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Chemical Geology 223

SIMS analyses of oxygen isotopes: Matrix effects in

Fe–Mg–Ca garnets

Daniel Vielzeuf a,*, Michel Champenois b, John W. Valley c,

Fabrice Brunet d, J.L. Devidal e

a CRMCN–CNRS, Campus de Luminy, case 913, 13288 Marseilles Cedex 9, Franceb CRPG–CNRS, 15 rue Notre-Dame des Pauvres, 54501 Vandoeuvre-les-Nancy, France

c Department of Geology and Geophysics, University of Wisconsin, Madison, WI 53706, USAd Laboratoire de Geologie–Ecole Normale Superieure — 24 rue Lhomond, 75231 Paris, France

e Laboratoire Magmas et Volcans, Universite Blaise Pascal — CNRS, 5, rue Kessler, 63038 Clermont-Ferrand, France

Received 9 November 2004; received in revised form 2 July 2005; accepted 25 July 2005

Abstract

Large instrumental mass fractionation (IMF) may occur during measurements of oxygen isotope ratios by SIMS. Part of this

fractionation depends on crystal structure and mineral composition. In order to improve the accuracy of SIMS measurements,

we gathered 6 commonly used garnet standards and prepared 6 others to adequately cover the composition range Alm0–73, Prp0–

99, Grs0–20. Electron microprobe analyses were performed at UBP-Clermont to check the chemical homogeneity of these

standards. Oxygen isotope compositions were determined by laser fluorination and mass spectrometry at UW-Madison. Ten

SIMS sessions and 336 d18O measurements at CRPG-Nancy, on a Cameca IMS1270 instrument, demonstrate that the standards

are homogeneous with external reproducibility of 0.3x (1r). In terms of d18O, SIMS measurements indicate that, during a

single session, IMF can vary up to 6.3x from one garnet standard to another. In most of the sessions, IMF can be correlated

with the grossular content. However, for a satisfactory correction scheme, we suggest the combination of the 3 main

components (Ca, Fe, Mg). This is done using a simple least square calculation routine. The correction coefficients determined

for each session can be used to calculate the IMF and correct the measured isotopic ratio of a garnet of known chemical

composition. This way, we were able to reproduce the d18O values of most of the Fe–Mg–Ca garnet standards within F0.6x.

Interestingly, the use of only 3 end-member standards (AlmCMG, PrpMM, GrsSE) plus a standard of intermediate composition

(e.g. UWG-2) is sufficient to reproduce d18O within the same precision. Thus, linear interpolation among end-member

standards is satisfactory in the case of the garnet solid-solutions. Two studies carried out on zoned garnets from the Alps

and the Pyrenees indicate that matrix effects become significant when variations in grossular contents are important (N10%). In

order to obtain reliable isotope ratio measurements on Fe–Mg–Ca garnets using a SIMS, we suggest a correction scheme using

at least 3 reliable end-member standards plus a standard of intermediate composition (a garnet standard closest to the average

0009-2541/$ - s

doi:10.1016/j.ch

* Correspondin

E-mail addre

(2005) 208–226

ee front matter D 2005 Elsevier B.V. All rights reserved.

emgeo.2005.07.008

g author.

ss: vielzeuf@crmcn.univ-mrs.fr (D. Vielzeuf).

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 209

composition of the analysed garnet). This allows cross-checking and incorporates a correction based on the variations in

composition of zoned crystals.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Ion microprobe; Oxygen isotopes; Matrix effects; Garnet standards

1. Introduction

A major advance in understanding the dynamics of

geological systems comes from the development of in

situ analytical techniques with micrometer (Am) spa-

tial resolutions. Secondary Ion Mass Spectrometry

(SIMS) allows the analysis of oxygen isotopic ratios

in minerals at a fine scale. However, large instrumen-

tal mass fractionation (IMF) occurs during such mea-

surements. Part of this fractionation may depend on

mineral type and composition, this is commonly

referred as a bmatrix effectQ (e.g. Eiler et al., 1997).In order to improve the precision and accuracy of

SIMS measurements, a better knowledge of the matrix

effect is required for each mineral group, this is

particularly important for those with multiple solid-

solutions. Indeed, such mineral series are particularly

interesting for petrological studies since they are able

to record changes of geological conditions through

major, trace and isotopic zoning which are often

combined, for instance in single zoned garnet crystals.

In such situations, it is important to determine whether

Fig. 1. Garnet standards in the Alm+Spe, Prp, Grs+And triangle.

oxygen isotopic heterogeneities are real or just instru-

mental artefacts associated with variations in major

element concentrations. As noted by Riciputi and

Paterson (1994) and Eiler et al. (1997), SIMS analysis

of zoned crystals is a difficult task because the varia-

tion of solid solution end-members and its potential

effect on oxygen ratio determinations cannot be cor-

rected using a single standard. On the other hand, the

linear interpolation among end-member standards

may introduce large errors in some cases (Eiler et

al., 1997). Thus, specific measurements to character-

ize the matrix effect in each mineral series must be

carried out.

The garnet group is a complex solid solution series

(see Table 2), particularly important for hydrothermal,

metamorphic and magmatic studies. In this paper, we

present 336 SIMS determinations of 18O/ 16O ratios in

twelve Fe–Mg–Ca (–Mn) garnets (Fig. 1), with

known and independently determined 18O/ 16O ratios.

The aim is to characterize specific matrix effects and

propose a simple and reliable correction scheme

applicable to this mineral group for oxygen isotope

analysis by SIMS. We did not focus our attention on

the manganese component in garnet, particularly

important for studying hydrothermal systems, since

the grossular–spessartine join has been considered

elsewhere (Jamtveit and Hervig, 1994; Riciputi et

al., 1998).

2. Garnet standards: major and trace element

contents, and oxygen isotope ratios

2.1. Origin

Five garnet standards, with previously determined18O/ 16O ratio, were gathered (Table 1). The following

garnets AlmSE, AlmCMG, GrsSE and SpeSE were

used by Eiler et al. (1997) in their study of matrix

effects in complex minerals. These are various gem

garnets, selected for their clarity and absence of

Table 1

Garnet standards analyzed for 18O/ 16O by SIMS

Name Main components Composition d18O per mila

2B3 Almandine–Grossular Alm66Grs20And7Spe4Prp3 6.9

AlmCMG Almandine–Pyrope Alm68Prp26Spe2And2Grs1 7.5

AlmSE Almandine–Pyrope Alm73Prp26And1 8.3

Bal509 Almandine–Pyrope Alm50Prp46And3Spe1 12.3

h114 Almandine–Pyrope Alm58Prp34And5Grs2Spe1 9.3

GrsSE Grossular Grs93And3Spe1Alm1TiAl1 3.8

PrpAA Pyrope Prp71Alm15Uv6And4Grs2Spe1 5.5

PrpAk Pyrope Prp67Alm20Uv4Grs4And4Spe1 5.5

PrpDM Pyrope Prp99And1 5.6

PrpMM Pyrope Prp65Alm23And5Grs4TiAl2Spe1 5.3

SpeSE Spessartine Spe94Alm6 5.4

UWG-2 Pyrope–Almandine Prp43Alm42Grs11And4Spe1 5.8

a Determined by conventional laser fluorination technique.

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226210

defects, bought at gemmological trade shows, for use

as diffusion samples (Elphick et al., 1985). The exact

origin is unknown except for the SpeSE sample com-

ing from Pala area in California. The fifth one UWG-2

is at present the best characterized garnet standard for

oxygen isotope analysis, prepared from a single large

porphyroblast in granulite facies mafic amphibolite

from the Gore Mountain mine, Adirondack Moun-

tains, NY, USA (Valley et al., 1995).

In addition to these, seven other garnet separates

were prepared and analysed for 18O/ 16O ratios (Table

1). PrpMM is derived from a gem quality single

garnet megacryst from the Monastery Kimberlite

pipe, South Africa (Moore, 1986). Another garnet

from Monastery Mine has already been used as an

oxygen standard by Harris et al. (2000). PrpDM

comes from a large porphyroblast of pyrope in a

quartzite from high-grade blueschists of the Western

Alps, Dora Maira massif, Italy (Chopin, 1984). PrpAA

was extracted from a garnet peridotite from Alpe

Arami in the Central Alps, Switzerland (Nimis and

Trommsdorff, 2001). PrpAk is a pyrope-rich garnet

from a garnet peridotite (Almklovdalen) in the Wes-

tern Gneiss Region of Norway (Medaris, 1984).

