PII S0016-7037(98)00117-3

Oxygen isotope geochemistry of the amphiboles: Isotope effects of cation substitutionsin minerals

MATTHEW J. KOHN1 and JOHN W. VALLEY

2

1Lawrence Livermore National Laboratory, Livermore, California 94550, USA2Department of Geology and Geophysics, University of Wisconsin, Madison, Wisconsin 53706, USA

(Received July29, 1997;accepted in revised form March3, 1998)

ABSTRACT—The occurrence of coexisting amphiboles in rocks and the likelihood of concurrent isotopeclosure allows equilibrium oxygen isotope fractionations among the amphiboles to be recovered from naturalsamples. Oxygen isotope analyses of mineral separates using laser fluorination show that coexisting amphi-boles increasingly partition18O in the order: hornblende,, gedrite, cummingtonite# anthophyllite. Theobserved fractionations at;575°C are:D(Ged-Hbl) 5 0.8‰, D(Cum-Hbl) 5 0.9, D(Cum-Ged)5 0.2,D(Ath-Ged)5 0.3, andD(Ath-Hbl) . 0.9. Previously published data for hornblende, actinolite, glaucophane,and garnet show thatD(Act-Hbl) ; 0.2,D(Gln-Grt) .. 1, andD(Hbl-Grt) ; 0. Thus, glaucophane stronglypartitions 18O relative to the calcic amphiboles. The fractionation between two amphiboles of arbitrarycomposition can be predicted from the known fractionations for mica endmembers, pyroxene endmembers,and exchange components such as CaAl(NaSi)21, NaAl(CaMg)21, CaMg21, MgFe21, FeMn21, KNa21,KAl( Si)21, and Fe31Al21. Applications of the exchange component method reproduce measured amphibolefractionations to within60.1 to60.2‰, whereas other predictive methods cause misfit for typical metamor-phic hornblende of$0.5‰ at 575°C. Although the isotope effects of cation exchanges may be small at high-T,they magnify dramatically for minerals formed in surficial, diagenetic, and low-T metamorphic environments.Different composition clays are predicted to have equilibriumd18O differences of 2–9‰. If the isotopefractionation can be determined for one mineral endmember, then calibrated exchanges allow accurateprediction of the isotope fractionations for intermediate compositions of most ortho-, ring-, chain-, andsheet-silicates. Copyright © 1998 Elsevier Science Ltd

1. INTRODUCTION

The isotope fractionation of compositionally intermediate min-erals is commonly assumed to be approximated by the linearcombination of the fractionations of endmember components.For example, the isotope fractionation of compositionally in-termediate plagioclase relative to an arbitrary phase is equal tothe proportionate contributions of the fractionations of end-member albite and anorthite (i.e., relative to quartz, lna(Qtz-Pl)5 XAnlna(Qtz-An)1 XAblna(Qtz-Ab)). To our knowledge, norigorous test of this assumption has ever been made for silicateseither experimentally or by the analysis of natural rocks (al-though see Tarutani et al., 1969, for Mg in calcite). Somereasons such tests have not been made include: (1) Bondstrengths are not strongly affected by mixing in solid solutions,and so physically these strengths should be approximated wellby linear combinations of the strengths of endmember compo-nents. (2) Isotope partitioning experiments for silicates requirepainstaking effort, and studies of compositionally intermediatecompounds would vastly increase the number of experimentsand their expense. (3) Studies of natural systems are plagued bydiffusional exchange of oxygen on cooling. For minerals withrapid oxygen diffusivity like plagioclase, the present dayd18Odepends not only on cation composition, but also on the phys-ical character of all the minerals in the rock (mineral modalabundances, grain sizes, and diffusivities) and cooling rate(e.g., Giletti, 1986; Eiler et al., 1992; Jenkin et al., 1994). Theuncertainties in correcting for diffusional exchange can over-whelm any differences in fractionation arising from cationcompositional differences.

Miscibility gaps circumvent many problems encountered inempirical studies because two or more species of the samemineral system may be present for analysis. This coexistence ispotentially useful because, for any one rock, the degree ofreequilibration for the different phases is defined by a single setof parameters (cooling history, modes, grain sizes, etc.). If thegrain sizes and oxygen diffusivities are similar in these phases,then reequilibration is controlled by the same parameters, andthe populations should in theory (Kohn and Valley, 1998a)retain an isotope fractionation equal to their mutual closuretemperature (Tc) as defined analytically by Dodson (1973).Although Tc will be different among samples because of vari-ations in cooling history, or grain sizes, isotope fractionationsshould show a systematic trend with cation composition.

Amphiboles are especially well-suited for studying the ef-fects of cation substitutions on isotope partitioning. There areseveral members of the amphibole group that coexist macro-scopically in many rocks, including gedrite, anthophyllite, ac-tinolite, cummingtonite, hornblende, and glaucophane. Consid-ered both together and individually, amphiboles span a largerange of cation compositions. The different amphiboles areoften also physically separable because of differences in colorand habit. Consequently, analysis of the isotope compositionsof coexisting calcic and Fe-Mg amphiboles was undertaken totest whether there are (1) differences in isotope compositionthat correlate with cation differences and (2) similarities be-tween measured isotope compositional differences and predic-tions. Just as experiments and theory examine the temperature-dependence of fractionations, the overall purpose of this studyis to examine the cation compositional dependence of isotope

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fractionations, specifically focusing on amphiboles, but recog-nizing the implications for other minerals.

Our results demonstrate significant isotope effects associatedwith cation exchanges, as well as good success in reproducingmeasured high-T fractionations using our new predictive ap-proach. Although isotope effects of cation exchanges are gen-erally less than 1‰ at T. 500°C, they increase strongly atlower T. Because the cation exchanges that operate in amphi-boles also occur in many other minerals, our data and predictiveapproach further imply strong control of isotope fractionationsby mineral chemistry in surficial, diagenetic, and low-T meta-morphic settings.

