Isotopic exchange in mineral-fluid systems. IV. The crystal chemical controls on oxygen isotope exchange rates in carbonate-H2O and layer silicate-H2O systems

Geochimica et Cosmochimica Acta, Vol. 64, No. 5, pp. 921–931, 2000 Copyright © 2000 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/00 $20.00 ⫹ .00

Pergamon

PII S0016-7037(99)00357-9

Isotopic exchange in mineral-fluid systems. IV. The crystal chemical controls on oxygen isotope exchange rates in carbonate-H2O and layer silicate-H2O systems DAVID R. COLE* Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6110, USA (Received April 29, 1999; accepted in revised form September 14, 1999)

Abstract—Oxygen isotope exchange between minerals and water in systems far from chemical equilibrium is controlled largely by surface reactions such as dissolution-precipitation. In many cases, this behavior can be modeled adequately by a simple pseudo-first order rate model that accounts for changes in surface area of the solid. Previous modeling of high temperature isotope exchange data for carbonates, sulfates, and silicates indicated that within a given mineral group there appears to be a systematic relationship between rate and mineral chemistry. We tested this idea by conducting oxygen isotope exchange experiments in the systems, carbonate-H2O and layer silicate-H2O at 300 and 350°C, respectively. Witherite (BaCO3), strontianite (SrCO3) and calcite (CaCO3) were reacted with pure H2O for different lengths of time (271–1390 h) at 300°C and 100 bars. The layer silicates, chlorite, biotite and muscovite were reacted with H2O for durations ranging from 132 to 3282 h at 350°C and 250 bars. A detailed survey of grain sizes and grain habits using scanning electron microscopy (SEM) indicated that grain regrowth occurred in all experiments to varying extents. Changes in the mean grain diameters were particularly significant in experiments involving withertite, strontianite and biotite. The variations in the extent of oxygen isotope exchange were measured as a function of time, and fit to a pseudo-first order rate model that accounted for the change in surface area of the solid during reaction. The isotopic rates (ln r) for the carbonate-H2O system are ⫺20.75 ⫾ 0.44, ⫺18.95 ⫾ 0.62 and ⫺18.51 ⫾ 0.48 mol O m⫺2 s⫺1 for calcite, strontianite and witherite, respectively. The oxygen isotope exchange rates for layer silicate-H2O systems are ⫺23.99 ⫾ 0.89, ⫺23.14 ⫾ 0.74 and ⫺22.40 ⫾ 0.66 mol O m⫺2 s⫺1 for muscovite, biotite and chlorite, respectively. The rates for the carbonate-H2O systems increase in order from calcite to strontianite to witherite. This order clearly reflects the influence of the change in cation chemistry, i.e., Ba ⬎ Sr ⬎ Ca. A similar pattern is observed for the layer silicate-H2O systems, where chlorite⬎biotite⬎muscovite. The link between cation chemistry and rate is more complicated in this case, but in general, the order follows a trend where Mg-Fe ⬎ K-Mg ⬎ K, with an associated increase in Si and Al, and decrease in hydroxyl. The isotopic-chemical relations suggest that oxygen isotope exchange behavior monitored experimentally in this study is the net result of bond-breaking and dissolution of the mineral, complex ion formation in solution and growth of the mineral, whose structure is controlled, in large part, by the lattice energy. We compared the rates against the electrostatic attractive lattice energies (neglecting the repulsive forces), normalized per number of cations. The correlations between rates and lattice energies are quite good for both mineral-H2O systems. The increase in rates correlated with a decrease in the electrostatic attractive lattice energies, i.e., the greater the lattice energy required to break up the crystal, the more sluggish the rates for both chemical and isotopic exchange. By establishing an unambiguous relationship between rate, lattice energy, and ultimately temperature, we can begin to develop empirical equations useful in predicting rates of isotopic exchange for minerals for which experimental data are lacking. Copyright © 2000 Elsevier Science Ltd where the mineral undergoes some form of heterogeneous chemical reaction such as dissolution-reprecipitation (e.g., Cole et al., 1983; Cole and Ohmoto, 1986; Cole, 1992). Our knowledge of the mechanisms and rates of isotopic exchange accompanying surface reactions comes principally from high temperature (ⱖ300°C)-high pressure (ⱖ1 kbar) partial isotope exchange experiments designed specifically to measure equilibrium fractionation factors rather than rates. A limited number of partial isotope exchange experiments on rock-fluid systems (Cole et al., 1987; Cole et al., 1992), calcite-fluid (Anderson and Chai, 1974; Chai, 1975; Beck et al., 1992; Cole, 1992), quartz-water (Matsuhisa et al., 1979; Matthews and Beckinsale, 1979; Matthews et al., 1983), and alunite-water (Stoffregen et al., 1994) were specifically designed to elucidate mechanisms and rates of exchange. Many of these systems can be modeled by a simple pseudo-first order rate model, modified from Northrop and Clayton (1966), that takes into account changes

1. INTRODUCTION

Critical to the interpretation of the extent of isotopic equilibrium and factors that influence exchange in natural systems is knowledge of the mechanisms and rates of isotopic exchange between minerals and fluids. Quantitative modeling of natural processes from stable isotope distributions among fluids and minerals is limited because of large gaps in experimentally derived isotope exchange rates for heterogeneous reactions involving important rock-forming minerals. In contrast to the recent gains made in our understanding of rates of experimental oxygen isotope exchange controlled by diffusion (e.g., Farver and Yund, 1990; Farver and Yund, 1991; Fortier and Giletti, 1991), far less is known about rates of exchange for systems

*Author to whom correspondence should be addressed (coledr@ ornl.gov). 921

922

D. R. Cole

in the surface area of the solid (Cole et al., 1983; Cole and Ohmoto, 1986). Preliminary modeling of the high temperature data indicated that within a given mineral group there appears to be a systematic relationship between rate and mineral chemistry for systems initially far from equilibrium (Cole et al., 1983; Cole and Ohmoto, 1986; Cole, 1994). For example, in the carbonate group, calcite and dolomite exchange oxygen much slower than either witherite (BaCO3) or strontianite (SrCO3). Si, Al, Na and K-dominated silicates generally exchange oxygen isotopes slower than the Ca, Mg, or Fe-rich silicates. In general, these trends suggest a correlation between increasing rate of oxygen isotope exchange and a decrease in the ratio of cation charge to cation radius. The relationship between exchange rate and mineral chemistry for systems controlled by chemical reaction is not entirely unexpected because numerous mineral dissolution-precipitation kinetic studies have demonstrated linear correlations between dissolution rates and a variety of parameters (e.g., crystal chemical; thermodynamic) such as metal-oxygen bond length (Dove and Czank, 1995), free energy of formation (Sverjensky, 1992) and mean electrostatic site potentials (Brady and Walther, 1989; Brady and Walther, 1992). Two problems plagued our original analysis of isotopic rates. First, the higher temperature exchange data (ⱖ500°C) for most phases undoubtedly involved a contribution from both recrystallization and diffusion. The diffusion component was not accounted for in a rigorous manner in our previous calculations based on the partial exchange results, hence the calculated rates were somewhat greater than they should be if exchange was controlled solely by chemical reaction. An additional problem involved the estimation of the initial surface areas, and how these change during the course of an experiment for cases where surface area measurements are lacking. If the starting grain size and its distribution are known, then a reasonable estimate can be made for the starting surface area. However, in the earlier analysis of rates, changes in surface area due to ripening were not taken into account. The overall theme of this paper is to investigate the crystal chemical controls on oxygen isotope exchange accompanying only chemical reaction. The specific objectives are three-fold. First, we present new experimental oxygen isotope exchange rate data on three metal carbonate-H2O subsystems: calcite (CaCO3), strontianite (SrCO3), and witherite (BaCO3) reacted with pure H2O at 300°C and 100 bars. Second, we describe new experimental isotope exchange rate data on three hydrous silicate-H2O subsystems: chlorite, biotite and muscovite reacted with pure H2O at 350°C and 250 bars. Special attention is paid to changes in surface area during reaction. Finally, we compare the measured rates of oxygen isotope exchange with crystal chemical parameters to test for linear correlations that might lead to empirical equations capable of predicting rates of exchange for other carbonates or layer silicates for which rate data are lacking. 2. EXPERIMENTAL METHODS The degree of isotopic exchange between either carbonates or layer silicates and pure H2O has been monitored as a function of time in a total of 25 experiments at 300° and 350°C, respectively. A brief summary is provided below of the details of the starting materials, experimental design and procedures used in these experiments. Table 1