Bal509 comes from a metapelitic granulite found as

a xenolith in a late Tertiary alkaline volcano from the

Velay area, Massif Central, France (Leyreloup et al.,

1977). b114 was extracted from a paragneiss of the

High Himalaya Crystalline Formation 1 of the Lam-

jung (Central Nepal). The paragenesis includes two

micas, garnet and kyanite (France-Lanord et al.,

1988). Finally, 2B3 was prepared from a Qtz–Kfs–

Cpx–Grt igneous rock within a diorite–norite complex

in the Pyrenees (Vielzeuf, 1984).

2.2. Chemical and physical properties

Garnet grains of the different standards were

mounted in epoxy. Depending on the original quality

of the garnet crystals and the abundance of mineral

inclusions, the grain size after light crushing or grind-

ing varies from 0.2 mm (UWG-2) up to 5 mm in the

case of gem quality garnets (e.g. PrpAA or PrpMM).

872 electron microprobe (EMP) analyses were per-

formed using a Cameca SX100 electron microprobe at

Universite Blaise Pascal, Clermont-Ferrand, in order

to precisely determine the chemical composition of

these garnets and check for their homogeneity. Oper-

ating conditions were 15 kV accelerating voltage, and

10 nA sample current. The counting times were 10 s

on peak and 5 s on the background. Three spectro-

meters were used simultaneously and the following

standards were used for calibration: natural albite (Si),

Al2O3 (Al), synthetic Fe2O3 (Fe), olivine (Mg), wol-

lastonite (Ca), MnTiO3 (Mn, Ti), Cr2O3 (Cr), and a

glass with 1000 ppm P2O5 (P). The ZAF correction

procedures were applied. For the calculation of struc-

tural formulae, the program VFNorm written by P.

Ulmer at ETH Zurich was used. Seven end-members

were taken into consideration (see Table 2). The low

standard deviations (1r) calculated for each element

confirm the absence of important chemical heteroge-

neities in these garnets. Molar weights were calculated

using the end-member proportions of each standard

Table 2

Chemical compositions, structural formulae and end-member proportions of the 12 garnet standards used in this study

Garnet end members

Mol. wt. (g/mol) Mol. vol. (cc/mol) Ionic por. (Z)a (%)

General formula of the major components: (X2+)3 ( Y3+)2 (SiO4)3

X2+ Y3+

Almandine Fe Al 497.76 115.3 25.1

Pyrope Mg Al 403.17 112.6 24.3

Spessartine Mn Al 495.03 118.1 26.2

Grossular Ca Al 450.45 125.3 27.3

Andradite Ca Fe 508.21 131.7 30.5

Uvarovite Ca Cr 500.53 130.7 –

Minor component:

Ti–Al garnet Ca3 Ti2 Al2Si O12 490.07 – –

Sample AlmCMG AlmSE PrpDM PrpAk PrpAA PrpMM GrsSE SpeSE 2B3 Bal509 h114 UWG-2

d18O (x) 7.5 8.3 5.6 5.5 5.5 5.3 3.8 5.4 6.9 12.3 9.3 5.8

Chemical compositions of the 12 garnet standards (wt.%)

SiO2 37.72 37.47 44.56 41.35 41.71 41.36 39.16 35.52 36.33 39.43 38.17 39.36

TiO2 0.02 0.00 0.02 0.10 0.12 0.92 0.54 0.09 0.04 0.02 0.01 0.06

Al2O3 21.57 21.42 25.30 22.39 22.23 21.66 22.21 20.40 19.86 22.55 21.73 22.38

P2O5 0.05 0.09 0.12 0.01 0.01 0.04 0.02 0.11 0.01 0.06 0.01 0.03

Cr2O3 0.02 0.00 0.01 1.54 2.07 0.03 0.02 0.00 0.00 0.06 0.03 0.01

Fe2O3 0.74 0.98 1.32 1.47 1.62 1.75 1.12 0.22 2.33 1.10 1.58 1.38

FeO 30.94 32.85 0.00 9.89 7.62 11.39 0.40 2.68 28.72 23.53 26.57 19.65

MnO 1.06 0.17 0.02 0.37 0.40 0.34 0.69 39.50 1.80 0.25 0.63 0.41

MgO 6.63 6.47 29.80 18.57 19.96 18.44 0.01 0.00 0.68 12.27 8.74 11.24

CaO 1.09 0.35 0.32 4.85 4.99 4.50 36.09 0.07 9.16 1.28 2.27 5.53

Total 99.84 99.80 101.47 100.54 100.73 100.43 100.26 98.59 98.93 100.55 99.74 100.05

Standard deviation (1r) in wt.%

Nb An. 68 95 53 117 56 205 33 22 51 58 36 78

SiO2 0.36 0.48 0.52 0.44 0.43 0.50 0.28 0.33 0.57 0.39 0.30 0.35

TiO2 0.02 0.02 0.03 0.04 0.04 0.05 0.06 0.04 0.03 0.03 0.02 0.03

Al2O3 0.14 0.21 0.21 0.24 0.15 0.19 0.15 0.14 0.26 0.18 0.17 0.17

Cr2O3 0.03 0.02 0.01 0.21 0.11 0.02 0.02 0.01 0.01 0.03 0.02 0.02

FeO2 0.29 0.32 0.31 0.28 0.28 0.29 0.08 0.10 0.41 0.23 0.36 0.47

MnO 0.06 0.04 0.03 0.04 0.04 0.04 0.03 0.20 0.12 0.04 0.14 0.04

MgO 0.09 0.20 0.30 0.16 0.18 0.13 0.01 0.01 0.05 0.12 0.37 0.15

CaO 0.05 0.04 0.21 0.14 0.14 0.08 0.22 0.02 0.31 0.07 0.19 0.25

Number of atoms on the basis of 12 oxygens

Si 2.9706 2.9634 2.9639 2.9643 2.9615 2.9790 2.9499 2.9705 2.9687 2.9622 2.9585 2.9618

Ti 0.0012 0.0001 0.0011 0.0053 0.0063 0.0499 0.0304 0.0056 0.0025 0.0014 0.0006 0.0031

Al 2.0015 1.9961 1.9836 1.8914 1.8599 1.8386 1.9714 2.0105 1.9128 1.9966 1.9851 1.9853

P 0.0031 0.0062 0.0066 0.0009 0.0007 0.0022 0.0012 0.0076 0.0005 0.0035 0.0009 0.0020

Cr 0.0015 0.0002 0.0004 0.0874 0.1161 0.0017 0.0011 0.0002 0.0001 0.0034 0.0019 0.0006

Fe3+ 0.0441 0.0580 0.0659 0.0793 0.0863 0.0951 0.0633 0.0141 0.1431 0.0623 0.0920 0.0782

Fe2+ 2.0375 2.1727 0.0000 0.5927 0.4525 0.6859 0.0255 0.1872 1.9629 1.4782 1.7222 1.2364

Mn 0.0709 0.0112 0.0010 0.0222 0.0243 0.0208 0.0438 2.7975 0.1243 0.0160 0.0410 0.0260

Mg 0.7778 0.7621 2.9547 1.9842 2.1127 1.9793 0.0007 0.0004 0.0831 1.3737 1.0092 1.2606

Ca 0.0918 0.0299 0.0228 0.3724 0.3798 0.3473 2.9128 0.0063 0.8020 0.1027 0.1884 0.4460

(continued on next page)

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 211

Table 2 (continued)

Sample AlmCMG AlmSE PrpDM PrpAk PrpAA PrpMM GrsSE SpeSE 2B3 Bal509 h114 UWG-2

d18O (x) 7.5 8.3 5.6 5.5 5.5 5.3 3.8 5.4 6.9 12.3 9.3 5.8

End members proportions

Grossular 0.007 0.000 0.000 0.038 0.022 0.042 0.929 0.000 0.196 0.001 0.016 0.109

Almandine 0.684 0.730 0.000 0.199 0.152 0.226 0.009 0.063 0.660 0.498 0.582 0.416

Pyrope 0.261 0.256 0.992 0.668 0.712 0.653 0.000 0.000 0.028 0.462 0.341 0.425

Spessartine 0.024 0.004 0.000 0.007 0.008 0.007 0.015 0.935 0.042 0.005 0.014 0.009

Andradite 0.022 0.010 0.008 0.040 0.044 0.047 0.032 0.002 0.072 0.031 0.047 0.040

Uvarovite 0.001 0.000 0.000 0.044 0.059 0.001 0.001 0.000 0.000 0.002 0.001 0.000

Ti–Al garnet 0.001 0.000 0.000 0.003 0.003 0.025 0.015 0.000 0.001 0.001 0.000 0.002

Mol. wt.

