Interpreting SrŒNd isotopic data from magmatic and ...janousek/abstracts/izoworkshop.pdf ·...

Voj těch Janou�ek: In terpre t ing Sr�Nd i so top ic da ta: numer ica l rec ipes

� 1 �

Interpreting Sr�Nd isotopic data from magmatic and metamorphic

rocks

Numerical recipes and exercises

!

Vojtěch Janou�ek Czech Geological Survey, Prague

�Where chaos begins, classical science stops�

James Gleick, Chaos


� 2 �

IMPORTANT CONSTANTS

Rb decay constant λRb = 1.42 × 10-11 y�1 [Steiger & Jäger, 1977]

Sm decay constant λSm = 6.54 × 10-12 y�1 [Lugmair & Marti, 1978]

e e = 2.7182818

Sr isotopic ratios 86Sr/88Sr = 0.11940 84Sr/86Sr = 0.056584 [Steiger & Jäger, 1977]

Rb isotopic ratio 85Rb/87Rb = 2.59265 [Steiger & Jäger, 1977]

Atomic weights of Sr 88Sr: 87.9056 amu 87Sr: 86.9088 amu 86Sr: 85.9092 amu 84Sr: 83.9134 amu [Faure, 1986]

Atomic weight of Rb 85.46776 amu [Faure, 1986]

Atomic weight of Sm 150.4 amu [Faure, 1986]

Atomic weight of Nd 144.24 amu [Faure, 1986]

UR � present-day Sr isotopic composition 87Rb/86Sr = 0.0816 87Sr/86Sr = 0.7045 [Faure, 1986]

CHUR � present-day Nd isotopic composition 147Sm/144Nd = 0.1967 [Jacobsen & Wasserburg, 1980] 143Nd/144Nd = 0.512638 [Wasserburg et al., 1981]

DM � present-day Nd isotopic composition 147Sm/144Nd = 0.222 143Nd/144Nd = 0.513114 [Michard et al., 1985]

Two-stage DM Nd model ages

143Nd

144Nd0DM = 0.513151

147Sm

144Nd0DM = 0.219

147Sm

144Nd0CC = 0.12

[Liew & Hofmann, 1988]

Note that all Nd isotopic data are based on normalization to 146Nd/144Nd = 0.7219


� 3 �

AIM

The primary objective of this short text written for a PG level isotopic workshop at the Charles University is to explain basic numerical approaches used in interpreting Sr�Nd isotopic data in igneous and metamorphic geochemistry. To demonstrate the usability of the theoretical principles and numerical recipes given, exercises are presented that are based on real as well as artificial data. A floppy disc with the data and software needed for the exercises accompanies this handout.

Enjoy!

Vojtěch Janou�ek

Prague, April 1999

CONVENTIONS

Notation (employed to make the formulae �simpler looking�)

I = 87Sr/86Sr or 143Nd/144Nd

R = 87Rb/86Sr or 147Sm/144Nd

All the constants needed for the exercises are given on the previous page

Most important formulae are shown in bold type

Pictographs used:

Exercise

Hints to the exercise

Associated data file

Important notice


� 4 �

1. RECALCULATION OF ELEMENTAL TO ISOTOPIC RATIOS

+

=

SrSr

SrRb

SrRb

86

87

86

87

43174.928535.0 [1.1]

+

=

NdNd

NdSm

NdSm

144

143

144

147

14252.053151.0 [1.2]

In the Central Bohemian Pluton, Czech Republic, occur numerous Hercynian granitoid intrusions, all of comparable age (~ 350 Ma). The detailed Sr�Nd isotopic study (Janou�ek et al., 1995) has shown that most of the individual intrusions had distinct sources. This fact, together with the influence of other processes (mostly beyond the scope of this text) accounts for their observed geochemical variability.

Using the data given below, calculate the 87Rb/86Sr and 147Sm/144Nd ratios for selected granitoids from the Central Bohemian Pluton and their country rocks.

