The effect of hydrogen, oxygen, and water fugacity on oxygen diffusion in alkali feldspar

Geochimica er Cosmochimica Acta Vol. 54, pp.

Oolb-7037/90/$3.00 t.00

2953-2964

Copyright 8 1990 Pcrgamon Pns plc.Printed in U.S.A.

The effect of hydrogen, oxygen, and water fugacity on oxygen diffusion in alkali feldspar JOHN R. FARVERand RICHARDA. YUND Department of Geological Sciences, Brown University, Providence, RI 029 12, USA (Received December 4, 1989; accepted in revisedform August 20, 1990)

Abstract-Oxygen self-diffusion in adularia and albite single crystals was studied hydrothermally at 650°C from 5 to 1500 MFa confining pressure using a combination of hydrogen/oxygen buffers, a hydrogen ion buffer, and variable mole fractions of water (dilution with CO*). Diffusion coefficients (D) were determined from “0 concentration profiles measured with an ion microprobe. There is a good correlation of the D values with water fugacity but not with oxygen fugacity, hydrogen fugacity, hydrogen ion concentration, nor confining pressure over the range for which these parameters could be fixed independent of the water fugacity. Oxygen diffusion must involve the transport of an oxygen-bearing species, and the results of this study suggest that the transport species is molecular water. The rate-limiting step for oxygen diffusion could be either the rate of migration of the molecular water in the crystal or the rate of exchange of its oxygen with the feldspar structure. While protons may play a role in the mechanism of oxygen diffusion in feldspar, above the concentration supplied by pure water additional protons have no measurable effect on diffusion rates. INTBODUCTION

Alternative interpretations of the YUND and ANDERSON ( 1978) results were proposed by NORTONand TAYLOR( 1979) and EWALD(1985). Incorporating additional data for oxygen diffusion in an albite (FREER and DENNIS,1982), EWALD (1985) interpreted the apparent pressure dependence of “0 exchange in feldspars as a two-stage process with a relatively fast water pressure dependent surface reaction followed by the pressure independent rate-limiting diffusion process. We have measured oxygen diffusion rates in single crystals of feldspar using an ion microprobe in order to demonstrate further that the exchange of oxygen between feldspar and a fluid involves solid-state diffusion, and more importantly to resolve the dependence of oxygen diffusion rate on confining pressure and water fugacity. This technique provides an accurate measurement of the surface and near-surface 18O/‘bO ratio, which is necessary to resolve whether surface reactions or dilfusional exchange is occurring (GILETTI, 1985), and it also provides the narrow uncertainty limits necessary to demonstrate the dependence of D on experimentally controlled fugacities and activities of various species. The mechanism of oxygen diffusion in silicates and the role of water on the diffusion mechanism remains an important question. Recent studies of oxygen diffusion in anorthite (ELPHICK et al., 1988) and in quartz (ELPHICK and GRAHAM, 1988) confirm that there is a dramatic difference between oxygen diffusion under “wet” versus “dry” conditions. While the presence of water or one of its components clearly increases the diffusion rate, the mechanism by which the water produces this effect remains poorly understood. A model proposed by ELPHICKand GRAHAM( 1988) calls upon fast transient protons which are transported through the silicate lattice much faster than the oxygen diffusion rate and which mediate in the oxygen jump mechanism. We have conducted experiments over a wide range of hydrogen, oxygen, and water fugacities, as well as a range of hydrogen ion activities and confining pressures, and these parameters have been varied independently in order to eval-

ROLE OF WATER on the rate of solid-state diffusional processes in silicate minerals is well established. In the presence of water or one of its components (H+, H30+, OH-), the rate of oxygen diffusion in many silicate minerals is increased and the activation energy decreased (e.g., FREER, 1981), the rate of Al/Si disordering (GOLDSMI-IX,1987,1988) and CaAl/NaSi interdiffision (YUND, 1986) in feldspars is increased, and the strength of quartz and feldspar in the dislocation creep regime is significantly reduced (GRIGGS and BLACK, 1965; GRIGGS, 1974; TULLIS and YUND, 1980). An understanding of the effect of water on diffusion rates in minerals is essential for the application of experimental data to geological problems. For example, oxygen isotope systematics can be used to constrain the thermal history of igneous or metamorphic rocks, or their interaction with migrating fluids as they cool (e.g., GILE?TI, 1986; FARVER, 1989). However, before closure temperatures or cooling rates can be calculated for various minerals, the effect of water fugacity (fluid composition, hydrostatic pressure, etc.) on oxygen diffusion rates must be known. The effect of water on oxygen diffusion in feldspar was first reported by YUND and ANDERSON (1974). Diffusion coefficients determined from bulk exchange experiments with i80-enriched water and fine, closely sized feldspar grains demonstrated increased oxygen diffision rates with increased confining pressure, contrary to the effect of pressure predicted on the basis of volume diffusion theory. YUND and ANDERSON ( 1978) suggested that “water” as molecular H20, OH-, or HsO+ in the feldspar structure was responsible for the enhanced oxygen diffusion rates and that the mechanism might be similar to that suggested by DONNAYet al. (1959). This process calls upon rapid diffusion of hydrogen ions which act to hydrolyze tetrahedral ion-oxygen bonds. Slower diffusing hydroxyl ions or water molecules could then exchange with these hydrolyzed lattice oxygens.

THE UNIQUE

2953

J. R. Farver and R. A. Yund

2954

uate their effect on the oxygen diffusion rates. The results, together with results from recent infra-red studies, help to identify the oxygen-hearing species involved in the solid-state diffusion of oxygen under hydrothermal conditions and provide the basis for a more detailed comparison with oxygen diffusion rates in other minerals as well as for other ions in feldspar.

6.