(g/mol)

472.4 473.6 404.0 431.3 428.5 422.5 447.1 495.2 485.5 453.8 465.7 452.3

a (A) 11.523 11.5208 11.456 11.5332 11.5297 11.5295 11.8749 11.6332 11.6258 11.5073 11.5267 11.5465

Mol. vol.

(cc/mol)

115.3 115.2 113.3 115.6 115.5 115.5 126.2 118.6 118.4 114.8 115.4 115.10

AMU (g/at.) 23.62 23.68 20.20 21.57 21.42 21.13 22.36 24.76 24.27 22.69 23.29 22.61

Z (%) 25.06 24.95 24.35 25.09 25.11 24.93 27.37 26.14 25.95 24.92 25.14 25.23

a Z values from Dahl, 1997.

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226212

and the molar weights of the theoretical end-members

reported in Table 2. These garnets adequately cover

the range Alm0–73, Prp0–99, Grs0–20. Out of this range,

results obtained on an almost pure grossular are also

reported. In addition, a sample of spessartine was

analysed and data will be provided but, as already

mentioned, emphasis will not be put on this compo-

nent. For a better visualization, the compositions of all

the garnet standards are plotted in a triangular diagram

Alm+Spe�Prp�Grs+And+Uv (Fig. 1).

X-ray diffraction data (powder and single crystal)

were collected at UBP-Clermont on a Sigma 2080

diffractometer using Cu–Ka radiation with an accel-

erating voltage of 40 kV and a filament current of 35

mA. Crystal fragments were analysed with a Gandolfi

X-ray camera. After exposure of 20 h, the XRD films

were scanned and diffraction lines extracted. Lattice

parameters were obtained with the non linear least

square cell refinement program Unitcell (Holland

and Redfern, 1997) based on 12 to 15 reflections.

For powder diffraction patterns, a silicon single-crys-

tal low background sample holder and Cu–Ka1 radia-

tion (focusing quartz-monochromator on incident

beam) were used. Step scanned data were acquired

in the range 16–808 2H with a step width of 0.028 anda counting time of 6 s per step. The cell parameters

were calculated using the Fullprof Rietveld refinement

software operating in profile-matching mode (Rodri-

guez-Carvajal, 1998).

2.3. Mass spectrometry oxygen ratio determinations

Oxygen isotope analyses by ion microprobe were

standardized against values determined by conven-

tional laser fluorination techniques at the University

of Wisconsin-Madison (Valley et al., 1995). From 1 to

2 mg of garnet were pre-treated with BrF5 overnight at

room temperature. Samples were then heated with

fresh BrF5 reagent using a CO2 laser (k =10.6 Am).

The evolved oxygen was purified cryogenically and

with hot Hg, before combustion to CO2, measurement

for analytical yield, and isotope analysis in a Finni-

gan/MAT 251 mass-spectrometer. On each day of

analysis, at least three aliquots of the UWG-2 garnet

standard were analyzed with the average precision of

F0.07x. Values were corrected to the accepted d18O

of UWG-2 (5.8x) as recommended by Valley et al.

(1995).

3. SIMS analytical techniques

Ion microprobe analyses were performed at

CRPG–CNRS (Nancy) using the French national

facility Cameca IMS 1270 instrument. Instrumental

conditions are described in detail by Rollion-Bard

(2001) and Rollion-Bard et al. (2003). Oxygen iso-

topes were analysed as O� ions produced by the

bombardment of the target by a 133Cs+ primary

Table 3

SIMS measurements of oxygen isotope ratios in 12 garnet standards, listed in order of analysis

d18OVSMOW

(x)

18O/ 16O(actual) Measured

d18O (x)

18O/16O(measured) aSIMS IMF

(x)

n r int.

(x)

r ext.

(x)

Counts on18O (millions/s)

