JOURNALOF GEOPHYSICALRESEARCH,VOL. 89, NO. B6, PAGES4047-4057,

OXYGEN SELF-DIFFUSION

IN QUARTZ UNDER HYDROTHERMALCONDITIONS Paul

F.

Dennis

Department of Geology, Imperial

Abstract.

Oxygen self-diffusion,

been monitored in single-crystal

Dox, has

temperature range 515ø-850øCunder hydrothermal relations

for

College

Si-O-Si

+ H20 •-•

Si-OH:HO-Si

(1)

quartz in the

conditions. In the beta field, between 700ø and 850øC, the data are represented by two linear Arrhenius

JUNE 10, 1984

transport

parallel

The net effect of this reaction is to replace the "strong" Si-O-Si bonds with a comparatively weak

silanol group[Griggs, 1967]. The structure is

and

considered

to depoly!n_erize in a manner analogous

perpendicularto c. Valuesfor DO (m2 s-1) are

to silicate glasses[Moulsonandroberts, 1960]

2.09 x 10-1! parallel to c and3.16 x 10-10 ?er-

and melts [Burnham; 1975! . However, indicated by McLaren et al. [1983] this modelas is unsatis-

pendicular to (10iO). Values for AH (kJ molTM) are 138.54

parallel

to c and 203.72

perpendicular

to (1010). At 7OOøC,in the total pressure range 11.5-1OO MPa, Dox is independent of water (f(H20)) and oxygen (f(02)) fugacities between the Ni-NiO and Fe30•-Fe203 buffers. The results are consistent with diffusion via a simple charged vacancy mechanism under an extrinsic point defect regime. Further experiments are required to confirm the nature of the mobile oxygen defect. A key aspect of the results is the observation that at the low water fugacities of the present experiments a hydrogen-containing defect appears to play no role in the oxygen transport mechanism. This is in contrast to other• published sets of data and leads directly to the requirement for detailed interlaboratory comparisons.

factory. The incorporation of an infrared active OH:HO species is structurally incompatible with the minimum Si-Si distance in quartz (0.303 nm). A large structural rearrangement would be required, resulting in a high energy defect that is

likely

to occur in low concentrations only. More

recently, Dennis [1981] suggestedthat hydrogen is incorporated

as a simple interstitial

species

(HI' , usingKr•ger-Vinknotation[Kr•ger, 1964]) with a shallow donor level.

Based upon limited

ESRdata [Nuttall and Weill, 1980], Hobbs[1981] and McLarenet al. [1983] further proposeda complex defect silicon lattice

cluster consisting site tetrahedrally

of a vacant coordinated

by

four hydroxylgroups((4H)si) . Hobbs[1981] assumed the defect

likely

to be a shallow

acceptor.

The

effect of these defects on the stoichio-

merryof ,quartz is discussedby Hobbs[1981, this

Introduction

issue]. Since, in all crystalline solids, diff-

There

is

now a considerable

literature

concer-

usion

coefficients

are

sensitive

to

defect

con-

ning the hydrolytic weakeningof single crystals

centrations [KrSger, 1964], they shouldprovide a

of quartz as a result of some sort of bulk interaction with water. A review of the experimental

sensitive monitor for the incorporation of a hydrogen based defect. The present self-diffusion data base for quartz, however, is too sparse to test these mod-

studies is given by Blacic and Christie [this

issue]. It has beenpresumed that the effects involve water related defects within the crystal, the weakening being correlated with a broad, structureless infrared absorption band in the

3 pmwavelengthregion [Kekulawalaet al., 1981]. However, the precise nature of the disorder is not clear, although there has been some specul-

els. Choudhury et al. [1965], Giletti et al. [1976], and Freer and Dennis [1982] have made preliminary determinations of Dox under hydrothermal conditions at temperatures in the range 6OOø-750øC. There is a poor agreement between the various

ation about the solution mechanism [ Griggs, 1967; Dennis, 1981; Hobbs, 1981, this

this issue; McLarenet al.,

issue;

Kirby,

1983]. The aim of the

•of water

trolled

related

defects

processes by monitoring

in

diffusion

con-

fugacities to a total pressure of 1OO MPa. The effect, if any, of a water-related defect on oxygen transport rates will depend on the mechanism o_f incorporation of hydrogen or hydrox-

self-diffusion lytic

by reaction

of a water molecule

with

however,

do

data base and broadens the hydro-

represents

an important

and

be noted.