Sample Intrusion Rb (ppm)

Sr (ppm)

87Sr/86Sr Sm (ppm)

Nd (ppm)

143Nd/144Nd

Sa-1 Sázava 76 555.8 0.70700 4.57 24.2 0.512476 Koz-2 Kozárovice 164.1 486.9 0.71258 5.91 31.7 0.512210 Bl-2 Blatná 185 439.1 0.71434 6.85 43.8 0.512101 Se-9 Sedlčany 308.1 307.8 0.72620 8.17 40.2 0.512080 Ri-1 Říčany 310.7 374.1 0.72154 4.06 24.1 0.512053 CR-1 shale 110 80.4 0.72596 3.3 17.3 0.512061 CR-5 paragneiss 160 86.4 0.74670 9.4 50.6 0.511880

[cbp.xls]

2. INITIAL RATIOS, AGES

( )1−+= ti eRII λ [2.1]

( )1−−= ti eRII λ [2.2]

+

−= 1ln1

RII

t i

λ [2.3]

Exercise 1-1


� 5 �

Calculate initial Sr isotopic ratios (87Sr/86Sri ) of the samples from the previous exercise for ages 350 and 300 Ma. Calculate the age of the Kozárovice granodiorite (Koz-2) assuming 87Sr/86Sri = 0.705.

[cbp.xls]

3. ISOCHRON AGES For calculation of ages (cf. eq. 2.3), initial ratios are obtained using:

• a mineral without the parent (radioactive) element (apatite � virtually no Rb),

• a mineral with very high contents of the radioactive element (lepidolite � Rb-rich),

• the isochron method.

Samples plot onto an isochron, if:

• they are cogenetic (identical source ⇒ the same initial ratio),

• they are of the same age,

• represented a closed isotopic system throughout their subsequent history.

In fact [2.1] ( )1−+= ti eRII λ

is an equation of a straight line in the form:

y = a + bx [3.1]

Where: a = intercept, b = slope.

Figure 3-1: Rb�Sr data for the Agua Branca adamellite, Brazil, plotted (a) on a conventional isochron diagram; and (b) on an �improved� isochron diagram after Provost (1990)

Exercise 2-1


� 6 �

It is apparent from [2.1] and Fig. 3�1 that a corresponds to the initial ratio of the whole cogenetic suite and the slope b of the isochron is expressed as:

( )1−== tetgb λα [3.2]

Giving a formula for isochron age:

( )1ln1+= bt

λ [3.3]

The isochrons are usually fitted using software given in Tab. 3�1. The algorithm utilizes weighted linear regression and follows York (1969).

The Rb�Sr isotopic composition of the Serra do Acari granite from Pará, Brazil, was determined by Xafi da Silva et al. (1985). We will use this granite as a case study showing how isochrons are plotted, as well as how isochron ages and initial ratios are obtained.

Calculate the age and Sr initial ratio for the Acari granite using simple linear regression (MS Excel). Then calculate the same parameters using weighted linear regression implemented by Provost (1990) and produce both conventional and

improved isochron plots. Compare results obtained in both cases. Which sample controls the regression and why?

Sample 87Rb/86Sr 1σ 87Sr/86Sr 1σ

AT-R-173 5.743 0.062 0.858993 0.000034 AT-R-167 22.290 0.280 1.290200 0.000050 AT-R-157 42.170 0.530 1.760370 0.000069 AT-R-165 61.230 0.980 2.248950 0.000140 AT-R-158 99.000 1.800 3.182530 0.000170 AT-R-169 232.000 3.300 6.548880 0.000470

[acari.xls, acari.sr]

Hints:

! Plot a diagram analogous to Figure 3�1a (if you dare, you can even plot error bars), ! Fit the data by linear regression, ! Intercept of the regression line equals to the sought initial ratio, ! Age can be calculated from the slope using eq. [3.3], ! Start ISOCHRON.EXE, import the data file provided on the floppy (acari.sr), ! Note the format of the *.SR data file: first line is ignored and is intended for

comments, the following lines contain: sample_number, 87Rb/86Sr, 1σ, 87Sr/86Sr and 1σ with several spaces in between,

! If in doubt, just press ENTER to accept the defaults offered by the program.

Exercise 3-1

Isochron Provost (1990) France Pascal

IsoPlot Ludwig (1993) USA QuickBasic

Table 3-1: Software used for geochronological calculations

[ISOCHRON.EXE]


� 7 �

4. EPSILON ND VALUES

The isotopic evolution of Nd in the Earth is described in terms of a model, called CHUR (Chondritic Uniform Reservoir: DePaolo, 1988), which is assumed to have Sm/Nd ratio equal to that of chondrites. This model is widely used for comparison of initial isotopic composition of a studied (usually igneous) rock with that of primitive mantle at the time of its generation. This is done by means of the ε-notation:

( )( )

400

00

1011

1×

−

−−−−

= tCHURCHUR

tSASAt

CHUR eRIeRI

λ

λ

ε [4.1]

Where: t refers to the time of the intrusion, 0 to the present, SA = sample, present-day composition of CHUR is: 147Sm/144Nd = 0.1967 143Nd/144Nd = 0.512638

(Jacobsen & Wasserburg, 1980).