2. ANALYTICAL TECHNIQUES AND SAMPLEDESCRIPTIONS

Over 500 thin sections of rocks with multiple amphiboles wereinspected from the collection of Dr. Frank S. Spear, and sixteen werechosen for this study, based on uniformity of mineralogy and grain size,lack of alteration and inclusions, and mineral assemblage. Fifteensamples are from Vermont and New Hampshire, USA, and one sampleis from Tierra del Fuego, Chile. One additional sample from the TauernWindow, Austria, was supplied by Dr. Jane Selverstone, and eightsamples from the Jackson County Iron Formation (JCIF) of centralWisconsin were obtained through the Geology archives at the Univer-sity of Wisconsin-Madison. Although amphibole compositions showsubstantial differences between samples, for simplicity we refer to theamphiboles as hornblende, actinolite, cummingtonite, anthophyllite,and gedrite based on their optical and chemical characteristics. Figure1 shows measured amphibole compositions projected onto an (Al1Fe31) 2 Ca 2 (Fe21 1 Mg 1 Mn) diagram and illustrates the majorcompositional fields on which our name assignments are based. Mostsamples are quite well characterized in terms of P-T-t evolution andamphibole compositions (Jones, 1978; Spear, 1980, 1982; Kimball,1981; Kimball and Spear, 1984; Selverstone and Spear, 1985; Spearand Rumble, 1986; Harrison et al., 1989; Spear and Harrison, 1989;Kohn et al., 1992, 1993, 1995; Smelik and Veblen, 1993; F. S. Spear,pers. commun., 1993; E. Smelik, pers. commun., 1993), and the peakmetamorphic temperatures for these rocks are:;450°C (CordilleraDarwin), ;475°C (Tauern Window),;550°C (JCIF), and 575–625°C(New Hampshire and Vermont amphibolites).

In the rocks from New Hampshire, Vermont, and Wisconsin, differ-ent amphiboles exist as both intergrown and discrete grains. Spear(1980, 1982), Kimball and Spear (1984), and Spear and Rumble (1986)have presented extensive textural, compositional, and petrologic evi-dence that the different amphiboles were in chemical equilibrium at thepeak of metamorphism. The only exceptions are trace amounts ofriebeckite in sample 1692-3 (Kimball and Spear, 1984), which was notseparated, and actinolite in samples CD-157E (Tierra del Fuego) andHF-13 (Tauern Window), which occurs only as patchy cores of largeamphibole grains with hornblende overgrowths. The systematic parti-

tioning of oxygen observed in this study for all coexisting amphibolesother than actinolite further supports the assumption of equilibrium.

Typically 10–20 grams of each sample were crushed and sizedbetween 150 and 250mm. Amphiboles were further purified by settlingin slightly dilute methylene iodide (r ; 3.2 g/cm3). Amphibole sepa-rates were then handpicked based on crystal color and habit. Analyseswere collected with the laser probe fluorination system at the Univer-sity of Wisconsin and were standardized using UW Gore MountainGarnet standards #1 and #2 (6.2‰ and 5.8‰ respectively, V-SMOW;Kohn et al., 1997; Valley et al., 1995). The analytical reproducibility onstandards during data collection was60.08‰ (1s). As described inKohn and Valley (1998a), although we routinely pretreat our samplesovernight with BrF5 to eliminate adsorbed water or organic residuesand to reduce analytical blanks, special efforts to assess chemicaleffects of this pretreatment showed no surface reaction, oxygen leach-ing, or F(OH)21 exchange and no dependence of isotope compositionon pretreatment time. Thus, compositions are not detectably biased bythe pretreatment procedure.

In a few samples, pure amphibole separates were not achieved, andso whereas the coexisting amphiboles were likely in cation and isotopeequilibrium, the reported values may be biased. Actinolite in theWisconsin samples contained abundant fine-grained inclusions ofquartz and/or magnetite, and so the reportedd18O values for theseactinolite analyses may be inaccurate. In rocks that contain gedrite1hornblende6 cummingtonite, it was not possible to separate gedritecompletely from intergrown anthophyllite. However, becauseD(Ath-Ged) is small (#0.3‰) in those samples where the two orthoamphi-boles were readily separated, a small anthophyllite impurity (,10%) insome gedrite separates should have had only a small effect on measuredgedrite composition (,,0.1‰). All gedrite analyses should, therefore,be accurate.

Yields on cummingtonite and gedrite were all within weighinguncertainties (; 6 3% for 1–2 mg) of 100%, but yields on hornblendewere routinely;96–98%. The slightly low apparent yields on horn-blende may simply be the result of weighing errors, but might also becaused by difficulty in controlling the reaction of high calcium phasesusing a CO2-laser extraction system. A typical problem is sputteringand slight loss of material, and yields for natural clinopyroxene usingthe same extraction system are routinely;96% (Kohn and Valley,1998b). Although yields of;95% are commonly reported for Nireaction vessels, we now recognize that the,100% yields with thelaser may be problematic: measured compositions of clinopyroxeneusing the UW laser probe fluorination system are systematically 0.360.2‰ (62s) lower thand18O values obtained by R. N. Clayton and T.Mayeda for the same materials using nickel reaction vessels at theUniversity of Chicago, when all analyses are corrected to yield thesame composition for a concurrently run standard. This interlaboratorydifference for clinopyroxene contrasts with garnet, which gives thesame compositions in the two systems when standardized to NBS-28quartz (Valley et al., 1995). Consequently, in order to match UCanalyses, clinopyroxened18O compositions collected at UW wouldhave to be corrected upward by;0.3 6 0.2‰ (Kohn and Valley,1998b). Hornblende and actinolite have uniformly better yields thanclinopyroxene and react with much less sputtering, so compositionalcorrections are undoubtedly smaller. Considering that the calcic am-phiboles can be described crystal-chemically as 50% clinopyroxeneand 50% sheet silicate, any corrections are expected to be;0.15 60.1‰. Because this borders on the analytical resolvability of fraction-ations, and because such a small difference would be nearly impossibleto resolve by comparing with analyses collected with externally-heatedNi-reaction vessels, we have chosen not to make corrections to thecompositions of the calcic amphiboles. However, our reportedd18Ovalues for hornblende and actinolite may be systematically too low byas much as 0.2‰, and this small systematic uncertainty does impactinterpretations of relative fractionations.