should

The accompanying paper in

and Yund [this issue ] also contribution

to this

area

a Experimental

02- ion to produce two OH- species that

are hydrogen

The results,

weakening debate.

this volumeby"Giletti

yl species [KrSger, 1964; Hobbs,1981]. Griggs [1967] proposedthat hydrogenentered the quartz lattice

data.

possible to determine whether incorporation of water from the vapour phase is responsible for the strong enhancement in exchange rates. The present work considerably enlarges the oxygen

oxygen self-diff-

usion coefficients (Dox) as a function of temperature (T), water (f(H20)), and oxygen (•(02))

bridging

of

erminations [Haul and DUmbgen, 1962; 'Schachtner and Sockel, 1977]. From these studies it is not

present work is to obtain information about the role

sets

indicate a significant enhancement of the oxygen self-diffusion rate when compared with the extrapolated results of high-temperature dry gas det-

Methods

bonded together:

Startiq• material. Two small, high clarity natural rock crystals from Madagascarwere used for the diffusion experiments, M3 and M12. Both the crystals have similar low total cation impurities (=0.02 mol %). Semiquantitative secondary ion mass spectrometer (SIMS) analyses for A1, K,

Copyright 1984 by the American Geophysical Union. Pape r number 3B1610. 0148-022 7/84/003B-1610505.

O0 404 7

4048

Dennis: Oxygen Diffusion

TABLE 1.

Semi-Quantitative

in Quartz

SIMS Analyses of the Starting

Material

Sample

A1

Ti

Li

K

Na

OH*

M3

28 (104)

2 (7)

58 (215)

7 (25)

14 (50)

68 (250)

M•

•

•

4 (•5)

• (?)

(S•)

(4•)

5• (•0)

All concentrations are expressedin units of atomsx 10-17 cm-3 and, in brackets, of atoms/10B Si atoms.

*Unpolarizedinfrared absorptionspectra at 20øC[Jones, 1978]. Li, Na, and Ti are presented in Table 1. The total hydrogen contents were determined by Jones

anneal at an ambientoxygenfugacity (2 x 104 Pa)

[1978] by using the completeroomtemperature

equilibrium with these conditions. To ascertain the extent of chemical potential gradient contri-

infrared

spectra.

Samplepreparation. oriented

with respect

The single crystals were to the c zone axis and

(10io) prism faces on a goniometerheadand sectioned with a precision diamond annular saw. Slices, approximmtely 1 mm thick, were cut para-

llel

to the basal plane (M3) and to (1010) (M12)

With orientations subsequently checked using the Laue back reflection X ray method. The cut surfaces were then ground using successive grades of SiC (to 12 •m), A1203 (to 8 •m), and diamond paste (to 1 •m) on an automated lap. The final polishing was carried out by hand using O.1 •m diamond paste on photographic paper. Pieces for experiments, approximately 2.0 x 2.0 x 1.Omm in size, were carefully broken off areas of polished sections free from pitting and visible scratching at x36Omagnification. To stabilize the damage due to mechanical

polishing [Atkinson and Taylor, 1978; Reedand Wuensch,1980; Sonderet al., 1981], all the fragments were wrapped in Au foil and annealed in air at 850øC for periods up to 1 month. Subsequent analyses of diffusion profiles indicated that this was long enough to relieve damaged surface layers. Where samples were not preannealed the isotope exchange profiles often exhibited a near-surface region of constant isotopic composition characteristic of solution/reprecipitation or recrystallization.

Hydrothermalexperiments. For the diffusion

experiments two or three quartz crystals (6-9 mg) were cleaned, loosely wrapped in Au foil and then sealed

in

3 mm O.D.

x O.1 mmwall

thickness

Pt

tubeswith 2-3 mgof water enrichedin 180, (180/(180 + 1BO) = 20%). To minimize convection and solution/reprecipitation [Kennedyet al., 1962] capsules were restricted to 1.5 cm in length and were placed in well characterised

pressurevessel hot spots (<1øCcm-1). At lower pressures longer capsules were necessary (e.g., 8 cm at 700øC and 11.5 MPa) and the crystals were

it

is assumed that

butions

to

the

the point

determined

defect

state

self-diffusion

is in

coeff-

icients, two samples (M12-OX4, M12-OXll) were preequilibrated prior to the isotope exchange runs. An identical procedure as outlined above was used with the substitution of distilled, deionised water of natural isotopic composition for the labeled water. After preequilibration the

samples were recovered, cleaned, and reloaded in a new capsule with labeled water and run at the equilibration conditions. In the experiments water fugacity was controlled by varying the total pressure in the range 11.5-100 MPa. Heating and cooling periods from

1OOøCbelow the required temperature represent less

than 2% of the total

anneal

time.