Partial melting of CHUR would produce melts with Sm/Nd ratios lower than CHUR (as Nd is more incompatible than Sm). On the other hand, the residue will be relatively enriched in Sm and have a higher Sm/Nd ratio (Fig. 4�1). This means that old igneous rocks formed by CHUR-like mantle melting should have present-day 143Nd/144Nd generally lower than CHUR and mantle domains depleted in melt will, with time, develop 143Nd/144Nd ratios higher than CHUR.

In general, if the εNd value is negative, the rock is thought to having been derived from (or assimilated a great proportion of) a material with Sm/Nd ratio lower than CHUR (e.g. old crustal rocks � Fig. 4�2). If, in turn, the εNd value is positive, then the rock came from a source with high time-integrated Sm/Nd ratio, such as residual mantle domains depleted in incompatible elements during a previous partial melting event (so-called Depleted Mantle, DM � DePaolo, 1988).

Partial melt

CHUR

CHUR

Residu

al so

lid (D

M)

T 0

Time

Partial melting

Figure 4-1: Isotopic evolution of Nd in a chondritic uniform reservoir (CHUR), igneous rock formed by its partial melting and the residual solid (after Faure, 1986)

Figure 4-2: Tentative Sr�Nd correlation diagram showing the approximate compositions of the most common crustal and mantle rocks (after Rollinson, 1993)


� 8 �

Calculate initial εNd values for the granitoid samples from the Central Bohemian Pluton (see exercises 1�1 and 2�1) assuming that their age is 350 Ma. Plot the initial 87Sr/86Sr ratios and εNd values into a diagram similar to Fig. 4�2 and briefly discuss the

possible sources of individual granitoid bodies, provided no assimilation, magma mixing or later disturbance of the Sr�Nd isotopic system has taken place.

[cbp.xls]

Hints:

! Epsilon values are calculated using eq. [4.1], ! Note that the intersection of both axes will be in εNd = 0 and the 87Sr/86Sr composition

of UR 350 Ma ago (see Page 2 for constants), ! Having trouble with interpretation? See Figure 4�2.

5. ND MODEL AGES

Single-stage ages

The single-stage Nd model ages provide an estimate of the time that a rock unit has had a different Sm/Nd ratio from that of the Earth�s mantle (represented by a model reservoir, typically either DM or CHUR: Fig. 5�1). The equation

TDM

TSA II = [5.1]

is solved for T (the so-called model age):

( ) ( )11 0000 −−=−− T

DMDMT

SASA eRIeRI λλ [5.2]

+

−−

= 1ln100

00

DMSA

DMSANdDM RR

IITλ

[5.3]

SAMPLE

DM

I = ( 143Nd/144 Nd)SA SampleDM Depleted mantle

T 0

Time

IT = I TDM SA

I0SA

I0DM

Partial melting

Figure 5-1: Theoretical concept of a single-stage Nd model age. Model age is the time in the past, when mantle evolution line (here is assumed depleted mantle) intersects with that for the given sample.

Exercise 4-1


� 9 �

Two-stage ages

The Nd model ages can be also calculated using the two-stage model of Liew and Hofmann (1988) which accounts for the fact that a great deal of rocks contain a significant proportion of a crustally-derived material. In the following formulae, the indexes DM, CC, SA refer to depleted mantle, average crustal reservoir and the sample, respectively. T = two-stage Nd model age, t = crystallization age of the sample, 0 refers to the present day (Fig. 5�2). As:

TDM

TCC II = [5.4]

( ) ( )11 0000 −−=−− TDMDM

TCCCC eRIeRI λλ [5.5]

+

−−

= 1ln100

00

DMCC

DMCC

RRII

Tλ

[5.6]

For the crustal and sample evolution lines: ( )100 −−= t

CCCCtCC eRII λ [5.7]

( )100 −−= tSASA

tSA eRII λ [5.8]

and because: tSA

tCC II = [5.9]

( )( )0000 1 CCSAt

SACC RReII −−−= λ [5.10]

From [5.6] and [5.10]) we finally get :

( )( )

( )

+

−−−−−

= 11ln100

0000

DMCC

DMCCSAt

SANdDM RR

IRReITλ

λ [5.11]

Where:

143Nd

144Nd0DM = 0.513151

147Sm

144Nd0DM = 0.219

147Sm

144Nd0CC = 0.12

Calculate single-stage TNd

CHUR and two-stage TNdDM model ages for the granitoid samples

from the Central Bohemian Pluton, in the second case assuming the intrusion age of 350 Ma.