Amphibole-talc fractionations were also investigated in several sam-ples. Samples Ches-2 to Ches-13 were obtained from the Chester talcquarry, Vermont, and aside from trace phases, contain only coarse-grained actinolite and talc, intergrown on a mm to cm scale. Thesesamples recrystallized at 575–625°C (based on thermobarometry fromsimilar structural levels in Vermont; Kohn and Spear, 1990; Ratcliffe etal., 1993; Kohn and Valley, 1994). Sample 14-1a is from the JacksonCounty iron formation (provided by UW archives; T; 550°C), and

Fig. 1. Measured amphibole cation compositions on a (Al1 Fe31)-Ca-(Fe1 Mg 1 Mn) plot showing principal compositional differencesand name assignments. Note that cummingtonite (monoclinic) andanthophyllite (orthorhombic) are readily distinguished in thin sectionby their optical properties and habit and in crushed samples by theirhabit and color.

1948 M. J. Kohn and J. W. Valley

K93-30C is from near Zermatt, Switzerland. The Swiss sample is aneclogitic rock that was overprinted by abundant coarse-grainedtalc1 actinolite at T; 450°C (Barnicoat, 1988; Barnicoat and Fry,1989).

3. RESULTS

Oxygen isotope compositions are given in Table 1 andplotted in Fig. 2. Mineral abbreviations are after Kretz (1983).Most of the amphibole data exhibit a very consistent compo-

sitional trend, such that the order of increasingd18O is: horn-blende,, gedrite, cummingtonite; anthophyllite. Garnetanalyses showD(Grt-Hbl) 5 0.1‰, similar to the 0.06 0.2‰fractionation observed by Kohn and Valley (1994, 1998a),from which we conclude that the measured fractionation be-tween garnet and typical metamorphic hornblende is nearlyzero. Actinolite compositions are more problematic. Fraction-ations between actinolite and cummingtonite in the Wisconsinsamples show much greater variation than any other amphibolepair, probably as a result of impure actinolite separates (seeabove). Fortunately, talc-actinolite and biotite-actinolite frac-tionations are quite consistent in nearly bimodal rocks fromwhich mineral separates were pure. As shown by Kohn andValley (1998a) for amphibolite-facies samples from Vermontand Ontario,D(Act-Bt) ; D(Hbl-Bt) 1 0.2‰. So,D(Act-Hbl)is small (;0.2‰), as expected from consideration of the iso-tope effects of cation exchange (see following).

1949Oxygen isotopes in amphiboles

Few analyses of glaucophane have been previously reported,and its isotope fractionation compared to other amphiboles isdifficult to constrain precisely. Data from Taylor and Coleman(1968) for garnet- and glaucophane-bearing rocks that equili-brated at;320°C (Oh et al., 1991) show an averageD(Gln-Grt)of ;1.7‰. Our data for a sample from Sifnos, Greece (Kohnand Valley, 1998b) that equilibrated at;470°C (Schliestedt,1980, 1986; Ridley, 1984) has a measuredD(Gln-Grt) of;1.4‰. The fractionations between hydrous and anhydroussilicates are very nearly linear in 1/T2 with an intercept of 0 (Tin kelvins; see discussion of Chacko et al., 1996), and thedifferences between a linear and a polynomial fit are,,0.1‰at T 5 300–800°C. AssumingD(Gln-Grt) has such a linear1/T2 dependence, at 575°CD(Gln-Grt) should be;1.0‰. Thatis, glaucophaned18O should be significantly higher than the

calcic amphiboles and at least as high as the Fe-Mg amphi-boles.

4. INTERPRETATION AND DISCUSSION

4.1. Effects of Diffusional Exchange

Interpretation of the measured amphibole fractionations (Ta-ble 1) requires assessment of post-peak diffusional exchange.As described by Eiler et al. (1992) and Kohn and Valley(1998a) the isotope fractionation preserved between two min-erals with identical grain-sizes and oxygen diffusivities reflectsequilibrium at a temperature that is defined mathematically bythe closure temperature equation of Dodson (1973). For oxygendiffusion rates determined experimentally in amphiboles ofdifferent composition (Farver and Giletti, 1985) and the mea-sured amphibole grain size in the samples analyzed (;1 mmdiameter), this temperature is;575°C. Although there may besmall differences in the effective amphibole closure tempera-tures for different rocks, the amphiboles in any one sampleprobably closed at about the same temperature, because: (1)The diffusivity of oxygen is similar in the different amphiboles(Farver and Giletti, 1985). (2) In any one rock, all the amphi-boles have approximately the same grain size and shape. Thehighest peak metamorphic temperatures are only 600–625°C,and for typical mineral modes of mafic amphibolites, isotopeexchange of any one amphibole over 25–50°C changes itsisotope composition by 0.1‰ or less. Thus, the isotope frac-tionations of the amphiboles should reflect peak or near-peakmetamorphic conditions to within 0.1‰ or better.

Amphibole exsolution is a special concern. As described bySpear (1980, 1982) and Smelik and Veblen (1993), hornblendeand cummingtonite from our samples typically contain only afew exsolution lamellae (#1%), but gedrite and anthophylliteexperienced pervasive exsolution over a range of temperatures.It is possible that exsolution physically decreased the effectivegrain size through the production of new incoherent grainboundaries, increased the diffusivity of oxygen during lower-temperature exsolution, and/or produced domains of differentdiffusional character in different amphiboles. These effectscould produce much lower effective closure temperatures thatmight differ for each amphibole and sample and bias relativefractionations. For example, as has been well documented byFarquhar and Chacko (1994) and Farquhar et al. (1996), gran-ulite-facies oxides undergoing oxy-exsolution can have closuretemperatures far below peak metamorphic conditions, whichthey ascribe to either an exsolution-enhanced decrease in dif-fusion domain size, or a commensurate increase in dislocationsand oxygen diffusion rates as exsolution proceeds.