Reported

temperatures are believed to be accurate to ñ5øC and pressures to ñ1.5 MPa. At the termination of the run charges were recovered and checked for leaks by repeated dry-

ing at 120øC and weighing. The presence of excess water was always checked on opening to ensure that the

buffered

conditions

were maintained

during

anneal.

Ion microprobe analysis.

Satisfactory

samples

were cleaned and prepared for analysis by using the improved techniques outlined by Freer and

Dennis [1982]. Oxygenisotope compositionas a function of depth beneath the sample surfaces was determined by ion-microprobe analysis, using an Atomika A-DIDA (Atomika Technische Physik GmbH, Munich, Federal Republic of Germany) quadrupole

equipped scanning ionmicroscope [Wittmaack,

1978]. Typical operating parameters were selected as follows: to avoid primary beam dilution effects

[Gilett et al.. 1978] the primaryion beamwas massfiltered 40 Ar+ , accelerated to 10 keV with a total maximum current of 150 nA, focussed into a spot of 50 •m diameter at the sample surface; to ensure flat bottomed craters and improve depth resolution

the

beam

was

rastered

an

area

of

approximately

Charges rub approximately on the Ni-NiO buffer were placed directly in externally heated, cold seal pressure vessels using water as a confining

from

[Colby, 1975; Wittmaack, 1977]. For depth profiles less than 0.2 Bmin total length the rastered

medium. For samples run at the Fe•O•-Fe20 • buffer the Pt capsules were sealed in 4 mm0.D. x 0.3 mm

area was increased to 1OOO x 1000 •m. With these primary beam parameters sputter rates varied from 0.16-O.04 nm s-1 and were constant with time dur-

wall

thickness

Au tubes

10-15 mg of water prior ure

with

the

buffer

mix

and

to loading in the press-

vessel.

Because all

the specimens were given a damage

ition

500 x 500 •m, with

over

then held at the cold end of the tube by a small crimp.

electronics the

central

the data acquis-

gated to accept secondary ions 8% of

the

total

crater

area

ing ghe analysis [Freer and Dennis, 1982; Dennis, 1982]. Negative

secondary ions at m/e values of 16,

Dennis: Oxygen Diffusion

in Quartz

4049

depth(IJm)

17, 18, and 28 were sequentially monitored by rapid peak switching. These correspond to the

o

species160-, (170- + 16OH-), 180-, and 28Si-,

o.1

i*-crystol surfoce

respectively. Monitoring all four masses allowed the determination of chemical homogeneity in the

sampleby giving a cation:total oxygen(180 + 1BO)ratio which remainedconstant throughoutthe analyses.

The count rates

for

the total

M12-OX3

oxygen

t..92 x10'21m2s -1

signal exceeded5 x 106 cps in all runs. No correction

was required

dilution [Giletti

et al

o.161

for primary beam

1978] or H20 massspec-

tral interference with•O JAriraet al., 1979; Jaoulet al., 1980].ThelowH•160 - ionyield and

high residual

vacuum (<2 x 10-ø torr)

produced

•rol

natural 180 abundancesin the tails of most profiles. An example of the raw data is illustrated in Figure la. The depths of sputtered craters were measured with

a Leitz

reflecting

Linnick

light

dual

beam

, 2.•,

microscope. Thallium green light

,,•

o

2.0 1.8

recorded.

Computationof diffusion coefficients.