PROCEDURES Sample Material Two natural feldspar samples were selected for this study: an adularia (Ab,.* AQ,~ 0r9& from Kristallina, Switzerland (AMNH #26545) and an albite (Ab9,., An,.* Or,.,) from Amelia Courthouse, Virginia, USA. Both samples are gem quality, clear crystals with welldeveloped cleavages and have been employed in other diffusion studies (Kristallina adularia: YUND and ANDERSON,1978; GILETTIet al., 1978; KRONENBERGet al., 1989. Amelia albite: KASPER, 1974; ANDERSONand KASPER, 1975; GILETTIet al., 1978). Thus, the results of this study may be directly compared to those of previous studies. A detailed chemical composition from neutron activation analysis of the adularia is presented in Table 1 (A. K. KRONENBERG,pers. commun.). Sample Preparation Experimental charges were prepared using crystallographically oriented pieces of feldspar sectioned with a low speed wafering saw. The sample was then cleaved along the (001) face using a razor blade. By using natural cleavage faces instead of a polished surface there was no enhanced exchange observed at the surface due to mechanical damage from polishing. A cleaved face also provides a very smooth planar surface for measuring the depth of individual bore holes. Both of these factors contribute to the improved reproducibility for the diffusion coefficient measurements, which is discussed in more detail later. Hydrothermal Runs Most of the experiments were typical two-oxide buffered, hydrothermal experiments (e.g., CHOU, 1987) and consisted of a cleaved (001) piece of feldspar (2 X 3 X 1.5 mm) loosely wrapped in Pt foil and weld-sealed in a thin-walled (-0.1 mm) Pt tube with 98 atom% “O-enriched water (6 to 12 mg for experiments at 5 to 350 MPa, 20 to 30 mg for experiments at ~-350 MPa). Approximately 15 to 20 mg of powdered feldspar was added to the experiments annealed at >350 MPa confining pressure in order to prevent shattering of the crystal during pressurization. The thin-walled Pt tube was weld-sealed in a thick-walled (-0.2 mm) Au tube together with - 100 mg of a two oxide plus water buffer.

Table

1.

Rb Mg Ba La Zr V MO Fe Ni AS Se Nd EU DY LU u

Trace

Element Chemistry of

119oi30 -7oot 9600*170 1.6f0.2 < 74 < 30 <6 46Oi.80 <48 <2 <2 16f2 < 0.05 <2 < 0.04 < 0.7

Cs Sr SC Ti IT I Cr Mll co :b” Ce Sm Tb Yb Th

Krislallina

Adularia’

5.7f0.3 790flOO 230f20 < 2600 0.19*0.05 <5 <27 0.9f0.2 <7 < 0.2
Concentrations are atoms per formula unit. in ppm. * from KR~NENBER~ (personal communicalion), determined by neutron activation i from GILETTI et al. (197s). dctcrmined by electron

microscopy

0

3

2

1

tog

4

P

WPa) FIG. 1. Water fugacities at 650°C over the range of confining pressures used in this study. Buffer assemblages are: WM = wustite + magnetite, MO = Mnz03 + Mn904, and NNO = Ni + NiO. The MO and NNO lines are coincident on this figure.

Three different hydrogen/oxygen solid oxide buffers were used in this study: wustite-magnetite (WM), Ni-NiO (NNO), and Mn30.,Mn203 (MO). The water fug&ties imposed by these buff& at 650°C as a function of pressure are shown in Fig. 1. These three buffers were selected because they effectively cover the range of oxygen and hydrogen fugacities expected in crustal environments. By using the solid oxide buffers a range of almost 10 orders of magnitude in hydrogen fugacity and nearly 20 orders of magnitude in oxygen fugacity was obtained in these experiments In addition, over the range of confining pressures employed (5 to 1500 MPa), the water fugacity was varied by over three orders of magnitude (Fig. 1). These fugacities were calculated using published data (HUEBNER, 197 1; RYZHENKO and VOLKOV,1971; PANKRATZ,1982). In the second type of experiment, Ag&04 was added to produce a known partial pressure of CO,, which allowed the fugacity of the water in the inner Pt tube to be varied independent of the confining pressure (HOLLOWAY et al., 1968; B~ETKHER et al., 1973). The silver oxalate decomposes at - 150°C to produce solid Ag and COZ gas. These experiments were all buffered at MO to ensure a high oxygen fugacity which minimizes the formation of other chemical species (i.e., CH.,) and allows accurate calculation of the fugacities of HZ0 and CO*. The fugacities of Hz0 and CO2 in the experiments were calculated using a modified hard-sphere Redlich-Kwong equation as proposed by KERRICKand JACOBS(1981) and JACOBSand KERRICK(198 1). All of the experiments were annealed at 65O’C and 100 MPa confining pressure. The mole fraction of CO2 was varied from 0.51 to 0.75 which yielded_&, = 19 to 37 MPa; this compares with 7 1 MPa for pure water at this temperature and pressure. The third type of hydrothermal run employed the Ag-AgCl hydrogen buffer of FRANTZand EUGSTER(1973). In these experiments, - 10 mg each of Ag filings, AgCl powder, and water were weld-sealed in a thin-walled Pt tube (2.5 mm OD). This tube was then placed in the 3.5 mm OD Pt tube with the P&wrapped sample and “O-enriched water. The experiments were all buffered at NNO because the AgAgCl buffer is well calibrated at those conditions (e.g., CHOU, 1978; FRANTZ and MARSHALL,1984). Hydrogen ion activities in these experiments were calculated using Eq. (12) and information in Table 4 of Franz and EUGSTER(1973), together with information in Table 6 of FRANTZ and MARSHALL (1984) for the specific run conditions and buffers of the experiments (200 MPa, 65O”C, NNO). The a”+ values calculated in this fashion compare well to calibrated values reported in CHOU ( 1978). The fourth type of hydrothermal run involved a pre-anneal with isotopically normal water at a higherf& than the diffusion anneal to produce, if possible, a different initial water concentration in the sample. The crystal was first annealed at 350 MPa for 48 h, then annealed at 50 MPa for 8 h with “O-enriched water. The charge was buffered at NNO for both anneals.