SESSION 1

h114 9.3 0.0020238 11.6 0.0020285 1.00228 2.3 11 0.1 0.6 8.5

PrpMM 5.3 0.0020158 7.4 0.0020200 1.00206 2.1 5 0.1 0.2 9.25

UWG-2 5.8 0.0020168 8.3 0.0020217 1.00244 2.4 4 0.1 0.2 7.56

PrpDM 5.6 0.0020164 6.4 0.0020181 1.00083 0.8 4 0.2 0.2 6.95

Bal 509 12.3 0.0020299 14.4 0.0020341 1.00209 2.1 3 0.1 0.2 8.18

SESSION 2

PrpMM 5.3 0.0020158 6.4 0.0020181 1.00111 1.1 3 0.1 0.2 9.78

h114 9.3 0.0020238 11.7 0.0020287 1.00238 2.4 3 0.1 0.6 10

UWG-2 5.8 0.0020168 7.4 0.0020201 1.00162 1.6 3 0.1 0.2 8.79

SESSION 3

PrpAk 5.5 0.0020162 3.3 0.0020119 0.99786 �2.1 6 0.2 0.3 5.45

PrpAA 5.5 0.0020162 4.0 0.0020132 0.99849 �1.5 7 0.3 0.6 5.17

PrpDM 5.6 0.0020164 2.0 0.0020092 0.99641 �3.6 4 0.2 0.4 4.59

Alm SE 8.3 0.0020218 3.6 0.0020125 0.99537 �4.6 5 0.2 0.5 5.34

Spe SE 5.4 0.0020160 2.9 0.0020110 0.99752 �2.5 3 0.4 0.2 5.36

Bal 509 12.3 0.0020299 9.3 0.0020238 0.99701 �3.0 6 0.2 0.4 5.15

2B3 6.9 0.0020190 6.3 0.0020178 0.99938 �0.6 4 0.3 0.2 5.32

Grs SE 3.8 0.0020128 4.4 0.0020141 1.00063 0.6 5 0.3 0.7 4.25

Alm CMG 7.5 0.0020202 4.8 0.0020148 0.99731 �2.7 4 0.3 0.3 5.53

h114 9.3 0.0020238 6.7 0.0020187 0.99746 �2.5 4 0.3 0.2 5.59

UWG-2 5.8 0.0020168 3.8 0.0020127 0.99796 �2.0 5 0.3 0.3 5.16

PrpMM 5.3 0.0020158 2.0 0.0020092 0.99673 �3.3 5 0.2 0.2 5.44

PrpDM 5.6 0.0020164 2.6 0.0020104 0.99702 �3.0 2 0.4 0.4 5.18

SESSION 4

PrpAk 5.5 0.0020162 4.6 0.0020144 0.99909 �0.9 3 0.3 0.3 5.29

h114 9.3 0.0020238 7.6 0.0020204 0.99829 �1.7 4 0.3 0.5 6

UWG-2 5.8 0.0020168 3.7 0.0020125 0.99786 �2.1 4 0.3 0.5 5.5

PrpAk 5.5 0.0020162 4.5 0.0020142 0.99899 �1.0 1 0.2 – 5.81

h114 9.3 0.0020238 8.3 0.0020218 0.99899 �1.0 1 0.2 – 6.57

UWG-2 5.8 0.0020168 3.9 0.0020129 0.99807 �1.9 1 0.3 – 6.04

Alm CMG 7.5 0.0020202 5.7 0.0020165 0.99817 �1.8 3 0.2 0.5 6.56

2B3 6.9 0.0020190 5.9 0.0020171 0.99905 �1.0 4 0.2 0.6 6.3

PrpAk 5.5 0.0020162 3.1 0.0020113 0.99757 �2.4 2 0.3 0.6 6.03

PrpAA 5.5 0.0020162 2.7 0.0020106 0.99720 �2.8 2 0.2 0.4 5.7

h114 9.3 0.0020238 7.6 0.0020205 0.99835 �1.7 2 0.2 0.4 6.76

UWG-2 5.8 0.0020168 4.0 0.0020133 0.99825 �1.7 2 0.3 1.4 6.2

Alm CMG 7.5 0.0020202 6.1 0.0020173 0.99856 �1.4 2 0.2 0.2 6.87

Grs SE 3.8 0.0020128 4.9 0.0020149 1.00105 1.0 2 0.3 0.8 5.44

2B3 6.9 0.0020190 5.2 0.0020155 0.99826 �1.7 2 0.3 0.4 6.43

Bal 509 12.3 0.0020299 8.8 0.0020229 0.99655 �3.4 2 0.2 0.3 6.25

Spe SE 5.4 0.0020160 1.7 0.0020087 0.99635 �3.7 2 0.2 0.2 6.15

Alm SE 8.3 0.0020218 3.8 0.0020127 0.99550 �4.5 2 0.2 0.5 5.89

PrpDM 5.6 0.0020164 0.5 0.0020062 0.99491 �5.1 3 0.3 0.8 5.15

SESSION 5

h114 9.3 0.0020238 6.8 0.0020188 0.99752 �2.5 3 0.1 0.2 –

PrpAk 5.5 0.0020162 3.8 0.0020128 0.99829 �1.7 3 0.1 0.3 –

(continued on next page)

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 213

Table 3 (continued)

d18OVSMOW

(x)

18O/ 16O(actual) Measured

d18O (x)

18O/ 16O(measured) aSIMS IMF

(x)

n r int.

(x)

r ext.

(x)

Counts on18O (millions/s)

SESSION 5

PrpAA 5.5 0.0020162 3.0 0.0020112 0.99752 �2.5 3 0.1 0.2 –

PrpDM 5.6 0.0020164 2.3 0.0020098 0.99673 �3.3 3 0.1 0.1 –

Spe SE 5.4 0.0020160 3.1 0.0020114 0.99770 �2.3 3 0.1 0.2 –

Bal 509 12.3 0.0020299 10.0 0.0020252 0.99771 �2.3 3 0.1 0.1 –

2B3 6.9 0.0020190 6.3 0.0020177 0.99935 �0.6 3 0.1 0.1 –

Alm CMG 7.5 0.0020202 5.3 0.0020158 0.99782 �2.2 3 0.1 0.1 –

UWG-2 5.8 0.0020168 4.1 0.0020133 0.99826 �1.7 3 0.1 0.1 –

h114 9.3 0.0020238 6.9 0.0020190 0.99760 �2.4 1 0.1 – –

SESSION 6

h114 9.3 0.0020238 7.4 0.0020201 0.99813 �1.9 4 0.1 0.3 –

PrpDM 5.6 0.0020164 3.9 0.0020129 0.99826 �1.7 4 0.1 0.1 –

Spe SE 5.4 0.0020160 3.9 0.0020131 0.99854 �1.5 3 0.2 0.1 –

Grs SE 3.8 0.0020128 7.8 0.0020209 1.00402 4.0 2 0.2 0.0 –

2B3 6.9 0.0020190 6.8 0.0020188 0.99987 �0.1 3 0.1 0.2 –

Alm CMG 7.5 0.0020202 5.8 0.0020168 0.99831 �1.7 3 0.1 0.1 –

UWG-2 5.8 0.0020168 4.8 0.0020147 0.99897 �1.0 3 0.1 0.3 –

PrpAA 5.5 0.0020162 4.6 0.0020143 0.99906 �0.9 3 0.1 0.3 –

Bal 509 12.3 0.0020299 10.9 0.0020271 0.99863 �1.4 3 0.1 0.2 –

PrpDM 5.6 0.0020164 3.6 0.0020124 0.99798 �2.0 2 0.2 0.0 –

PrpDM 5.6 0.0020164 3.3 0.0020119 0.99774 �2.3 3 0.2 0.2 –

SESSION 7

PrpDM 5.6 0.0020164 4.2 0.0020137 0.99863 �1.4 3 0.1 0.2 –

h114 9.3 0.0020238 8.3 0.0020218 0.99898 �1.0 3 0.1 0.1 –

UWG-2 5.8 0.0020168 5.4 0.0020160 0.99961 �0.4 3 0.1 0.1 –

2B3 6.9 0.0020190 6.9 0.0020190 0.99996 0.0 2 0.1 0.0 –

PrpAk 5.5 0.0020162 4.5 0.0020141 0.99896 �1.0 3 0.1 0.0 –

PrpDM 5.6 0.0020164 3.5 0.0020123 0.99793 �2.1 3 0.2 0.2 –

PrpAk 5.5 0.0020162 4.3 0.0020138 0.99879 �1.2 3 0.1 0.1 –

h114 9.3 0.0020238 7.6 0.0020205 0.99835 �1.7 2 0.1 0.0 –

PrpDM 5.6 0.0020164 3.7 0.0020126 0.99810 �1.9 1 0.1 – –

SESSION 8

PrpMM 5.3 0.0020158 �1.2 0.0020027 0.99349 �6.5 4 0.3 0.4 3.47

h114 9.3 0.0020238 2.2 0.0020095 0.99293 �7.1 5 0.3 0.5 3.35

Bal 509 12.3 0.0020299 6.4 0.0020180 0.99415 �5.8 3 0.2 0.5 3.47

PrpDM 5.6 0.0020164 �0.4 0.0020043 0.99400 �6.0 3 0.2 0.3 3.24

UWG-2 5.8 0.0020168 1.0 0.0020072 0.99522 �4.8 3 0.3 0.4 –

SESSION 9

PrpAA 5.5 0.0020162 0.2 0.0020057 0.99476 �5.2 4 0.2 0.3 5.61

PrpDM 5.6 0.0020164 0.4 0.0020061 0.99487 �5.1 4 0.2 0.2 5.12

Alm SE 8.3 0.0020218 2.5 0.0020101 0.99421 �5.8 4 0.2 0.2 5.92

Spe SE 5.4 0.0020160 1.2 0.0020076 0.99583 �4.2 3 0.2 0.1 6.38

Bal 509 12.3 0.0020299 7.5 0.0020202 0.99525 �4.8 3 0.2 0.1 5.9

PrpMM 5.3 0.0020158 1.5 0.0020082 0.99623 �3.8 3 0.2 0.0 6.12

2B3 6.9 0.0020190 4.4 0.0020140 0.99749 �2.5 3 0.2 0.2 6.52

Grs SE 3.8 0.0020128 3.1 0.0020114 0.99931 �0.7 4 0.2 0.2 5.39

Alm CMG 7.5 0.0020202 3.6 0.0020124 0.99614 �3.9 3 0.2 0.1 6.5

h114 9.3 0.0020238 5.4 0.0020160 0.99611 �3.9 4 0.2 0.3 6.64

PrpAk 5.5 0.0020162 1.9 0.0020090 0.99641 �3.6 4 0.2 0.4 6.32

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226214

Table 3 (continued)

d18OVSMOW

(x)

18O/ 16O(actual) Measured

d18O (x)

18O/16O(measured) aSIMS IMF

(x)

n r int.

(x)

r ext.