,

P412-OX3

2.2

(% = 540 rim) was used and accurate measurements made from suitable photomicrographs. Under optimum conditions accuracies to better than +0.O1 pm were

i

o

interference

,-,16 i

Self-

diffusion of the 180 isotope may be modeled by transport into a semi-infinite medium from a fluid phase held at constant isotopic composition. The length of all exchange runs was such that the rate of the phase boundary (solid/vapor)

'

1.2

,-,10 ._

O8

exchangereaction could be neglected [Freer and Dennis, 1982]. Under these conditions the general solution

to Fick's

first

law may be approximated

0.2

by [Crank, 1975]

o

•t) ) (Cx-C1) =erfc(•/•

(2)

(Co - c•)

whereCx, CO,and C1 are, respectively, the 180 concentration at a distance x beneath the crystal surface, in the fluid phase and at x --• in the

crystal (0.2% -- natural 180/(180 + 160) composition); the

t is the hydrothermal run time and D is

diffusion

coefficient.

A plot of erfc-1 (Cx - C1)/(C0- C1) versusx yields

a straight

line

with a slope equal to

1/2(Dt)l/2. An exampleof the reduceddata for

run M12-OX3 is illustrated in Figure lb. The corresponding raw data are plotted in Figure la. Results

Lattice

tracer

diffusion.

The

results

of

the

experiments are presented in Table 2. It is first necessary to establish that these represent tracer

diffusion

coefficients.

As indicated

ear-

lier it is assumed that the damage anneal equilibrates the defect chemistry with an ambient f(02). On changing the f(02) or f(H20), as in the isotope exchange experiments, the quartz nonstoi-

chiometrymaychange[Hobbs, this issue] . Equilibration must proceed by mass transport via diffusion of the relevant defect species from the gas-solid interface into the bulk of the crystal or

vice

possible

versa.

To determine

chemical potential

the

effect

gradients

of

these

on the

measured values of Dox, the two runs marked with an asterisk

in Table

2, M12-OX4 and M12-OXll,

received a thermodynamic anneal prior to the isotope exchange experiment. A comparison of results

for

runs

M12-OX1

with

M12-OX4

and M12-OX3

o.1

o.161

depth

Fig. (at60), Oxygen isotope ratios 180/(11• 0+ asa function of •epthin sample M12-OX3after hydrothermalexchangeat 700øCand 100 MPa for 1.6 x 10 $ s. Measured ratios are shown by the open symbols and the solid line represents the best fit to the data determined using the inverse error function plot illustrated in Figure lb. Only data in the depth range 0 to 0.1 pm were used in the least squares fitting procedure. The slope of the regressed line in

Figure lb is equal to 1/2(Dr)L7•2.Points to note are (1) the precision of the data, (2) the natural isotopic composition (0.2%) recorded without background subtraction in the tail of the profile, and (3) the good fit of the theoretical profile to the experimental data. with M12-OXll shows an agreement between the diffusion coefficients to better than 20%, Table 2. This similarity between equilibrated and nonequilibrated samples shows that if chemical pot-

ential gradients exist, they are eliminated rapidly, and that there is little or no mixing of the oxygen isotopes during this process. Thus the results represent true tracer (self) diffusion. The operation of lattice diffusion mechanisms is supported by the excellent fit of the data points in a depth profile to a single error function distribution as in Figures la and lb. Mixed lattice, grain boundary, and dislocation transport often results in a complex profile characterized by several superposed error function dis-

tributions [see Atkinsonand Taylor, 1978]. Alternative

isotope exchange mechanisms, e.g.,

sol-

4050

Dennis: Oxygen Diffusion

TABLE 2.