Despite the observed exsolution and previous studies ofoxides, we believe all the amphiboles analyzed probably pre-serve high temperature fractionations for the following reasons:first, compositions of exsolved vs. unexsolved amphiboles areinconsistent with differential isotope resetting. The moststrongly exsolved amphiboles (anthophyllite and gedrite) occurin relatively felsic bulk compositions and have typicald18Ovalues lower than the bulk rock. Consequently any additionaldiffusional exchange with feldspar and quartz after the clino-amphiboles closed would have lowered orthoamphiboled18O,leading to a smallD(Ged/Ath-Hbl) and a largeD(Cum-Ged/Ath). Yet, this prediction is the reverse of what we observe.

Fig. 2. (a) Gedrite composition vs. hornblende, cummingtonite, andanthophyllite compositions. (b) Cummingtonite compositions vs. horn-blende, gedrite, and actinolite compositions. Data are systematic over alarge range ofd18O and showD(Ged-Hbl) ; 0.8‰, D(Cum-Hbl) ;0.9‰, andD(Cum/Ath-Ged); 0.2‰. Analytical errors (62s) areapproximately the size of the symbols.

1950 M. J. Kohn and J. W. Valley

One reason why orthoamphibole exsolution may not stronglyaffect oxygen isotope exchange concerns the interplay of de-creasing temperature and exsolution-related dislocations onoxygen diffusivities. As shown in Smelik and Veblen (1993)and Treloar and Putnis (1982), the highest-temperature exso-lution lamellae form along the amphibole 010 plane at T# ;500°C and are typically coherent. If this type of exsolutiontruly does not increase dislocation densities, then isotope ex-change might not be significantly facilitated, because oxygendiffusion along the lamellae boundaries would be no faster thanthrough the bulk crystal. Although the morphology of thelower-temperature exsolution lamellae and their boundaries(Smelik and Veblen, 1993) does suggest an increase in dislo-cation densities, temperatures by then may have been too lowfor diffusion to affect isotope compositions. An alternativeexplanation relies on the observation that oxygen diffusionrates in amphibole are;1000 times faster parallel to c thanperpendicular to it (Farver and Giletti, 1985). Because exsolu-tion lamellae are ubiquitously parallel to c (Smelik and Veblen,1993), domain lengths parallel to c are unaffected, and closuretemperatures may remain high.

Second, measured fractionations show no dependence onbulk composition or mineralogy. The bulk compositions en-countered in this study show a wide range from mafic amphi-bolites (60% or more hornblende6 cummingtonite6 gedrite)to felsic metavolcanic rocks (20% gedrite1 anthophyllite6 hornblende). If different amphiboles have different closuretemperatures, then the observed relative amphibole fraction-ations in different rocks should either be nonsystematic or showa dependence on rock type. The constancy of observed frac-tionation among all the samples studied suggests that differen-tial blocking is not a problem. Because the clinoamphibolescummingtonite and hornblende are relatively unexsolved, theirfractionations should reflect peak or near-peak metamorphictemperatures. The systematic isotope partitioning of the ortho-amphiboles with respect to the clinoamphiboles independent ofrock type implies that all amphiboles have similar closuretemperatures and that all amphibole fractionations likely reflectpeak or near-peak temperatures.

Finally, the one clear compositional anomaly (hornblende) isleast affected by exsolution (#1%; E. Smelik, pers. commun.,1993). If this tiny amount of exsolution in hornblende caused amajor problem in the multiple-amphibole assemblages, then wewould expect some systematic difference in the hornblendefractionations compared to rocks in which hornblende is theonly amphibole and is, therefore, probably unexsolved (be-cause it is nonsolvus). The similarity ofD(Grt-Hbl) in bothmultiple-amphibole and mono-amphibole samples (Kohn andValley, 1994, 1998a) suggests that minor exsolution has notresulted in substantial reequilibration.

4.2. Comparison with Bond-Strength Predictions

A semi-empirical approach (the modified increment method)has been used by Richter and Hoernes (1988), Zheng (1993),and Hoffbauer et al. (1994) to predict oxygen isotope fraction-ations for hydrous minerals. All three studies give similarpredictions for relative fractionations among amphiboles, butthe predictions of Richter and Hoernes (1988) are closest to ourmeasured data. The results of these calculations at T5 575°C

(Fig. 3a) confirm that the magnitude of observed fractionationsis predicted fairly well for gedrite, anthophyllite, and cumming-tonite. Hornblende and actinolite, however, are predicted tohave similar compositions to the other amphiboles (e.g.,Zheng’s calculations at 575°C showD(Ath-Hbl) ;0.3‰ andD(Ged-Hbl) ;20.2‰)), yet thed18O value of hornblende issystematically 0.5–1.0‰ lower than the Fe-Mg amphiboles,and actinolite compositions are probably similar to hornblende.The reverse problem is encountered with the electrostatic ap-proach (Smyth and Clayton, 1988; Smyth, 1989), which, for

Fig. 3. Predicted fractionation between amphiboles vs. measuredfractionation. (a) Predictions based on bond-strength calculations ofRichter and Hoernes (1988). Predicted fractionations for anthophyllite-gedrite and cummingtonite-gedrite are in reasonable agreement withmeasurements, but predicted gedrite-hornblende and cummingtonite-hornblende fractionations are systematically more than 0.5‰ differentfrom measurements. (b) Predictions based on calibrated exchangecomponents (this study), showing improved agreement with measure-ments. Solid symbols show no correction to measured hornblendecompositions, dashed symbols show correction of 0.2‰ for isotopecompositions of calcic amphiboles.

