Oxygen isotope fractionation in quartz, albite, anorthite and calcite

0016-7037/89/$3.oLl+

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Oxygen isotope fractionation in quartz, albite, anorthite and calcite ROBERT N. CLAYTON,’ JULIAN R. GOLDSMITH’

and TOSHIKO K. MAYEDA’

‘Enrico Fermi Institute, Department of Chemistry and Department of the Geophysical Sciences, Universityof Chicago, Chicago, IL 60637, U.S.A. ‘Department of the Geophysical Sciences, University of Chicago, Chicago, IL 60637, U.S.A. ‘Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, U.S.A.

(Received August 23, 1988; accepted in revisedform December 30, 1988)

Abstract-Laboratory

measurements of equilibrium oxygen isotope fractionation in quartz, albite, anotthite, and calcite have been carried out by anhydrous exchange between silicates and calcite at temperatures of 600°C and above. Exchange in these systems is as rapid as exchange between silicates and water. Fractionation factors can be summarized

in the following equations: Aoc = 0.38 - 1067-’ AAw = -0.57.1067-’ AAnc = - 1.59. IO?‘-’ from which the silicate-pair fractionations are readily obtained. These results are compared with published theoretical estimates as well as data derived from hydrothermal experiments. Some significant differences are found. In particular, it is difficult to reconcile all of the hydrothermal data either with theotetical calculations or with the pratnt experimental data. The new exwriments orovide an intemallv consistent set of fractionation factors suitabk for isotopic thermometry and for test of disequilibrium in natural systems. INTRODUCIlON

dependence of the fractionation factor is complicated for aqueous systems as a consequence of the high vibmtional frequencies of the water molecule (CLAYTON, 1961) so that one is unable to take advantage of the usually simple tempemture dependence in analyzing the data. We have found that both of these limitations can be avoided by using calcium carbonate instead of water as the common exchange medium. Most common silicates undergo rapid oxygen isotope exchange with calcium carbonate at temperatures above 600°C and pressures of 15 kilobars (MAYEDA et al., 1986). In this paper, we present results for exchange of calcium carbonate with quartz, albite. and anorthite. These experiments provide new measurements of quartz-albite, quartz-anorthite, and albiteanorthite fractionations which can be compared with data from earlier hydrothermal experiments (CLAYTON et al., 1972; O’NEIL and TAYLOR, 1967; MATSUHISAet al., 1979) and with theoretical calculations (KIE~R, 1982). At sufficiently high temperatures’ the isotopic fractionation between a pair of anhydrous phases should be linear on a graph of Ina versus l/T’, and should pass through the origin (BIGELEISENand MAYER, 1947). “Sufficiently high” must be defined in terms of the ratio of highest vibrational frequency in the mineral, o, to the temperature T. For values of hm/ kT > 2, significant departures from linearity occur. In the silicatecarbonate systems, the largest frequency is the asymmetric stretch in calcite, at 1470 cm-‘. At the lowest temperatures in this study, 6OO”C, the value of hcw/kT for this frequency is 2.4, so that we are entering the non-linear regime at the lower temperatures. Based on the calculations of KIEFFER (1982), departures from linearity in silicate-calcite equilibria are likely to be less than 0.1 k at temperatures above 600°C. However, the equilibrium curves presented here should not be extrapolated linearly to lower temperatures, as

THERMODYNAMIC data necessary for understanding the oxygen isotope distributions among minerals in a rock consist of a set of equilibrium isotopic fractionation factors for all pairs of rock-forming minerals at all temperatures of interest (UREY, 1947). For example, the isotopic fractionation between quartz and albite is given by the equilibrium constant, a, for the isotope exchange reaction: THE FUNDAMENTAL

‘/tSi’“Or + ‘/sNaAlSis’*Os P

‘/zSi’*02 + l/sNaAlSir’60a,

( rso/ 160)Q cY= (‘R0/‘60)Ah * These quantities can be measured in the laboratory and can also be estimated theoretically by the methods of statistical mechanics (UREY, 1947). Existing laboratory calibrations are incomplete in that several important minerals have not yet been studied, temperature. ranges are limited, and some internal inconsistencies exist (MATSUHISAet al., 1979; MATTHEWSet al., 1983a). Existing theoretical calculations require approximations that limit their accuracy for purposes of geologic thermometry (KIEFFER, 1982). Although the desired data are mineral-pair fractionations, it is, in general, not practical to equilibrate a pair of silicate phases directly, since the fine grain size necessary to achieve adequate exchange rates makes clean physical separation of the products extremely difficult. Almost all of the published data on mineral fractionations have been determined by exchange of single minerals with water at pressures of 1 to 20 kilobars and combining two sets of such experiments for different minerals to get mineral-pair fractionations (MATTHEWS et al. 1983a). There are two fundamental limitations to this approach: (I) many minerals are unstable, or melt or dissolve excessively in the presence of water, and (2) the temperature 725

126

R. N. Clayton, J. R. Goldsmith and T. K. Mayeda

considerable errors will arise. This is especially true for the albite-caicite system, for which the temperature coefficient even changes sign on decreasing temperature (KIEFFER, 1982).