(x)

Counts on18O (millions/s)

SESSION 9

UWG-2 5.8 0.0020168 2.3 0.0020098 0.99653 �3.5 3 0.2 0.1 6.51

PrpAA 5.5 0.0020162 1.8 0.0020089 0.99635 �3.6 2 0.2 0.0 –

UWG-2 5.8 0.0020168 2.0 0.0020092 0.99623 �3.8 2 0.2 0.3 –

h114 9.3 0.0020238 5.2 0.0020156 0.99595 �4.1 1 0.2 – –

PrpAA 5.5 0.0020162 1.9 0.0020091 0.99645 �3.6 1 0.2 – –

SESSION 10

h114 9.3 0.0020238 9.7 0.0020247 1.00040 0.4 4 0.1 0.3 7.35

UWG-2 5.8 0.0020168 6.4 0.0020179 1.00055 0.5 3 0.1 0.2 7.31

2B3 6.9 0.0020190 10.0 0.0020253 1.00312 3.1 3 0.1 0.1 7.96

Spe SE 5.4 0.0020160 6.7 0.0020186 1.00128 1.3 3 0.1 0.2 8.31

h114 9.3 0.0020238 10.0 0.0020252 1.00065 0.7 3 0.1 0.4 7.96

Alm CMG 7.5 0.0020202 8.0 0.0020212 1.00049 0.5 3 0.1 0.3 8.3

Alm SE 8.3 0.0020218 8.3 0.0020219 1.00004 0.0 3 0.1 0.3 8.15

Bal 509 12.3 0.0020299 12.8 0.0020309 1.00052 0.5 3 0.1 0.4 7.98

PrpDM 5.6 0.0020164 6.3 0.0020177 1.00065 0.6 3 0.1 0.1 7.05

h114 9.3 0.0020238 10.0 0.0020253 1.00070 0.7 3 0.1 0.2 8.5

Grs SE 3.8 0.0020128 7.3 0.0020199 1.00351 3.5 3 0.1 0.7 7.5

PrpAk 5.5 0.0020162 5.9 0.0020169 1.00035 0.3 3 0.1 0.3 8.29

PrpMM 5.3 0.0020158 4.9 0.0020151 0.99964 �0.4 3 0.1 0.4 8.35

PrpAA 5.5 0.0020162 6.7 0.0020186 1.00117 1.2 3 0.1 0.4 8.33

h114 9.3 0.0020238 9.8 0.0020249 1.00053 0.5 3 0.1 0.2 8.84

(mean values). See Table A in electronic supplementary material for detailed analytical results.

aSIMS=[18O/16O(measured)] / [18O/ 16O(actual)].

IMF = Instrumental Mass Fractionation.

n = number of independent spot analyses on a given standard.

r int. = average of the 1 standard error of n *30 cycles in a single standard (internal precision).

r ext. = 1 standard deviation of n independent spot analyses on a given standard (spot to spot reproducibility).

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 215

beam at 10 kV with a 5 nA sample current. The size of

the oval spots varied from 30 to 50 Am with a depth of

about 2 Am. The normal incidence electron flood gun

was used to compensate sample charging during ana-

lysis (Slodzian et al., 1987). Secondary negative ions

of O were accelerated at 10 kVand analysed at a mass

resolution of about 5000 using the circular focusing

mode of the IMS 1270 and a transfer optic of 150 Am.

There is no species interference on the 16O� and 18O�

peaks at this mass resolution. The position of the

energy window was �25F60 eV which corresponds

to the optimized acceptance of the ions by the spectro-

meter. Measurements of O isotopes were conducted in

multicollection mode (secondary ions counted simul-

taneously) using two off-axis Faraday cups (L’2 and

H1). The measurements were performed with ion

intensities in the range 3 to 8d 106 counts/s on the18O� peak (see Table 3). The typical acquisition time

was 2 s for oxygen analysis during each of the 30

cycles that comprise one 60 s analysis. The gains of

the L’2 and H1 Faraday cups were systematically

inter-calibrated at the beginning of each analytical

session using the built-in amplifier calibration routine,

derived by Cameca from the Finnegan hardware

developed for solid source mass spectrometry (de

Chambost, 1997).

Previous studies on matrix effects in complex

minerals (Hervig et al., 1992; Eiler et al., 1997; Rici-

puti et al., 1998) were conducted using a SIMS with

high-energy filtering technique and a single collector.

For this study, we used a multicollector large radius

instrument (Cameca IMS 1270). On such a machine,

both the internal precision (i.e. within the 30 cycles in

one spot) and external reproducibility (from spot to

spot in a given grain) are improved for various rea-

sons: (1) the transfer optics located in the secondary

column between the sample and the electrostatic sec-

tor have been optimized in the IMS1270 and provides

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226216

better ion transmission; (2) higher total counts on 18O

give better precision; (3) the multi-collection mode

allows simultaneous counting of the two isotopes,

while ions are counted one after the other in single

collection mode. In other words, in multi-collection

mode, an isotopic ratio is determined from the same

ablated material while, in mono-collection mode, the

isotopic ratio is determined from two slightly different

ablated materials; (4) multi-collection allows faster

measurements (about 3 min instead of 15) which

improves the quality of the measurement in the case

of instrumental drift. Previous work with a single

Fig. 2. Instrumental Mass Fractionation (IMF x) as a function

IMF=d18O(measured)�d18O(actual). Error bars correspond to the external

the height of the symbol is larger than the error bar.

collector demonstrated that the external precision on

homogeneous standards was limited by counting-sta-

tistics down to 0.3x for ca. 1 h analyses. Therefore,

one of the main improvements of the multi-Faraday

measurements is high count rates and better counting

statistics limits within an acceptable time period (a

few minutes); (5) the use of Faraday cup detectors

instead of an electron multiplier is required for high

signal intensities (greater than ca. 1 million counts/s).

A Faraday detector has the disadvantage of having a

higher background noise than an electron multiplier

and some care must be taken to optimize the signal /

of major components in garnet in two analytical sessions.

precision (or reproducibility) of the measurements. In most cases,

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 217

noise ratio. For instance, on the instrument we used,

we found that a signal z5d 106 counts/s on 18O is

adequate to obtain good analyses in garnet. On the

other hand, the use of Faraday detectors eliminates

problems related to aging of an electron multiplier

detector, which can be a major cause of instrument

drift in previous analyses.

4. Results

336 SIMS measurements were carried out during

10 different sessions from September 2001 to Novem-

ber 2002 (Table 3, and Table A in electronic supple-

mentary materials). Each spot measurement consists

of 30 acquisition cycles lasting 2 s each. As cycles

accumulate, the average d18O is calculated together

with a standard deviation; cycles outside the 2r inter-

val are discarded. On the remaining cycles, a new

average d18O is calculated (the final result) with its

standard deviation. This standard deviation divided by

the square root of the number of retained cycles gives

a standard error of the mean commonly referred to as

internal precision (rint). It reflects the stability of the

signal from a block to another within a given spot

measurement. For each standard, an average of 3

different spots (n) was analyzed in a row. rint listed

in Table 3 is the average rint of the n measurements.

On the other hand, rext is the standard deviation on

the n measurements (spot to spot external precision

referred to as reproducibility). Note that contrary to

internal precision, external precision is calculated as a

standard deviation and not a standard error of the

mean (Fitzsimons et al., 2000). Data are reported in

Table 3 as the average measured and actual 18O /16O

ratios, together with their d18O notation in per mil

variations relative to the Standard Mean Ocean Water

(SMOW), whose 18O/ 16O ratio equals 2.00520*10�3

(Baertschi, 1976). The average Instrumental Mass

Fractionation (IMF) is expressed as an alpha ratio:

aSIMS=(18O /16Omeasured) / (

18O/ 16Oactual). The IMF is

also reported in units per mil, calculated according to

the following relationship: [(18O/ 16Omeasured)� (18O /16Oactual) / (

18O/ 16Oactual)] *1000.

According to the data listed in Table 3, the stan-

dards are isotopically homogeneous with a spot to

spot reproducibility of d18OV0.3x (1r) for most

garnets, except for AlmSE and GrsSE (rext=0.37

and 0.49x, respectively). In terms of d18O, SIMS

measurements indicate that, during a single session,

IMF can differ up to 6.3x from one garnet standard to

the other. The difference remains small between al-

mandine, pyrope and spessartine end-members (b2x).

