All?gre Claude J. Isotope Geology

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bombarding 1 mg of carbon with a stream of cesium ions, the ﬂow of

ions is 15

ions per second.

(a) For the same intensity of current of

C, how many

C ions are obtained per unit

time for 1 mg of carbon aged 55 ka?

(b) If the measurement lasts 20 minutes, what is the uncertainty on the age determina-

tion? Compare it with the error on the measurement of the present-day

Cratio.

decide the difference to be measured with the present day must be at least ﬁve

times greater than the uncertainty?

(d) If we wanted to make the same measurement by counting  radioactivity and the

maximum counting time for a sample was 8 days, how much carbon would need to

be puriﬁed?

(ii) We wish to use the

238

U–

230

Th method to test the

C age of corals assumed to be about

55 000 years old. To simplify, we ignore the

234

238

U fractionation and assume that

(

230

Th)

¼0. The dating equation is written:

230

232

238

232



ð1  e

230

Þ:

Given that the uncertainty on the

230

Th/

232

Th ratio measurement is 1% and that the uncer-

tainty on the

232

Th and

238

U measurements is about 5ø, what is the uncertainty on the age?

Is this a good method for checking the results obtained by

C in this age range?

5 We are confronted with the geological situation shown in the section in Figure 5.38.

A geological formation of foliated and folded gneiss is cross-cut by a granodiorite which is

itself foliated.

(i) We wish to measure the age of the gneiss and to do so we make a series of

Rb/

measurements on the whole-rock. The results are given in Table 5.9. The Sr concentrations

of the various facies are very similar. Calculate the

Rb/

Sr age using a simple least-

squares method (without experimental uncertainties).

(ii) We determine the age of the granite by U–Pb methods applied to zircons from the granite.

Table 5.10 shows the results. Calculate the U–Pb age again by the simple least-squares

method and the concordia method. How would you interpret the result in geological

terms? Can you give a brief geological history of the region?

Rb-

(Whole rock)

U-Pb

(Zircons)

Figure 5.38 Geological formation of gneiss cross-cut by granodiorite.

217 Problems

6 A granite from south-eastern Canada is dated by various methods. The apparent age

results are:

Can you reconstruct the geological history of this granite and explain the ages measured?

7 We can determine the Permian–Triassic boundary at a given location. A granite cross-cutting

the Permian formation but with pebbles at the base of the Triassic is dated 243 5 Ma. The

Triassic is dated by two basalt ﬂows located in a section 100 m above the Permian–Triassic

boundary at 229 8 Ma and another 200 m above the Permian–Triassic boundary at

215 3 Ma. What is the approximate age of the Permian–Triassic boundary? What is the

error on the age determination at 218 3 Ma?

8 You are asked to explore the possibility of using the U–He chronometer.

(i) What time-span do you think best corresponds to the potential of the method?

(ii) What types of rock or mineral do you think are interesting a priori?

9 Half a century ago the question of the origin of granite was a subject of much debate. The

American Bowen showed by laboratory experiment around 1930 that rock of granitic com-

position could be made from basaltic magma (which we know is itself the product of partial

melting of the mantle). Bowen and Winkler in Germany showed, again by experiment, that

the melting of detrital sediments (shales and sandstones) to which sodium has been added

Table 5.9 Samples from the gneiss in Figure 5.38

Sample

Sr/

Rb/

1 0.713 0.0005 0.1 0.0005

2 0.718 0.0005 0.35 0.0005

3 0.719 0.0005 0.45 0.0005

4 0.722 0.0005 0.6 0.0005

5 0.724 0.0005 0.8 0.0005

6 0.723 0.0005 0.9 0.0005

Table 5.10 Samples from the granite in Figure 5.38

Sample

206

U*/

238

207

Pb*/

235

A 0.3 0.01 5 0.3

B 0.26 0.01 4 0.3

C 0.24 0.01 3.5 0.3

D 0.2 0.01 2.5 0.3

Method U–Pb

concordia

Rb–Sr

whole

rock

Sm–Nd

whole

rock

Rb–Sr on

biotite

Ar–

Ar Rb–Sr on

muscovite

Apparent

age (Ga)

2.8 0.1 2.7 0.1 2.7 0.1 1.7 0.2 1 0.1 1.7 0.2

218 Uncertainties and results of radiometric dating

also gives rise to a granitic magma. Subsequently, other experiments showed that the partial

melting of ‘‘wet’’ basalts produced granitic ﬂuids.

These experimental data were supplemented by ﬁeld observations and then more recently

Sr/

Sr measurements supporting the idea that almost all continental granites result

from the remelting of continental crust. The model of granites derived directly from the

mantle was abandoned. Yet, in the middle of the mid-Atlantic ridge, in Iceland, the famous

Hekla volcano has spewed out lava of granitic composition (rhyolites). The

Sr/

Sr ratios of

about 0.7032 give no clear answer to their origin as they are similar to those of many basaltic

lavas of Iceland.

The Icelander Sigmarsson studied the (

230

Th/

232

Th,

238

232

Th) ratios of these rhyolites

with the

230

Th–

238

U isochron diagram. The mantle beneath Iceland is in secular equilibrium,

corresponding to

238

232

Th ratios of 1.1 to 1.3 (in activity). The oldest basalt crust of Iceland

has (active)

238

232

Th ratios ranging from 0.9 to 1.1. It too is in secular equilibrium. The

rhyolites have a

230

Th/

232

Th ratio of 0.95 and

238

232

Th of about 0.8. What do you think is

the origin of this rhyolite?