Since the oxygen isotopic fractionations between quartz and feldspar are small at the temperatures of igneous and metamorphic rocks, this mineral pair is not a good choice for isotopic thermometry. It is, however, an excellent choice for monitoring open system behavior, since the equilibrium constant is not very sensitive to temperature, and the rates of isotopic exchange with external fluids are much greater for feldspar than for quartz. Disturbance of the quartz-feldspar equilibrium as a measure of interaction tith external fluids has been extensively exploited by TAYLOR (e.g., TAYLOR, 1977). Clearly, in order to deal with disturbance of equilibrium, it is necessary to know the ~uilib~um const?nt. The literature is full of examples of quartz-alkali feldspar fractionations in the range of 1.0 to 2.0%0, which are all casually referred to as being “in the igneous range”. However, such a range of fractionation represents a temperature range of about 300”, and cannot be properly interpreted without a precise knowledge of the equilibrium fractionation as a function of temperature and of the chemical composition of the feldspar. EXPERIMENTAL METHYLS The principle of the experiment is simple and straightforward: to hold a dry, powdered mixture of a silicate and carbonate at the desired temperature and pressure until isotopic equilibrium is established, and then to analyze the product minerals separately. Proof of isotopic equilibrium is obtained by “bracketing” the final equilibrium distribution by choice of the isotopic com~tions of the starting materials in a pair of otherwise identical experiments. The weights of the carbonate and of the silicate components used in each experiment were chosen to contain the same number of oxygen atoms, and ranged from approximately 10 to 26 mg each. The mix was m&led under reagent-grade acetone in a small agate mortar three times to dryness. Each 20 to 50 mg charge was loaded into a capsule made from 3/32” gold tubing (runs QC6 to 18 and AC16 and I7 were encapsulated in platilium) and dried at I IO to 120°C before sealing. The capsules were weighed before and after each experiment to be sure that the charges had remained isolated from the surrounding solid high-pressure medium. Many of the samples were black or grey at the outer surface when the capsules were cut open at the conclusion of the experiment. This was probably caused by carbon produced from small amounts of residual organic matter derived from the acetone or by minor reduction of the carbonate. Small changes in PC of the carbonate were observed (column 9 in Tables 2,3,4), consistent with either of these m~hanisms. Higher temperatures that could have eliminated the carbon were not used in heating the samples prior to sealing because of the problem of partial dissociation of the carbonate and/ or oxygen exchange with the atmosphere. Heating the open capsules in a CO, atmosphere to avoid dissociation was impractical because of the problem of isotopic exchange with the gaseous CO,. The isotopic exchange reaction was carried out in piston-cylinder apparatus. NaCl pressure cells were used, except for runs AC16 and 17, in which the pressure medium was soft g!ass. Temperature was controlled and measured with chrome!-alume! thermocouples. One of the advantages of reacting components in a high-pressure device in which pressure is applied externally to the sample capsule is that the individual phases or grains are forced into intimate contact. Thus, intergranular diffusion is mechanically aided, aside from other possible accelerating factors induced by the pressure per se. All of the experiments were made at pressures well above those at which thermal and reactive dissociation of the carbonate would take place, and in the stability fields of the starting phases. SEM and X-my dif-

fraction m~surements on repren~ntative run products showed that no new phases were present. Experiments at 600°C and 15kbar are very close to the calcite-aragonite equilibrium curve (GOLDSMITH and NEWTON,1969). This should not affect the data, however, for no measurable isotopic Fractionation between calcite and aragonite has been observed at these temperatures and pressures (CLAYTON ef al., 1975).

The grain size of starting materials was mostly in the I to f0 pm range. The run products were sintered “rocks” of intimately intergrown carbonate and silicate with grain size also in the 1 to IO pm range. The products were crushed and ground, and then reacted with 100%phosphoric acid for two days at 25°C in the standard procedure for isotopic analysis of carbonates. The residual silicates were washed repeatedly with distilled water to remove acid and were then dried at 1lo’% before analysis. For those silicates such as anorthite and olivine, which dissolve partially during long acid treatment, it is necessary to take a separate aliquot of the run product and dissolve the calcite in 2N acetic acid for two hours at room temperature, using occasional ultrasonic agitation. The residual silicates were washed and dried. Oxygen was extracted from the silicates by reaction with BrFS (CLAYTONand MAYEDA,1963) and was isotopically analyzed as CO1 on a double-collecting mass spectrometer. Isotopic material balance between reactants and products was checked in each experiment to determine the quality of the analyses. Isotopic equilibrium was approached from opposite directions by appropriate choice of starting materials. The comp~itions ofstarting materials are given in Table I. The column headed “A? in Tables 2, 3 and 4 gives the initial “fractionation” between sili&e and carbonate for each run. In cases in which isotopic equilibrium was not achieved in a set of two or three experiments under the same conditions, the method of NORTHROPand CLAYTON (I 966) was used to extrapolate to the equilib~um fm~tionation and to calculate the percent exchange. An imp&ant assumption ofthis procedure is that the rates of chemical reaction must be the same in each member of the set. Although this assumption is readily satisfiedin hydrothermal experiments, it is not so obviously true in solid-solid exchange, in which particle size and surface effects may be important. Iin almost all of the data reported here, the extent of exchange exceeded 90%, so that errors in the extrapolation procedure cannot be very large. Another possible source of systematic error is in the use of synthetic minerals or metastable polymorphs as the starting materials. In such cases, the chemical driving force for phase change is much larger than the isotopic energy differences and may lead to a disequilibrium kinetic isotope effect. These questions are addressed in the discussion of the experimental data.

EXPERIMENTAL RESULTS 1. Quartz-calcite Exchange between quartz and calcite was measured in six sets of experiments from 600 to 1000°C. The experimental conditions and results are given in Table 2, and fractionations as a function of temperature are plotted in Fig. 1. With quartz as the starting material, TABLE 1

Calcite K2

2.66

Calcite JI.3

9.94

Calcite C

17.65

C&ire B

28.74 9.60 21.06

Albite Floras Creek

12.82

Albitc syntheac

16.90 12.04

127

Oxygen-isotope fractionation between silicates and calcite TABLE 2

data from the quartz runs will be used. The data can be fit very well with a straight line through the origin with a slope of 0.38 (Fig. I). 2. Albite-calcite

Qcl3

ICC0

I6

24

Q

-794

0.14

-0.17

QC I4

ICC0

16

24

Q

-0.34

0 19

-0.33

QCI

800

15

96

Q

-7 94

0.02

-0.211

-0.04

Qc2

800

15

96

Q

690

0.51

0.07

-0.33

Qc6

Boo

IS

96

Q

-0.34

0 35

0.03

-0.3Y

QCS

700

15

240

Q

-7.94

-0.10

0.06

QC4

700

I5

240

Q

6.90

079

.0.03

-0.25

QC5

700

15

240

Q

-0.34

0 32

0.13

-0.22

QC7

700

I5

240

Cl

1a.t5

0.51

-0.05

-0.30

QCII

700

15

240

CT

10.95

0.61

-0.02

-0.11

QCl7

600

I5

264

Q

690

2.31

0.26

-0.23

Qcl8

600

I5

264

Q

-0.34

0.29

0.09

-0 II

QCE

600

15

240

Cr

10.95

0.95

0.05

-0.03

600

I5

240

Cl

-7 49

0.42

-0.03

-0.15

lcc0ln[(l

+

&

0 19

%.a

0 32

94.0

0 I’)

-006

QCl2

(1)&-lmlidvDhJed

YY.3

3. Anorthite-calcite 1000

0 5h

72.1

li 53

97 I

0 65

(3) MB. - mslenal balance = Upducrs) - S’v,

/(I +A,.

