All?gre Claude J. Isotope Geology

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total

Sr 1 þ



 atomic mass of Sr:

If we wish to make a precise calculation, we must recalculate the atomic mass of strontium

because the

Sr/

Sr ratio is not exactly that of the standard samples, which is 0.709. This is

not an easy operation because we must calculate the atomic mass of each isotope (or look it

up in tables).

We shall ignore this difﬁculty. The standard isotope ratios are:

Rb=

Rb ¼ 2: 5926;

Sr=

Sr ¼ 8:3752;

Sr ¼ 0:056 584:

The atomic mass of Sr is 87.613 and of Rb is 85.35.

We therefore ﬁnd:



mass

 0:341;

which gives:



Earth

¼ 0:031

Exercise

Calculate the relation between the

147

Sm/

144

Nd ratio and the Sm/Nd gravimetric chemical

ratio.

Answer

Read on!

6.2.4 Position of granites in the (Sr, Nd) diagram

Analysis ofgranites ofvarious ages initiallyby teams in Paris and Cambridge (1978^80) (see

Alle

gre and Ben Othman,1980; O’Nions et al., 1983; Ben Othman et al.,1984) showed, as

expected,muchwiderdispersionofisotoperatiosthanforthemantle.Insteadofhavingasim-

plealmostlinearcorrelation asforoceanicbasalts,continentalgranites, gneisses, andgranu-

lites de¢ne a fairlybroad domain, but in a‘‘symmetrical’’positionto thebasalts relativeto the

reference point of the primitive mantle (Figure 6. 12). This pattern of distribution of points

representing the continental crust is the outcome of two combined e¡ects: for one thing, the

continentalcrustismadeupoftectonicsegmentsofdi¡erentages¢ttedtogetherlikeamosaic;

for another, in the complex pro cesses occurring in the continents (erosion, sedimentation,

metamorphism, hydrothermalism, anatexis, folding), fractionation between Rb and Sr and

b etween Sm andNd aredi¡erent andsotheisotopicresultsarevaried.

The precise atomic mass of an isotope is not just the number of neutrons neutron mass þnumber of

protons proton mass, expressed as a unit of mass (1/12 of

C), because the bonding energy

E ¼mc

, related to the energy of formation of the atomic nucleus, must be subtracted.

239 Strontium–neodymium isotopic coupling

6.2.5 Back to the isotope evolution diagrams

We can now plotthe isotope evolution diagram for the

Sr/

Sr ratio versus time for basalt

and granite.The novelty is that we can now plot the straight line of isotope evolution of th e

Earth, that is, of the primitive mantle as the reference since none of Rb, Sr, Nd, or Sm is

incorporated i n th e Earth’s core.

Figure 6. 13 shows that granites, which constitute most of

the continental crust, are situated above the primitive mantle, and oceanic basalts below,

withthe MORB being the mostextreme.

BymeasuringtheRband Srcontents ofthe continentalcrust,we canestimatetheslopeof

the straight line of evolution for the continents as equal to l

Rb=



.The

Rb/

ratios of continental rocks range from 0.5 to 3.The value1is a good average. Conversely, the

Rb/

Sr ratios of MORBs are very low (0.001). The straight line of evolution of the

MORBsource medium is virtuallyhorizontal.

As said, the continents are made up of segments of tectonic provinc es that are pieced

together and formed at di¡erent times. It is th erefore a seri es of vectors of evolution that

must be considered and which lie behind the wide dispersion of the present-day

Sr/

isotope ratios (Figure 6. 1).

Let us try to construct an analogous diagram for the

143

Nd/

144

Nd ratio. To do this, we

mustmeasurethe comp osition ofgraniteswhichturn outtohaveverynegative"parameters

(the Bulk Earthbeing taken as the referencewith "

Earth

¼0).Whenwe plotthe resultson the

Nd isotope evolution diagram, we observe a similar distribution as for Sr but in revers e.

The values of the granites are below those of the pr imitive mantle and the basalt values

above,withtheMORBlyingfurthestout,withthehighest "parameters (Figure6. 13).

143

Nd/

144

Granites

Present-day

Bulk Earth

Oceanic

basalts

0.7050.700

0.513

0.512

0.511

0.510

0.509

0.710

Sr/

Figure 6.12 Position of granites in the (Sr, Nd) isotope correlation diagram. Notice the domain is much

broader than that of basalt. The straight lines of evolution of oceanic basalts and of the Earth’s primitive

mantle are shown.