Table 1. Chemical composition of chlorite and mica starting materials (weight% oxides). Oxide

Chloritea

Biotiteb

Muscovitec

SiO2 Al2O3 FeO MgO CaO Na2O K2O TiO2 MnO H2Od F Cl

24.75 22.05 25.46 15.30 0.36 0.10 0.30 0.16 tr. 13.84 0.02 0.05

35.79 14.90 26.74 5.91 0.61 0.55 9.27 2.23 0.05 2.90 0.67 0.27

46.48 35.22 1.40 0.41 0.01 1.02 9.84 0.08 0.08 4.86 0.28 tr.

a

Garnet-chlorite schist, Vermont Biotite pegmatite, New York c Muscovite pegmatite, India d RF induction heating, water reduction via U, and hydrogen manometry b

summarizes the chemical compositions of the layer silicates; chlorite, biotite and muscovite. Experimental conditions and isotopic results are given in Table 2 and Table 3 for the carbonate-H2O and layer silicate H2O systems, respectively.

2.1. Starting Materials and Solids Characterization Three compositionally different reagent-grade carbonates (Mallinckrodt) were used in this study; calcite (#3983), witherite (#8220) and strontianite (#3736). The Sr and Ba carbonates were used as is without further processing (e.g., sieving, washing, etc.). Both of these phases are very fine-grained with mean grain diameters of 0.32 ⫾ 0.06 (1␴) and 0.59 ⫾ 0.35 (1␴) ␮m for strontianite and witherite, respectively. Kr-BET surface area analysis of these two phases yields specific surface areas of 2.753 m2 gm⫺1 for strontianite and 1.401 m2 gm⫺1 for witherite. SEM observations reveal that both of these phases have an irregular, blocky crystal habit. The calcite has been used in previous studies (e.g., Cole, 1992), and is much coarser in grain size due to hydrothermal pre-treatment. The original material was reprocessed for this study by dry-sieving, sizing to ⬍38 ␮m, and repeated settling in order to elutriate the fine fraction. Well-formed equant-shaped rhombs of calcite have a mean diameter of 7.52 ⫾ 3.52 (1␴) ␮m and a N2-BET specific surface area of 0.512 m2 gm⫺1. Laser particle size analysis indicated that over ⬃90% of the calcite grains were less than ⬃15 ␮m in diameter. Pyncometer measurements gave densities for calcite, strontianite and witherite of 2.71, 3.72 and 4.30 gm cm⫺3, respectively. The layer-silicates, chlorite, biotite and muscovite, were derived from natural sources. These starting materials were examined by X-ray diffraction (XRD) and SEM, and were chemically characterized by both X-ray fluorescence (XRF) and wet chemical methods (Table 1). Water was liberated from each solid by RF induction heating at ⬃1200°C, then reduced by reaction with hot U-metal (Godfrey, 1962). Water contents were determined from capacitance manometry of H2 (Bigeleisen et al., 1952). All three were crushed, dry-sieved, sized to less than ⬍38 ␮m, washed and repeatedly settled in order to elutriate the fines. The elutriation process, when combined with sonication, was only partly successful because SEM images revealed the adherence of a small percentage of ultrafine particles on many of the larger grains, particularly in the case of the chlorite. Laser particle size analysis and SEM images indicated that greater than 75% of the particles for all three phases ranged from between 1 and 10 ␮m in diameter. The mean grain diameters were 9.75 ⫾ 2.5 (1␴), 1.73 ⫾ 1.25 (1␴), and 4.50 ⫾ 2.15 (1␴) ␮m for chlorite, biotite and muscovite, respectively. Kr-BET analysis yielded specific surface areas of 3.89, 22.10 and 8.63 m2 gm⫺1 for chlorite, biotite and muscovite, respectively. The high surface areas reflect the greater micro-porosity of these layered phases. Pyncometer

Isotopic exchange in mineral-fluid systems

923

Table 2. Experimental parameters and oxygen isotope exchange rates for the systems calcite - H2O; strontianite - H2O; witherite - H2O at 300°C, 100 bars.

Cap. no.

P T°C (bars)

Time (h)

Soln. mass (a)

Solid mass (a)

X (b)

X (b)

␦ (c)

0.956 0.845 0.847 0.956 0.848 0.845 0.848

0.044 0.155 0.153 0.044 0.152 0.155 0.152

⫺55.37 ⫺55.45 ⫺55.29 ⫺55.42 ⫺55.17 ⫺55.11 ⫺55.07

o fl

o s

f fl

␦ (d) f s

nfl0 nso n ⫹ nso o fl

(e)

F (f)

New A (m2) (g)

1n r (h)

d៮ (i)

1. Calcite 226 167 247 127 155 137 237

300 300 300 300 300 300 300

250 250 250 250 250 250 250

137 299.93 138.5 89.38 288 87.69 522 300.52 790 90.08 1025.5 88.42 1073 90.00

25.36 30.22 29.26 25.44 29.88 29.92 29.84

6.58 6.26 6.12 5.61 5.42 5.10 4.87

0.7274 0.7664 0.7436 0.7297 0.7600 0.7587 0.7591

0.014 0.018 0.024 0.030 0.038 0.045 0.050

2. Strontianite C61 C9 C27

300 300 300

100 100 100

271 695 1390

100.87 203.28 199.32

37.45 0.880 0.120 ⫺33.81 7.46 75.34 0.881 0.119 ⫺33.29 ⫺11.32 75.02 0.879 0.121 ⫺33.15 ⫺11.91

0.6700 1.3481 1.3399

0.546 4.891 ⫺18.95 ⫾ 0.62 0.639 9.433 AF ⫽ 0.2063 0.654 9.055

0.966 1.035 1.099

3. Witherite C49 C5 C23

300 300 300

100 100 100

271 695 1390

103.90 51.06 0.881 0.119 ⫺34.56 ⫺9.61 211.04 101.57 0.884 0.116 ⫺33.86 ⫺15.29 203.36 101.09 0.880 0.120 ⫺33.52 ⫺17.08

0.6841 1.3643 1.3526

0.479 3.116 ⫺18.51 ⫾ 0.48 0.634 6.014 AF ⫽ 0.2767 0.687 5.827

2.65 2.78 2.91

1.297 ⫺20.75 ⫾ 0.44 1.545 AF ⫽ 0.0157 1.494 1.296 1.517 1.515 1.511

7.54 7.54 7.56 7.59 7.63 7.66 7.66

(a) Mass of starting fluid (fl) and solid (s) in mg. (b) Mole fraction of fluid oxygen and calcite oxygen. (c) Final oxygen isotope composition of fluid calculated from mass balance; initial fluid value ⫽ ⫺55.55‰ for calcite; ⫺36.89‰ for strontianite and witherite; ‰ VSMOW. (d) Final oxygen isotope composition of solid; initial value ⫽ ⫹7.28‰ (calcite); ⫹15.2‰ (strontianite); ⫹7.68‰ (witherite). (e) Ratio of product of number of moles of O in fluid (fl) and solid (s) to the sum of the moles in the system (⫻103). (f) Fraction of oxygen isotope exchange, ⫽ (␣i ⫺ ␣f)/(␣i ⫺ ␣eq), with ␣eq from O’Neil et al. (1969) ⫽ 1.006192 (calcite), 1.004961 (strontianite), 1.003599 (witherite). (g) Total surface area, m2 (⫻102), estimated from mean grain diameters; see text for details. (h) Rate constant, moles O m⫺2 sec⫺1, from pseudo-first under model; AF is the regression agreement factor ⫽ 公⌺(Fmeas ⫺ Fcalc)2/nmeas ⫺ nvar where Fmeas and Fcalc are the measured and calculated fractional exchange, nmeas and nvar are the numbers of measurements and variables (nvar ⫽ 1). (i) Mean grain diameters, in microns, determined from SEM images; initial mean diameter (in ␮m): calcite ⫽ 7.52; strontianite ⫽ 0.32; witherite ⫽ 0.59.