- &Ow~ams).

- S”C,.

(5) loo/m = percent cxdungc. (6) A = cruqda~cd

Exchange between anorthite and calcite was measured in three sets ofexperiments from 600 to 800°C. The experimental conditions and results are given in Table 4, and fractionations as a function of temperature are plotted in Fig. 3. The rate of exchange was even faster than that of albite. A best-fit straight line, constrained to go through the origin, has a slope of -I .59. DISCUSSION

The results of the present experiments can be compared with (a) the results of previous hydrothermal experiments, and (b) theoretical calculations. It is found that some significant discrepancies exist, and an attempt at their solution is presented.

(2) A( = fmll valw. (4) A’*

Exchange between albite and calcite was measured in five sets of experiments from 600 to 800% The experimental conditions and results are given in Table 3, and fractionations as a function of temperature are plotted in Fig. 2. Exchange was more tapid with albite than with quartz, with complete equilibration being achieved at 700 and 800°C in three days. Two different albite starting materials were used: one, a natural albite from Floras Creek, Oregon; the other, a synthetic albite. The data for the two starting materials agree within their analytical uncertainties and are all included in the following discussion. A best-fit straight line, constrained to go through the origin, has a slope of -0.57.

equilibrium frxuOnancm.

1. Quartz-calcite the percentage of exchange ranged from 72 at 600°C to 99 at IOOO”C. Experiments in which cristobalite was recrystallized to quartz at 600 and 700°C showed almost complete exchange. However, the fractionations measured in the cristobalite runs appear to be systematically a little larger than in the quartz runs at the same temperature, suggesting that a small nob-equilibrium effect may occur in the conversion of cristobalite to quartz. In the following discussion only the

A hydrothermal experimental value for the quartzcalcite fractionation can be determined from the quartz-water data of CLAYTON et al. (1972) and the calcite-water data of O’NEIL et al. (1969) at 500°C. This value, shown by the square in Fig. I, lies 0.2960above the extrapolation of the present data. As will be seen below, this near agreement is probably fortuitous. Results of two theoretical calculations for quartzcalcite fractionations are shown in Fig. 1 (SHIRO and SAKAI, 1972;

TABLE 3 l

l

Cuorlz -coIcde

t (hr) Mvrnl

A,

A,

M.B

A”C

-0.36

+0.22

-0.44

-0.43

+O.OY

-0.54

Run *

TPCI

P(kbar)

AbC3

803

13

73

FC

IO08

AbC4

800

I3

72

FC

2 85

AKII

8M

I3

72

Syn.

6.85

-0.55

+0.24

.O.M

AbC12

800

I3

74

Syll.

-0.74

-0.62

+0.07

+0.04

0

Cr~stobohte -coIclte

AK2

700

II

73

FC

-0.65

+0.27

-0.22

0

Hydrothermal

AbCI5

700

II

76

FC

I008

-0.65

0.00

-0.22

1

FIG. I. Isotopic fractionation between quartz and calcite. Heavy line is a linear least-squares fit to the experimental data, constrained to pass through the origin. Two theoretical calculations are shown for comparison (SHIROand SAKAI, 1972; KIEFFER, 1982). The open square at 500°C is based on hydrothermal experiments of O’NEIL n al. (I 969) and CLAYTON ef al. (I 972).

2 85

AbC6

700

I6

71

Syn.

14.10

-0.55

l0.13

-0.33

AK7

700

I5

71

Syn.

-0.74

-0.57

-0.07

-0.13

AbClO

7M

I5

75

Syn.

14.10

-0.48

+0.34

-0.14

AbCB

6al

I5

98

Syn.

14.10

+0.24

-0.15

AK9

600

I5

96

Syn.

.0.74

io.05

.o. IO

*Symbols 8%m Table 2.

+,.I, -0.64

-lWm

A

YY 0

-0 46

99. I

-0 62

100

-0 65

99 6

-0 57

88 2

.U63

728

R. N. Clayton, J. R. Goldsmith and T. K. Mayeda

YO

Temperolure "C 7TO .600 -5oc ,

KIEFFER ( 1982) by 3. 1O.-’due to a rounding error (WEFFER, personal communication). In addition, the partition function ratios for a-quartz of KAWABE (1979) are seriously in error due lo some kind of miscalculation. Recalculation using his vibrational frequencies yielded values of In(Q’/Q), which are larger by 1.75 to 1.80 - IO-’ at all temperatures. The apparent large isotopic differences between a- and /l-quartz in KAWABE’S calculations result fro mthis error. Since the a-8 transition occurs at 960°C at 15 kilobars (COHENand KLEMENT, 1967). all but the lOOO”C run in the present experiments were in the field of aquartz. We see no evidence for an isotopic discontinuity corresponding to the a-/3 transition.

~0.5

. Nolurol olblle 0 Synthellc olblle

j

I

2. Albite-calcite _,DU_.

.._

0

0.5

I

I

I.5

,,kO, -2

2.0

FIG. 2. Isotopic fractionation between albite and calcite. Heavy line is a linear least-squareslit lo the experimental data, constrained lo pass through the origin. The theoretical calculation of KIEFFER (1982) is shown for comparison. The open square at 500°C is based on hydrothermal experiments of O’NEIL and TAYLOR (1967). O’NFII. et al. (1969)and MATSUHISA ef al. (1979).