We shall use the terms ‘‘Earth,’’ ‘‘Bulk Earth,’’ and ‘‘primitive mantle’’ interchangeably when speaking

of Rb/Sr or Sm/Nd ratios, since the corresponding ratios are all identical.

240 Radiogenic isotope geochemistry

Topin downthe quantitative evolutionsof

143

Nd/

144

Nd ratios,wehavesoughtto evaluate

the

147

Sm/

144

Nd ratios of th e two‘‘symmetrical’’ reservoirs: the continental crust and the

mantle, which is the MORB source. For the crust, the

147

Sm/

14 4

Nd ratios are close

(0.10^0.12). For the MORB source, the

147

Sm/

144

Nd ratios range from 0.15 to 0.3. Unlike

with

Sr/

Sr, the evolutionofthe MORBsources intermsof

147

Sm/

144

Ndis notahorizon-

tal line.

On this basis, a si mple geo dynam ic model can be developed.The continental crust has

di¡erentiated at the expense of the m antle probably through volcanism or magmatic pro -

cesses related to subduction.T he continental crust is enriched (compared with the mantle)

in elements such as potassium, rubidium, cesium, rare earths, thorium, and uranium.

According to the plate tectonics paradigm, the continents ‘‘£oat’’ on the mantle and are

never swallowed up again by it: the enriche d elements of the continental crust aretherefore

stored atthe Earth’s surface.Thus theyare removed from theupper mantle, which is conse-

quentlydepletedin these elements.

Measurements of concentrations reveal that the continental crust is greatly enriched in

Rb an d less so in Sr.Therefore, the Rb/Sr ratio of the continental crust is far higher than

that remaining in the mantle after extraction (residual mantle). Likewise, the continental

cru st is much more enrich ed in Nd than in Sm, and so the Sm/Nd ratio of the continental

cru st is lowerthan inthe residual m antle.T his explains the origin ofthe inverseisotope cor-

relation.T he di¡erences in chemicalbehavior between the Rb^SrandSm^Nd syste ms are

important in dispersion. As Figure 6.1 4 shows, the Sm/Nd ratio is just as widely dispersed

in MORBs as it is in granite, whereas the dispersion of Rb/Sr is very di¡erent in the two

media (MORB values showing little dispersion). This is because of the properties of rare

earths, which areverysimilar to eachother.

Extraction ofelements by the conti nental crust atthe expense of the mantle is a complex

geologicalprocessthat mustbe evaluatedbutwhichprobablyinvolves magmaticprocesses.

MORB

Bulk

Earth

Continental

crust

MORB

+10

0.7025

0.7050

0.7100

0.7125

0.7150

0.7175

0.7200

–20

Sr/

Earth

4.55 Ga present day

Time

4.55 Ga present day

Time

Continental

crust

Figure 6.13 Isotope evolution diagrams inferred directly from the (Sr, Nd) isotope correlation. These

diagrams show how we can imagine the surface part of the Earth evolved, with continental crust having

preferentially extracted some elements and a depleted oceanic mantle (MORB source) as a result of that

extraction. Positions in the isotope evolution diagrams are ‘‘symmetrical’’ relative to the Bulk Earth.

241 Strontium–neodymium isotopic coupling

Geological mapping(seePlate5) andthe isotopic dispersion ofcontinentalrockssuggest

that this di¡erentiation of the continents has been going on throughout geological time in

successive episod es.The upper mantle fromwhich the continental cr ust has been extracted

and which is termed ‘‘deplete d’’ mantle (that is, depleted in certain elements such as potas-

sium, uranium, thorium, rubidium, etc.) is therefore the residue of this extraction process.

Buttheupper mantle is alsoinvolved inthe gigantic process ofplate tectonics.It is therefore

a medium in which convection processes occur, with transport of matter over great dis-

tan ces but also with vigorous mixing. This medium is th erefore relatively homogeneous,

which explains thenarrowisotopic spreadof MORBs in Figure 6. 1.