measurements gave densities for chlorite, biotite and muscovite of 2.80, 3.00 and 2.83 gm cm⫺3, respectively. 2.3. Experimental Techniques Tables 2 and 3 summarize the experimental conditions used in the study of isotopic exchange between carbonates—H2O and layer silicates—H2O, respectively. Calcite, strontianite, and witherite were reacted with pure H2O for various durations (137⫺1390 h) at a temperature of 300°C and pressures of 100 bars. The layer silicates were reacted with pure H2O for durations of between 132 and 3282 h. Experiments were carried out in noble metal (Au; Pt) capsules loaded into Ti-alloy pressure vessels housed in an Al-block furnace. The total time to reach run temperature (controlled to ⬃1°C) was approximately 20 min., and runs were quenched isobarically in an ice bath to below 25°C in less than one min. SEM observations showed no evidence of crushing of grains during the heat-up cycle, and fine-grained quench products were not observed in any experiment. A typical charge containing carbonate and H2O consisted of ⬃25–75 mg of carbonate and between 90 and 200 mg of H2O (O mole ratio of ⬃4 to 6) loaded under a positive pressure of argon. Approximately 250 –350 mg of layer silicate were reacted with about 700 mg of H2O (O mole ratio of ⬃4.5). These experiments were also loaded under a positive argon pressure in order to eliminate the oxidative effects of air. Capsules were reweighed after quenching to check for leaks, and punctured under vacuum. Each water was cryogenically separated and sealed under vacuum in a glass ampule. Each solid run product was examined with both XRD and SEM. The SEM images were used to document the changes in grain habit and mean grain diameter relative to the starting material.

2.4. Analytical Methods Oxygen isotope analysis of the starting materials and run products was done using standard techniques: phosphoric acid extraction of carbon and oxygen from the carbonates at 25°C (McCrea, 1950); and conventional silicate oxygen extraction by bromine pentafluoride at 600°C, followed by conversion to CO2 (Clayton and Mayeda, 1963). The following acid fractionation factors were used for the calcite, strontianite and witherite, respectively; 1.01025, 1.01047, and 1.01095 (Sharma and Clayton, 1965). Starting silicate materials and run products were heated to 100 –150°C in Ni reaction vessels for about three h under vacuum in order to remove adsorbed and interlayer water, prior to higher temperature (⬎500°C) BrF5 extraction. If gas yields did not meet or exceed 98 –99% of the expected value, the gas was rejected. Oxygen isotope compositions of starting waters and a select number of run waters were determined using the CO2-water equilibration method of Epstein and Mayeda (1953). The value of ␣CO2-H2O was taken to be 1.0412 (1985 IAEA Consultants Group Meeting). Measurements are reported in the usual “␦” notation in parts per thousand (‰) relative to Vienna Standard Mean Ocean Water (VSMOW). Pure H2O with a ␦18O value of ⫺24.79‰ (VSMOW) was used in experiments involving the layer-silicates. The oxygen isotope values for the chlorite, biotite and muscovite are 7.72, 6.45 and 10.50‰, respectively. Two different pure waters were used in the carbonate experiments; a ⫺55.55‰ H2O reacted with the calcite (␦18O ⫽ 7.27‰, VSMOW), and a ⫺36.89‰ H2O reacted with strontianite (␦18O ⫽ 15.20‰, VSMOW) and witherite (␦18O ⫽ 7.68‰, VSMOW). The total error for oxygen isotope analysis (including extraction and mass spec reproducibility) is approximately ⫾0.1‰ (1␴) for all waters, ⫾0.25‰ for silicates, and ⫾0.1‰ for carbonates.

924

D. R. Cole

Table 3. Experimental parameters and oxygen isotope exchange rates for the systems chlorite - H2O; biotite - H2O; muscovite - H2O at 350°C, 250 bars.

(e)

F (f)

6.26 5.99 5.54 4.43

0.6364 0.6770 0.6650 0.6630

0.044 0.065 0.08 0.119

0.940 0.993 0.952 0.880

⫺22.40 ⫾ 0.89 AF ⫽ 0.0819

10.5 10.75 11.05 11.88

⫺24.22 ⫺23.59 ⫺23.41 ⫺23.10

3.69 0.68 0.11 ⫺1.48

0.7011 0.6891 0.6919 0.7117

0.10 0.21 0.24 0.29

7.136 5.965 5.835 5.370

⫺23.14 ⫾ 0.74 AF ⫽ 0.1569

1.91 2.24 2.31 2.59

⫺24.75 ⫺24.59 ⫺24.52 ⫺24.48

10.08 9.35 9.12 8.84

0.6639 0.6520 0.6673 0.6566

0.014 0.041 0.05 0.06

2.269 2.148 2.178 2.101

⫺23.99 ⫾ 0.66 AF ⫽ 0.0432

4.58 4.73 4.81 4.88

Solid mass (a)

Cap. no.

T°C

P (b)

Time (h)

X (b)

X (b)

␦ (c)

1. Chlorite OC-7 1 4 7

350 350 350 350

250 250 250 250

132 669 1384 3282

713.60 702.47 686.76 698.08

252.97 273.32 268.74 266.82

0.839 0.826 0.825 0.829

0.161 0.174 0.175 0.171

⫺24.55 ⫺24.42 ⫺24.33 ⫺24.11

2. Biotite E F G H

350 350 350 350

250 250 250 250

168 669 1384 3282

705.05 711.21 699.10 719.35

355.17 347.44 350.61 360.70

0.821 0.825 0.821 0.822

0.179 0.175 0.179 0.178

3. Muscovite A B C D

350 350 350 350

250 250 250 250

168 669 1384 3282

696.36 699.17 692.49 702.77

268.09 262.48 270.07 264.19

0.828 0.825 0.821 0.822

0.179 0.175 0.179 0.178

o fl

o s

nfl0 nso n ⫹ nso

New A (m2) (g)

Soln. mass (a)

f fl

␦ (d) f s

o fl

1n r (h)

d៮ (i)

(a) Mass of starting fluid (fl) and solid (s) in mg. (b) Mole fraction of fluid oxygen and layer silicate oxygen. chlorite: 0.03007 moles O gm⫺1; biotite; 0.02406 moles O gm⫺1; muscovite: 0.029913 moles O gm⫺1. (c) Final oxygen isotope composition of fluid calculated from mass balance. Initial fluid value ⫽ ⫺24.79‰. (d) Final oxygen isotope composition of solid. Initial chlorite ⫽ ⫹7.72‰; biotite ⫽ 6.45‰; muscovite ⫽ 10.50‰; ‰ VSMOW. (e) Ratio of product of number of moles of O in fluid (fl) and solid (s) to the sum of the moles in the system (⫻102). eq eq (f) Fraction of oxygen isotope exchange, F ⫽ (ai ⫺ af)/(ai ⫺ aeq), achl ⫽ 0.999698 (Cole and Ripley, 1999); abio ⫽ 0.998 (Bottings and Javoy, eq 1975); ␣musc ⫽ 1.002844 (O’Neil and Taylor, 1969; corrected for “salt effect” with data from Horita et al., 1995). (g) Total surface area, m2, estimated from mean grain diameters; see text for details. (h) Rate constant, moles O m⫺2 sec⫺1, from pseudo-first order model; AF is the regression agreement factor (see notes from Table 2 for definition). (i) Mean grain diameters, in microns, determined from SEM images; initial mean diameter (in ␮m): chlorite ⫽ 9.75; biotite ⫽ 1.73; muscovite ⫽ 4.50.