Self-diffusion of 0 in aduhuia and albite All experiments were annealed at 650°C in Rene metal cold-seal vessels from 5 to 350 MPa confining pressure, and in a solid medium apparatus from 840 to 1500 MPa. For the solid-medium sample assembly a stepped furnace was used to minimize vertical temperature gradients, and NaCl was used as the confining medium. Run temperatures in the cold-seal vessels were measured using Chromel/Alumel thermocouples, which were calibrated against known melting points and are accurate to < +S’C. Run temperatures in the solid medium apparatus were measured using Pt/Pt-Rh thermocouples and are accurate to +lO’C. Pressures in the cold-seal vessels were measured using Bourdon-tube pressure gauges and are accurate to eO.2 MPa for experiments at 5 to 25 MPa, and +l MPa for experiments at 50 to 350 MPa. The confining pressures in the solid medium apparatus were measured using an external transducer, and due to the strength of NaCl the values reported are probably maximum values but ~100 MPa higher than the true pressure on the sample, and all of the experiments were done with the piston-out technique (JOHANNES,1978; HOLLAND,1980). In all experiments the presence of water in the charges after the anneal was confirmed by observing fluid when the tube was opened and by weight loss after drying. The presence of both oxide phases in the buffer at the end of an experiment was confirmed by X-ray diffraction analysis, as was the presence of both Ag and AgCl in the AgCl-buffered experiments.

+ 5 +

‘+ -t ‘80

Profiles of “0 concentration versus depth into the crystal were measured using a Cameca IMS 3f ion microprobe at the MIT-BrownHarvard reaional facilitv. Details of the techniaue have been described previously~GILEr’rr et-al., 1978; GILET~IandYUND, 1984; FARVER and GILETTI, 1985). The sputtering employed a 50 pm diameter primary beam of O- ions with an accelerating voltage of 13.1 KeV. The rastered area was a square - 150 pm on a side, and O+ ions were analyzed A mechanical aperture, centered on the sputtered area, was introduced into the ion optics to limit the actual area from which data were collected to a circle 68 pm in diameter. Masses 18, 16, 17.5 (background), and 30 (Si) were measured while sputtering the sample. Bore hole depths were determined using an optical interferometer and monochromatic green light (wavelength 544 nm). A representative depth profile obtained for oxygen diffusion in adularia is presented in Fig. 2a. The apparent‘*Oconcentrationat

the surface(-50%) is lessthan the actualconcentration(-98%) due to dilution of the sputtered sample oxygen by isotopically normal oxygen from the primary beam. Previous workers (e.g., GILETTIet al., 1978) have demonstrated that after the first few tens of nanometers of sputtered crystal this dilution is constant with depth, and D values obtained for quartz using an AS primary beam and an O- primary beam yield identical results (KRONENBERGet al., 1987). The effect of using the observed concentrations rather than those corrected for primary beam dilution is not significant in the calculation of the diffusion coefficient; rather, the length of the gradient is the important parameter (e.g., GILETTIet al., 1978). Data from the depth profiles were reduced using the diffusion equation for transport normal to the surface of a semi-intinite volume (CRANK, 1956):

cxco-

X

_=erf- Cl

G

2(Dt)‘”

where C, = the concentration at some depth, x; Co = the initial concentration in the feldspar; C, = the concentration at the crystal surface; D = the diffusion coefficient; t = the duration of the anneal; and erf = the error function. Taking the inverse error function of the data from a depth profile (Fig. 2a), a linear array is obtained, as shown in Fig. 2b. A least-squares linear regression is fit to the data, and the slope of the line is proportional to 2(Dt)“*.

RESULTS The experimental results are presented in Table 2 along with the corresponding run conditions and D values calcu-

’

1qJq

+

+ +

+ +

2-

++ ++ ++

l-

01 0.0

+++++

++++++++++

I

0.5

0.25

0.75

1.0

Depth km) 2

erf -l

Diffusion Profiles

2955

1

U.”

0.25

0.5

0.75

Depth(I-W FIG. 2. (a) Representative profile of I80 concentration versus depth into an adularia crystal after a hydrothermal anneal at 650°C and 100 MPa confining pressure buffered at MO. (b) Data from (a) calculated as the inverse error function of the ‘*O concentration versus depth into the crystal. The solid line is a least squares linear regression fit to the data. All points after the nineteenth in (a) were averaged to yield the initial “0 concentration of the adularia.

lated from the depth protiles. Results are grouped into sets of bores made on different regions of a crystal, and the average of these is the D value assigned to that experiment. Uncertainties in the calculated D values take two forms: variation among a set of bores into the same crystal and the difference in average D values for different experiments annealed at the same conditions. While it is not possible to determine statistically valid uncertainties for such a small data set, the reproducibility of the D values provides a useful framework for this evaluation. Replicate analyses for an individual crystal yield a maximum standard deviation in D of 35% ofthe mean, with most replicate analysis having standard deviations of ~10% of the mean. A comparison of D values obtained from different crystals annealed under identical run conditions yields a maximum standard deviation of 23% of the mean. It is important to note that these reproducibilities are significantly less than the factor of 2 uncertainty for D values estimated in most other studies of oxygen diffusion in single crystals measured by similar techniques (GILETTIet al., 1978; GILETTI and YUND, 1984; FARVER and GILETTI, 1985, 1989; FARVER, 1989). The use of natural cleaved surfaces combined with buffered experi-

J. R. Farver and R. A. Yund

2956 Table

2.

Pressure

Diffusion Buffer’

Coefficients

Oxveen

(m*/s

WM I,

5

Feldsoar

log

x.10”)

Krisfollino 5

in

D

Duration (sets)

(MPa)

fur

D

(mean)

to&! fHz0

tw

ali+

(MPa)

(moles/kg)

4dularia

57 600

0.154 0.153 0.151

-18.82

0.308

-19.67

64 800 II

0.457 0.421 0.367

-18.38

0.691

-19.67

7.5

WM

64 800

0.218 0.215 0.226

-18.66

0.484

-18.15

11

WM

43 200

I,

II

0.334 0.401 0.412

-18.42

0.651

-16.71

25

WM

1.14 1.09 1.08

-17.96

1.008

-13.51

1.77 1.76 1.81

-17.75

1.615

-9.43

502

NNO

39 600 I,

29 400

1003

M3

36 000

1.19 1.25 1.30 1.13 1.12

-17.92

1.292

-9.34

1004

hKJ

36 000

1.50 1.57 1.35

-17.83

1.419

-9.30

100’

h4L?