It seems that MORBs are samples from the part of the mantle that is most a¡ected by

extraction of the contin ental crust. As MORBs crop out at the ocean £oor along oceani c

ridges, itis assumed thatthis reservoir is the upper part ofthe mantle (as con¢rmed nowby

tomographic imageryobtained byseismology).

In contrast, OIB comes from the more primitive, deeper mantle; it is c ontaminated as it

crosses the upper mantle and so its isotopic compositions lie midway between those of

MORBandthose ofthe more primitive mantle (Figure 6. 15).

6.2.6 Evolution of time in the (Nd, Sr) isotope diagram and the

question: geochemical differentiation or mixing?

Intheforegoingreasoning,toillustrate changesinthe Srand Nd isotope ratios, we returned

to the diagrams of isotope ratios versus time, adding an essential component, the reference

constituted by the straight lines of evolution of the Bulk Earth (Alle

gre et al., 1979). Can

these evolutionsnotbe shown di rectlyon the (Sr, Nd) isotope diagram? Ofcourse they can,

and this presentation has the advantage of clearly situating the isotope domains observed.

135

Rb/

Granitoids

0.1 0.2 0.3

147

Sm/

144

MORB

Granitoids

Figure 6.14 Statistical distribution of

Rb/

Sr and

147

Sm/

144

Nd ratios in MORB and granitoids.

242 Radiogenic isotope geochemistry

ThestraightlineofevolutionoftheEarthsystem canbe drawn.Thetwoevolutionequations

are:



Earth

143

144

143

144



147

144



Earth

Eliminatingtgives:

143

144



143

144







147

144



Earth



Earth

0:196  6:54  10

12

0:091  1:42  10

11

¼ 0:9919:

Therefore in the

143

Nd=

144

Nd;

Sr=



diagram, the evolution is a straight line with

a slope very close to unity. This straight line is graduated in time, of course. The two

straight lines of evolution leading to the average of the continental crust and of the resi-

dual mantle, the MORB source, can be drawn. Their slopes can be easily calculated

and are equal to :

147

144



Depleted

upper mantle

Continental crust

MORB

OIB

Primitive

deep mantle

Figure 6.15 The standard model of the mantle. The mantle is separated into two layers: the MORB

derived from the upper layer and the OIB from the deeper layer. The upper layer is depleted in some

elements by extraction of the continental crust. Thedeeperlayerismoreprimitive (that is, closer

to the value of the Bulk Earth). The continents are made up of a series of provinces of varied ages

243 Strontium–neodymium isotopic coupling

With the approximate values for the continental crust and the primitive mantle, we ¢nd the

slope of the straight line of evolution of the d epleted mantle is very, very steep (more than

100) and thatofthe c ontinental crustis closeto0.05.

Exercise

Given that the slope of the straight line of evolution of the depleted mantle is very high and

the extreme value of MORB is

143

Nd/

144

Nd ¼0.513 50 and

Sr/

Sr ¼0.7021, what is the

minimum age of differentiation of the crust–mantle?

Answer

The age is greater than 2 Ga.

On the basis of this reasoning, we can trace the curves of evolution of the depleted mantle

and the continental crust (Figure 6. 1 6), assuming that the continental crust has been

extracted in a series of episodes.When the theoretical models are compared with experi-

mentaldata, a questionarises.Howcanwe explainthe dispersionofvaluesfor the continen-

tal crust andthelesse r dispe rsion ofbasalts?

A priori, there are two hypotheses: di ¡erentiation or mixing ?(ora combination of the

two ?).Were there multiple crust^mantle di ¡erentiations giving rise to di¡erent pieces of

cru st and leaving di¡erent pieces of depleted mantle? Or, on the contrary, are all the inter-

mediate points the result of mixing between two extreme components? Before discussing

these questions, we need to know how a mixture is represented in the (

143

Nd/

14 4

Nd,

143

Nd/

144

Granites

continental

crust

Granites

continental

crust

Present-day

Bulk Earth

Mixing

Depleted

mantle

1 Ga

2 Ga

Oceanic

basalts

0.7050.700

0.513

0.512

0.511

0.510

0.509

143

Nd/

144

0.710

Sr/

0.7050.700

0.513

0.512

0.511

0.510

0.509

0.710

Basalts

MORB

Figure 6.16 Diagram of (Nd–Sr) isotope evolution over geological time. (a) We have supposed that the

continental crust was extracted in a series of episodes and that the residual mantle reﬂected these

extractions in a continuous, gradual manner. (b) We have supposed the extraction episodes of pieces of

continents were followed by mixing phenomena both in the residual mantle to the left of the straight

line of evolution of the Earth and in the continental pieces (one case is shown, to the right of the straight

line of evolution of the Earth). After Alle

gre

.(1979).