3. RESULTS

The extent of fractional approach to oxygen isotope equilibrium in these experiments can be expressed in the familiar form of F, as derived by Northrop and Clayton (1966): F ⫽ (␣i ⫺ ␣f)/(␣i ⫺ ␣eq)

(1)

where the ␣’s are the isotopic fractionation factors between either carbonate or layer silicate and water at time t (␣f), at t ⫽ 0 (␣i), and at t ⫽ ⬁ (␣eq). The oxygen isotope equilibrium fractionation factors (␣eq) for the carbonates and layer silicates are described in Tables 2 and 3, respectively. The experiments described by O’Neil et al. (1969) for carbonates and by O’Neil and Taylor (1969) for muscovite used electrolyte solutions to enhance the exchange rates. In the case of the carbonate experiments, O’Neil et al. (1969) used NH4Cl at a modestly low concentration of 0.56 molal, whereas NaCl (or KCl) solutions used in the muscovite experiments ranged from 2 to 3 molal. The isotope salt effect for NH4Cl is not well constrained at 350°C and a correction has not been applied to the O’Neil et al. (1969) carbonate experiments, but this is not the case for NaCl (or KCl) in the muscovite experiments. The following expression was used to make this correction: 103 1n ␣musc⫺H2O ⫽ 103 1n ␣musc-salt soln ⫺ 103 1n ⌫

(2)

The fractionation for the oxygen isotope salt effect, 103 ln ⌫, is approximately ⫺0.6‰ at 350°C and 3 molal NaCl (or KCl)

[see Horita et al., 1995 for a definition of ⌫ as a function of T, salt type, and concentration]. The relationships between the extent of oxygen isotope exchange and time are clearly evident in Figure 1 and Figure 2 for carbonates and layer silicates, respectively, where F is plotted against time in hours. There is a measurable increase in the F values with increasing time for all three carbonate phases reacted hydrothermally at 300°C. The F-values can exceed as much as 0.5– 0.6, as in the case of witherite and strontianite, or as low as less than 0.1 for calcite (Fig. 1a). The increase in the F-values with increasing time is very pronounced for witherite and strontianite (Fig. 1a). The rate of change in F is initially steep, but tends to flatten out somewhat with increasing time. The inflection in slope for F versus time occurs after 270 h for witherite and strontianite. In the case of the coarser-grained calcite, the increase in F values is rather constant with time and shows no inflection. The magnitudes and rates of change in F-values versus time are much less striking for the layer silicates reacted at 350°C (Fig. 2a). Total exchange (F) was only about 0.06 for muscovite, 0.12 for chlorite, and 0.29 for biotite after 3282 h of reaction. The F-values for these three phases exhibit steady increases with increasing time, but generally no major rapid increases early in the reaction. The greatest initial increase in F was observed in the system biotite-H2O, which experienced exchange to F values of 0.1 and 0.21 at 168 and 669 h, respectively (Fig. 2a). The biotite exchange at 669 h was

Isotopic exchange in mineral-fluid systems

Fig. 1. (a) Summary of the data for total F (fraction of 18O/16O exchange) plotted against time in hours for the systems: witherite (BaCO3)-H2O, strontianite (SrCO3)-H2O, calcite (CaCO3)-H2O reacted at 300°C, 100 bars. Equilibrium fractionation factors used to calculate F are from O’Neil et al. (1969). Solid square ⫽ witherite; solid diamond ⫽ strontianite; solid circle ⫽ calcite. (b) Ratio of mean grain diameter of run product to mean grain diameter (␮m) of starting material plotted against time in hours. The symbols are the same as described for (a).

approximately four times greater than for chlorite and nearly five times greater than muscovite at the same time. A detailed survey of grain sizes and grain habits was conducted using SEM images, wherein we measured the diameters of between 50 and 100 grains of each phase at each given run condition. These results, summarized in Tables 2 and 3, are shown in Figures 1b and 2b, where we plot the ratios of the mean grain diameter to mean starting grain diameter (d៮ /d៮ o) versus time. The trends observed in these plots are similar in many respects to those exhibited in the companion Figures 1a and 2a. In general, there is a sympathetic increase between the mean grain diameter and the fraction of exchange with increasing time. This correlation is most evident for witherite, strontianite and biotite. Strontianite and witherite both exhibit profound grain ripening, with mean grain diameters increasing by factors of 3 and 4.5 after 271 h of reaction, respectively (Fig.

925

Fig. 2. (a) Summary of the data for total F (fraction of 18O/16O exchange) plotted against time in hours for the systems: chlorite-H2O, biotite-H2O, muscovite-H2O reacted at 350°C, 250 bars. Equilibrium fractionation factor for chlorite from Cole and Ripley (1999), biotite from Bottinga and Javoy (1975), muscovite from O’Neil and Taylor (1969). Solid square ⫽ biotite; diamond ⫽ muscovite; solid circle ⫽ chlorite. (b) Ratio of mean grain diameter of run product to mean grain diameter (␮m) of starting material plotted against time in hours. The symbols are the same as described for (a).

1b). SEM evidence indicates that smaller grains have undergone dissolution with transfer of mass to the larger grains. Presumably the total number of grains decreased during this process. The mean grain diameter of calcite did not increase by more than a few percent because of its much coarser initial diameter and lower solubility, compared to witherite and strontianite. The layer silicates sustained much less grain ripening compared to the Sr and Ba carbonates (Fig. 2b). We have direct SEM evidence of the dissolution of the finer grains and small, but measurable increases in the grain size of coarser grains. The greatest change was observed in biotite with mean grain diameters increasing by factors of roughly 1.29, 1.35 and 1.5 at 669, 1384, and 3282 h, respectively. Chlorite, whose mean grain diameter was the coarsest of the three layer silicates, experienced the next greatest change, with a maximum increase of

926

D. R. Cole

about 1.2 times the initial size attained at 3282 hours of reaction. Muscovite exhibited the smallest change, only an ⬃8 –10% increase in mean diameter at the longest run time of 3282 h. As with the carbonates, the trajectories of increasing change in grain diameter mimicked very closely the trends observed in the fraction of exchange, F (Fig. 2a). 4. DISCUSSION