KIEFFER, 1982). Neither is a good match to the experimental data. There are substantial differences among the various Calculations for quartz. A calculation based on the vibrational frequencies of KAWABE (1979). combined with the calcite data of KIEFFER(1982), gives the best fit to the experimental data (to be discussed further below). It is very important in comparing calculated partition function ratios with experimental fractionation at high temperatures to verify that the calculated fractionations go exactly to zero in the high temperature limit. In cases in which all isotopic frequency shifts are calculated froni a force-field model, the isotopic partition function ratios do not, in general, go to zero, but extrapolate to a value on the order of +3 - lO-4 in In(Q’/Q). Since these erron are of the same magnitude as the mineral-pair fractionation at 600 to 800”, they must be removed in order to compare theory with experiment. This is best done by using a product rule to calculate at least one of the frequency shifts (BECKER, 1971; KIEFFER, 1982). It was found necessary lo decrease the values of SHIRO and SAKAI (1972) for aquartz by 3. IO-’ due to this effect, and to increase the values of

The present experimental data for albite-calcite are in serious disagreement with the hydrothermal experiments at 500°C. shown by the square in Fig. 2 (O’NEIL and TAYLOR, 1967: MATSIJHISA er al., 1979: O’NEIL ef al., 1969). This temperature was chosen as the highest temperature at which reliable calcite-water data are available, and also a temperature at which the albite-water data of O’NEIL and TAYLOR ( 1967) and MATSUHISA et al. ( 1979) are in excellent agreement with one another. The disagreement between the hydrothermal experiments and the direct albite-calcite exchange will be discussed in the sections “Quartz-albite” and “Albiteanorthite” below. The only published theoretical calculations for albite are those of KIEFFER(I 982). The agreement of her calculation with the present experiment is excellent, which suggests that the small disagreement seen in the quartz-calcite system results from the calculated quartz partition function ratio being loo small. 3. Anorlhile-calcite An experimental point for anorthite-calcite hydrothermal exchange at 500°C can be obtained from the data of O’NEIL

Temperature

800 700

I

1

“C

5oc

6tKl

I

-.--l-

Anorlhlte Colclle

!-

1

TABLE 4 .

Run*

TO3

P(kbu)

t(hr)

Mum-d

AC16

SO0

II

72

AC17

800

II

x2

SY”.

AC18

800

II

72

SYn

A,

A,

MR

A’V

lcO/“l

1

SYn

AC9

700

9

72

SW

206

-172

-0 02

0 In

AC10

700

9

72

Syn

-533

.I 26

-0 OS

-0 20

-25i IN,

ACII

700

9

73

SYn

206

AC12

700

9

72

SYn

-553

AC14

600

12

IY2

SYn

AC15

600

11

IS0

SYn

206

-lb0

+Ulb

-0 08

-1 38

+0.19

-0 II

-207

-5s3 -244

r” 36 +004

“II -0 “4

9s

I ,v

.’ ..

.;

1..

__..L

05

I

I5 ,06

,‘!

__J 20

FIG. 3. Isotopic fractionation between anorthite and calcite. Heavy line is a linear least-squaresfit 10 the experimental data, constrained 10 pass through the origin. The theoretical calculation of KIEFT~R ( 1982) is shown for comparison. The open square at 500°C is based on hydrothermal experiments of O’NEII. and TAYLOR ( 1967). O’NEIL (‘1 ul. ( 1969) and MATSUHISA er al. ( 1979).

Oxygen-isotope fractionation between silicates and calcite

and TAYLOR (1967), MATSUHISAet al. (1979), and O’NEIL et al. (1969), and is shown by the square in Fig 3. As was the case for the albite-calcite system, this data point lies far above the extrapolation of the present experimental results. The agreement of the anorthite-calcite results with the calculations of KIEFFER (1982) is excellent. SILICATE PAIRS I. Albite-anorthite

The albite-calcite and anorthite-calcite experimental dam can be combined to give an albite-anorthite fractionation, shown as a Iunction of temperature in Fig. 4. Four separate determinations of this fractionation are Seen to be in very good agreement: the present work (heavy line), the hydrothermal experiments of MATSUHISAet al. (1979), the theoretical calculations of KIEFFER (1982), and the empirical relationship given by BOTT~NGAand JAVOY (1973), which is based on the hydrothermal experiments of O’NEIL and TAYLOR (1967). The results of the various experiments are expressed in the following equations: AA,._*”= 1.02 - 106T-2

(this work)

AA,_,” = 1.09 - 106Te2

(MATSUHISAet al., 1979)

A,,,._,,”= 0.76 - 106Te2

@‘NEIL and TAYLOR, 1967)

+ 0.41. The two sets of hydrothermal experiments were carried out under quite different conditions; the O’NEIL and TAYLOR ( 1967) experiments involving cation exchange at one kilobar in water-dominated charges, and the MAIWHISA et al. (1979) experiments involving exchange at 7 to 12 kilobars with small quantities of pure water. The agreement among three quite different experiments, and their agreement with theoretical calculations, supports the conclusion that the equilibrium

AlbIle -Amnth~ie

3 d 0.5

I /

OO

/

/

/

/

/

//

/

I

0.5

I

1.0 106T-2

I

1.5

2.0

FIG. 4. Isotopic fractionation between albite and anorthite. Heavy line is derived by combination of albite-calcite and anorthite-calcite results. Agreement is good among alI four estimates: I(IE!=FER (1982) theoretical calculation; MATWHISAet al. (1979) hydrothermal experiments; BOTTINGA and JAVOY(1973), based on the hydrothermal experiments of O'NEIL and TAYLOR(1967).