Experimental

in Quartz

Conditions

and Results

logf(O2),ôlog f(H20),ôPreanneal RunTime, Profile logDox,Orient-

Run

TøCBufferõ P, MPa Pa

Pa

Time,105 s 105 s

M3-OX2 M3-OX3 M3-OX4 M3-OX5 M3-OX6 M3-OX7 M3-OX8 M3-OX9 M3-OXll M3-OX12 M3-OX14

595 849 711 710 695 708 515 824 703 708 697

NNO NNO NNO NNO NNO NNO NNO NNO NNO NNO MH

1OO 1OO 100 40 50 75 1OO 1OO 20 11.5 1OO

-14.31 - 7.83 -10.93 -10.99 -11.37 -11.02 -17.22 - 8.32 -11.17 -11.O5 - 6.41

7.81 7.94 7.89 7.55 7.63 7.78 7.68 7.94 7.27 7.04 7.88

6.0828 1.4544 4.0776 4.0296 4.8828 4. 2906 10.3254 O. 8346 1.5822 4.4856 4.1385

M12-OX1 M12-OX3 M12-OX4* M12-OX5 M12-OX6

852 697 846 760 591

NNO NNO NNO NNO NNO

1OO 1OO 1OO 1OO 1OO

- 7.76 -11.29 - 7.88 - 9.73 -14.44

M12-OX7a M12-OX7b M12-OX8 M12-OXll* M12-OX14 M12-OX15

690 690 708 703 747 694

NNO NNO NNO NNO MH MH

40 40 11.5 1OO 1OO 1OO

-11.51 -11.51 -11.O5 -11.14 - 5.17 - 6.49

7.63 7.88 7.95 7.91 7.80 7.54 7.54 7.04 7.87 7.91 7.88

0.7920 1.5504 O.7782 1.6679 4.8786 2.3754 2.3754 4.4856 1.4812 1.4512 1.6412

Length,pm m2s-1 ation 2.36 4.42 2.30

-18.66 -17.17 -18.21

•! c •l c •! c

1.77

-18.10

l! c

1.82 1.83 1.22 1.77 2.O1 2.18 1.79

-18.13 -18.O2 -19.49 -17.24 -17.99 -18.O9 -18.12

I! I• t! •l •! •! •,

0.6]. 0.16

-•8.82 -20.31

.m.(].o!o) .J.(101_O)

0.63 0.22 0.09 O.15 O.14

-18.91 -19.71 -21.O2 -20.37 -20.44

.L(1010) _L(1010) _L(1010) _L(1010) _L(1010)

0.22 0.15

-20.33 -20.33

.L(1010) ..t.(101_0)

0.20 0.16

-19.76 -20.36

.4.(1010) A(1010)

c c c c c c c --

M3 0{c)

1.59OO

5.1845

and M12 (l(1010).

õNNO-Ni-NiO oxygen buffer; MH-Fe304-Fe203 oxygenbuffer. ôOxygen fugacities werecalculated by using the data of Huebner[ 1971]. Water fugacities werecalculated usingthe method outlinedby Edgar[ 1973]. Theequilibriumconstantfor formationof water, Kw, wastaken fromRobieet al. [1978]; the hydr_ogen fugacity coefficient from ShawandWones[1964] and the water fugacity coefficient from Holser [1954]. *See

text.

ution/reprecipitation

and recrystallization,

are

expected to yield a step function 180 profile beneath

the crystal

Precision results

is

surface.

and accuracy. estimated

The precision

from

a consideration

of the

formed

of

experience on the Imperial College SIMS system. Assuming that ion bombardment-induced profile

the

uncorrelated errors during the exchange anneal and ion probe analysis. The diffusion coefficient is determined from an equation of the form

D -- p2.t-1

(3)

whereP represents I/slope of the erfc -1 versus depth plot, Figure ib, and t is the isotope exchange run time. Accordingly, the relative ision of D, 4D/D, is given by

= A diffusion

run

prec-

+

started

(4)

and

finished

as

soon

as

the temperature passed through 10øC below the required cycles.

within period

temperature The sample,

on the heating however,

and cooling

was at a temperature

1OOøCof the run temperature for a further of approximately 30 min. Therefore •t/t is

estimated

as

+0.02

diffusion

time

at

the

most

of 23 hours.

for

the

Contributions

these errors in (4) gives an estimated precision in D of the order 4D/D = +25%. This is in agreement with the limited duplicate experiments per-

shortest

to 4P/P

mainly arise from the precision of the crater depth determinations. Measurements from photomicrographs indicate 4P/P is equal to +0.02 (+1 standard deviation) in the worst cases. Applying

to

date

and

in

accord

with

the

accumulated

broadeningis minimal [Giletti et al., 1978; Freer and Dennis, 1982], significant inaccuracies may still result from solution damage at the surface of the samples. For instance, specimens oriented parallel to (OOO1) exhibit strong hydrothermal etching resulting in a high density

(2.5 x 103 cm-2) of pits, 1-2 pm in diameter and 0.2 •m_deep. Samples with faces oriented parallel to (1010) exhibit no such pitting, but minor scratching to a depth of O.1 •m is observed. This is thought to be due to etching of dislocation damage generated during polishing. The effect of solution damage on the determined values of Dox is not known and remains a possible important factor determining the absolute accuracy of the results. This point will be returned to in the discussion.