4.1. Solubility, Mass Transfer and Surface Area Changes The results of the SEM examination of the reaction products indicate that dissolution and reprecipitation control isotopic exchange between carbonates and H2O and layer silicates and H2O. It is clear that the fraction of exchange (F) correlates with the extent of measurable grain recrystallization, which in turn must be related to a change in the total surface area of the solid with increasing time. Similar results were obtained by Anderson and Chai (1974) for oxygen isotope exchange in the system: calcite-H2O-NaCl for temperatures between 300 and 700°C. Greater degree of recrystallization for certain phases is a direct reflection of their higher solubilities compared to phases exhibiting lesser amounts of regrowth. For example, experimental solubilities of Ba and Sr-carbonates reacted with pure H2O are significantly greater (1 to 2 orders of magnitude) than those measured for calcite and dolomite under similar hydrothermal conditions (100 –300°C) (Rimstidt, 1997). Low temperature experimental studies on the solubilities of layer silicates in pure H2O indicate that biotite should be somewhat more soluble than muscovite (Lasaga, 1998); reliable solubility data on chlorite are not currently available. In this present study, starting grain sizes are not uniform among the various phases, but qualitatively, the relative magnitudes of regrowth through mass transfer follow the general solubility trends described above. The magnitude of mass transfer associated with ripening is controlled by a number of factors including temperature, pressure, fluid composition, initial grain size, grain size distribution, and growth mechanism. For example, a two-fold increase in mean grain size corresponds to about 80% mass transfer for diffusion-controlled growth, but only about 55% for screwdislocation growth (Chai, 1975). In the case of Ba and Srcarbonates, a significant amount of the solid has gone through the ripening process. The maximum increase in mean grain diameter exceeds a factor of 4 for witherite reacted for the longest time, 1390 h. Systems that exhibit this much mass transfer should approach isotopic equilibrium, but clearly in this study, they do not. The data suggest that a significant percentage of the larger grains contain unexchanged cores. Thin section analysis of witherite and strontianite run products using optical (oil immersion) and electron backscatter methods indicates the presence of faint outlines within larger grains that may be the remnants of original grain edges of starting material. The core diameters encompass the full range of possible grain sizes observed in these materials, as well as cases where small, unreacted grains become sutured together and covered by overgrowths. This behavior is less obvious for the layer silicates where the maximum increase in mean grain diameter does not exceed 1.5 for biotite reacted for the longest duration of 3282 h. Thus, the F values represent some proportion of unexchanged cores and perhaps equilibrated overgrowths.

The development of any rate model used to describe these results should account for the change in total surface area. There are a number of methods that can be used to address this issue. Obviously, the most accurate method is to measure the surface areas of the run products with N2 or Kr BET. However, this is not possible because our sample size is prohibitively small. In their study of oxygen isotope exchange between alunite and water, Stoffregen et al. (1994) assumed as a first approximation that total surface area, A, is a linear function of F, the fraction of exchange where A ⫽ Ao (1–F); Ao is the initial surface area. This relationship has not been confirmed experimentally. In the absence of measured surface areas, the most common approach utilizes the mean grain size and geometry of the grains, such as sphere, plate or cylinder. The calculated surface areas are typically less than the measured surface areas, with the magnitude of the difference dependent on mineral type, surface roughness and grain size distribution. For example, Leamnson et al. (1969) presented results for silica that clearly showed the calculated surface areas were underestimated by 3 to 4 times compared to the BET values. Similarly, White and Peterson (1990) presented comparisons between measured and geometrically-calculated surface areas that showed a systematic underestimation of true surface area by a factor of 5 or more when using the geometric approach. However, they documented a linear, empirical relationship between BET measured surface areas corrected for mineral density (m2 cm⫺3) and mean particle size (cm) for a variety of mineral types, e.g., carbonates, oxides, and clays. Some mineral groups (e.g., carbonates) appeared to have a distinctive trajectory. Surface area estimates in this study for carbonate and layer silicate run products are obtained from a similar approach as described by White and Peterson (1990). Data on BET surface areas and mean grain diameters for starting carbonates and layer silicates used in the experiments were combined with similar data from solids not selected—i.e., dolomite (BET ⫽ 0.365 m2 gm⫺1; 12.0 ␮m diameter), chlorite (BET ⫽ 14.6 m2 gm⫺1; 2.63 ␮m), and biotite (BET ⫽ 13.30 m2 gm⫺1; 2.90 ␮m). We have normalized the BET values to density (A⬘; m2 cm⫺3) for each phase and fit these data against the mean grain diameters (d៮ ; in cm). For carbonates, the linear regression equation is log A⬘ (m2 cm⫺3) ⫽ ⫺1.7647 ⫺ 0.6105 (log d៮ )

(3)

with an R2 of 0.996 (n ⫽ 4). For layer silicates, the linear regression equation is log A⬘ (m2 cm⫺3) ⫽ ⫺2.095 ⫺ 1.0404 (log d៮ )

(4)

with an R2 of 0.998 (n ⫽ 5). The mean grain diameters measured for each run product are used to estimate the specific surface areas, which are converted to total surface areas (Tables 2 and 3) by dividing by mineral density, then multiplying by sample mass. This empirical approach does not imply any unique geometry for the grains, but simply compares the mean diameters with a set of “standard” minerals of the same mineral group whose BET surface areas have been accurately determined. Note also these estimates are for physical, not reactive, surface areas.

Isotopic exchange in mineral-fluid systems

4.2. Rates of Oxygen Isotope Exchange The correlation between increase in grain growth and fraction of oxygen isotope exchange with increasing time in our experiments is confirmatory evidence that reaction involving chemical exchange at the mineral-H2O interface is promoting isotopic exchange. The actual exchange process may, indeed, occur in solution between dissolved carbonate or silicate species and H2O in a manner similar to silica and H2O as proposed by Bottinga and Javoy (1987). However, it is unlikely that this step is rate controlling. There have been numerous rate studies of 18O/16O exchange between carbonate and bicarbonate ions and H2O that demonstrate relatively rapid rates of equilibration, with half-lives on the order of hours or tens of hours (e.g., Poulton and Baldwin, 1967; Gamsjager and Murmann, 1983). Further consideration of rates must account for surface processes. Typically, the reaction order is determined from F versus time data (Cole and Ohmoto, 1986), which leads to the development of a rate model. These data were tested with a number of general rate-order models, e.g., zero, first, pseudo-first, and second-order, using ORGLS, a general least-squares regression program (Busing and Levy, 1962; Busing, 1970). The layer silicate-H2O oxygen isotope exchange reactions were fit slightly better using a pseudo-first order model, whereas the carbonate-H2O data were described about as equally well with either pseudo-first or second order models. The difference between these two models was not great so for the purposes of this discussion a pseudo-first order dependency was adopted. This is reasonable because a number of mineral (rock)-fluid systems exhibit this type of behavior (e.g., Kusakabe and Robinson, 1977; Cole et al., 1983; Cole and Ohmoto, 1986; Cole, 1992). Although the model is not necessarily suited for the treatment of all the partial exchange data, it does serve as a useful framework for the comparison of rate data from systems where surface areas are changing due to chemical reaction. Cole et al. (1983) modified a simple isotope exchange rate model derived by Northrop and Clayton (1966) to account for surface areas. The model does not account for anisotropic exchange behavior. The overall rate, r, can be expressed in the following equation with inclusion of a factor, A, representing the total surface area (m2) of the solid; r ⫽ [⫺1n(1 ⫺ F) WS]/(W ⫹ S) A t

(5)

where W and S represent the total moles of oxygen in the H2O and solid, respectively, at P and T; t is the run time in seconds; and r is in units of moles O m⫺2 s⫺1. The measured F-values (Tables 2 and 3) together with data on the total surface area, the mass of the H2O and solid, and the duration of each run are used to compute the isotopic rate constants. These values (in the form of ln r) are summarized in Tables 2 and 3 along with agreement factors (AF) that reflect the goodness of fit to this model. Stoffregen (1996) points out that this model is useful for interpreatation of experimental data, but does not provide a physically meaningful description of exchange controlled by dissolution/reprecipitation leading to Ostwald ripening. However, this approach requires data on interfacial free energies and chemical reaction rates that are lacking for many hydrothermal mineral-fluid systems. The isotopic rates (ln r) for the carbonate-H2O system are