129

constants for fractionation among albite-anorthite-calcite and albite-anorthite-water are well established in the range 600 to 8OO“C. The source of the discrepancies seen in Figs. 2 and 3 involving hydrothermal data on albite-calcite and anorthitecalcite fractionations must therefore lie in the hydrothermal calcite-water value at 500°C. This difference is well beyond the stated experimental uncertainties in the data and implies some systematic error in the calcite-water result at 500°C. It is not obvious how such a large error could arise. 2. Quartz-albite The quartz-calcite and albite-calcite experimental data can be combined to give a quartz-albite fractionation, shown as a function of temperature in Fig. 5. The results are virtually identical with the relationship given by B~ITINGA and JAVOY: AAh_,&” = 0.95 * 10T2

(this work)

AAbAn= 0.97. 106TV2. (BOTTINGAand JAVOY, 1973) The Bottinga-Javoy equation was based on hydrothermal experiments of CLAYTON et al. (1972) (quartz-water) and O’NEIL and TAYLOR (1967) @bite-water). The data of CLAYTONet al. (1972) fell into two groups: (1) runs in which the same fractionation factor was reached from opposite directions, implying attainment of isotopic equilibrium, and (2) runs in which only partial equilibration occurred. The latter gave extrapolated equilibrium fmctionations which were systematically larger than the former. The data from partial equilibration experiments were used to derive the relationship presented by BOTTINGA and JAVOY(1973). If the agreement between the present results and the BOTTINGAJAVOY (1973) equation is taken to mean that both are correct, then the equilibrated experiments for quartz-water of CLAYTONet al. (1972) as well as both equilibrated and partially exchanged experiments of MATSUHISAet al. (1979) must produce fractionations that are systematically low. As in the case of calcite-water, the discrepancies are far greater than the stated analytical uncertainties. From the present data on quartz-albite fractionation and the data of MATSUHISA et al. ( 1979) for albite-water, values expected for quartzwater equilibrium can be calculated. These are shown in Table 5, and are compared with various measured values. It is seen that most of the data from hydrothermal exchange experiments are 0.4 to 0.9% lower than the expected values. The data for quartz synthesized from silica gel and for partial exchange between quartz and water give satisfactory agreement with the expected values at 500°C. It is this agreement which leads to the agreement of the Bottinga-Javoy equation and the data from the present experiments. It should be noted that the discrepancies among the different experimental methods do not arise from uncertainty in the C02-Hz0 fractionation factor. In the experiments of MATSUHISA et al. (1979), all water analyses were done by fluorination, and all three mineral systems were studied in the same time period with the same analytical techniques. The theoretical calculation of quartz-albite fmctionations shown in Fig. 5 (KJEEEER,1982) gives values lower than the present experiments by 0.2 to 0.4%. This is consistent with the conclusion presented earlier that Kieffer’s quartz partition function ratios are a little too small.

730

R. N. Clayton, J. R. Goldsmith and T. K. Mayeda TABLE

Temperature “C 800 700 600 500

5

I

I

I

I

Quartz-Anorthite

QJarlz-dbitc

1.59

1.25

l.Oa

ThlS work

AM.-wm

1.52

0.86

0.55

Marsuhsa ct al. (1979)

Qwmwam

3.11

2.11

I.55

Fm

2.24

1.33

0.69

Clayton et al. c1972)

Pmidcxchm~cQ-W

2.36

I23

1.05

Matsuhisa et al. (1979)

cdobdia

2.20

I.62

1.14

Matsllhlsa et al. (1979)

Fipilibntcd

r&w

QW

Silica gel gw

3 08

_

Partial exchange @W

3.25

1.6

2.5-

QAbandAbW

c s Q 2.0-

Clayton et al. (1972) _

1.5 -

claylo”crd.(1972,

/

/

/

/

I

I

0

0.5

3. Quartz-anorthite

Ao_A”= 1.97. 106Tw2. The constant in the corresponding Bottinga-Javoy equation is 2.02. All of the discussion in the previous section on quartzalbite applies verbatim to quartz-anorthite. As was pointed out in the presentation of data for mineral pairs in the previous section, there are some large discrepancies between the results of the present experiments and those of previously described hydrothermal experiments. No systematic errors of such magnitude are recognizable internally within either data set. Theoretical calculations are probably not sufficiently accurate to be used to recognize which of the sets of experimental results is more reliable.

1000

Temperature“C 800 700 600

500

Quartz -AlbIle

/

/

/

I

I 1’

I I

00'

1.5

2.0

IO6 T-*

The quartz-calcite and anorthite-calcite experimental data can be combined to give a quartz-anorthite fractionation, shown as a function of temperature in Fig. 6. The result can be written as:

/

1.0

0.5

I

1.0 106T-2

I

1.5

2.0

FIG. 5. Isotopic fractionation between quartz and albite. Heavy line is derived by combination of quartz-calcite and albite-calcite results. Agreement is good with line of BoTTINGA and JAVOY (1973), based on the hydrothermal experiments of O’NEIL and TAYLOR (1967) and CLAYTON et al. (1972). Agreement is poor with the calculated line of KIEF’FER (1982) and the results of hydrothermal exchange by MATSUHISA etal. (1979).

FIG. 6. Isotopic fractionation ments for Fig. 5 apply.

between quartz and anorthite.

Com-

It may be instructive to compare the available data on hydrothermal isotopic equilibration at 500°C (Table 6). The data for albite-water and anorthite-water, obtained in two different laboratories, are in excellent agreement. Furthermore, the albite-anorthite fractionation derived from these measurements is 1.76, which is in agreement with the value of 1.77 determined from the silicate-calcite exchange experiments and with the calculated value of 1.9 (KIEFFER, 1982). It may be safe to conclude that the albite-anorthite fractionation at 500°C is well established. The quartz-albite fractionation determined from equilibration of quartz and water (CLAYTON et al., 1972; MATSUHISA et al., 1979) is 0.81, in contrast to the value of 1.59 determined by extrapolation of the silicate-calcite exchange data. The larger value is clearly preferred if natural igneous quartz-feldspar pairs are near equilibrium. We tentatively conclude, therefore, that the quartz-water equilibration experiments give systematically low values for reasons as yet unknown. The quartz-water fmctionations measured on quartz synthesized from silica gel (CLAYTON et al., 1972; MATTHEWS and BECKINSALE, 1979) lead to quartz-albite fractionations of 1S7, in excellent agreement with the silicatecalcite experiments, but these observations should not be taken as a general endorsement of mineral synthesis procedures for measurement of equilibrium isotope effects. The albite-calcite fractionation determined using the O’NEIL et al. (1969) value for calcite-water is -0.02, in contrast to the value of -0.95 determined by extrapolation of the direct albite-calcite exchange experiments and the value of -0.7 calculated by KIEFFER (1982). A value of 2.43 for the calcite-water fractionation at 500°C is required to reconcile the discrepancy. No calcite-water exchange experiments have given values this high. It may be that the solubility of calcite was excessive in the NH&l solutions used by O’NEIL et al. (1969). However, the experiments of CLAYTON et al. (1975) were done with only calcite and distilled water, and yielded lower, not higher, fractionation factors. The reason for the discrepancy remains a mystery. In the remainder of this discussion, it will be assumed that

