at that time, and then bordering parts to the north and west whose

mo del age is 2^2.3 Ga. It can be seen that the 1.8 Ga materials also extend into the pro-

vince to the south in New Mexico and Texas dated 1.2^1.5 Ga. Heading west, towards the

Rocky Mountains, the Berkeley team traced isoclines with the same "

(0) value showing

that when movi ng fro m the continent toward the oceanic margin s, "

(0) becomes

increasingly positive, that is ever closer to mantle values (Figure 6.34). The percentages

of mantle material in the make-up of the granite can be calculated: they increase from

east to west.

These two examples show how continental tectonic segments are built up by addition to

an cient sediment. Probably through subduction processes, as shown in the Rocky

3 2 1 0

Nd model age (Ga)

Geological age of emplacement (Ga)

Recent

granites

Straight line of concordance

Figure 6.32 Model ages of granites of varied geological ages. After Alle

gre and Ben Othman (1980); Ben

Othman

. (1984).

272 Radiogenic isotope geochemistry

Mountains, but with reworkingand reuseofoldersediment.Ifasimilarstudyis made inthe

Himalayas, that is, in a collision range, the geographical distribution is markedlydi¡erent

butthe division between newly formed crust and recycled crust remains.The same goes for

allofEuropewherethe Caledonian,Hercynian,and Alpine orogenies essentiallyreworked

an cientpieces ofcontinentalcrust,someofwhich areveryold, as re£ected by the N d model

ages calculatedongranitesorsediments.

Wethereforehavetwoverydi¡erentsituations:



continents that have grown through new segments, which are very clearly mapped as in

Nor th Americaor Scandinavia;



continentswhereitis di⁄culttoidentifylarge age provincesbecause everything hasbeen

mixed and recycled,as in Europeand the middl e partof As ia.

200 km

32°

36°

40°

122°

114° 106°

Pacific

Ocean

SAF

= 1.7–1.8 Ga

= 1.8–2.0 Ga

> 2.7 Ga

M.R.

G.C.

PENOKEAN

1.8 Ga

ALGOMAN

2.3-3 Ga

CENTRAL

1.2+1.5 Ga

0.53

1.8

1.2

< 1.4 Ga

= 2.0–2.3 Ga

Pacific

Ocean

Figure 6.33 Study of Colorado granites by the model age method. Top: tectonic provinces (see Plate 5).

Bottom: provinces mapped by neodymium model ages. The two distributions do not coincide. The

difference can be explained by reworking. After Bennett and DePaolo (1987).

273 The continental crust–mantle system

Remark

The main mechanisms of continental growth seem to be well understood. One question remains.

We have drawn a general map of the tectonic provinces. The Colorado study gives details of one

speciﬁc case. There is no doubt that continental crust in a given continent is extracted during

mountain-building episodes of well-deﬁned ages. But is this true at the scale of all the continents?

Does not the combination of all orogenies lead to continuous extraction?

Australian detritalzircons

These ideas about dual mechanisms of formation of continental crust ^ reworking of old

materialandformation ofnewsegmentsofcontinentmaterial ^ arewonderfullyillustrated

byworkonAustraliandetritalzirconsbyChris Hawkesworth’s Bristolteamusingthelatest

insitu isotope analysistechnology (Hawkesworthand Kemp,20 06).

+6 +2

–2

–6

–10

–14

–18

–2

–6

Pacific

Ocean

500 km

100

500

Distance (km)

Percentage of mantle

Nd in granites

750

000

SAF

1.63 Ga

0.18 Ga

0.91 Ga

1.5 Ga

1.63 Ga

}

Figure 6.34 Neodymium isotope study of the Rocky Mountains in California. The curves of the "

isotope ratios are plotted. An E–W curve is shown below. The proportion of mantle decreases very

rapidly eastwards. After Farmer and DePaolo (1983).

274 Radiogenic isotope geochemistry

This work began with the analysis of detrital zircons. Zircons (ZrSiO

), which are prime

minerals for U^Pb radiometr ic dating, are extremely resistant to erosion.They are engen-

deredbytheformation ofgraniticrocks.They withstandweatheringvery well andaretrans-

ported mechanically and mix with clastic sediments (sandstones and, to a lesser extent,

shales). They may undergo a second phase of e rosion and be re-sedimented. At that ti me

they can mix with zirconsborn in a newgeneration ofgranites.Thus, a sandstone may con-

tain zircons ofvarious ages.This pseudo-immortality of zircons was revealed in studiesby

Le de nt et al.(1984), whowere attempting to determine a mean age for continental crustby

analyzing a zircon population. Using grain-by-grai n zircon analysis,Gau dette et al.(1981)

showedthe reweremanyepisodesofgranitization recordedin asinglepopulationofdetrital

zircons. But such studies us ing conventional methods were time-consuming and tedious.