927

⫺20.75, ⫺18.95 and ⫺18.51 moles O m⫺2 s⫺1 for calcite, strontianite and witherite, respectively. If surface area changes were not accounted for, the ln r values for strontianite and witherite would be greater by 0.7 and 0.8 ln units, respectively. The error (1␴) for calcite-H2O is only about 0.44 ln units, but roughly ⫾0.6 for strontianite and ⫾0.5 for witherite. The rate for calcite-H2O is in good agreement with the data of Cole et al. (1983) and Cole (1992). Previous work on witherite and strontianite involved partial exchange experiments where recrystallization resulted from interaction with a solution containing 0.56 molal NH4Cl, so a direct comparison with our results is not possible. The oxygen isotope exchange rates for the layer silicate-H2O system are ⫺23.99, ⫺23.14 and ⫺22.40 moles O m⫺2 s⫺1 for muscovite, biotite and chlorite, respectively. Note that the AF values for these results (Table 3) indicate a somewhat better fit to the pseudo-first order model compared to the AF values calculated for the carbonate-H2O system (Table 2). Rates would be only 0.14, 0.18 and 0.28 ln units greater for muscovite, chlorite and biotite, respectively, if surface area changes are ignored. The errors (1␴; analytical, estimates of ␣eq, and total surface areas) for these rates range from ⫾0.66 ln units (muscovite) to ⫾0.89 (chlorite). Cole et al. (1983) estimated a ln r value of approximately ⫺21 moles O m⫺2 s⫺1 for paragonite-KCl at 350°C (O’Neil and Taylor, 1969); ⬃3 orders of magnitude faster than our new muscovite-H2O result. 4.3. Crystal Chemical Considerations A relationship between the rates of oxygen isotope exchange and mineral chemistry is evident from these new experimental results. The rates for the carbonate-H2O systems increase in order from calcite to strontianite to witherite. This order clearly reflects the influence of the change in cation chemistry, i.e., Ba ⬎ Sr ⬎ Ca. A similar pattern is observed for the layer silicate-H2O systems, wherein the chlorite rate of oxygen isotope exchange exceeds biotite, which in turn, is faster than muscovite. The link between cation chemistry and rate is more complicated in this case, but in general, the order follows a trend where Mg-Fe ⬎ K-Fe ⬎ K, with an associated increase in Si, Al and decrease in hydroxyl. Cole and Ohmoto (1986) observed trends in isotopic rates mimicking the approximate order of nucleation (precipitation) rates for neutral to slightly acidic systems, where carbonates ⬎ alkali feldspars ⬎ quartz ⬎ micas. Our new experimental results confirm part of this ranking where the carbonate-H2O oxygen isotope exchange rates are 2–3 orders of magnitude faster than those measured for the layer silicate-H2O systems. Correlations between reaction rates and one or more mineral chemistry parameters have precedent in both the chemical and geochemical literature (e.g., Gamsjager and Murmann, 1983; Casey and Westrich, 1992; Sverjensky, 1992; Lasaga, 1998). Casey and Westrich (1992) demonstrated linear correlations among increasing dissolution rates of orthosilicates (Me2SiO4), increasing divalent cation radii (Ca, Mg, Be), and increasing rate of water exchange from the solvent into hydration spheres of corresponding dissolved cations. Sverjensky (1992) showed that surface reaction-controlled dissolution rates of isostructural groups of divalent metal oxides and orthosilicates, when used with a modified Hammet equation, yield coefficients char-

928

D. R. Cole

acteristic of the specific crystal structure, which turn out to be very similar to the coefficients obtained by regression of standard free energies for the same mineral groups. The most relevant of these to our work are the results of Brady and Walther (1992), who described a silicate dissolution model involving the breaking of oxygen bonds that bind silicon to mineral surfaces reacted with neutral and basic pH solutions. They observed a good correlation between the normalized rate of silicon release with the mean site potential of oxygen sites bound to Si in the mineral structure. The isotopic - chemical relations suggest that the oxygen isotope exchange behavior monitored experimentally in this study is the net result of bond-breaking and dissolution of the mineral, complex ion formation in solution, and regrowth of the mineral. The structure of the mineral is determined by the tendency of the atoms to take up positions whereby their total potential energy is reduced to a minimum (West, 1984). This tendency may be expressed in terms of the lattice energy—i.e., the energy required to separate all ions in the crystal to infinite distance. The lattice energy depends upon the balancing of electrostatic forces between ions of opposite charge and the internuclear repulsive forces. The greater the lattice energy, the greater the energy required to break up the crystal into constituent ions, and the more sluggish the rate. The Born-Mayer treatment, described by West (1984), of the equilibration of attractive and repulsive forces in an ionic solid, is given as U ⫽ [⫺A e2 Zct Zo N/rct ⫹ ro] ⫹ BNe⫺r/p ⫺ CNr⫺6 ⫹ 2.25Nhv omax

(6)

where the first term is the Coulomb attractive force (85–90% contribution to total), the second term is the Born repulsive force (10 –15% contribution), the third term is the van der Waals force (⬃1% contribution) and the last term accounts for the zero point vibration (⬃1% contribution). N is Avogadro’s number, A the Madelung constant (structure dependent), Zct and Zo, the valence of the cation and oxygen, respectively, rct ⫹ ro the interatomic distance between cation and oxygen, e the electronic charge, vomax the highest occupied vibrational mode, and B, C, ␳, and h are constants. Focusing on the dominant first term of this relationship, we observe that for isostructural phases, i.e, where Zct, Zo, e and A are constant, the electrostatic lattice energy is inversely dependent on the cation-oxygen interatomic distance, i.e., bond strengths increase as bond lengths decrease. This may explain our qualitative observation noted above regarding the relationship between isotopic rates and cation chemistry. To test this relationship further, we investigated the correlation between ln r and a normalized electrostatic lattice energy of each mineral. We define the normalized electrostatic lattice energy (U⬘) as U⬘ ⫽ ⌺ (ni Ui)/2 ␯ct

(7)

where Ui is the electrostatic site potential for each cation and anion site, ni is the number of each site in the crystal, and ␷ct is the number of cations per formula unit in each phase. By normalizing the lattice energy to the number of cations, direct comparisons can be made between rates and U⬘ for a given

Fig. 3. Oxygen isotope exchange rates for metal carbonates (a) and layer silicates (b) reacted with pure H2O at 300 and 350°C, respectively, plotted against the normalized electrostatic lattice energy (U⬘). U⬘ represents the sum of electrostatic site potentials for each cation and anion normalized by dividing by the number of cations per formula unit in each phase. The symbols for experimentally determined rates are the same as described for Figures 2 and 3. The good correlations exhibited in these plots suggest that the method may be used to predict rates of other phases common to a given mineral group. Lattice energies have been calculated for phases for which rate data are lacking. These have been projected to the lines regressed through the experimental data and are shown as open symbols.

mineral group (Fig. 3a,b). Site energies, computed for oxygen by Smyth (1989) and for cations by Smyth and Bish (1988) for silicates and carbonates were used to calculate the total electrostatic lattice energy (⌺ (ni Ui ) / 2). The sum of all site energies in the crystal will yield twice the total electrostatic energy of the crystal, since each atom pair is counted twice in the procedure. This is accounted for by dividing by 2 in Eqn. (7). Electrostatic energies reported in electron volts have been converted to kcal mol⫺1 by multiplying by 23.05. The ionic model specifically excludes nearest-neighbor repulsive forces, van der Waals attractive forces, the distortion energies of electron distributions, and dynamic effects of lattice vibrations (the second, third and fourth terms in Eqn. 6). The more