Conversely, the maximum difference is found between

AlmSE or PrpDM on one side and GrsSE on the other

side. In most of the sessions, IMF can be correlated

with the grossular (+andradite) content and, to a lesser

extent, with the pyrope component. The results

obtained on two representative sessions (#6 and 9)

are shown in Fig. 2. Summarizing, a significant matrix

effect is observed on oxygen isotope SIMS measure-

ments of Fe–Mg–Ca garnets and the grossular compo-

nent plays a major role in causing this effect.

5. Discussion

5.1. Correction scheme

The correlation between the calcium content of the

garnet and IMF may appear good enough to generate

a simple correction scheme. However, we prefer a

correction scheme combining the 4 main end-mem-

bers [Alm, Prp, Grs, Spe] for the following reasons:

(1) this is a general, easy to adapt, multivariate correc-

tion scheme taking into account all of the garnet

components; it considers compositional effects that

may have been overlooked by the user; (2) detailed

analysis of the results of standard measurements and

the design of a new specific correction scheme for

each session are not required; (3) contrary to the

appearance, the calculation of correction coefficients

in the proposed multivariate analysis is extremely

simple and requires a single line of Matlab script;

(4) the use of the same routine to calculate correction

coefficients facilitates the objective comparison of

results obtained during different sessions. This multi-

variate correction scheme is based on the following

relationship M[IMF]=M[conc] *M[w, x, y, z]. The left

hand side member of this equation (M[IMF]) is a 1

column, s line, matrix with the measured IMF for each

standard, M[conc] is a 4 column, s line matrix with the

Alm, Prp, Grs+And, Spe contents for each standard,

and M[w, x, y, z] is a 1 column, 4 line matrix of

unknown parameters related to Alm, Prp, Grs+And,

Spe, respectively (s is the number of standards mea-

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226218

sured in a given session (e.g. s =11 for session 6 and

s=16 for session 9). Knowing IMF and the concen-

trations, the matrix M[w, x, y, z] can be determined by

solving the set of s equations:

IMF1 ¼ wAlm1 þ xPrp1 þ y Grsþ Andð Þ1 þ zSpe1

IMF2 ¼ wAlm2 þ . . .

IMFs ¼ wAlms þ xPrps þ y Grsþ Andð Þs þ zSpes

using a simple least square method. A Matlab script of

the routine we used to determine the w, x, y, z

correction coefficients, together with a worked exam-

ple are given in the Appendix A.

Once determined, the w, x, y, z coefficients can be

used to determine the IMF and correct the measured

oxygen isotopic ratio of any Fe–Mg–Ca (–Mn) garnet

of known chemical composition.

It is important to note that the coefficients used to

relate instrumental mass fractionation to mineral

chemistry differ slightly from day to day in both

their absolute and relative values. This is due to

instrumental conditions that may vary from day to

day. Thus, an accurate determination of oxygen iso-

tope ratios in a sample requires a calibration of the

instrument using standards during the same session,

before and after the analysis of the sample to check

for instrumental drift. For this purpose, the sample

and the standards are ideally held on the same

sample holder (preferably, mounted and polished

together in the same preparation) to avoid changing

sample mounts, breaking vacuum, and possible

changes of instrumental conditions (Valley et al.,

1995).

In order to test this scheme, the correction coeffi-

cients were determined for each session, and then

used to recalculate the IMF required to correct the

measured value of d18O for each standard. An exam-

ple of this calculation is given in the Appendix A.

Results for sessions 6 and 9 are reported in Fig. 3 as

the difference between recalculated and actual d18O

values (D). The average standard deviation of the

mean D for all the sessions equal 0.6 x with varia-

tions from 1.12 to 0.25 for the worst and best sessions

(#4 and #7), respectively.

Interestingly, the use of only 5 standards (4 end-

members: AlmCMG, PrpDM, GrsSE, SpeSE and 1

standard of intermediate composition: UWG-2) is suf-

ficient to calculate the M[w, x, y, z] matrix without alter-

ing the results in a significant way. In addition, if we

exclude the manganese-rich standard (SpeSE) from the

calculation, there is no significant effect on the recal-

culation of the d18O of all the standards, but SpeSE, and

the D are identical to the ones shown in Fig. 3A and B.

This is simply due to the fact that all of our standards,

but one, are poor in spessartine component.

To summarize, for manganese-poor garnets (spes-

sartine contents b5%), 3 end-member standards such

as AlmCMG, PrpDM, GrsSE, plus a standard of

intermediate composition (e.g. UWG-2), are sufficient

to obtain reliable and accurate isotope ratio measure-

ments on Fe–Mg–Ca garnets using a IMS1270 instru-

ment. A major consequence of this result is that the

linear interpolation among end-member standards is

satisfactory in the case of the garnet solid-solutions.

Using this correction scheme, 75% of the d18Oestimates on the garnet standards were reproduced

within F0.6x of their actual value, 85% within

F1x, and 95% within F2x . These are indications

of the accuracy of the measurements we can expect

for SIMS measurements of oxygen isotopes in garnets

under the present operating conditions. It is important

to note that in most petrological studies, for instance

in the case of zoned minerals, precision of the mea-

surement is more important than its accuracy. In this

respect, the SIMS is an extremely powerful instrument

as variations as low as 0.3x in a crystal can be

considered as significant (Cavosie et al., 2005; Viel-

zeuf et al., 2005, and Fig. 5C).

5.2. IMF, mean atomic mass and molar volume

It is beyond the scope of this paper to discuss the

physical processes responsible for isotopic matrix

effects. However exploring the possible correlations

between physical properties of the minerals and IMF

might prove helpful in the debate. In their contribu-

tion to the determination of the matrix effects in

complex minerals on SIMS analyses of oxygen iso-

topes, Eiler et al. (1997) following Hervig et al.

(1992) noted a significant correlation between IMF

and mean atomic mass (AMU) of the minerals, even

if they consider that this correlation remains unsui-

table for a correction scheme (see also Riciputi et al.,

1998). In Fig. 4A and B, the instrumental mass

fractionations for measurements of sessions 6 and 9

have been plotted against the mean atomic mass. A

Fig. 3. Differences between recalculated and actual d18O values in the garnet standards measured in two analytical sessions:

D=d18O(recalculated)�d18O(actual). Error bars correspond to the external precision (or reproducibility) of the measurements. In most cases, the

height of the symbol is larger than the error bar. The 2r standard deviation of the mean is shown as dashed lines.

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 219

poor positive correlation can be found for the Fe–

Mg–Mn garnet solid-solution and, most importantly,

the representative point of the grossular garnet lies

far off the trend. Thus, we conclude that, contrary to

previous studies, but on a different type of SIMS,

there is no significant correlation between IMF and

AMU in the Ca–Fe–Mg garnet solid-solution. The

correlation between IMF and molar volume is more

convincing and incorporates the grossular end-mem-

ber as well (Fig. 4C and D). It has been suggested

that closeness of atomic packing in a crystal structure

exerts a major control on ion diffusivities such that

compact structures tend to inhibit volume diffusion

while open structures enhance it (Dowty, 1980; For-

tier and Giletti, 1989; Dahl, 1997). Ionic porosity (Z)

is the fraction of a mineral’s unit-cell volume not

occupied by ions (see Table 2), and thus an indica-

tion of the degree of compactness in a mineral. In

Fig. 4E and F, IMF has been plotted against the ionic

porosity Z for the two sessions 6 and 9. A positive

correlation exists but is not better than the previous

IMF vs. molar volume correlation; it remains unsui-

table for a correction scheme.

The instrumental mass fractionations reported by

earlier studies of matrix effect in garnet cannot be

directly compared to those of this study because of

differences in conditions of analysis. Previous studies

used a single electron multiplier detection system on

a Cameca ims-4f operated at lower secondary poten-

tial and a high energy offset (Eiler et al., 1997;

Schulze et al., 2003). The IMFs measured by Eiler

et al. (1997) are in the range 50–60x for garnets

while those in the present study do not exceed 7x.

These authors report the greater difference of IMF

Fig. 4. Instrumental mass fractionation versus mean atomic mass (AMU), molar volume and ionic porosity (Z) in sessions 6 and 9. Error bars

correspond to the external precision (or reproducibility) of the measurements. In most cases, the height of the symbol is larger than the error bar.