Water fu•acity dependenceat 7OOøC. Figure 2 represents

the results,

listed

in Table 2, for

Dox as a function of f(H20) at a constant f(O 2)

(-•10-11 Pa). Within the experimentalrange a

dependence

of the

D = f(H20) TM

form

m = -O.11 +O.29 m -- 0.O1 +O.51

({}c) (œ(1010))

(5)

Dennis: OxygenDiffusion in Quartz

is indicated.

From the linear

regression

results,

700øC

Dox is observed to be approximately independent of f(H20). It must be emphasised, however, that

-18

the limited experimental range and small sample size has resulted in a large uncertainty in the slope determination at the 95% confidence level.

-19 ß

Oxygen fugacity dependenceat 700øC. Only

at

the

Ni-NiO

buffer.

diagram are the results

Included

in

form

T#m s•ud•

o •,,, .,. ,,,,,

-21

i

i

i

-1•

of an independent study

mined under a similar f(H20) but considerably more oxidizing conditions. Within the combined experimental range an f(02) dependence of the

J. (10TO)

-20

the

[Giletti andYund, this issue]. Thesewere deter-

.... ,.......... *..../-........... t" I1œ

three experiments were conducted at an oxygen fugacity fixed by the Fe30•-Fe203 buffer, Table 2. Two of these were at 700øC. The results are plotted in Figure 3 with the equivalent data determined

4051

i

-12

i

i

i

-10

i

-8

,

i

-6

,

i

-•

i

-2

,

,

,

0

,

2

•o9f(O2) (Pa)

Fig. 3. Measured values of log Doxas a function of log f(02)

at 700øC. The closed symbols repre-

sent data from this

study (Table

2) and the open

symbols are data taken from Giletti

and Yund

[this issue]. The f(O2) for the latter results m = -0.02 m =-0.02

D • f(02) TM

+0.02 +0.04

is observed. The results clearly be f(O2)-independent, with little

was calculated

(•c) (œ(1010))

(6)

indicate Dox to experimental

from the equilibrium

constant

for

formationof water at 700øC[Robieet al., 1978] and the total pressure, P = 100 MPa. The slopes for both orientations clearly indicate f(O2)-independent behavior for tracer diffusion.

uncertainty, in the 100-10-1! Pa range. Temperature dependence.

All

the results

are

plotted as a function of inverse temperature in Figure 4. Data in the temperature range

700ø-850øCplot on two straight lines characteristic of the two transport directions. well described by the Arrhenius law

These are

••-7•2

the activation enthalpy for oxygen self-diffusion, R is the gas constant, and T the absolute temperature. A linear regression of data in the

giving values for Do and AH, is summ-

in Table

95% confidence

3. The errors

ed in this

temperature

are quoted at the

level.

Results at 6OOøCand 515øC were omitted from the best fit procedure. Moreover, too few data have been collected in the alpha field to (1) estimate an empirical activation enthalpy and (2) provide statistical evidence for the observed

Comparison with other data. For comparison with the present determination, all other sets of data are summarized in Table 4 and Figure 5. Gil-

etti and Yund[this issue] monitoredthe diffusion coefficient in single crystal quartz at 100MPa total pressure under conditions fixed by a fluid constrained to the bulk composition of pure H20. In the beta field their values of the activation enthalpy for diffusion are

142 kJ mo1-1 (lie) and 205 kJ mo1-1 (A(10[O)). These results are in excellent agreement with those of the present study. Moreover, there is also a very good agreement between the two sets

of preexponential imental

logfH2 0(Po) i

....

8 i

i

i

I

700øC

11]

•

,•, 20 '

PI12(J.c)

--,

t-tz,

p

21

I

constants, lying within exper-

of each other,

for

transport

both

data

available

further

discussion

is

not

warranted.

-t-tt

19

error

parallel and perpendicular to c, Figure 5 and Table 4. Correspondence in the alpha field is only reasonable, Figure 5, but in view of the limited

Ni-NiO buffer

•

range.

(?)

whereDO is the preexponentialconstant, AHis

arized

pared with those of Giletti and Yund[this issue]. Clearly, further detailed work is requirDiscussion

Dox= Doexp[-AH,•

beta field,

departures from the extrapolated high-temperature data. The data in the alpha field should be com-

i i I , , i ,,i , , i , , , ,,16 log (Po) fH 2

Fig. 2. Measuredvalues of log Dox as a function of log f(H20) at 700øC and the Ni-NiO oxygen buffer. Both transport directions show approximately f(H20)-independent behavior, though the associated errors in the slope determinations are

large at the 95%confidence level (equation (5)).