[cbp.xls]

Hints:

! Necessary parameters of both models are given on Page 2, ! Single-stage CHUR Nd model ages are obtained using eq. [5.3], ! Two-stage DM Nd model ages are calculated by eq. [5.11].

SAMPLE

CC

DM

I = ( 143Nd/144 Nd)

DM Depleted mantleCC Average crustSA Sample

T t 0

Time

I t = I tSA CC

IT = I TDM CC

I 0SA

I 0CC

I 0DM

Partial melting

Figure 5-2: Theoretical concept of a two-stage Nd model age. An intermediate reservoir with Sm/Nd ratio of typical crustal rocks (CC) is assumed.

Exercise 5-1


� 10 �

6. BINARY MIXING

A. Major and trace elements

Mixing of two components, A, B. For fraction f of the component A:

f AA B

=+

[6.1]

Concentration of any element in the mixture is:

BBABAM cccffcfcc +−=−+= )()1( [6.2]

For two elements, X and Y (Faure, 1986):

Y XY YX X

Y X Y XX XM M

A B

A B

B A A B

A B

=−−

+−−

( )( )

[6.3]

which is an equation of a straight line on the X�Y plot.

A1 Major-element based mixing test

Equation [6.2] corresponds to a straight line in the diagram of cA�cB versus cM�cB with the slope being equivalent to the proportion of the component A (mixing test sensu Fourcade and Allègre, 1981 � see Fig. 6�1a).

A2 Trace-element based mixing test

Castro et al. (1990) used the theoretical proportions obtained from the major-element based mixing test for calculation of theoretical contents of trace-elements in the suspected hybrid. Then they compared the calculated and observed trace-element contents (see Fig. 6�1b).

Although eq.[6.2] should also work for the trace elements, it must be borne in the mind that the fractionation following the magma-mixing could have dramatically altered the original trace�element contents. Therefore incompatible

elements should be preferably used for this purpose.

In the Central Bohemian Pluton, associated with the Kozárovice granodiorite are K-rich pyroxene- and amphibole-bearing monzonitic rocks (e.g. Lučkovice melamonzonite�monzogabbro). In a quarry SE of Kozárovice small bodies of biotite�amphibole quartz monzonite occur, whose hybrid origin is strongly supported by both the field evidence and presence of disequlibriun textures on a mineral scale.

a

c-c

MB

c -cA B-10 100 20

-10

10

0

20

Si

Ti Al

Fe2+ Fe3+Mn

MgCa

NaK

HY

BRID

/ BA

SIC

0

1

2

3

Ba Rb Sr Zr Hf Ce Y Ni CoLa Cr

b

Figure 6-1: Mixing test for the Kozárovice quartz monzonite (Janou�ek et al. � in print; presumed end-members Kozárovice granodiorite and associated monzogabbro). The trace�element diagram (b) compares the actual composition of the hybrid (filled symbols) with calculated composition (empty symbols) using proportions from the mixing test for the major elements (see Exercise 6�1).

Exercise 6-1


� 11 �

Using major-element compositions given below, test whether the quartz monzonite could have originated by magma mixing between Kozárovice granodiorite and Lučkovice monzogabbro. Given that the granodiorite contains 1154 ppm and the

monzogabbro 2329 ppm Ba, calculate the expected Ba concentration in the quartz monzonite.

A: Kozárovice granodiorite

M: Quartz monzonite B: Lučkovice monzogabbro

SiO2 64.60 59.58 49.21 TiO2 0.57 0.72 1.02 Al2O3 14.99 14.8 13.69 FeO 2.79 4.08 6.96

Fe2O3 1.27 1.69 2.47 MnO 0.08 0.14 0.15 MgO 2.37 4.11 8.53 CaO 3.44 5.33 9.74 Na2O 3.12 2.84 1.89 K2O 4.34 4.19 3.61

[koza.xls]

Hints:

! Plot a diagram analogous to Figure 6�1a, ! Fit the data by linear regression (forcing the intercept to zero), ! The quality of the fit is shown by the correlation coefficient, ! Slope of the regression line gives the proportion of the acid end-member, ! For this value of f, calculate the Ba contents in the mixture using eq. 6.2.