39 600

1.80 1.74 1.87

-17.74

1.571

-9.24

28 800

2.40 2.45

-17.62

1.607

-7.69

2.52 2.38 2.47

-17.61

1.607

-7.69

3.46 2.98 3.00

-17.50

1.850

-7.69

100

100

WM

WM

57 600

57 600 1,

100 II

100

NNO

28 800 II

4.45 2.68

-17.45

1.848

-7.69

200

NNO

25 200

5.39

-17.27

2.038

-5.52

200

NNO6

23 820

5.00 4.72

-17.31

2.038

-2.69

3.90 3.44 3.16

-17.46

2.038

-2.69

6.33 7.08 7.27 7.14

-17.16

2.328

-4.87

8.86 10.7 12.4

-16.97

2.949

-3.94

200

350

840 I,

NIV06

21 600 II

M>

21 600

II

I,

M) I, II

21 600

1200 11

M II II

28 800

16.0 14.6 14.6 15.3

-16.82

3.342

-3.63

1500

WM

28 800

21.9 22.0 23.5

-16.65

3.618

-3.45

24.4 23.1

-16.62

3.618

-3.45

23.5 25.7 24.1

-16.61

3.648

-3.4s

II 1500

1500

WM II

43 200

ho I<

36 000 I,

Self-dithnion of 0 in adularia and albite

2951

Table 2. (Continued) Pressure

Buffer’

D

Duration

(sets)

(MPd

(m*/s

log D xlO1*) (mean)

Amelia 100 II

100 II II

WM II II

28 800 II II

II

”

WM II

28 800 II

II

II

log a”+

1% fmo (MPa)

(moles/kg)

Albite

1.01 1.15 1.17 1.30

-17.94

1.607

-7.69

1.21 1.28 1.35

-17.89

1.607

-7.69

1.14 1.17 1.34 1.29

-17.91

1.850

-7.69

100 11 II n

MI I. II

28 800 I n

1450 II

M) II

36 000 II

9.32 14.3

-16.93

3.598

-3.48

1500 II II

WM I. II

21 600

7.78 8.46 8.94 8.51

-16.07

3.618

-3.45

I,

II

II

All at 65O’C. trsnspon normal 10 (001) IWM = wustitc + magnctile +wstcr MO = Mn>O, + Mn20, + ~stcr NNO = Ni + NiO + water 2prc-annealed 8, 350 MPa “X co1 = 0.75 4x co1 = 0.66 ~xco~=o.51 6Ag + A&l + water

cleavage

mental conditions and annealing conditions that provide relatively long depth profiles is believed to be the reason for the significantly improved reproducibility of the results presented in this paper. DISCUSSION

Before discussing the effects of the various parameters on the oxygen diffusion rate in feldspar, it is necessary to first establish that the measured transport is by lattice diffusional exchange. Establishing the mechanism of exchange in these experiments is important because, as noted earlier, the results of the bulk exchange experiments of YUND and ANDERSON (1978) have been m-interpreted by EWALD (1985) as evidence of a two-step process of a pressure-dependent surface hydrolysis reaction followed by diffusional exchange. The ability to measure surface and near-surface ‘*O/‘6O ratios in single crystals by the ion microprobe depth profiling technique allows for accurate discernment of surface reaction effects. Other authors have discussed the advantages of this technique for studies of dilhtsional transport in minerals (e.g., GILETTI et al., 1978; FREER and DENNIS, 1982; GILETTI, 1985). The depth profile and corresponding inverse error function plot presented in Fig. 2 are typical of all of the depth profiles reported in this paper. A surface reaction process such as solution-reprecipitation would yield a step function for the depth profile (e.g., GILETTI, 1985). Clearly, Fig. 2 shows no indication of surface reaction and the excellent fit of the data to the error function, which is the solution to the diffusion equation for the conditions employed, demonstrates a diffusional exchange process. In addition, there was no variation in the surface ‘sO/‘6O ratios as a function of confining pressure as required for the surface reaction proposed by EWALD(1985). Thus, the oxygen transport process mea-

face.

sured in this study is lattice diffusion and the variations in D values are not the result of surface hydrolysis. It bears emphasis that the “0 concentration measured in the depth profiles is the “0 concentration of the crystal and is not influenced by the small amount of water (- 1100 ppm, KRONENBERGand YUND, 1988) present in the adularia. Hence, any gradient in the concentration of water in the feldspar due to the chemical diffusion of water is too small to have a measurable effect on the igO concentrations determined in the depth profile analysis. The reported diffusion coefficients represent the self-diffusion of oxygen in feldspar and not the diffusion of water, although water molecules may be the means of “0 transport, as described below. The YUND and ANDERSON( 1974, 1978) studies reported increased oxygen diffision rates with increased water pressure for the same adularia used in this study. In contrast, FREER and DENNIS( 1982) reported no pressure dependence for oxygen diffusion in albite in hydrothermal experiments annealed at 650°C and up to 800 MPa. To assess whether the effect of water on oxygen diffusion is different in different feldspar compositions, buffered experiments using Amelia albite were also done. The results (Table 2) demonstrate a similar increase in the oxygen diffusion rate with increasing confining pressure for albite as for adularia. It is not apparent why FREER and DENNIS (1982) did not observe the pressure dependence of D, but the effect may not have been evident because of the uncertainties and limited number of their data. The results of this study indicate that the water effect is not unique to adularia, and the following discussion is applicable to any feldspar. Natural feldspar samples typically contain from tens to thousands of ppm water (DEER et al., 1963); the adularia used in this study contains - 1100 ppm water (KRONENBERG and YUND, 1988). The presence of water in the feldspar poses