Isotopic exchange in mineral-fluid systems

negative the U⬘ values, the greater the electrostatic lattice energy. Site potentials for both oxygen and cations are available for a number of phases, including calcite, strontianite, witherite, and muscovite. Cation site potentials from annite were used as a proxy for the biotite, along with oxygen site potentials from phlogopite since none have been calculated for annite. Site potential data for chlorite are not available. As a proxy for cation site potentials, we have used data on amesite (a septochlorite) given by Smyth and Bish (1988), and oxygen site potentials from brucite and talc (Smyth, 1989), weighted according to their proportions in chlorite. Although Mg-bearing amesite, brucite, and talc were used in the site potential calculations, the Mg sites are typically only a few 10’s of kcal mol⫺1 greater than corresponding Fe sites, so no attempt has been made to correct for these small differences. The oxygen isotope exchange rate (ln r) for each phase has been plotted against its normalized electrostatic lattice energy in Figs. 3a and b for carbonates and layer silicates, respectively. Data on Fig. 3a demonstrates a good linear relationship between ln r and U⬘, where rates increase (witherite ⬎ strontianite ⬎ calcite) with decreasing electrostatic lattice energy. This is despite the fact that witherite and strontianite are in a different structural group from calcite, i.e, aragonite group (orthorhombic) versus calcite group (trigonal), respectively. Qualitatively, the decreasing lattice energy reflects an increase in the rct ⫹ ro distances, where rBa ⫹ rO ⫽ 2.80 Å, rSr ⫹ rO ⫽ 2.65 Å and rCa ⫹ rO ⫽ 2.36 Å. Similarly, we observe a good correlation between an increase in the isotopic exchange rate, ln r for chlorite ⬎ biotite ⬎ muscovite, with decreasing electrostatic lattice energy (Fig. 3b). This order is consistent with the model and reflects, in part, a greater proportion of Si-O and Al-O bonds in muscovite compared to either chlorite or biotite. The order is also consistent with the order in the rate of weathering of micas, where Fe-rich, silica-poor varieties react much faster than their more alkali and silica-rich counter parts (Brady and Walther, 1989). Note that structurally, biotite and muscovite belong to the mica group, whereas chlorite belongs to the chlorite series. Despite this difference, the correlation between rates and U⬘ is very good. The correlations presented in Figure 3 are generally only valid when temperature, pressure, and initial fluid chemistry are the same and only minor structural differences exist among phases being compared, i.e., isostructural or close to it. Additionally, it is important that the stoichiometry of the phase remains unchanged during the reaction. Our experiments for both carbonate-H2O and layer silicate-H2O have met these requirements. The good correlations observed in this study suggest the possibility of using this approach to predict the rates of oxygen isotope exchange for phases for which data are lacking. To illustrate this point, we have calculated the normalized electrostatic lattice energies for a number of carbonates and layer silicates from site potential data given by Smyth and Bish (1988; cations) and Smyth (1989; oxygen), and projected these to the least squares regression lines given in Figure 3. The order of rates predicted for carbonate-H2O oxygen isotope exchange (Fig. 3a), from fastest to slowest, is witherite (Ba) ⬎ strontianite (Sr) ⬎ cerrusite (Pb) ⬎ rhodocrosite (Mn) ⬎ calcite (Ca) ⱖ dolomite (Ca, Mg) ⬎ magnesite (Mg). This order

929

follows approximately the magnitude in the rct ⫹ ro distances, from greatest to smallest. The order for the layer silicates, from fastest to slowest, is chlorite ⬎ biotite ⬎ phlogopite ⬎ margarite ⬎ paragonite ⱖ muscovite. Qualitatively, this order follows a pattern of increasing Si, Al, Na, K and Ca and decreasing Mg and Fe. The order of oxygen isotope rates for these layer silicates parallels the order for decreased dissolution rates described by Brady and Walther (1989) that is used to explain the inverse mineral reaction series sequence of surface weathering. 5. SUMMARY

Oxygen isotope exchange between minerals and fluids in systems initially far from chemical equilibrium are controlled largely by surface reactions such as dissolution-precipitation or transformation of one phase to another. In our previous studies we have demonstrated that this behavior can be adequately modeled by a simple pseudo-first order rate model that takes into account changes in surface area. Oxygen isotope exchange rate constants estimated from a variety of partial exchange experiments, corrected for the presence of salt, can be ranked in the following approximate order: carbonates ⱖ sulfates ⬎ pyroxenes/amphiboles ⬎ alkali feldspars ⬎ quartz ⱖ alkali micas. Interestingly, the order for silicates follows approximately a decrease in the ratio of non-bridging oxygens to tetrahedrally coordinated cations. This relationship between isotopic exchange rates and crystal chemistry is not entirely unexpected, since numerous chemical kinetic studies have reported correlations between mineral dissolution rates and a variety of crystal chemical parameters, most notably, oxygen site potentials. We proposed that similar types of relationships should exist between isotopic exchange rates and the crystal chemical properties of common rock-forming minerals. In order to test this idea, we conducted oxygen isotope exchange experiments in the systems, carbonate-H2O and layer silicate-H2O at 300 and 350°C, respectively. Witherite, strontianite and calcite were reacted with pure H2O for varying lengths of time (271–1390 h) at 300°C and 100 bars. Similarly, chlorite, biotite and muscovite were reacted with pure H2O for durations ranging from 132 to 3282 h at 350°C and 250 bars. Data, in the form of fraction of exchange (F) versus time, were adequately fit using a pseudo-first order rate model. These rate data were compared against the electrostatic lattice energies (neglecting the repulsive forces) for each phase, normalized per number of cations. The correlations between rates and lattice energies are quite good for both mineral-H2O systems. In both cases, we observe an increase in rates correlated with a decrease in the electrostatic attractive lattice energy. The increase in oxygen isotope rates also closely follows the increase in solubility and dissolution rates reported for these minerals. The isotopic— chemical relations suggest that the oxygen isotope exchange behavior monitored experimentally is the net result of bond-breaking and dissolution of the mineral, complex ion formation in solution, and in particular, mineral growth, the most likely rate-limiting step. The greater the lattice energy required to break up the crystal into its constituent parts, the more sluggish the rates of both chemical and isotopic exchange. Although the results may seem intuitive, it is important to point out that by establishing an unambiguous relationship between

930

D. R. Cole

rate, lattice energy, and ultimately, temperature, we can being to develop equations capable of predicting rates of isotopic exchange for minerals for which experimental data are lacking. Clearly, more experimentation is needed to further test the model.

Acknowledgments—This work was sponsored by the Geosciences Program, Division of Engineering and Geoscience, Office of Basic Energy Sciences of the U.S. Department of Energy, under contract number DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation. The author gratefully acknowledges the assistance of D. Coffey for operation of the SEM, S. Fortier for conducting a number of carbonate experiments, J. Horita for analysis of metal carbonates, and E. M. Ripley for analysis of chlorites. The author wishes to thank Juske Horita, David J. Wesolowski, and Timothy Burch for comments and suggestions that greatly improved earlier versions of this paper. Appreciation is extended to John Valley and an anonymous reviewer for their insightful comments that also improved the paper.