B. Radiogenic isotopes (after Faure, 1986)

B1 Using a single isotopic ratio

The mixing equation for the isotopic ratios is:

−+

=

M

BB

M

AAM c

fcIc

fcII )1( [6.4]

Eqs [6.2] and [6.4] can be, after eliminating f, developed into:

( )

( ) BA

BBAA

BAM

ABBAM cc

IcIccccIIccI

−−

+−−

= [6.5]

and this is an equation of a hyperbola in the c�I (e.g. Sr�87Sr/86Sr) space.

In the isotope-based modelling of the binary mixing are frequently used plots such as 1/Sr�(87Sr/86Sr)i (i.e. age-corrected Sr isotopic ratios), where the mixing hyperbola changes into a straight line. For suite of co-genetic rocks, a non-zero slope of this line implies that some sort of open process has played a role, such as magma mixing or wall-rock contamination. On the other hand, samples that


� 12 �

originated from the same magma by various degrees of fractional crystallization only preserve identical initial isotopic ratios (forming horizontal lines).

Eqs [6.2] and [6.4] can be, after eliminating cM, combined into a formula for f. The parameter f can be calculated if the isotopic compositions and element concentrations for both end-members as well as the isotopic composition of the presumed hybrid are known:

( )

BBAABAM

MBB

cIcIccIIIcf

+−−−

=)(

[6.6]

Plot the theoretical mixing hyperbola between granite and basalt, whose compositions are given below. Calculate the 87Sr/86Sr ratio of a mixture, containing 50 % of the granite. Calculate proportion of the granite in a mixture that has 87Sr/86Sr = 0.71200.

A: granite B: basalt

Sr 160 ppm 318 ppm 87Sr/86Sr 0.73691 0.70362

Hints:

! Calculate the Sr concentrations (eq. [6.2]) and isotopic composition (eq. [6.4]) of the hybrid for various proportions of the granite (f = 0�1)

! Plot the results in the Sr�87Sr/86Sr diagram ! Check the results in the 1/ Sr�87Sr/86Sr plot � they should form a straight line ! Proportion f of the granite end-member is obtained using eq. [6.6].

B2 Using a pair of different isotopic ratios (Sr�Nd)

Taking into account that [6.2]

)1( fcfcc BAM −+=

the equation [6.4] can be rewritten as:

)1(

)1(fcfc

fcIfcIIBA

BBAAM −+

−+= [6.7]

Both Sr and Nd isotopic compositions can be calculated for pre-set values of the parameter f and the corresponding mixing hyperbola plotted in the 87Sr/86Sr � 143Nd/144Nd space.

General equation of this mixing hyperbola is derived from two equations [6.7], one for Sr and one for Nd, by solving both equations for f and equating the results:

Exercise 6�2


� 13 �

A SrSr

B SrSr

NdNd

C NdNd

D

where

A NdNd

Nd Sr NdNd

Nd Sr

B Nd Sr Nd Sr

C SrSr

Nd Sr SrSr

Nd Sr

D NdNd

SrSr

Nd Sr NdNd

Sr

M M M M

BB A

AA B

A B B A

AB A

BA B

A BA B

B

87

86

87

86

143

144

143

144

143

144

143

144

87

86

87

86

143

144

87

86

143

144

87

0

+

+

+ =

=

−

= −

=

−

=

−

:

86SrNd Sr

AB A

[6.8]

Straight line is obtained for a special case when B = 0, i.e.

( / )( / )Sr NdSr Nd

A

B

= 1 [6.9]

Plot the theoretical mixing hyperbola between granite and basalt in the 87Sr/86Sr�143Nd/144Nd isotopic correlation diagram. Calculate 87Sr/86Sr and 143Nd/144Nd ratios of a mixture containing 60 % of the granite. Compositions of the end members are:

A: granite B: basalt

Sr 160 ppm 318 ppm 87Sr/86Sr 0.73691 0.70362

Nd 31 ppm 18 ppm 143Nd/144Nd 0.51212 0.51300

Hints:

! Likewise in the previous example, calculate Sr and Nd isotopic compositions of the presumed hybrid for various proportions of the granite (eq.[6.4]),

! The isotopic compositions of the hybrid for various values of f are obtained using eq. [6.7], ! Plot the results in the 87Sr/86Sr�143Nd/144Nd diagram, ! Check the results in the 1/ Nd�143Nd/144Nd plot � they should form a straight line.