J. R. Farver and R. A. Yund

2958

the possibility that the “water effect” may be influenced by the initial concentration of water in the crystal and thus is a function of the hydrothermal history of the sample. To address this question, one experiment was done by first annealing the sample at 350 MPa for 48 h using isotopically normal water in order to impose a greater water concentration. The sample was then annealed at 50 MPa for 8 h using ‘*O-enriched water. Both anneals were at 650°C and buffered at NNO. The diffusion coefficient obtained agrees with that for a run at the same conditions but without the first anneal (Table 1). Thus, if any changes occurred in the starting water concentration in the crystal due to the pre-anneal, there is no effect on the diffusion rate. Only the conditions of the diffusion anneal are important. The important question is how “water” produces such a large increase in the oxygen diffusion coefficients in feldspar and other silicates. In addition to molecular water, hydrothermal experiments contain Hz, 02, H+ (or HSO+), and OHspecies. The fugacity or activity of each of these species in a hydrothermal experiment is a function of the temperature, pressure, and the influence of external buffers (e.g., CHOU, 1987). By independently varying the hydrogen, oxygen, and water fugacities, confining pressure, and hydrogen ion activity, the effect of each of these parameters on the oxygen diffusion rate in feldspar was evaluated. The results indicate that oxygen diffusion rates correlate with the water fugacity and are independent of fH2, ,fo2, OH+, kH-,and confining pressure in so far as these parameters could be varied independent of the water fugacity. The apparent correlation of D with an+ and confining pressure is due to these parameters being dependent on the water fugacity in the pure water experiments. Fugacity of Water The oxygen diffusion coefficients for adularia determined in this study are plotted in Fig. 3 as a function of the water

._

(m */set)

FIG. 4. The oxygen diffusion coefficient as a function of the water fugacity ., 3. For _ for albite at 650°C. Svmbols are as described in Fie. reference, the dashed curve is the trend defined by the adularia data in the previous figure.

fugacity of the experiment.

There is an excellent

correlation

of log D with log f Hflfor all of the experiments. The more limited data for albite are shown in Fig. 4 and yield a similar correlation with water fugacity. The excellent correlation of oxygen diffusion coefficients with water fugacity provides an important constraint on the oxygen diffusion process in feldspar which was not apparent from previous studies. Having established this correlation, the effect on D of the other parameters to the extent that they could be evaluated independent of the water fugacity will be considered. Confining Pressure In hydrothermal experiments, evaluating the effect of water fugacity on the oxygen diffusion rate independent of the effect of confining pressure is difficult. One way is to anneal the samples at low confining pressures (< 10 MPa) where the partial pressure of the water is low and the partial pressure of hydrogen imposed by the WM buffer becomes significant. In this fashion, the MO and WM buffers fix significantly different water fugacities at a constant confining pressure (Fig. 1). In order to vary the water fugacity at a high constant confining pressure, a known partial pressure of CO2 was added to three of the charges, which significantly decreases the water fugacity in the experiments (KERRICK and JACOBS,198 1). Values of log D for oxygen in adularia, as determined in

-17 i

logD

log/ (H*O) WW

I logf W *O’ Pa)

FIG. 3. The oxygen diffusion coefficientas a function of the water fugacity for adularia at 650°C. The symbols distinguish different buffering assemblages: open circles = Mn203 + MnsO,, open diamonds = wustite + magnetite, open squares = Ni + NiO, filled circles = Mn203 + MnX04 with C02, filled diamonds = Ni + NiO and Ag + AgCl, and filled squares = Ni + NiO pm-annealed (see text for details). Uncertainties on the data are approximately the size of the symbols.

this study, are plotted against log P,,r in Fig. 5. While a positive trend with a good correlation is apparent in Fig. 5, when the fugacity of water was varied while keeping the confining pressure constant, the apparent correlation of D values with the confining pressure is lost. This can be seen in Fig. 5 at P,,, = 100 and 5 MPa, where the range in D values obtained is greater than a factor of 3, well’outside uncertainty limits. By varying the water fugacity of the experiments independent of the confining pressure it is clear that it is not the confining pressure that causes the increased D values but water fi,tgacity which varies with the confining pressure (Fig. 1). Early hydrothermal bulk-exchange experiments (YUND and ANDERSON, 1974, 1978) demonstrated an increase in

Self-diffusion of 0 in adularia and albite

2959

Most recently, it has been suggestedthat the increased Si/

WD (m 4sec)

1 II

0

1

2

3

4

P tMPa) log

FIG. 5. The oxygen diffusion coefficient as a function of the confining pressure for adularia at 650°C. Symbols are as described in Fig. 3. the oxygen diffusion coefficient in adularia with increased confining pressure. The increase in D with increasing confining pressure reported by YUND and ANDERSON (1974,1978) is real but is actually due to the correlation of D with the water fugacity. Their experiments were not buffered and CO1 was not added in order to vary the water fugacity independent of the confining pressure.

Al disordering rate in feldspar is due to proton-activated, transient O-H bonding (GOLDSMITH, 1988) and that the rate of oxygen diffusion in quartz is increased due to fast proton transients (ELPHICKand GRAHAM, 1988). These studies suggest that diffusion rates should correlate directly with H+ activity (au+) in hydrothermal experiments. The apparent correlation with confining pressure would then be due to the dissociation of water into H+ and OH- ions with increased pressure (HOLZAPFEL, 1969; QUIST, 1970; MARSHALLand FRANCK, 1981). Figure 7 is a plot of the au+ in a pure water system at 650°C over the range of confining pressures employed in this study. The au+ was calculated from Eq. (4) of MARSHALL and FRANCK (198 1) using molar volume data from BURNHAMet al. (1969). The change in au+ over this pressure range is greater than 17 orders of magnitude. The large change in au+ with pressure is an appealing means to increase diffusion rates by the process mentioned above. However, if the change in au+ is responsible for the increased oxygen diffusion rates observed in this study, there should be a direct correlation of log D with an+. In order to test this correlation, a hydrogen ion buffer was employed to fix the au+ of experiments independent of the

Fugacity of Hz and 02

Plots of log D versus log fuI and logfo, are shown in Fig. 6a and b, respectively. These data include a range of - 10 orders of magnitude in fnZ and -20 orders of magnitude in f%;hence, any dependence of D on either fugacity should be readily observed. These results demonstrate that, at a constant water fugacity, there is no correlation of oxygen diffision rate with either Hz or Oz fugacities. The results for a given buffer are vertical or nearly so because the log D values reflect the variation of water fugacity with confining pressure for these experiments (Table 2). The results for a given buffer plot along a vertical line on Fig. 6b because the oxygen partial pressure is essentially independent of confining pressure, whereas on Fig. 6a the data points have a slight positive slope because fH2 varies slightly with confining pressure. The absence of any correlation argues that these species do not play a significant role in the oxygen diffusion mechanism. This is consistent with previous results for oxygen diffusion in quartz (ELPHICK and GRAHAM, 1988).