Oxygen-isotopefractionationbetweensilicatesand calcite

A

System

Albite-water

Ancnhiawarcr

ltcfcnncc

1.51 f 0.21

O’Ncil and Taylor (1967)

1.52 k 0.14

Matsuhisa er al. (1979)

1.4Of0.17

Matthews et al. (1983b)

-0.28 f 0.10

O’Neil md Taylor (1967)

-0.28 f 0.08

Matsuhisaet al. (1979)

731

section above, it was shown that the quartz-water and calcitewater experimental results are in disagreement with the results of sikate-calcite exchange. An even Iargerdiscmpancy is seen if the experimental silicate-water equilibria are compared with the fmctionations calculated from statistical mechanics.

TABLE 7

MT-2

PC

cab&

M-1’

QJaW2

Albite

Anuthite

QlWz-water

2.26 f 0.06

CllyW

qdlibratcd

2.31 f 0.07

Mnlsuhisa et al. (1979) 0.5

1141

5.79

5.99

5.97

5.48

3.08 k 0.26

ClayIon et al. (1972)

0.6

1018

6.92

7.15

7.14

6.56

5.91

3.02 cxwpolatcd

Matthews and Becidnsalc (1979)

0.7

922

8.05

8.3 1

8.31

7.64

6.88 7.84

ct al. (1972)

2.01 inwpolatal

Clayton (l%l)

1.50fO.12

O’Ncil n al. (1969)

1.19fO.12

claymnnal.(l975)

the present set of experiments gives the best available estimate of the oxygen isotope fractionation factors among quartz, albite, anorthite, and calcite at temperatures of 600 to 800°C. Extrapolation to temperatures outside the experimental range is best accomplished using theoretical calculations as extrap olation formulas. Since the available calculations do not exactly match the experimental results, it is necessary to apply some correction procedures to bring them into agreement. The simplest procedure is to apply a multiplicative factor to the calculated values. This preserves the proper high-temperature behavior and the curvature of the plots of ln(Q’/Q) versus Te2 at lower temperatures. Partition function ratios for the four minerals have been determined as follows: (1) Quartz-Recalculated using KAWABE’S (1979) Ikequencies and a multiplicative factor of 1.008; (2) Albite-KIEFFER’s (1982) results and a factor of 0.992; (3) Anorthite-KlEFFER’S (1982) results unchanged, (4) Calcite-KlEFFER’s (1982) results unchanged. It is seen that corrections of less than 1% are sufficient to bring calculations and experiment into agreement. The partition function ratios (as 1000 ln(Q’/Q)) are listed in Table 7. The isotopic fractionation between any pair of minerals at a given temperature is obtained (as 1000 lnar) as the algebraic difference between entries in the table. MINERAL-WATERFRACX’IONATIONS In the previous sections, it was shown that the silicatecalcite exchange experiments permit the derivation of an internally consistent set of isotopic fractionation factors over a range of several hundred degrees. Furthermore, the experimental values are in close agreement with statistical mechanical calculations of the fractionation factors, so that ap plication of very modest “correction factors” to the latter permits construction of a table of partition function ratios which may be used to estimate fractionation factors beyond the temperature ranges covered experimentally. For broadest geological applicability, this table should include water as well as the solid minerals. Attempts to incorporate water into the scheme reveal serious difficulties. In the “Discussion”