Exercise 6-3

[mix.xls]


� 14 �

CITED REFERENCES AND FURTHER READING

Textbooks an monographs in bold, asterisks indicate the (inevitably subjective) importance of the given reference

** Albarède, F. (1995): Introduction to the Geochemical Modeling. � Cambridge University Press, pp. 1�543.

** Arndt, N.T.; Goldstein, S.L. (1987): Use and abuse of crust-formation ages. Geology 15, 893�895.

* Bowen, R. (1988): Isotopes in Earth Sciences.� Elsevier, London, pp. 1�647.

** DePaolo, D.J. (1988): Neodymium isotope geochemistry.� Springer, Berlin, pp. 1�187.

** Dickin, A.P. (1995): Radiogenic Isotope Geology.� Cambridge University Press, Cambridge, pp. 1�452.

** Faure, G. (1986): Principles of Isotope Geology.� J. Wiley & Sons, Chichester, pp. 1�589.

* Fourcade S, Allègre CJ (1981) Trace elements behavior in granite genesis: a case study. The calc-alkaline plutonic association from the Querigut Complex (Pyrénées, France). Contrib. Mineral. Petrol. 76: 177�195.

** Geyh, M.A.; Schleicher, H. (1990): Absolute age determination.� Springer Verlag, Berlin, pp. 1�503.

* Hradetzky, H.; Lippolt, H.J. (1993): Generation and distortion of Rb�Sr whole-rock isochrons � effects of metamorphism and alteration.� Eur. J. Mineral., 5, 1175�1193.

* Jacobsen, S.B., Wasserburg, G.J. (1980) Sm�Nd evolution of chondrites. Earth Planet. Sci. Lett. 50, 139�155.

Janou�ek V, Rogers G, Bowes DR (1995) Sr�Nd isotopic constraints on the petrogenesis of the Central Bohemian Pluton, Czech Republic. Geol. Rdsch. 84: 520�534.

** Kullerud, L. (1991): On the calculation of isochrons.� Chem. Geol. (Isotope Geoscience Section), 87, 115�124.

* Liew, T.C.; Hofmann, A.W. (1988): Precambrian crustal components, plutonic associations, plate environment of the Hercynian Fold Belt of central Europe: indications from a Nd and Sr isotopic study. Contrib. Mineral. Petrol. 98, 129-138.

** Ludwig, K.R. (1993): Isoplot, a plotting and regression program for radiogenic-isotope data, version 2.60.� US Geological Survey Open-File Report 91�445, pp. 1�40.

** Lugmair, G.W.; Marti, K. (1978): Lunar initial 143Nd/144Nd: differential evolution line of the lunar crust and mantle.� Earth Planet. Sci. Lett. 39, 349�357.

* Michard, A., Gurriet, P., Soudant, M.; Albaréde, F. (1985): Nd isotopes in French Phanerozoic shales: external vs. internal aspects of crustal evolution.� Geochim. Cosmochim. Acta 49, 601�610.

** Provost, A. (1990): An improved diagram for isochron data.� Chem. Geol. (Isotope Geoscience Section), 80, 85�99.

** Rollinson, H.R. (1993): Using geochemical data: Evaluation, presentation, interpretation. Longman, London, pp 1�352.

** Steiger, R.H., Jäger, E. (1977): Subcommission on geochronology: convention on the use of decay constants in geo- and cosmochronology. Earth and Planetary Science Letters, 36, 359�362.

* Wasserburg, G.J., Jacobsen, S.B., DePaolo, D.J.; McCulloch, M.T.; Wen,T. (1981): Precise determination of Sm/Nd ratios, Sm and Nd isotopic abundances in standard solutions Geochim. Cosmochim. Acta 45, 2311�2324.

** Wilson, M. (1989): Igneous Petrogenesis. Unwin Hyman, London, pp 1-466

Xafi da Silva, J.J., Alberto dos Santos, C., Provost, A. (1986): Granito Serra do Acari: geologia e implacação metalogenética (folha Rio Mapuera, NW do estado do Pará). Proc. 2nd Symp. on Geology of Amazônia, Belém, Vol. 2. Soc. Bras. Geol., São Paulo, pp. 93�109.


� 15 �

** York, D. (1969): Least-squares fitting of a straight line with correlated errors.� Earth Planet. Sci. Lett. 5, 320�324.

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