REFERENCES Anderson T. F. and Chai B. H.-T. (1974) Oxygen isotope exchange between calcite and water under hydrothermal conditions. In Geochemical Kinetics and Transport. (ed. A. W. Hofmann et al.) 634, 219 –227, Carnegie Inst. Wash. Pub. Beck J. W., Berndt M. E., and Seyfried W. E. (1992) Application of isotopic doping techniques to evaluate the reaction kinetics and fluid/mineral distribution coefficients: An experimental study of calcite at elevated temperatures and pressures. Chem. Geol. 97, 125– 144. Bigeleisen J., Perlman M. L., and Prosser H. L. (1952) Conversion of hydrogenic materials to hydrogen for isotopic analysis. Anal. Chem. 24, 1356 –1357. Bottinga Y. and Javoy M. (1975) Oxygen isotope partitioning among minerals in igneous and metamorphic rocks. Rev. Geophys. 13, 401– 418. Bottinga Y. and Javoy M. (1987) Comments on stable isotope geothermometry: The system quartz-water. Earth Planet. Sci. Lett. 84, 406 – 414. Brady P. V. and Walther J. V. (1989) Controls on silicate dissolution rates in neutral and basic pH solutions at 25°C. Geochim. Cosmochim. Acta 53, 2823–2830. Brady P. V. and Walther J. V. (1992) Surface chemistry and silicate dissolution at elevated temperatures. Am. J. Sci. 292, 639 – 658. Busing W. R. (1970) Least-squares refinement of lattice n-orientation parameters for use in automatic diffractometry. In Crystallographic Computing (ed. F. M. Ahmed) pp. 319 –330, Munksgaard. Busing W. R. and Levy H. A. (1962) ORGLS, a general Fortran least squares program. ORNL-TM 271. Casey W. H. and Westrich H. R. (1992) Control of dissolution rates of orthosilicate minerals by divalent metal-oxygen bonds. Nature 355, 157–159. Chai B. H.-T. (1975) The Kinetics and Mass Transfer of Calcite Hydrothermal Recrystallization Process. Ph.D. Thesis, Yale University, New Haven, 203 p. Clayton R. N. and Mayeda T. K. (1963) The use of bromine pentafluoride in the extraction of oxygen from oxides and silicates for isotopic analysis. Geochim. Cosmochim. Acta 27, 43–52. Cole D. R. (1992) Influence of solution composition and pressure on the rates of oxygen isotope exchange in the system: Calcite-H2ONaCl at elevated temperatures. Chem. Geol. 102, 199 –216. Cole D. R. (1994) Oxygen isotope exchange rates in mineral-fluid systems: Correlations and predictions. Min. Mag. 58A, 189 –190. Cole D. R. and Ohmoto H. (1986) Kinetics of isotopic exchange at elevated temperatures and pressures. In Stable Isotopes in High Temperature Geological Processes. (ed. J. W. Valley et al.) Rev. Mineral. 16, 41–90. Cole D. R. and Ripley E. M. (1999) Oxygen isotope fractionation between chlorite and water from 170 to 350°C: A preliminary

assessment based on partial exchange and fluid/rock experiments. Geochim. Cosmochim. Acta 62, 449 – 457. Cole D. R., Mottl M. J., and Ohmoto H. (1987) Isotopic exchange in mineral-fluid systems: II. Oxygen and hydrogen isotopic investigation of the experimental basalt-seawater system. Geochim. Cosmochim. Acta 51, 1523–1538. Cole D. R., Ohmoto H., and Jacobs G. K. (1992) Isotopic exchange in mineral-fluid systems. III. Rates and mechanisms of oxygen isotope exchange in the system: Granite-H2O-NaCl-KCl at hydrothermal conditions. Geochim. Cosmochim. Acta 56, 445– 466. Cole D. R., Ohmoto H., and Lasaga A. C. (1983) Isotopic exchange in mineral-fluid systems: I. Theoretical evaluation of oxygen isotopic exchange accompanying surface reactions and diffusion. Geochim. Cosmochim. Acta 47, 1681–1693. Dove P. M. and Czank C. A. (1995) Crystal chemical controls on the dissolution kinetics of the isostructural sulfates: Celestite, anglesite, and barite. Geochim. Cosmochim. Acta 59, 1907–1915. Epstein S. and Mayeda T. K. (1953) Variation in O18 content of waters from natural sources. Geochim. Cosmochim. Acta 4, 213–224. Farver J. R. and Yund R. A. (1990) The effect of hydrogen, oxygen, and water fugacity on oxygen diffusion in alkali feldspar. Geochim. Cosmochim. Acta 54, 2953–2964. Farver J. R. and Yund R. A. (1991) Oxygen diffusion in quartz: Dependence on temperature and water fugacity. Chem. Geol. 90, 55–70. Fortier S. M. and Giletti B. J. (1991) Volume self-diffusion of oxygen in biotite, muscovite, and phlogopite micas. Geochim. Cosmochim. Acta 55, 1319 –1330. Gamsjager H. and Murmann R. K. (1983) Oxygen-18 exchange studies of aqua- and oxo-ions. In Advances in Inorganic and Bioinorganic Mechanisms, 2. (ed. A. G. Sykes), 317–380. Academic Press, New York. Godfrey J. D. (1962) The deuterium content of hydrous minerals from east-central Sierra Nevada and Yosemite National Park. Geochim. Cosmochim. Acta 26, 1215–1245. Horita J., Cole D. R., and Wesolowski D. J. (1995) The activitycomposition relations of oxygen and hydrogen isotopes in aqueous salt solutions. III. Vapor-liquid water equilibration of NaCl solutions to 350°C. Geochim. Cosmochim. Acta 59, 1139 –1151. Kusakabe M. and Robinson B. W. (1977) Oxygen and sulfur isotope equilibria in the BaSO4-HSO⫺ 4 -H2O system from 110 to 350°C and applications. Geochim. Cosmochim. Acta 41, 1033–1040. Lasaga A. C. (1998) Kinetic Theory in the Earth Sciences. Princeton University Press, 811 p. Leamnson R. N., Thomas J., and Ehrlinger H. P. (1969) A study of the surface areas of particulate microcrystalline silica and silica sand. Ill. State Geol. Surv. Cir. 444, 12 p. Matsuhisa Y., Goldsmith J. R., and Clayton R. N. (1979) Oxygen isotopic fractionation in the system quartz-albite-anorthite. Geochim. Cosmochim. Acta 43, 1131–1140. Matthews A. and Beckinsale R. D. (1979) Oxygen isotope equilibration systematics between quartz and water. Am. Mineral. 64, 232–240. Matthews A., Goldsmith J. R., and Clayton R. N. (1983) On the mechanisms and kinetics of oxygen isotopic exchange in quartz and feldspars at elevated temperatures and pressures. Bull. Geol. Soc. Amer. 494, 396 – 412. McCrea J. M. (1950) The isotopic chemistry of carbonates and paleotemperature scale. J. Chem. Phys. 18, 849 – 857. Northrop D. A. and Clayton R. N. (1966) Oxygen isotope fractionation in systems containing dolomite. J. Geol. 64, 174 –196. O’Neil J. R. and Taylor H. P., Jr. (1969) Oxygen isotope equilibrium between muscovite and water. J. Geophys. Res. 74, 6012– 6022. O’Neil J. R., Clayton R. N., and Mayeda T. K. (1969) Oxygen isotope fractionation in divalent metal carbonates. J. Chem. Phys. 51, 5547– 5558. Poulton D. J. and Baldwin H. W. (1967) Oxygen exchange between carbonate and bicarbonate ions and water. I. Exchange in the absence of added catalysis. Can. J. Chem. 45, 1045–1050. Rimstidt J. D. (1997) Chapter 10. Gangue mineral transport and deposition. In Geochemistry of Hydrothermal Ore Deposits, 3rd Edition. (ed. H. L. Barnes), 487–515.

Isotopic exchange in mineral-fluid systems Sharma T. and Clayton R. N. (1965) Measurement of O18/O16 ratios of total oxygen in carbonates. Geochim. Cosmochim. Acta 29, 1347– 1353. Smyth J. R. (1989) Electrostatic characterization of oxygen sites in minerals. Geochim. Cosmochim. Acta 53, 1101–1110. Smyth J. R. and Bish, D. L. (1988) Crystal Structures and Cation Sites in Rock-Forming Minerals. Allen and Unwin, 386 p. Stoffregen R. (1996) Numerical simulation of mineral-water isotope exchange via Ostwald ripening. Am. J. Sci. 296, 908 –931. Stoffregen R. E., Rye R. O., and Wasserman M. D. (1994) Experimen-

931

tal studies of alunite: II. Rates of alunite-water alkali and isotope exchange. Geochim. Cosmochim. Acta 58, 917–929. Sverjensky D. A. (1992) Linear free energy relations for predicting dissolution rates of solids. Nature 358, 310 –313. West A. R. (1984) Solid State Chemistry and its Applications. John Wiley & Sons, New York, 743 p. White A. F. and Peterson M. L. (1990) Chapter 35. Role of reactivesurface area characterization in geochemical kinetic models. In Chemical Modeling of Aqueous Systems II (ed. D. C. Melchior and R. L. Basset) Amer. Chem. Soc. Symp. Series 416, 461– 475.