The two encircled dots in Fig. 4D correspond to 2 measurements outside the F1x interval at the beginning of the session (see Fig. 3).

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226220

between almandine and pyrope (ca. 16x) and no

difference between pyrope and grossular. On the

other hand, we observe almost no difference between

almandine and pyrope and the largest difference

between pyrope and grossular (ca. 6x). Previous

studies of instrumental mass fractionations accompa-

nying oxygen isotope analyses of garnets and other

silicates (Hervig et al., 1992; Eiler et al., 1997;

Riciputi et al., 1998) employed a high energy offset

technique in which only ions sputtered from the

sample surface with kinetic energies above ca. 250

eV were accepted for analysis. This was done to

make the isotope ratio measurements more stable

and less susceptible to subtle surface charging, and

also to minimize isobaric molecular interferences.

The high energy ion population is a small fraction

(less than 1 part in 1000) of all sputtered ions. There

is a pronounced mass dependence of the transfer of

kinetic energy from the primary ion beam to this

population. This mass dependence contributes to the

large overall IMF and the strong dependence of IMF

on atomic mass (for instance, see the data on Na–Al-

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 221

silicate glasses with various sputter rates in Eiler et

al., 1997). On the other hand, this population of ions

has relatively weak interactions with other ions near

the sample surface, and so charge transfer reactions

that may re-neutralize them are less important as a

control on matrix effects. Therefore, differences in

electrochemistry among various cations do not man-

ifest themselves; at least not noticeably. The present

study has been conducted at the opposite extreme.

With the IMS1270, isobaric interferences are

removed with high mass-resolution above 2500 and

a high energy offset is not required. Thus a larger

proportion of ions ejected from the same surface

with near-zero kinetic energies is analyzed. This

population more closely approaches the isotopic

composition of the bulk material, but is more subject

to charge-transfer reactions in the ion cloud just

above the sample surface. Thus, it has a smaller

instrumental mass fractionation, but matrix effects

are still significant and show no simple dependence

on mass. These issues are discussed in Eiler et al.

(1997), and explained in more detail in papers by

Slodzian et al. (1980) and Shimizu and Hart (1982).

Fig. 5. A: Electron microprobe X-ray image (Cameca SX100, Clermont) of

location of the analytical traverse (black line). B: Electron microprobe cal

Thus, there is no theoretical reason why the larger

IMFs measured by 4f can be simply scaled down to

make predictions for the present study. It is neces-

sary to make the instrumental corrections for this and

other studies using the results of standards run at the

same conditions and calibrated by standard analyses

that bracket sample analyses in the same session of

analysis.

6. Applications

6.1. Garnets from the Ursuya massif (western

Pyrenees)

In a plutonic complex from the Pyrenees, we

discovered composite garnets with two main growth

zones: a core relatively poor in calcium (Grs 7–9%)

and a more Ca-rich rim (Grs 12–14%). A SIMS

study carried out at Nancy indicates that d18O is

higher in the core (12–14x) than in the rim (7–

12x). In addition, a traverse at the core/rim interface

shows a progressive transition for both the grossular

calcium in a composite garnet from the Pyrenees (sample U822) and

cium traverse. C: d18O traverse along the same profile.

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226222

and the oxygen isotopic ratios (Fig. 5). We inter-

preted these features in terms of chemical relaxation

by diffusion for both calcium and oxygen isotopes

(Vielzeuf et al., 2005). In such a study, it is critical

to determine if the d18O variations are real or an

artefact linked to the variations in IMF due to gros-

sular content.

The SIMS traverse was performed during session 9

and intercalated between analyses of PrpAA and

UWG-2 (see Fig. 3). Table 4 provides the measured

d18O values and the composition of the garnet along

the traverse. The measured values of d18O were cor-

rected using two methods: a single standard calibration

with UWG-2 (i.e. applying a constant instrumental

correction of 3.6x), and a multi-standard calibration

as discussed in the text (i.e. applying instrumental

corrections dependent on composition). The correction

factors determined for session 9 are given in Table 4.

The two methods generate identical results (maximum

difference b0.2x), which means that the d18O varia-

tions measured in these garnets are real and not the

Table 4

d18O SIMS measurements in a zoned Pyrenean garnet

Distance

(Am)

Grs

(x)

Prp

(x)

Alm

(x)

Spe

(x)

Measured d18O

(x)

83 13.1 22.6 61.7 2.6 6.4

153 13.3 22.7 61.5 2.5 6.2

288 13.5 22.6 61.4 2.5 6.6

390 13.3 22.9 61.0 2.8 6.3

492 13.3 23.2 60.6 2.9 7.3

559 12.4 22.8 62.2 2.5 6.9

627 12.7 22.4 62.2 2.8 6.6

712 12.4 21.9 63.0 2.7 7.6

780 11.3 23.8 62.0 2.9 7.0

797 11.3 23.8 62.0 2.9 7.2

848 10.9 24.2 62.5 2.4 8.0

915 9.9 24.8 62.8 2.4 8.4

966 9.4 24.4 63.4 2.8 9.0

1034 8.4 24.2 64.7 2.6 9.0

1153 7.7 25.2 64.6 2.5 8.5

1220 7.6 25.2 64.0 3.1 8.9

1373 7.7 25.2 65.0 2.2 9.9

1526 7.7 25.2 64.9 2.2 9.6

1644 7.8 24.4 65.5 2.3 9.8

1763 7.9 25.3 64.3 2.5 10.0

1898 8.1 24.8 64.7 2.4 10.6

2017 8.5 22.1 66.6 2.8 10.8

Comparison of corrections with the UWG-2 standard on one side and the

Correction coefficients: w =�0.0372, x =�0.0473, y =�0.0053, z =�0.0

result of chemical zoning. This example suggests that,

though a correction is still needed to correct d18O vs.

SMOW, the variation of matrix effect in zoned Fe–

Mg–Ca garnets can be neglected if the variation in

end-member components is less than 10%. This is a

direct consequence of the fact that, under the present

operating conditions, the maximum difference of IMF

between end-member standards is not very large and

never exceeded 7x.

6.2. Garnets from the Dora Maira massif (Western

Alps)

In the framework of a study of minor elements,

HREE, and d18O distributions in UHP garnets from

the Dora-Maira massif (Brunet et al., 2003), we col-

lected SIMS data on garnets from gneisses intercalated

within coesite-bearing whiteschists (e.g. Compagnoni

and Hirajima, 2001). These measurements were made

during session 6 (Table 5). One of the garnet crystals

we studied (sample DM94-09) is strongly zoned (Fig.

Corrected d18O

with UWG-2 (x)

Calculated IMF

with matrix (x)

Corrected d18O

with matrix (x)

10.0 �3.5 10.0

9.8 �3.5 9.7

10.2 �3.5 10.1

9.9 �3.5 9.8

10.9 �3.5 10.8

10.5 �3.6 10.4

10.2 �3.6 10.1

11.2 �3.6 11.1

10.6 �3.6 10.6

10.8 �3.6 10.9

11.6 �3.6 11.6

12.0 �3.7 12.0

12.6 �3.7 12.7

12.6 �3.7 12.7

12.1 �3.7 12.2

12.5 �3.7 12.7

13.5 �3.7 13.7

13.2 �3.7 13.3

13.4 �3.7 13.5

13.6 �3.7 13.7

14.2 �3.7 14.3

14.4 �3.7 14.5

matrix correction scheme on the other side.

416.

Table 5

d18O SIMS measurements in a zoned garnet (DM94-09) from a UHP terrane in the Alps (Dora Maira)

Analysis

number

Grs (%) Prp (%) Alm (%) Spe (%) Measured d18O

(x)

Corrected d18O with

2B3 IMF=0.13xCalculated IMF

with matrix (x)

Corrected d18O

with matrix (x)

51 50 1 41 6 6.7 6.9 1.3 5.5

52 21 3 70 5 7.2 7.3 �0.5 7.7

53 22 3 69 5 6.9 7.0 �0.5 7.4

54 22 3 69 5 7.5 7.7 �0.5 8.0

55 21 3 70 5 7.2 7.3 �0.5 7.7

56 21 3 70 5 7.1 7.2 �0.5 7.6

57 44 1 47 6 5.9 6.0 0.9 5.0

Comparison of corrections using the 2B3 standard with the matrix correction scheme (session 6).