4.94

0.8

845

9.17

9.47

9.47

8.70

0.9

781

10.28

10.62

10.61

9.76

8.79

1.0

727

11.38

11.76

11.75

10.80

9.74

1.1

680

12.48

12.89

12.89

11.85

10.69

1.2

640

13.57

14.03

14.01

12.89

11.63

1.3

604

14.65

15.16

15.13

13.93

12.56

1.4

572

15.72

16.26

16.24

14.95

13.49

1.5

543

16.78

17.34

17.35

15.97

14.42

1.6

518

17.85

18.44

18.45

16.99

15.34

1.7

494

18.90

19.54

19.54

18.00

16.25

1.8

472

19.94

20.63

20.63

19.01

17.16

1.9

452

20.99

21.73

21.72

20.02

18.07

2.0

434

22.01

22.81

22.76

21.01

18.97

2.1

417

23.04

23.88

23.86

22.00

19.88

2.2

401

24.05

25.02

24.91

22.98

20.76

2.3

386

25.07

26.06

25.96

23.96

21.66

2.4

372

26.07

27.10

27.02

24.94

22.54

2.5

359

27.08

28.14

28.06

25.91

23.43

2.6

347

28.07

29.18

29.11

26.88

24.30

2.7

336

29.06

30.22

30.13

27.84

25.18

2.8

325

30.04

31.26

31.16

28.79

26.04

2.9

314

31.01

32.29

32.18

29.74

26.91

3.0

304

31.99

33.32

33.20

30.69

27.77

3.1

295

32.95

34.36

34.2 1

31.63

28.63

3.2

286

33.92

35.36

35.21

32.57

29.48

3.3

277

34.87

36.36

36.22

33.50

30.33

3.4

269

35.82

37.36

37.21

34.43

31.18

3.5

262

36.77

38.36

38.20

35.35

32.02

3.6

254

37.72

39.36

39.19

36.28

32.86

3.7

247

38.65

40.35

40.17

37.20

33.70

3.8

240

39.58

41.34

41.14

38.10

34.53

3.9

233

40.50

42.32

42.12

39.01

35.36

4.0

227

41.43

43.31

43.08

39.92

36.18

4.2

215

43.26

45.24

45.01

41.71

37.81

4.4

204

45.07

47.17

46.91

43.49

39.44

4.6

193

46.86

49.07

48.79

45.25

41.05

4.8

183

48.63

50.96

50.66

47.01

42.66

5.0

174

50.39

52.84

52.51

48.74

44.24

5.5

153

54.73

57.46

57.07

53.03

48.16

6.0

135

58.96

61.97

61.53

57.22

52.00

6.5

119

63.11

66.40

65.90

61.33

55.77

7.0

105

67.17

70.76

70.20

65.38

59.48

7.5

92

71.15

75.05

74.41

69.34

63.13

8.0

81

75.06

79.26

78.54

73.25

66.7 1

8.5

70

78.90

83.39

82.60

77.08

70.23

9.0

60

82.68

87.44

86.59

80.86

73.71

9.5

51

86.40

91.44

90.53

84.58

77.14

10.0

43

89.99

95.38

94.33

88.18

80.46

10.5

36

93.57

99.26

98.14

91.79

83.78

11.0

29

97.16

103.07

101.95

95.39

87.10

11.25

25

98.93

104.96

103.81

97.17

88.74

*Quam-1 ulctiti se text fe dcuils.

from frequencies of Kawabc (1978); Qupm-2

trOm Kkffcr

(1982).

R. N. Clayton, J. R. Goldsmith

732

A comparison of theoretical and experimental fmctionations has been made for the albite-water system, i.e., one which was considered weII behaved on the basis of agreement between laboratories and its “correct” determination of the albite-anorthite fractionation. The “theoretical” curve shown in Fig. 7 was determined by taking the albite partition function ratios in Table 7 (derived from the calculations of KIEFFER, 1982) and the water partition function ratios given by MTTINGA and JAVOY (1973). The theoretical curve has the expected crossover and minimum, and extrapolates smoothly to zero at infinite temperature. The experimental data of O’NEIL and TAYLOR (1967) and MATSUHISA et al. (1979). shown as individual measurements, agree well with one another, except at the highest temperature, but are in gross disagreement with the calculated curve. The same systematic dilTerences are seen for all of the silicate-water systems studied: the experimental fractionations are 1.5 to 2960more positive than the theoretical calculations. This phenomenon was first noted by BOTTINGA (1968) for the calcite-water system: the same calculations which give good agreement with experiment at 25°C give poor agreement at 500°C. He suggested that the disagreement might result from uncertainty in the calculation due to the non-ideality of water vapor under the experimental conditions. The statistical-mechanical calculations Of BOlTINGA (1968) and BOTTINGA and JAVOY (I 973) are based on vibrational frequencies of water vapor at room temperature. From these calculated values of partition function ratios, it is possible to estimate the ratios for liquid water by using experimentally determined liquid-vapor fractionations (FRIEDMAN and O’NEIL, 1977). As temperatures are increased from room temperature, these liquid-vapor fractionations necessarily approach zero as the critical temperature is approached. It has generally been assumed that the partition function ratios

Temperature 800 700

1

4 3

-31 0

l

I

“C

600

500

I

CONCLUSIONS

O’Neil and Taylor 119671

,‘P

I 1.0

I 1.5

are well approximated by the ideal-gas values above the critical temperature. However, the laboratory hydrothermal equilibration experiments have been carried out under pressures in the range of 1 to 10 kilobars, corresponding to water densities in the range 0.23 to 1.10 g cmm3 (KENNEDY and HOLSER, 1966). At these high densities, intermolecular interactions must be significant, so that the ideal-gas approximation may be inadequate. The effects of hydrogen bonding between water molecules are complicated, with some vibrational frequencies being increased and others decreased with respect to those in isolated molecules (AYERS and PULLIN, 1976). It appears likely that no single set of spectroscopic parameters (vibrational frequencies and isotopic frequency shifts) will suffice to calculate the isotopic partition function ratios for water over a wide range of temperatures and pressures. The oxygen isotopic fractionation between natural hydrothermal minerals and water is often used to estimate the isotopic composition of hydrothermal fluids which are no longer present, in order to determine their provenance or to estimate water-rock ratios (see review by CRISS and TAYLOR, 1986). Due to the uncertainties discussed above, care must be taken in the selection of mineral-water fractionation factors for this purpose. In the temperature range 400 to 800°C. the experimental albite-water data of O’NEIL and TAYLOR (1967) and of MATSUH~SA et al. ( 1979) may provide the best available estimates of the partition function ratios for water at pressures of one kilobar or more. At low temperatures (
I

0 Matsuhtsa et al II9791

I 0.5

and T. K. Mayeda

I 2.0

I 2.5

I

IO6 T-’

FIG. 7. Isotopic fractionation between albite and water. The calculated curve is based on the albite partition function ratios of KlEFFXR (1982) (as modified and tabulated in Table 7) and the water mtition function ratios of BOTrINGA and JAVOY (1973). The dashed curve labelled “BJ” is the BOIIINGA and JAVOY fit to the data of O’NEIL and TAYLOR (19671 in the interval 500 to 800°C. The dashdot curve labelled “hiGc” is a two-segment fit to the data of MATSUHISA a al. (1979). The experimental data are consistently more positive than the calculated curve by I.5 to 2.0%. The same is true for all measured mineral-water systems.The discrepancy may lie in the non-ideality of water at the temperatures and pressuresof the experiments.