10 Calculate the range of application of the

238

U–

206

Pb dating method for rocks and minerals

with the chemical ratios shown in the table below, given that the isotopic measurement is

affected by several relative uncertainties 

of 10

3

,10

4

, and 10

5

Draw the graphs corresponding to Figure 5.35. Calculate for the Rb/Sr ratio, and for U–Pb

applied to whole rocks and the main minerals that can be dated by this method.

Type of rock or

mineral

Granite Basalt Ultramaﬁc Zircon Sphene

U/Pb 0.2 0.1 0.05 100–10 2

219 Problems

CHAPTER SIX

Radiogenic isotope geochemistry

Our main concern in the previous chapters has been to calculate geological (or cosmo-

logical) ages and to clarify their geological meanings. In the next chapters we are going to

address isotope geochemist ry, which has a markedly di¡erent viewpoint although it is

based on the same physical laws and on the s ame equations.We are going to look not at age

but at the isotope ratios measured and the ways in which their natural variations may be

inter prete d.

This chapter, then, focuses on isotope ratioswhosevariationsarise m ainlyfrom radioac-

tive decay. Chapter 7 will be aboutisotopevariations caused by physical and chemical pro-

cesses. Examination of the variations in isotopic ratios will lead us to develop a

methodologyinwhichtheseratios areusedas tracersfor majorgeological andgeodynamic

phenomena. The purpose of these studies is therefore to determine the major structures

and exchanges of matteroccurring (or having occurred) among the major terrestrial reser-

voirs (crust, mantle, core, and atmosphere). The notion of age will crop up again, but in a

much moregeneral context, although in complete conti nuity withthe earlierchapters.

6.1 Strontium isotope geochemistry

6.1.1 Continents and oceans: granite and basalt

The natural isotopic composition ofstrontiumvaries with

Rb d ecay. Systematic collation

Sr/

Sr isotope compositions ofterrestrial basalt and granite (basaltbeing an isotopic

‘‘messenger’’fromthe mantle while graniteis a sample ofcontinental crust) revealsverydif-

ferent distributions. Strontium isotope ratios for granites from the various continents are

highly variable, ranging from 0.705 to 0.850 and more. Strontium isotope ratios for basalts

are much more uniform.They rangefro m 0.7020 to 0.7070 and foroceanic basalts from just

0.7022 to 0.7045.

Let us get these orders of magnitude clear. ‘‘Ordinary’’ analytical precision on the

Sr/

Sr isotope ratio is at least1.5 10

4

(relative) and therefore, on ratios close to 0.7, the

u ncertainty isbetter than10

4

(absolute).This means that0.7022 canbe distinguished from

0.7021 for certain. For granite, variations range from 0.850 to 0.705, corresponding to1500

measurement units. Foroceanic basalts, the range is 25 measurement units, or a dispersion

ratio of 60 timeslessthan forg ranites.

This di¡erence in the distributions of strontium isotope ratios between continents and

mantle can be explain ed by th e geological history of the two reservoirs from which granite

Plate 1 Periodic table of the elements. The isotopes most commonly used in isotope geology are indicated.

Magnet

Multicollector

Ion

beams

Ion

beams

Electrostatic

analyzer

Multi-filament

turret

Plasma

generator

Source

Plate 2 Modern mass spectrometers. In each case, the mechanical components are shown at the top and the ion

beam pathways below. Top: TIMS (thermal-ionization mass spectrometry). At the source, a turret allows several

samples to be tested in succession; at the collector, multicollection allows the various beams from different

isotopes to be analyzed without scanning. Bottom: ICPMS (inductively coupled plasma mass spectrometry). In

addition to the magnet, an electrostatic analysis sorts the ions by energy levels. The source is a plasma generator.

Multicollection is used as in TIMS.

Plate 3 Actual laboratory equipment. Top: A Cameca ion probe. Bottom: A clean room where samples

are prepared.

90 180

120 60

90 0

6060

Dark red 0-1 Ma

Medium red 1-4 Ma

Light red 4-9 Ma

Orange 9-20 Ma

Brown 20-35 Ma

Light brown 35-52 Ma

Yellow 52-65 Ma

Green-yellow 65-80 Ma

Light green 80-95 Ma

Medium green 95-110 Ma

Dark green 110-125 Ma

Green-blue 125-140 Ma

Blue 140-160 Ma

Purple 160-180 Ma

Plate 4 Map of ocean ﬂoor ages. After Sclater, Jaupart, and Garlson (1980).

0.25 - 0 Ga

0.7 - 0.25 Ga

1.7 - 0.7 Ga

2.5 - 1.7 Ga

3.8 - 2.5 Ga

3.8 - 1.7 Ga

Plate 5 Map of age provinces of continents. Top: world map. Bottom: more detailed map of North

America. After Hofmann (personal communication, modiﬁed).

3.8

3.6

3.2

2.8

Present day

Formation

of the Earth

Hadean

Archean

Isua formation

Greenland

Barberton

Great Canadian

orogeny

Cambrian

Phanerozoic time

West-African

orogeny

Proterozoic

Grenville

orogeny

Pan-African

orogeny

Eoarchean

Paleoarchean

Mesoarchean

Neoarchan

4.0

4.5

2.5

1.6

1.0

0.55

Paleoproterozoic

Mesoproterozoic

Neoproterozoic

Big Bang

Precambrian times

Plate 6 Geological timescales. Left: Precambrian times. Right: Phanerozoic times.