1951Oxygen isotopes in amphiboles

tremolite and pargasite (5 hornblende) indicatesD(Tr-Prg) ;1.25‰ at T5 575°C. This value is larger than the measuredfractionations between amphiboles reported in this study (allD’s # 1‰) and is not consistent with measured hornblende-biotite and actinolite-biotite fractionations in restricted bulkcompositions, which suggestD(Tr-Hbl) ; 0.2‰.

The poor prediction of hornblende fractionations is perplex-ing given the good consistency among measurements and pre-dictions for the other amphiboles. Analytical uncertainties arean unlikely explanation, as they are much smaller than themismatch. Exsolution and preferential reequilibration of horn-blende are also not likely responsible for the observed fraction-ations. Oxygen bonding in hornblende is crystallographicallysimilar to the other amphiboles, and although there are likelydifferences in specific oxygen bond strengths depending on siteoccupancies, those differences are not reflected overall bysystematic major differences in mean bond lengths or sitedistortions. The measured hornblende cation compositions arenot anomalous and can be readily represented by simple com-binations of endmember components. None of the amphiboleshave appreciable F or Cl (F. Spear, pers. commun.; this study).Although it is possible that hornblende has more oxy-compo-nent than the other amphiboles, calculations using the modifiedincrement method suggest that this component cannot be re-sponsible for the observed differences. If hornblende were fullydehydrated and the other amphiboles were fully hydrated, horn-blende is predicted to have a higherd18O by 0.6‰ than theother amphiboles.

The most reasonable remaining explanation for the mismatchbetween predicted and measured hornblende compositions isthat the predictions are inaccurate for compositionally interme-diate amphiboles like hornblende. This is worrisome becausethe cation substitutions that operate in amphiboles to producecompositionally intermediate species, such as CaAl(NaSi)21,Si(NaAl)21, NaAl(CaMg)21, AlAl(MgSi) 21, and Fe31Al21,also occur in other mineral groups, such as the feldspars, micas,pyroxenes, clays, and chlorites. Therefore, if the fractionationtrends of the intermediate amphiboles cannot be approximated,then presumably neither can similar trends in a wide variety ofother compositionally intermediate minerals.

4.3. Toward a New Predictive Model

To interpret thed18O differences among the amphiboles andto provide a predictive model, we have used crystal-chemicalprinciples and the compositional basis of the amphibole solidsolution series to develop a calibrated set of isotope exchangecomponents that can be applied to any mineral group. The twoissues we address are: (1) Can the isotope fractionations ofendmember amphiboles be estimated from linear combinationsof fractionations for sheet silicates and pyroxenes?, and (2) Canexchange components be calibrated and applied in combinationwith endmember amphibole fractionations to reproduce theobserved fractionations of intermediate amphiboles? If so, thenin principle, the same isotope exchange components can beapplied to any mineral group to estimate the isotope fraction-ations of compositionally intermediate compounds.

4.3.1. Endmember amphibole fractionations

As described in detail by Thompson (1981), the amphibolecrystal structure can broadly be considered to consist of a micamodule flanked on either side by a pyroxene module. Thus,tremolite [Ca2Mg5Si8O22(OH)2] can be considered not onlycompositionally but also crystallographically as a linear com-bination of one talc [Mg3Si4O10(OH)2] plus two diopside[CaMgSi2O6]. This implies that to a first order, the isotopefractionation of tremolite should be half-way between diopsideand talc, because half of tremolite’s oxygens are contributed bythe talc module, and half by the two diopside modules. Weknow of no measurements of thed18O of coexisting talc andpyroxene, nor of any appropriate rocks in which to make thismeasurement. Nonetheless, from a variety of observations fromtalc-, pyroxene-, and amphibole-bearing rocks, we believe thatwe can verify within uncertainty the expected linearity of theisotope fractionations. For simplicity, in this comparison weassume no fractionation between Fe- and Mg-endmembers, sothat actinolite and tremolite do not differ isotopically.

The first step is to identify the fractionation between actin-olite and diopside,D(Act-Di). One approach is to combineexperimental calibrations for biotite and diopside (Chiba et al.,1989; Chacko et al., 1996) with the empirically retrieved frac-tionation for actinolite and biotite (D(Bt-Act) ; 0.1‰; Kohnand Valley, 1998a). The expectedD(Act-Di) is then ;0.6 60.8‰ (2s) at 575°C. This value agrees with preliminary ex-perimental results for tremolite (R. N. Clayton, pers. commun.,1996), which, when combined with diopside fractionations(Chiba et al., 1989) suggestD(Act-Di) ; 1.1 6 0.4‰ (2s) at575°C. If the actinolite fractionation can be predicted from talcand diopside fractionations, thenD(Tlc-Act) 5 D(Act-Di), sothe second step in testing this hypothesis is to determinewhetherD(Tlc-Act) is 0.5–1.0‰ at 575°C. As shown by thedata from the amphibolite-facies samples,D(Tlc-Act) ; 0.960.2‰ (2s), in agreement with the theoretical expectations. Asdiscussed above, it is possible that the measuredd18O values ofthe calcic amphiboles are analytically biased by as much as0.2‰. If so, then a small 0.2‰ correction increasesD(Act-Di)to ;0.8‰, and decreasesD(Tlc-Act) to ;0.7‰.

4.3.2. Calibration of isotope exchange components

Isotope exchange components are an extension of the prin-ciple espoused by Thompson (1982) that the cation composi-tions of intermediate minerals can be expressed in terms of oneadditive component and a linear combination of independentexchange components. The extension to isotopes is that eachcation exchange component has an associated isotope effect.Therefore, if the fractionation of an endmember mineral isknown, and the effects of the cation exchange on isotopepartitioning can be calibrated from natural or experimental dataon endmembers, then the isotope fractionation of any interme-diate mineral can be predicted within the composition spacedefined by the exchanges.