244 Radiogenic isotope geochemistry

Sr/

Sr) diagram.We have spoken of mixing in the isochron diagrams but not yet in the

caseofpaired isotope ratios.

6.2.7 Mixing in isotope ratio correlation diagrams

Im agine we have two reser voirs characterized by their isotope ratios noted here R and 

(e.g.,

Sr/

Sr and

143

Nd/

144

Nd). How is a mixture represented in the (R , )diagram?Ifwe

write the equations of the mixture M between two extreme reservoirs (1) and (2), where A

and B areth e two chemical elementswhose ratios areunderc onsideration, weget:

¼ R

þ R

ð1  x



¼ 

þ 

ð1  y

where x

¼ m

þ m

and y

¼ðm

Þ=ðm

þ m

Þ; C

and C

being the concentration s of element A in poles 1 and 2, and C

and C

being the concen-

trations for element B. Let us calculate the mixing equation in the (R, )diagram.

Combining thetwo equations for th e tworatiosgives:

 R



¼ K



 



 



;

with K ¼ðC



ðC

Þ. If the denominator of the two ratios is identical (as is the

case, for example, with l ead isotopes whose denominator is common lead,

204

Pb), the m ix-

ing equation is a st raight l in e.The same is tr ue ifthe denominators are di¡erent, but K ¼1,

thatis, ifthe chemical ratios ofthe two elements are identical for1and 2 (for example i f Nd/

Sr is constantinbothsystems).

Generally, when K is di¡erent from1, the mixing curve is a hyperbola whose shape varies

with K (Figure 6. 17). However, if K is not too di¡erent from 1, the mixing curve is almost a

straight l i n e. (We shall make much use ofthisproperty in what follows.) This is generally the

casefor mixturesbetween mantlerocksorbetween continentalrocksfor the Nd^Sr system.

Exercise

We suppose a granite has been formed from a mixture of a basalt intrusion and pre-existing

acidic rock. The characteristics of the basalt magma are "

¼þ10,

¼7ppm,

Sr/

Sr ¼0.7025, and

¼300 ppm; those of the pre-existing rock are: "

¼20,

¼20 ppm,

Sr/

Sr ¼0.725, and

¼100 ppm. Calculate the mixing curve for the various

granite facies, supposing the

crust

magma

ratio varies from 0.1 to 1. (See Figure 6.18.)

Answer

Table 6.3 Mixing curve

Number

crust

mantle

Sr/

1 0.1 –18.98 0.719 00

2 0.25 –17.58 0.715 200

3 0.5 –15.53 0.711 50

4 0.75 –13.75 0.709 33

5 1 –12.2 0.708 12

245 Strontium–neodymium isotopic coupling

Di¡erentiation results in straight lines, while the mixtures in the Nd^Sr isotope dia-

grams are almost straight lines. By virtue of a powerful mathematical theorem by

which, in a linear (or near-linear) system, when there are two solutions, any combina-

tion of the two solutions are also solutions, there is no means of distinguishing by

Sr/

K =

= 0.1

(Sr/Nd)

0.5

100

+10

K = 10

0.705

K = 2

= 1

= 0.5

= 0.1

0.703 0.7040.702

Figure 6.17 Theoretical mixing diagram between two poles 1 and 2 in the (Nd, Sr) isotope diagram for

various values of relative concentrations of Nd–Sr of 1 and 2. Parameters are shown in the ﬁgure:

the ratio of Sr/Nd chemical ratios, the ratio of Nd concentrations is taken as 0.1, and the result is

graduated in mass ratio

0.708

–12

–14

–16

–18

0.710

0.712 0.714 0.716 0.718

Sr/

Figure 6.18 Representation of the various granite facies resulting from the crust–mantle mixture in the

exercise above.