Oxygen isotopic exchange between silicates (quartz, albite, anorthite) and calcite at pressures of 10 to I5 kilobars is as rapid as exchange between these silicates and water at comparable temperatures and pressures. This makes it possible to determine equilibrium isotopic fractionation factors in anhydrous silicate-calcite systems at temperatures from 600°C upward. By combining the results of these experiments for different silicates, the equilibrium fractionations between silicate pairs can be deduced. These experiments have several advantages over conventional hydrothermal exchange: ( I ) “quench products” from aqueous solution are avoided; (2) melting or excess solubility of minerals is avoided; (3) the fiactionations have temperature dependences which are readily calculable from statistical thermodynamic theory, so that extrapolation beyond the experimental temperature range is possible. A set of isotopic partition function ratios for quartz, albite, anorthite, and calcite has been tabulated for temperatures from 25 to 1141°C. These ratios can be used to estimate mineral-mineral fractionation factors for any pair of the tabulated phases. The factors so calculated are in agreement with all of the experimental results reported here, and in agreement, with small modifications, with calculated factors

Oxygen-isotope fractionation between silicates and calcite

of KIEFFER (1982). There are significant discrepancies, however, with some of the fractionation factors derived from previously published hydrothermal experiments. The reasons for the discrepancies are unknown. There is generally good agreement with the silicate-pair fractionations presented by J~OITINGAand JAVOY (1973) based on independent sets of experiments. Theoretical estimates of the equilibrium isotopic fractionations between minerals and water can be made by combining the partition function ratios for minerals with the calculated values for water (B~TTINGA and JAVOY, 1973). The calculated fiactionations am systematically 1.5 to 2.0960less positive than experimental values for all systems studied. There are three possible explanations: (I) all hydrothermal experiments give systematically incorrect results; (2) all calculations for solid phases give partition function ratios which are too small by a large factor; or (3) the calculated partition function ratios for water are too large by a large factor ( - 15%). By virtue of our ignorance of the effects of pressure (and consequent hydrogen bonding) on water, it is easiest to suggest that the calculation for water under supercritical conditions is the source of error. Direct spectroscopic studies of water at high pressures and temperatures should reveal the extent of such effects. Uncertainties in mineral-water fractionation factors make it more difficult than was previously believed to estimate the oxygen isotopic compositions of hydrothermal fluids in ore deposits and other natural systems in which the fluids are no longer present. The rates of exchange in silicate-carbonate systems at high pressures are surprisingly large. Experiments are under way in an attempt to determine the exchange mechanism. These experiments include the measurement of the pressure dependence ofexchange rates and the rates ofexchange between silicates and carbon dioxide gas at high pressures (CHACKO ef al., 1988). These experiments have shown that isotopic exchange between potassium feldspar and carbon dioxide proceeds to 64% of completion at 600°C and IO kilobars in 24 hours with no change in grain size or morphology of the feldspar observable by SEM. There was also no change in the degree of Al/Si ordering in the microline. It is clearly of great importance to determine the exchange rates and mechanisms for application to natural carbonatesilicate assemblages. research was supported by NSF grants EAR 8316812 (Clayton), EAR 8616257 (Clayton), and EAR 8507819 (Goldsmith). We thank Susan W. Kieffer for tabulations of her calculated isotopic partition function ratios. We thank Hitoshi Chiba for critical comments.

Acknowledgemenfs-This

Editorial

handling: J. R. O’Neil

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isolated water species-Ill. Infrared spectra and assignments of ‘“0 containing monomer and dimer water species in argon matrices. Specwochim. Acta 32A, 1689-1693. BECKERR. H. (197 I) Ph.D. thesis. Univ. Chicago. BIGELEISEN J. and MAYERM. G. (1947) Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 13.26 I 267. B~TTINGA Y. (1968) Calculation of fractionation factors for carbon

733

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J. R., KAREL K. J., MAYEDAT. K. and NEWTOKR. C. (1975) Limits on the effect of pressure on isotopic fractionations. Geochim. Cosmochim. Acto 39, I l97- 1201. COHENL. H. and KLEMENTW. (1967) High-low quartz inversion: Determination to 35 kilobats. J. Geoohvs. Res. 72.4245-425 I. CRISP R. E. and TAYLORH. P. JR. (1986) Meteor&hydrothermal systems. In Stable Isotopes in High Temperawe Geological Processes(eds. J. W. VALLEY,H. P. TAYLOR,JR. and J. R. O'NEIL), pp. 373-324. Mineralogical Society of America. FRIEDMANI. and O’NEIL J. R. (1977) Compilation of stable isotope fractionation factors of geochemical interest. In Dafa ofGeochemisfry (ed. M. FLEWHER), U.S. Geological Survey Prof. Paper 440KK. U.S. Government Printing Ollice, Washington, DC. GOLDSMITH1. R. and NEWTONR. C. (1969) P-T-X relations in the system CaCOr-MgCO, at high temperatures and pressures. Amer. J. Sci. 26lA, 160- 190. KAWABE1. (1979) Lattice dynamical aspect of oxygen isotope partition function ratio for alpha quartz. Geochem. J. 13, 57-67. KENNEDY G. C. and HOLLERW. T. (1966) Pressure-volume-temperature and phase relations of water and carbon dioxide. In Handbook of Physical Constants. pp. 37 1-384. Geol. Sot. Amer. Mem. 97, New York. KIEFFER S. W. (1982) Thermodynamics and lattice vibrations of minerals: 5. Applications to phase equilibria, isotopic fractionation, and high-pressure thermodynamic properties. Rev. Geophys. Space Phys. 20, 827-849.

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MAYEDAT. K., GOLDSMITH J. R. and CLAYTONR. N. (1986) Oxygen isotope fractionation at high temperatures (abstr.). Terra Cognira 6, 261.

NORTHROPD. A. and CLAYTO~~; R. N. (1966) Oxygen isotope fractionations in systems containing dolomite. J. Ceil. 74, 174-196. O’NEIL J. R.. and TAYLORH. P. (1967) The oxvaen isotooe and cation exchange chemistry of feldspars.‘Amer. Miierol. 52,’ l4141437. O’NEIL.J. R., CLAYTONR. N. and MAYEDAT. K. (1969) Oxygen isotope fractionation in divalent metal carbonates. J. Chem. Phys.

51,5547-5558. SHIROY. and SAKAIH. (1972) Calculation of the reduced partition function ratios of a,gquartz and calcite. Bull. Chem. Sot. Japan 45,2355-2359.

TAYLORH. P. JR. (1977) Water/rock interactions and the origin of H20 in granite batholiths. J. Geol. Sot. 133, 509-558. UREY H. C. (1947) The thermodynamic properties of isotopic sub stances. J. Chem. Sot. (London), 562-58 I.