-17 log D

(m2/sec)

Debate about the role of hydrogen ions (protons) in increasing lattice diffusion rates in silicates can be traced to ~XNNAY et al. (1959) who suggested that bridging oxygens would be attacked by H+ ions forming an SiOsOH tetrahedron and incomplete SiO: tetrahedron. By breaking Si-0 bonds in this fashion, the energy required to move silicon and aluminum ions in the disrupted tetrahedra is greatly reduced. A similar model of hydrolysis of Si-0 and Al-O bonds by H+ ions has been proposed to explain the so-called hydrolytic weakening of quartz (GRIGGS and BLACIC, 1965) and feldspar (TULLIS and YUND, 1980).

0

0

0 D

0

00 . e

-18

_,I Y. . . -10

I

.

.

,

.

,:“. ...

0

-5

Wf W2) (MPa)

0 0 0

-17 t

v .

WD

(m2/se~) Activity of Hydrogen

I I

Q 0 0

t

--,.; -30

0 .

.,....,,.

;.

-20

-10

0

lOOf to21 wpa)

FIG. 6. (a) The oxygen diffision coefficient as a function of the hydrogen fugacity for adularia at 650% Symbols are as described in Fig. 3. (b) The oxygen diffusion coefficient as a function of the oxygen fugacity for adularia at 65O’C. Symbols arc as described in Fig. 3.

J.

2960

R. Farver and R. A. Yund

I

iOQD n0rmallzBd to IOQf(H2D)= 1.85 (MPa)

FIG. 7. Hydrogen ion activity of pure water at 650°C over the range of run pressures employed in this study calculated from Eq. (4) Of MARSHALL and FRANCK (198 1) using molar volume data from BURNHAM et al. (1969).

FIG. 9. The oxygen diffusion coefficient normalized to a constant water fugacity of 71 MPa (the f&o fixed by the MO buffer at 100 MPa confining pressure) as a function of the hydrogen ion activity for adularia at 650°C. Symbols are as described in Fig. 3.

water fugacity and confining pressure. The buffer was the Ag + AgCl hydrogen buffer developed by FRANTZand EUGSTER (1973). With this buffer the an+ is fixed at a significantly greater value than in the experiments with pure water. The results are plotted in Fig. 8 as log D versus log OH+. It would appear from Fig. 8 that the diffusion coefficients show at least a modest correlation with &f. However, this apparent correlation is due to the variation in f&o in the experiments, and when D values are normalized to a constant water fugacity, as shown in Fig. 9, it is clear that there is no correlation with an+. This lack of correlation indicates that it is the water fugacity and not the hydrogen ion activity that is the important parameter for oxygen di&sion over the range of conditions employed in this study. It is important to note that the evidence that D values do not correlate with &+ comes from the buffered experiments with pure water as well as the experiments with the Ag + AgCl buffer. As stated earlier, at confining pressures < 10 MPa, the water fugacities imposed by the MO and WM buffers diverge significantly (Fig. 1) because the partial pressure of hydrogen in the WM buffered experiments becomes signifi-

cant relative to the partial pressure of water. Calculating the an+ from the dissociation constant of water by the equation of MARSHALLand FRANCK ( 198 1) assumes a pure water system. Certainly, this is not strictly the case in the low confining pressure WM buffered experiments. However, the effect of the relatively high partial pressure of H2 in these experiments would be to increase the au+ relative to the values calculated for the pure water system. Thus, the au+ values plotted in Figs. 8 and 9 for the WM buffered experiments at < 10 MPa confining pressure are minimum values, and the true values would yield a greater deviation from a correlation of an+ with the oxygen diffusion rate. It is useful to note that the activity of hydroxyl ions (@u-) also varied greatly over the range of experimental conditions and buffers employed. However, as with au+, there is no correlation of D values with en-. Thus, in feldspar at least, the activity of OH- species does not play a significant role in the oxygen diffusion process either. IMPLICATIONS The correlation of the oxygen diffusion rate with water fugacity, along with other recent experimental results, suggests a mechanism for oxygen diffusion in feldspar under hydrothermal conditions. A discussion of this mechanism along with oxygen diffusion in other minerals and the diffusion of other species in feldspar follows.

l 0 Q 0 IOQ

D

0

.

. .

,B

(m%ec)

-18

?

0

Q

Mechanism of Oxygen Diffusion in Feldspar

0 0

-1s -25

0

....I*

1

-20

-15

-10

.

.

.

.

I

-5

.

.

.

*

0

IOQa ( ,.,+I (mokslkQ) FIG. 8. The oxygen diffusion coefficient as a function of the hydrogen ion activity for adularia at 650°C. Symbols are as described

in Fig. 3.

The process of oxygen exchange between crystal and fluid can be thought of as consisting of two steps: the transport of oxygen through the crystal structure by some oxygen-bearing species and the exchange of ‘*O from the transport species with I60 in the structure. Either step could be rate limiting, although evidence cited below suggests that the exchange of oxygens is the slower step. In either case the exchange rate could be enhanced by protons acting to hydrolyze and thereby weaken the Si-0 and Al-O bonds as previously proposed (e.g., GOLDSMITH, 1988).