For example, the cation compositions of plagioclasefeldspars can be described in terms of the additive componentanorthite and the exchange component NaSi(CaAl)21 (plagio-clase exchange). Thus, Ab40 plagioclase5 anorthite1 0.4Na-Si(CaAl)21, or more generally for plagioclase of arbitrary

1952 M. J. Kohn and J. W. Valley

composition (AbX), AbX 5 anorthite 1 X * NaSi(CaAl)21.Isotopically, the effect of plagioclase exchange on feldspars hasbeen calibrated experimentally (Clayton et al., 1989) and showsthat at 575°C albite and anorthite should differ by 1.46‰(fractionation factors recalculated by Chiba et al., 1989). There-fore, at 575°C, the isotope composition of AbX plagioclaserelative to anorthite is equal to the isotope composition ofanorthite1 X * 1.46‰, or for Ab40 plagioclase,D(Ab402An)5 0.58‰.

For amphiboles, cation compositions can be modeled in termsof the additive component cummingtonite [Mg7Si8O22(OH)2],and the cation exchange components: NaSi(CaAl)21 (plagioclaseexchange), NaAl(CaMg)21 (jadeite exchange), KNa21, MgCa21,FeMg21, FeMn21, KAl( Si)21 (K-edenite exchange), Fe31Al21,MgTi(Fe31)22, F(OH)21, and Cl(OH)21. These exchanges werechosen because their isotope effects can be calibrated experimen-tally, theoretically, or from natural assemblages. Once these ex-changes are calibrated, isotope partitioning can be predicted forany two amphiboles within the cation composition space.

The ‰z O notation.In the following discussion, we definethe isotope unit notation of ‰z O (permil z oxygen) for thefractionation associated with exchange components. The use ofthis notation arises because each exchange is calibrated usingone mineral group with a specific number of oxygens (such asplagioclase: eight oxygens), whereas the exchange can be ap-plied to other mineral groups with different numbers of oxy-gens (such as amphibole: twenty-four oxygens). At a giventemperature, the fractionation of two mineral endmembers thatdefine an exchange component can be multiplied by the numberof oxygens in those endmembers to result in the units ‰z O.The isotope effect of the cation exchange on any mineral canthen be determined by dividing by the number of oxygens in

that mineral. For example,D(Ab-An) 5 1.46‰ at 575°C(Clayton et al., 1989; Chiba et al., 1989), and because albite andanorthite each have eight oxygens, this leads to a value of11.7‰z O at 575°C for the exchange NaSi(CaAl)21. Thisvalue is independent of the formula unit chosen for plagioclase.For example, a sixteen-oxygen formula unit would involve twoNaSi(CaAl)21 exchanges to describe the compositional differ-ence between endmember albite and anorthite. So, the ex-change value for one NaSi(CaAl)21 exchange would be calcu-lated as 1.46‰ * 16(oxygens)/2(exchanges)5 11.7‰z O.

The utility of this approach can be seen if one wishes to estimatethe fractionation between two phases that are also related by theplagioclase exchange, such as the white micas paragonite[NaAl2AlSi3O10(OH)2] and margarite [CaAl2Al2Si2O10(OH)2] at575°C:

D~Pg-Mrg! 511.7‰ z O

12 O p.f.u.5 0.98‰.

That is, complete operation of the plagioclase exchange at575°C affects feldspar by;1.5‰, but cannot affect the micasby more than;1.0‰ because the isotope effect is distributedamong more oxygen atoms.

Values for the exchanges considered above for amphibolesand their uncertainties are tabulated in Table 3. The exchangesKNa21, FeMg21, and FeMn21 are constrained by experiments,natural data, and theoretical considerations and are not thoughtto contribute significantly to isotope fractionation (e.g., O’Neiland Taylor, 1967, 1969; Matthews et al., 1983; Richter andHoernes, 1988; Smyth and Clayton, 1988; Smyth, 1989; Kohnand Valley, 1998b; this study). Experiments show that theplagioclase and jadeite exchanges are moderately important,

1953Oxygen isotopes in amphiboles

and at 575°C have values of 11.7‰z O and 8.8‰z O, respec-tively (Matthews et al., 1983; Clayton et al., 1989; Matthews,1994). In the amphiboles (twenty-four oxygens p.f.u.), fulloperation of one of these exchanges would lead to composi-tional shifts of 0.4–0.5‰. Of great interest is the octahedralexchange (Fe,Mg)Ca21, because it is commonly believed thatsimple substitutions between divalent cations of similar massshould have a negligible effect on oxygen partitioning. How-ever, consideration of electrostatic potentials (Smyth and Clay-ton, 1988; Smyth, 1989), experimental data for the pyroxenes(Chiba et al., 1989; Rosenbaum et al., 1994), and measureddifferences in fractionations among natural clinopyroxene, or-thopyroxene, and garnets of different cation composition (Kohnand Valley, 1998b) yield a very consistent value for this ex-

change of;4‰ z O. Experimental and natural data for frac-tionations among fluorphlogopite, hydroxybiotite, ilmenite, andhematite (Garlick and Epstein, 1967; Taylor and Coleman,1968; Chacko et al., 1996) suggest values of;5‰ z O for(Fe,Mg)TiFe22

31 and ;6‰ z O for F(OH)21 and Cl(OH)21 at575°C, although the exchanges are negligible for the amphibolecompositions considered here. Natural data for clinopyroxenevs. grossular-rich and andradite-rich garnets indicates thatFe31Al21 has an exchange value of;4.5‰ z O (Kohn andValley, 1998b).

An important, but previously uncalibrated exchange is K-edenite, KAl( Si)21, which describes the compositional differ-ence between talc [(Fe,Mg)3Si4O10(OH)2] and biotite[K(Fe,Mg)3AlSi3O10(OH)2]. The measured talc-actinolite and

1954 M. J. Kohn and J. W. Valley

actinolite-biotite fractionations at;600°C for bimodal amphi-bole-sheet silicate samples suggest a talc-biotite fractionationof ;0.8, or;10‰ z O for this exchange (twelve oxygens). Themagnitude of the isotope effect for K-edenite exchange shouldbe similar to that of NaSi(CaAl)21 (11.7‰z O), because thesame tetrahedral Al-Si substitution occurs in both exchangesand probably dominates the isotope effect. Furthermore, al-though the mineral structures are somewhat different, the cationcompositions of albite and quartz define a quasi Na-edeniteexchange, and the experiments of Clayton et al. (1989) suggestan isotope difference of;1.3‰ at 575°C, or;10.4‰z O(8 oxygens).