This approach was revolutionized by the team from the Australian National University

when Bill Compstonand Ia nWi llia ms (1984) developedthe SHRIMPion probefor U^Pb

isotope analysis of zircons. Advances in automation mean that 500 zircons can now be

mounted on a plate and their U^Pb analyses completed in a matter of days. It was with this

methodthatthe Australianteamdiscovered th e existence ofzircons aged 4.3 Ga and even a

few grains aged 4.4 Ga in Precambrian clastic sediments.T hey also made a further discov-

erythathadbeen suspected for so metime. Zircongrainshave complexindividu al histories.

Around an ancient core, which is often rounded by e rosion, newgrowth zones have devel-

opedgivingthezircon crystalsthe appearanceofadoublepyramid.Thezirco n crystalscon-

tain arecordofthe di¡e rentperiods oftheir individualhistories.

This is proof, if any were needed, that some granites were forme d from the remelting of

earlier sediments, which themselves contained detrital zircons. These ancient zircons

acted as seed crystals for newadditions of zircon around them. A single zircon may tell the

complexgeological historyofaregion!

The Bristol team working in conjunction with the Australian National University team

tooka sandstone fromthe Primary period (400 Ma)as their starting point. After mechani-

cally separating the zircons, they analyzed the U^Pb ages of several hu ndre d zircons.They

alsoan alyzedthe cores ofzirconsfrom agranite dated 430 Ma.Theyobtaine d agesbetween

3.2 Ga and the age of the gran ite. A whole series of ages, with maxima and min i ma, is

shown in Figure 6.35.

Theythenu sedthefactthatzircons arerich in hafnium(Hfis theelementjustbelow Zr in

the periodic table) and very poor in lutetium.They thus managed toanalyze the Hf isotope

composition and calculate their model age for ea ch zircon, in the same way as is done for

Nd.This yielded a model age at which the material from which the zircon d erives became

separated from the mantle.The high H f content of zircon meantthis analysis could be per-

formed by laser ablation followed by ICPMS analysis. But they added a further crite rion.

They analyzed the

O isotope comp osition of zircons with an ion probe. As we shall

see in the next chapter, basic magmatic rocks have very constant

O compositions

with  varying from 5.5 to 6.5.They therefore selected z ircons grains with 

O < 6.5. In this

way zircons derived from materials extracted from the mantle could be selected.This dou-

ble-sorting process yielded an extraordinary result.The model ages were clustered around

twovaluesof2 Gaand 3.2 Ga (Figure 6.36).

The conclusion is that new continental crust was only formed from the mantle at these

two periods. However, conti nental crust (granites) has formed throughout geological

275 The continental crust–mantle system

Hf model age

(δ

O<6.5‰)

Gondwana

sedimentary

rocks

4.0

3.0

2.0

1.0

1.0 2.0 3.0 4.00

Age (Ga)

Number

Nd model age (Ga)

U-Pb crystallization age

Nd model age

Figure 6.35 Composite zircon age diagram. The histogram in black shows the crystallization ages

determined on different zircons using an ion probe. The histogram in blue is the model age of

hafnium computed for individual zircons with 

O < 6.5. The blue curve is the neodymium model

age obtained on Australian sediments. After Hawkesworth and Kemp (2006).

Bulk Earth

Hf model age

176

Lu/

177

Hf = 0.021

= 0.75

176

Lu/

177

Hf = 0.017

= 0.94

Zircon

Lu/Hf ratio

of average crust

depleted mantle

–30

–20

–10

1 000 2 000 3 0000

Age (Ma)

U–Pb age (Ma)

(t)

500

1000 1500 2000 2500

depleted mantle

Figure 6.36 How hafnium model ages are obtained by laser ablation ICPMS. Zircons on spot size on the

left. The principle of hafnium model age competition. Results for Australian zircons.

276 Radiogenic isotope geochemistry

histor y, as shownbyU^Pb dating, but these episod es were merely the reworkingofancient

cru st. Newthingswere made outofold!