Self-diffusion of 0 in adularia and albite

There are several oxygen-bearing species present in sufficient concentration in a hydrothermal experiment to be significant for transporting oxygen in the crystal; these include 02, HzO, H30+, O-‘, and OH-. We have observed, however, that the oxygen diffusion rate correlates only with water, fugacity, suggesting that water molecules are the oxygen-bearing species in the diffusion process. Size and charge considerations also indicate that molecular water should diffuse more rapidly than other oxygen-bearing species. Oxygen molecules are probably too large to move easily in the structure, and HrO+ is large as well as charged. At the conditions of these experiments, the effective radii of 0m2, OH-, and Hz0 are similar, about 0.135, 0.176, and 0.154 nm, respectively (SHANNON and PREWITT, 1969; NIGHTINGALE, 1959; KRYNICKIet al., 1979). The important difference is the formal charge assigned to each species and that a charged species must be electrically compensated in a crystal by an oppositely charged species or other defect. Recent models of hydrothermal oxygen diffusion in silicates have emphasized the control of the crystal structure and size of the migrating species for determining relative diffusion rates (FORTIER and GILETTI, 1989). However, the charge on the diffusing species must play an even greater role, as shown by the relative diffusion rates for alkalis and Si in feldspar (e.g., FOLAND, 1974; YUND and SNOW, 1989), and for Mg and Si in olivine (e.g., BUENING and BUSECK, 1973; JAOUL et al., 1981). Thus, a relatively large but uncharged species may diffuse faster than a smaller, highly charged one. The suggestion that water molecules transport oxygen from the fluid into the crystal is also consistent with the identification by IR and near-IR spectroscopy of water molecules as the dominant hydrogen-bearing species in feldspars (HOFMEISTERand ROSSMAN, 1985a,b; BERAN, 1986; KRONENBERG et al., 1989). HOFMEISTER and ROSSMAN(1985a,b) and BERAN(1986) report that molecular water may substitute for K in the M-site of K-feldspars, but the lack of correlation of oxygen diffusion rates with oxygen fugacity indicates that if the concentration of any vacancy is related to the oxidation state of iron (or any multivalent ion), the vacancies do not significantly affect the rate of migration of water molecules. The lack of any evidence for a vacancy mechanism suggests that water migration may involve the relatively large interstitial sites in the feldspar structure (SMITH, 1974). Whatever the oxygen-bearing transport species is, it must also exchange oxygens with the feldspar structure. This exchange may be greatly enhanced if protons are present to hydrolyze and thereby weaken the Si-0 and Al-O bonds as suggested by GOLDSMITH(1988) and ELPHICKand GRAHAM ( 1988). In studies of the effect of water on oxygen diffusion in quartz, ELPHICKand GRAHAM (1988) proposed that fast proton transients, which may be unquenchable, move rapidly through the crystal structure. They suggest that the proton transients may bc undetectable except by direct observation at experimental temperatures and pressures, and may differ from hydrogen species identified in quenched quartz samples. They do not, however, discuss how the protons in the structure are charge balanced. Perhaps the concentration of protons required is very small and local charge balancing can be achieved by the minor impurities present in natural crystals.

2961

There is no correlation of oxygen diffusion rate with an+ over the range of experimental conditions employed in this study (Fig. 8), although there could be a lower, critical concentration of hydrogen ions required to enhance the exchange process (CHACKO and GOLDSMITH, 1988). Thus, the large difference in the oxygen diffusion rates for feldspar in anhydrous versus hydrothermal conditions may result from the ability of water to supply protons as well as serving as the oxygen-bearing species. The oxygen-bearing transport species, which the results of this study suggest is molecular water, has to diffuse faster than the observed diffusion rate for oxygen. Once the “0 from a water molecule has exchanged with the structure, the water molecule must return to the surface or exchange its oxygen with another water molecule bearing an ‘*O. On average each diffusing water molecule has to travel twice as far as the length of the diffusion profile; hence, its diffusion coefficient would be four times faster than the measured rate for oxygen. If the rate limiting step is the exchange of oxygen with the feldspar structure, then the rate of water diffusion could be even greater than four times the measured oxygen diffusion rate. The diffusion rate of “water” in feldspar and other minerals is not known. IR and near-IR spectroscopy has been used to determine hydrogen diffusion rates by measuring changes in O-H stretching modes (“sharp band absorbance”) in quartz (KR~NENBERG et al., 1986), olivine (MACKWELL and KOHLSTEDT,1990), and feldspar (KRONENBERGet al., 1989). However, determining water uptake rates by measuring changes in the broad band absorbance (H-O-H bending modes) has been greatly hindered by the low solubility of water in most silicate minerals. An upper limit for water diffusion in a synthetic quartz of lo-l2 m2/sec at 9OO”C, 1500 MPa, and a solubility of 100 H/ lo6 Si has been suggested by GERRETSENet al. (1989). This D value is approximately one order of magnitude less than hydrogen diffusion in quartz at the same temperature and 2.5 MPa confining pressure (KATS, 1962). The difference between the diffusion rates for hydrogen and water in feldspar and other minerals remains to be determined, but the diffusion rate of water is not as slow as the oxygen diffusion rate and could be much faster. The concentration of water in the feldspar structure probably correlates with the water fugacity, a correlation which has been reported for quartz (CORDIERand DOUKHAN,1989). The correlation of oxygen diffusion rates with water fugacity would then reflect the increased probability of exchange of an I60 in the feldspar structure with an **O-bearing water molecule due to the increased concentration of water in the feldspar at higher water fugacities. The rate at which a lattice oxygen is exchanged with a water molecule need not depend upon water content; however, the total number of exchanges with ‘*O-bearing water molecules, and thus the net flux of “0 into the crystal, should increase with increasing water content in the crystal. Comparison with Oxygen Diffusion in Other Minerals Increased oxygen diffusion rates in minerals due to the presence of water are not limited to feldspar and have been reported from hydrothermal experiments for quartz (GILE~I

2962

J. R. Farver and R. A. Yund

and YUND, 1984; ELPHICK and GRAHAM, 1988), hornblende and GILETTI, 1985), and apatite (FARVERand GILETTI, 1989). In a companion study (FARVER and YUND, 1990) oxygen diffusion rates in quartz have been measured under conditions similar to those used in this study. Again, when varied independent of the water fugacity there was no correlation of D with fn2 , fo,, an+, &H- , nor confining pressure. However, there was a strong, positive correlation with fHlo . This suggests that the oxygen-bearing transport species under hydrothermal conditions may be similar in quartz and feldspar, and perhaps for other oxides and silicates as well. (FARVER