4.3.3. Applications to mineral fractionations

In order to test our calibrations, we deconvoluted amphibolecompositions in terms of the additive component cummingto-nite and the exchanges considered above. Before showingresults for all samples, it is illustrative to first consider com-positions for endmember amphiboles (tremolite and glauco-phane) as well as for compositions that closely approximateintermediate amphiboles (hornblende and gedrite). Two typicalhornblende and gedrite compositions from Spear (1982) areNa

0.5Ca1.6 (Fe,Mg)3.6 Fe0.6

31 Al2.7 Si6.3 O22 (OH)2 and Na0.4

Ca0.1 (Fe,Mg)5.9 Fe0.031 Al2.4 Si6.6 O22 (OH)2, respectively (e.g.,

samples 77-56C and 77-57). The most important exchangesthat distinguish these two amphiboles are (Fe,Mg)Ca21 andAlFe21

31. A high ferric iron content in hornblende but not in theother amphiboles is supported by Mo¨ssbauer determinationsreported by Kimball (1981; actinolite and cummingtoniteFe31 5 0.0) and Spear (1982; hornblende Fe31/(Fe211Fe31);0.23 and gedrite Fe31/(Fe211Fe31) , 0.05).

The predicted relative fractionations among the amphibolescan be determined by multiplying the projected compositionsby the calibrated values of those exchanges as listed in Table 3.For tremolite, its cation composition is given by 1 cumming-tonite-2 MgCa21, and its isotope composition is given by

d18OTr 5 d18OCum 12~24 6 1.4!‰ z O

24 O p.f.u.

5 d18OCum 2 0.36 0.1‰.

That is,D(Cum-Tr);0.3 6 0.2‰ (62s) at 575°C because ofthe isotope effect of CaMg21 exchange. For glaucophane, itscomposition is given by 1 cummingtonite-2 MgCa21 12NaAl(CaMg)21, and its isotope composition is

d18OGlc 5 d18OCum 122~4 6 1.4! 1 2.0~8.86 1!‰ z O

24 O p.f.u.

5 d18OCum 1 0.46 0.15‰

or D(Glc-Cum);0.4 6 0.3‰. That is, glaucophane should parti-tion oxygen similarly to the Fe-Mg amphiboles, as inferred abovefrom previously published data and our new measurements.

Of more interest are the fractionations relative to intermedi-ate amphiboles like gedrite and hornblende. The idealizedisotope composition for gedrite is given by

d18OGed5 d18OCum 1

21.0~11.760.5! 1 1.0~8.861! 2 0.4~1062! 2 0.1~4.562!

24 O p.f.u.‰zO

or D(Cum-Ged); 0.3 6 0.1‰, and for hornblende yields

d18OHbl 5 d18OCum 1

21.4~11.760.5! 1 1.6~8.861! 2 0.3~1062! 2 0.6~4.562! 2 1.8~461.4)

24 O p.f.u.‰zO

which impliesD(Cum-Hbl) ; 0.6 6 0.3‰, D(Ged-Hbl);0.36 0.3, andD(Act-Hbl) ; 0.36 0.2‰. Predicted fractionationsfor the natural amphibole pairs (Fig. 3b) show a significantimprovement over bond-strength predictions. ObservedD(Ath-Ged) andD(Cum-Ged) is 0.26 0.3‰ compared to a predictedfractionation of;0.2–0.25‰, and the predictedD(Act-Hbl) of0.3‰ is similar to that determined from measured fraction-ations between biotite and the calcic amphiboles (which implyD(Act-Hbl) ; 0.2‰). The agreement between the predictedand measured fractionations of Fe-Mg amphiboles vs. horn-blende is also substantially improved, decreasing the predictivemismatch from 0.5 to 1.0‰ (Fig. 3a) to;0.3‰ (Fig. 3b). Thissmall remaining difference between predicted and measuredfractionation of Fe-Mg amphiboles vs. hornblende is encom-passed by 2s uncertainties. However, these fractionations areapparently not predicted as well as the relatively small frac-tionations between either coexisting Fe-Mg amphiboles or be-tween their calcic counterparts.

There are several possible reasons for this remaining dis-crepancy: first, systematic analytical error. As described above,there may be a systematic analytical error of as much as;0.2‰ for the calcic amphiboles. If so, this inaccuracy erad-icates much of the;0.3‰ discrepancy between measured andpredicted compositions (Fig. 3b). Fractionations between horn-blende and the Fe-Mg amphiboles are then reproduced to;0.2‰ (well within uncertainties), whereas the good agree-ment with retrievedD(Act-Hbl) is unaffected. Unfortunately,although we favor this explanation on crystallographic andanalytical grounds, such a small systematic error is nearlyimpossible to evaluate by comparison with data collected fromexternally-heated Ni reaction vessels.

Second, differences in fractionation between ortho- andclino-amphibole crystal structures. This possibility is supportedby the average measuredD(Ath-Cum) of ; 0.25‰ and bydifferences in measuredD(Cum-Ged) andD(Ath-Ged), whichimply D(Ath-Cum) of ;0.15‰. However, the large fraction-ation observed for the two clinoamphiboles, cummingtoniteand hornblende, is unexplained. Furthermore, in three of thefour samples containing both anthophyllite and cummingtonite,anthophyllite is significantly coarser grained, and the finer-grained cummingtonite may have been reset to lowerd18Ovalues during cooling by exchange with higherd18O phases(e.g., talc or feldspar). In the more equigranular samples con-taining gedrite, the typical variability in measured fraction-ations of60.22 0.3‰ (2s) implies that the smallD(Ath-Cum)is not statistically significant.