Correction coefficients: w =�0.0183, x =�0.0195, y =0.0424, z =�0.0145.

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 223

6) with an almandine-rich core (Alm70Grs20Py5Sp5)

and a grossular-rich rim (Grs50Alm41Py1Sp6). The rim

is interpreted as a high-pressure overgrowth zone. A

SIMS transect across this garnet shows d18O ranging

from 7.7x in the core down to 6x in the rim (Fig. 6).

These values were obtained using a single standard

correction (2B3) and a constant IMF equal to �0.13

x. When the multi-standard regression is taken into

account, the d18O values at the rim drop to 5.0–5.5x(IMF=+0.9 and +1.3x, respectively) whereas the

core values increase by about 0.3x (IMF=�0.5x).

Fig. 6. Scanning electron microprobe X-ray image (Hitachi S-2500,

ENS-Paris) of Ca, and location of the SIMS d18O point analyses in

a garnet from a UHP metamorphic terrane in the Italian Alps

(sample DM94-09, Dora Maira). The average compositions of

core and rim are indicated in black and white, respectively.

Thus, the use of the multi-standard correction

increases the difference in d18O between the core

and the rim and yields d18O ratios that are consistent

with laser-based oxygen data for garnets from the Dora

Maira country-gneisses (8.7–8.8x, Sharp et al., 1993)

and whiteschists (5.6x, Sharp et al., 1993, and this

study — PrpDM). In addition, this example shows that

matrix effect becomes significant when variations in

grossular content are large (N10%). Garnets from the

UHP series in the Alps are a typical case where special

care should be taken for d18O SIMS measurements

because (i) garnets are strongly zoned in calcium, and

(ii) grossular contents in garnets vary significantly (0%

to 70%) from one rock to another at a decimeter scale

(Shertl et al., 1991).

7. Conclusions

In order to obtain reliable and accurate oxygen

isotope ratio measurements on Fe–Mg–Ca garnets,

zoned crystals especially, using a SIMS, we suggest

the application of a correction scheme using at least 3

reliable end-member standards such as PrpDM,

AlmCMG and GrsSE, plus a standard of intermediate

composition (e.g. UWG-2 or the garnet standard clo-

sest to the average composition of the analysed garnet).

This allows (i) the control on the result obtained with a

single standard and (ii) incorporates a correction based

on the variations in composition of zoned crystals. The

fact that linear interpolation among end-member stan-

dards applies in the case of the garnet solid-solutions

implies that the complete compositional field can be

covered with a limited number of standards. Some of

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226224

the garnet standards used in this study (PrpMM, PrpAk,

PrpAA, PrpDM, Bal509, UWG-2) are available and

will be provided upon request.

Acknowledgements

This work has been supported by CNRS–INSU

through grants IT 2001/021 and IT 2002 to DV and

FB. We thank J. Craven, S. Elphick, C. Graham, B.

Devouard, V. Trommsdorff, E. Krogh, A. Leyreloup

and C. France-Lanord for providing valuable garnets

or garnet-bearing rocks. The final stage of this study

was carried out while DV was on a sabbatical leave

from CNRS at Caltech with a financial support

provided by E.M. Stolper. The manuscript benefited

from discussions with M. Chaussidon, E. Deloule,

R. Hervig, and C. Rollion-Bard. We thank J. Eiler

and an anonymous reviewer for their constructive

comments. [PD]

Appendix A. A Matlab routine and a worked

example for the determination of the coefficients

to calculate IMF

Input data: session 6 (see Tables 1 and 2)

Measured IMF Alm Prp Grs+And Spe

h114 �1.87 58.2 34.1 6.3 1.4

PrpDM �1.74 0 99.2 0.8 0

SpeSE �1.46 6.3 0 0.2 93.5

GrsSE 4.02 0.9 0 96.1 1.5

2B3 �0.13 66 2.8 26.8 4.2

AlmCMG �1.69 68.4 26.1 2.9 2.4

UWG-2 �1.03 41.6 42.5 14.9 0.9

PrpAA �0.94 15.2 71.2 6.6 0.8

Bal509 �1.37 49.8 46.2 3.2 0.5

PrpDM �2.02 0 99.2 0.8 0

PrpDM �2.26 0 99.2 0.8 0Correction coefficient for almandine (w): �0.0183

for pyrope (x): �0.0195

for grossular+andradite ( y): 0.0424

for spessartine (z): �0.0145

MATLAB script: lines beginning with d%T are

comments.

clear;

%Input: Measured IMF values

IMF =[�1.87; �1.74; �1.46; 4.02; �0.13;

�1.69; �1.03; �0.94; �1.37; �2.02; �2.26];

%Input: Molar fractions (in %) almandine, pyrope,

grossular+andradite, and spessartine

XMOL=[58.2 34.1 6.3 1.4; 0 99.2 0.8 0; 6.3 0 0.2

93.5; 0.9 0 96.1 1.5; 66 2.8 26.8 4.2; 68.4 26.1 2.9

2.4; 41.6 42.5 14.9 0.9; 15.2 71.2 6.6 0.8; 49.8 46.2

3.2 0.5; 0 99.2 0.8 0; 0 99.2 0.8 0] ;

%Calculation of the correction coefficients:

%In matrix notation, IMF and XMOL are two

matrices and X is the unknown matrix such that

XMOL*X=IMF.

%MATLAB uses a division terminology (a back-

slash \) to describe the solution of a general system of

simultaneous equations. The following expression

X=XMOL\ IMF denotes the solution of the matrix

equation XMOL*X=IMF. The dimension compatibi-

lity conditions require matrices XMOL and IMF to

have the same number of rows. The solution X has the

same number of columns as IMF and its row dimen-

sion is equal to the column dimension of XMOL. The

matrix XMOL need not to be square: if XMOL is m-

by-n, then there are 3 cases: m=n, square system,

MATLAB seeks an exact solution, mNn, the system

is overdetermined, MATLAB finds a least square solu-

tion (most common case in our situation). mbn, under-

determined system, MATLAB finds a basic solution

with at most m nonzero components.

X=XMOL\IMF

%Checking the calculated values of IMF using the

correction coefficients

IMFR=XMOL *X

%Difference between measured and calculated

IMF

D=IMFR� IMF

mean (D)

std (D)

plot (D,’ob’);

axis ([1 11 �3 +3]);

Results: Correction coefficients for session 6:

%End of program.

Recalculation of IMF (e.g. h114):�0.0183d 58.2 �0.0195d 34.1+0.0424d 6.3�0.0145d 1.4=�1.48.

D: (difference between recalculated and actual

d18O values)=�1.48+1.87=0.39x.

D. Vielzeuf et al. / Chemical Geology 223 (2005) 208–226 225

Summary:

Session 6 Actual d18O Measured d18O IMF Recalculated IMF Recalculated d18O D

h114 9.3 7.41 �1.87 �1.48 8.9 0.4

PrpDM 5.6 3.85 �1.74 �1.90 5.7 �0.1

SpeSE 5.4 3.93 �1.46 �1.46 5.4 0

GrsSE 3.8 7.84 4.02 4.04 3.8 0

2B3 6.9 6.77 �0.13 �0.19 7.0 �0.1

AlmCMG 7.5 5.8 �1.69 �1.67 7.5 0

UWG-2 5.8 4.76 �1.03 �0.97 5.7 0.1

PrpAA 5.5 4.55 �0.94 �1.40 5.9 �0.4

Bal509 12.3 10.91 �1.37 �1.68 12.6 �0.3

PrpDM 5.6 3.57 �2.02 �1.90 5.5 0.1

PrpDM 5.6 3.33 �2.26 �1.90 5.2 0.4

Average 0

r 0.25

Appendix B. Supplementary data

Supplementary data associated with this article

can be found, in the online version, at doi:10.1016/

j.chemgeo.2005.07.008.

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