Comparison with Diffusion of Other Ions in Feldspar It is useful to compare the role of water in oxygen diffusion in feldspar with its role in alkali and Al/Si dithtsion. The presence of a trace amount of water (or its components) has a pronounced effect on solid-state processes in feldspars, including Al/B disordering rates (YUND and TULLIS, 1980; GOLDSMITH, 1987, 1988), the interdiffusion rate of NaSi/ C&Al in plagioclase (YUND, 1986; YUND and SNOW, 1989) and hydrolytic weakening in the dislocation creep regime (TULLE and YUND, 1980). The exception appears to be the rate of alkali interdiffision which shows no “water effect” (e.g., YuND, 1983; BRADY and YUND, 1983; HOKANSONand YUND, 1986), although it should be noted that the total range in pressure in these studies was only from 50 to 200 MPa. The yield stress of fine-grained (- 150 pm) quartz and feldspar aggregates is significantly lowered by the addition of water, and this weakening occurs within a few hours or less at 900-1000°C and 1500 MPa (TULLIS and YUND, 1980, 1985). It is not known whether the weakening involves hydrogen or water, but the diffusion rate of either may be sufficiently rapid to account for the rapid weakening. This weakening is observed only at confining pressures above - 500 to 700 MPa for both quartz (KRONENBERGand TULLIS, 1984) and feldspar (TULLISand YUND, 1980), indicating a strong dependence on water pressure or fugacity. A recent study has shown that water at high pressure enhances the climb rate of dislocations in quartz (TULLISand YUND, 1989), and, because climb must involve all of the ions in a structure, the climb rate is probably limited by the diffusion rate of tetrahedral ions rather than that of oxygen. The much lower diffusion rates of tetrahedral ions compared to oxygen are consistent with their large formal charges (Al+’ and Sie4). The migration rate of both may be enhanced by weakening of the AI-0 and Si-0 bonds by protons. Since the migration of water molecules is not directly involved, it is not surprising that the rate of Al/Si diffusion demonstrates a dependence on an+, rather than f&o, over a wide range of conditions (GOLDSMITH, 1987, 1988; YUND and SNOW, 1989). In the case of alkali diffusion, the hydrolyzation of K-O bonds may be much less important than that of Al-O and Si-0 bonds, as the strength of the K-O bond is less and each K is bonded to approximately nine oxygens. In addition, if alkali diffusion occurs by a vacancy mechanism, the number of alkali vacancies would be the rate limiting factor and this need not correlate with the water fugacity.

Application of Oxygen Ditbsion Data Oxygen diffusion data are now available for most major rock-forming minerals as well as many accessory minerals. These data have been employed to constrain the thermal history of rocks using the oxygen isotope systematics of their mineral constituents (e.g., GILE~I, 1986; FARVER, 1989). An important question in these applications is the magnitude of the effects of fluid composition and pressure (depth) on the oxygen diffusion kinetics, because these greatly affect the calculated closure temperatures and cooling rates. The results of this study suggest that the effect of fluid pressure on the closure temperature for oxygen diffusion in feldspar (and probably other silicates) may be significant and should be considered in the application of oxygen diffusion data. Most of the published diffusion data from hydrothermal experiments have been determined at 100 to 200 MPa for pure water systems. For upper crustal applications (50 to 200 MPa) where Pauid = Ptoti, and the fluid is essentially pure water, the correction for fluid pressure and composition would be minor and would likely introduce uncertainties in the calculated closure temperatures that are less than the uncertainties associated with the temperature dependence of D. However, changes in both fluid pressure and composition often associated with metamorphism could yield widely different oxygen diffusion rates in silicate minerals especially if the fluid becomes anhydrous (i.e., COZ rich) or absent due to the extraction of a partial melt as suggested for some granulite grade metamorphic terrains (e.g., FROST and FROST, 1987). Results from oxygen diffusion studies in quartz (FARVER and YUND, 1990) show a similar dependence on water fugacity, and, if the mechanism of oxygen diffusion is similar for other minerals, they are likely to show a similar dependence on fluid composition and pressure. CONCLUSIONS Over the range of conditions employed, oxygen diffusion in alkali feldspar occurs by a solid-state mechanism and there is no evidence of a pressure dependent surface reaction. The presence of water produces a similar effect in adularia and albite, and thus is not peculiar to any one feldspar composition. Over a very large range of hydrogen and oxygen fugacities, there is no effect on the oxygen diffusion rates in feldspar. While protons may play a role in the mechanism of hydrothermal oxygen diffusion in feldspar, the oxygen diffusion rate shows no increase when the proton activity is increased independent of the water fugacity. However, the oxygen diffusion rate shows an excellent correlation over nearly four orders of magnitude of water fugacity, and this is the cause of the apparent correlation of D with confining pressure noted in earlier studies. The correlation of oxygen diffusion rate with water fugacity, together with recent IR data and size and charge considerations, suggests that the oxygen-bearing transport species for oxygen diffusion in feldspar is molecular water. With increasing water fugacity the concentration of water molecules may increase and provide a greater number of oxygen atoms to exchange with the feldspar structure. Although neutral

Self-diffusion of 0 in adularia and albite water molecules appear to be the species which transports oxygen in the feldspar structure, the rate of oxygen diffusion may be limited by either the rate of diffusion of the water molecules or the rate at which they exchange their oxygens with the feldspar structure. Acknowledgments-We

wish to thank Jan Tnllis, Andreas Kronenberg, and Bruno Giletti for their helpful comments on the manuscript.

We also wish to thank Bruno Giletti for use of the Au-coater and optical interferometer. This manuscript benefited from comments by reviewers Tom Anderson and Tom Chacko and Associate Editor Robert Bodnar. The research was supported by NSF grants EAR8306162 and EAR-8607097 (Earth Sciences Section). Editorial handling:

R. J. Bodnar REFERENCES

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