246 Radiogenic isotope geochemistry

analyzing the exper imental data which of di¡erentiation or mixing predominate in

explaining th e Sr^Nd isotope correlation diagram as a whole. Geological considera-

tions suggest that both phenomena are involved in the dispersion of the points

observed. In the mantle, magma arises from di¡erentiation which separates a magma

composition from that of a residue. Conversely, convection in the mantle results in

mechanical mixing. In the continental crust, the formation of granites as well as the

erosion cycle, chemical sedimentation, an d metamorphism also correspond to chemical

di¡erentiation. Sedimentation and tectonic folding are mixing pro cesses. These two

phenomena probably occurred in the past and in recent periods (genesis and transfer

of magma). We asked the question: di¡erentiation or mixing ? The answer seems to b e

di¡erentiation and mixing. There’s a simple example of a non-uni que solution, or, if

you like, of quantitative uncertainty.

6.2.8 The Sr–Nd–Hf system

Wehavejust explored the coherence within the Nd^Sr isotope systems.We aregoing toadd

tothis the

176

Lu ^

176

Hfsystem, whichwi ll strengthen the cohesion withoutcontributingany

fundamental new information.

Lutetium is a heavy rare earthwhile hafnium hasgeochemical proper ties closetothose

of light rare earths. Lutetium-176 disintegrates into

176

Hf at a de cay rate l ¼1.94 10

11

1

. It was only natural, then, to try to connect the variations in

176

Hf/

177

Hf isotope

composition w ith the variations observed in

143

Nd/

144

Nd. But this endeavor was

long unsuccessful because of di⁄culties in correctly analyzing the isotope composition

of Hf in the low amounts in which it occurs in rocks. This di⁄culty was overcome in

1980 by Patchett and Ta t s u m o t o (1980), working for the U.S. Geological Survey

in Denver. Since th en, a substantial amount of rock has been me asured by teams at

the Un iversity of Arizona at Tucson an d the E

cole Normale Supe

rieure in Lyon and the

result is an extraordinarily coherent correlation between the isotope compo sitions of Nd

and Hf (Figure 6. 1 9). This correlation is important because it strengthens cohesion

(Bl ichert-Toft and Albare

de, 1997; se e also Patchett,1983;Ve r v o o r t and Bl ichert-Toft,

1999). It shows that the isotopic variations ob served for Nd are not the outcome of s ome

property peculiar to Nd but that they obey more general rules. As we did w ith Nd, we

de¢n e:

ð0Þ¼

176

177



176

177



176

177



 10

The c onstants required for these calculations are:

Ratio at 4:55 Ga ð

176

Hf=

177

HfÞ

¼ 0:279 78

Present-day Bulk Earth ð

176

Hf=

177

HfÞ

¼ 0:282 95:

247 Strontium–neodymium isotopic coupling

The value of (

176

Lu/

177

Hf)

can be c alculated from the growth of the (

176

Hf/

177

Hf)

ratios,

giving

¼ 0:036.

Exercise

Three rocks (1, 2, and 3) are measured with

176

Hf/

177

Hf isotope compositions of 0.2835,

0.2832, and 0.281, respectively. Calculate "

(0). Can you identify the rocks from the Nd–Hf

correlation?

Answer

¼þ19, "

¼þ8.8, and "

¼68.9.

1 ¼MORB, 2 ¼OIB, and 3 ¼very old granitoid rock.

6.3 The continental crust–mantle system

Examination of the regularities and c orrelations in Sr^Nd^Hf system s sparked the idea

thatthefunda mentalprocessbehind chemicaldi¡erentiationoftheupper partoftheplanet

was the extraction of continental cr ust and its repercussions on the mantle.We shall try to

look more closely at this process in quantitative terms using the model developed by

Alle

gre,Hart,andMinster(1983a).

MORB

OIB

0 Ma

> 0.09 Ma

< 0.8 Ma

> 1.15 Ma

0.2835

0.2830

0.2825

0.2820

0.2815

0.5110 0.5114 0.5118 0.5122 0.5126 0.5130

MORB

OIB

Continental material

143

Nd/

144

176

Hf/

177

Figure 6.19 Modern (Nd, Hf) isotope correlations after data from Patchett and Tatsumoto (1980) and

Vervoort and Blichert-Toft (1999). The correlation is excellent and extends linearly to rocks of the

continental crust for which only a few points are shown.

248 Radiogenic isotope geochemistry