This new method, once extende d to various region s of the planet, will indicate exactly

how continental crust formed. Did it form continuou sly throughoutgeological tim e, more

or less in relation with the activity of subduction zones, but in di ¡erent geographical loca-

tions? Ordid itformworldwide duri ng speci¢c episodesof intense activity?

When a histogram is drawn ofgeological ages measured on the various continents, peaks

arefound at600 Ma,11 00 Ma ,1600 Ma,2100 Ma,2 700 Ma,and 3200 M a.Theirdispersion is

100 Ma on average.What do these peaks mean? Are they the h eartbeat of the planet or the

re£ectionthatsomeregionslikeChinaorIndiaarestil lunder-explored?Studiesofthewestern

United States by the team from Berkeley seem to show that the formation of new continental

crust is also associated geographically with reworking processes. But is this a general result?

We can entertain high expectations of the results of this research because the method devel-

oped at Bristolandatthe Australian National Universitysuggeststhatwenowhavethe means

tosolvetheproblem.

6.4 Isotope geochemistry of rare gases

There are ¢ve rare gases.They form the ¢nal colu mn of the periodic table of the elements:

helium (He), neon (Ne), argon (Ar), krypton (Kr), an d xenon (Xe). Some isotopes of rare

gas es are produced bylong-period radioactive processes and so causevariations in isotope

abundance (Tables 6.5 and 6.6).Wehavealready referred to

He and

Ar when dealing with

geochronology (Chapter 5).The decay schemes leading to rare gas isotopes are recalled in

Table6.7.

All rare gas atoms share the common property of having their outer electron shell satu-

rated and so being chemically inert. They are transported by physical processes only and

tend to migrate upwards, towards the atmosphere where they accumulate. In the atmo-

sphere, theirbehavior varies dependingontheiratomic mass.

Helium, avery light element, is not retained by the E arth’s atmosphere as its mass is too

low.Itescapes continuouslyintospacelike(andwith) hydrogen. Neonisretainedbythe pre-

sent-day atmosphere, but it is thought that some n eon was lost in the Earth’s early history.

Argon,krypton,and xenon areretainedbytheatmosphere.Howcanthe escapeoftheseele-

ments be interpreted? As a ¢rst approximation, it can be understood quite simply. For an

objecttoescapefrom theEarth, itsvelocity mustexceedthe Earth’sgravitational attraction.

Since1/2 mV

¼mg R,thevelocityV

mustbe greater than

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2gR

. Now, acceleration due to

gravity is g 10 m s

2

and the Earth’s radius R is 6400 km, therefore the escape velocity is

¼11.28 km s

1

Letus supposethat escapeisby thermal means only.

kT and V

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

3kT

Hence:

3kT

ð11:2kms

1

where k is Boltzmann’s constant, Tis absolutetemperature, and m is mass.

277 Isotope geochemistry of rare gases

Table 6.5 Composition of the atmosphere

Isotope Atomicabundance (%)

Helium

30.000140

4 100

Neon

20 90.50

21 0.268

22 9.23

Argon

36 0.3364

38 0.0632

40 99.60

Krypton

78 0.3469

80 2.2571

82 11.523

83 1 1 .477

84 57.0 0

86 17.398

Xenon

124 0.951

126 0.0887

128 1.919

129 26.44

130 4.070

131 21.22

132 26.89

134 10.430

136 8.857

Majorgases

Molecular

mass Fractionby volume

Totalbalance

Bymass (kg) By volumeatstandard

temperatureandpressure

28.0134 0.78014 3.866 10

3.0 93 10

31.9988 0.2 0948 1.185 10

8.298 10

44.0 099 (3.40)  10

4

2.450  10

1.24 8 10

He 4.0026 (5.24 0.05)  10

6

3.707 10

2. 07 6 10

Ne 20.179 (1 .8 1 8 0.004)  10

5

6.484 10

7.2 02 10

Ar 39.948 (9.34 0.01)  10

3

6.594 10

3.700  10

Kr 83.8 0 (1.14 0.01)  10

6

1.688 10

4.5 16 10

Xe 1 3 1.30 (8. 7 0. 1 )  10

8

2. 019 10

3.4 46 10

Table 6.6 Rare gases in sea water

Concentration(atstandardtemperature andpressure)

He (1 0

8

)Ne(10

7

)Ar(10

4

)Xe(10

8

)

Surface seawater (25 8C) 3.7 1.47 2.26 0.65

Deepwater (48C) 4.22 1.85 3.51 1.1

278 Radiogenic isotope geochemistry