Third, errors in the values for the isotope effects of exchangecomponents. Because the main difference between gedrite andhornblende cation compositions is along the (Fe,Mg)Ca21 andFe31Al21 exchange vectors, this explanation implies that one

1955Oxygen isotopes in amphiboles

or both of these values are incorrect. The isotope effect of(Fe,Mg)Ca21 is well-studied in a variety of mineral systems,including the pyroxenes which directly constitute half the am-phibole structure; it is unlikely that the value for this exchangeis significantly in error, and propagation of likely uncertaintiesleads to differences in predicted fractionations of only;0.1‰.The calibration for Fe31Al21 is based on a study of calcicgarnets (Kohn and Valley, 1998b), and because the octahedralsites in garnet and amphibole are not directly analogous, it ispossible that the isotope effect of Fe31Al21 is underestimated.However, the value for Fe31Al21 would have to be;15‰ z Oto account for the discrepancy, making it even more importantthan tetrahedral exchanges. Such a large value for a simpleoctahedral substitution seems unlikely.

Fourth, errors in closure temperature. If coexisting amphib-oles have similar closure temperatures significantly lower than;575°C, then the measured fractionations between amphiboleswould be increased. However, this argument requires an am-phibole Tc # 400°C. Given higher likely closure temperatures,and the systematic fractionations observed between amphibolesand minerals like garnet with very slow diffusivities, such a lowclosure temperature for these amphiboles is unacceptable.

Fifth, nonlinearity in the fractionation of compositionallyintermediate minerals. Possibly, the isotope composition of anintermediate mineral is not approximated well by the linearcombination of endmember components. The systematic frac-tionations observed experimentally among compositionally re-lated tectosilicates (quartz-albite-anorthite; Clayton et al.,1989) as well as empirically for the orthosilicates (kyanite-staurolite-chloritoid; Kohn and Valley, 1998a), talc-actinolite-diopside (this study), and noncalcic amphiboles (this study)suggests that deviations from linearity for structurally similarsilicates are unlikely.

4.3.4. Implications for low-temperature minerals

The data and model described here for high-T metamorphicrocks have significant implications for isotope fractionations atlower-T. For example, oxygen isotope compositions of pedo-genic clays have been shown to track local waterd18O (Law-rence and Taylor, 1971, 1972), and clays are now being usedfor paleoclimatic research (e.g., Bird and Chivas, 1988, 1989;Stern et al., 1997). Clays show an enormous range of cationcomposition, which theoretically should translate into a widerange of fractionation factors at low T. Although the tempera-ture coefficients of cation exchanges are not yet known forextrapolating from metamorphic to diagenetic conditions, themagnitude of cation substitution effects can be roughly esti-mated assuming a linear 1/T2 dependence (T in kelvins). Sucha simple 1/T2 dependence has been found, for example, in somecarbonates in the range 10–450°C (O’Neil et al., 1969; Kimand O’Neil, 1997), although some minerals instead show a 1/Tdependence. Based on our calibrated isotope exchanges, typicalexchanges as celadonite (AlAlMg21Si21), Fe31Al21, and di-octahedral-trioctahedral (Al2Mg23) at 25°C could have isotopeeffects as large as 2.4‰, 4.2‰, and 8.9‰, respectively, inclays. Inasmuch as changes in climate have been ascribed to3–5‰ differences in clayd18O (e.g., Taylor, 1974; Stern et al.,1997), clearly cation compositions of clay minerals must be

determined prior to interpretation of isotope results, for exam-ple as was done by Stern et al. (1997).

5. CONCLUSIONS

This study is the first systematic analysis of the composi-tional dependence of isotope fractionations for a single silicategroup and demonstrates significant differences among the am-phiboles in oxygen isotope fractionations. There is a systematicenrichment in18O in the order hornblende,, gedrite, an-thophyllite ; cummingtonite. Semi-empirical methods (Rich-ter and Hoernes, 1988; Smyth and Clayton, 1988; Smyth, 1989;Zheng, 1993; Hoffbauer et al., 1994) predict well the relativepartitioning between endmembers like anthophyllite and cum-mingtonite, but reproduce only poorly the actual isotope parti-tioning of compositionally complex, intermediate members likegedrite and hornblende. In contrast, calibrated isotope ex-changes predict isotope fractionations more accurately in theamphibole solid solution series. If the isotope partitioning of anendmember mineral can be determined experimentally, empir-ically, or through the addition of mineralogically valid struc-tural modules, then the partitioning of intermediate composi-tions can be better estimated through the addition of isotopeexchange vectors.

Future empirical and experimental studies could further re-fine the influence of cation exchanges through the systematicanalysis of the micas, chlorites, clays or feldspars that areextremely common and show extensive solid solution andsolvus behavior. Finally, we note that few oxygen isotopestudies also report cation compositions of the materials ana-lyzed. The high analytical precision and spatial resolutionavailable through laser fluorination analysis makes the isotopeeffects of cation composition more readily resolvable and im-portant for petrologic interpretations, and points to a greaterneed for full chemical characterization of minerals.

Acknowledgments—Our most sincere thanks are due Dr. Frank S.Spear for providing many of the samples used in this study as well asunpublished amphibole compositions. We also thank Jane Selverstonefor sending a sample with coexisting actinolite and hornblende, MikeSpicuzza for help in the stable isotope lab, and James Farquhar andthree anonymous reviewers for their comments. MJK thanks Drs.Donald Miller and Frank S. Spear for providing use of rock grindingequipment and mineral separation facilities and materials at RPI. Thiswork was supported by NSF grants EAR 9316349 (MJK), EAR9105709 (JWV) and EAR 9304372 (JWV), DOE grant FG02-93ER14389 (JWV), and by a grant from the DOE Office of BasicEnergy Sciences (to F. J. Ryerson) at LLNL under the auspices ofcontract W-7405-Eng-48.

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