Comparing the detailed trace element chemistry of the crystals used and the annealing conditions for both studies

indicates

a large variation

with

the exception of the A1 content and the f(H20). The agreement between the results, therefore, can only be rationalized in terms of (1) intrinsic (thermal) diffusion, or (2) extrinsic diffusion with Dox dependent on the A1 content, the water fugacity or both. In view of this

observation,

it

is surprising

that attempts to further characterise the diffusion mechanismby monitoring the variation of

Doxwith water fugacity has produced widely differing results. imental error,

In the present work, within experDox is observed to be independent

of f(H20) in the range 11-77 MPa, at 700øC. In contrast, Giletti and Yund [this issue] have rep-

4052

Dennis: Oxygen Diffusion

TøC 800

7OO

,

600

,

with 5:1 solid:fluid weight ratio in the charge has already been noted (see Results, Precision and Accuracy). These may be expected to be somewhat more severe at 350 MPa. The question is to what extent, if any, do microscopic solution phenomena affect the diffusion profile? Matzke

550

,

,

16

H3 (uc)

17

[1976, 1982] has indicated that surface roughening and relaxation in actinide dioxides during the early stages of isotope exchange anneals may be responsible for erroneous results. In experiments, this is evident as an initial fast tracer penetration showing correct error function behav-

18

--

19

•

20

H12LLc)

o• 21 ,

•

ior. In a time dependent study of Dox at 100 MPa, Giletti and Yund [this issue] have reported a

22

beto

i

i

0-9

otpho

i

1-0

similar behavior. For instance, transport •rhomb the determined reased by a factor of 2 for an exchange anneal time from 2 to experiments, however, have not higher pressures in either this

i

1.1

Giletti

1.2

103/TøK

Fig. 4.

Log Dox as a function of reciprocal tem-

perature. The solid lines represent a least quares fit to the data in the beta field. Values for the activation parameters in the Arrhenius law

are

summarized

in

Table

3.

orteda marked dependence with Dox• f(H20)1'1 over a slightly The

reason

for

the

different

results

is

Both

studies

a range of f(H20) number of results.

have

examined

conditions

too

to

for

the

is of the right

different

results.

At

determined Two other

diffusion determinations

coefficients. of the

tracer

diffus-

conditions

have

beenmade. Freer and Dennis [ 1982] determined Dox, •lc, at 600ø and 750øCunder identical conditions

to the present

study. The preliminary

act-

determination

but the preexponential

con-

stant is a factor of 104 x smaller. No attempt

the present determination. Outside these limits different dependencies may well exist. To adequately resolve this problem there is a requirement for data covering a much wider range of f(H20) conditions than hitherto considered. 2. At the high total pressures (350 MPa) used

and Yund [this issue] quartz exhibits solubility

account

this stage there is a strong requirement to study in more detail the effect of microscopic changes in surface geometry, by whatever mechanism, on

present

the slopes of

Giletti and Yund[this issue] are compatiblewith

significant

The magnitude of the effect

ivation enthalpy (138 kJ mo1-1) is close to the

restricted

isotherms in a plot of log Dox versus f(H20) cannot be determined with any degree of precision (e.g., see equation (5)). As a result, within experimental error and in the overlap of conditions studied (22.5-77 MPa f(H20)), the results of

by Giletti

time.

ion of oxygen under hydrothermal

with only a limited

Consequently

and Yund [this issue]. It is difficult,

order

the

not

at 800øC and value of Dox decincrease in the 30 hours. Similar been repeated at study or that of

therefore, to assess whether the reported values of Dox represent correct results or experimental artefacts due to too short an exchange anneal

wider range from 22.5 to 225 MPa.

apparent. There are, however, two important possibilities that require verification by further experiments; 1.

in Quartz

(>1.6 wt.%) in water at

has yet been made to duplicate the experiments on this particular crystal and the results should be

treated with caution. Choudhury et al. [ 1965] used

a combination

of

the

nuclear

reaction

180(p, •)15N with microsectioning to determine tracer diffusion profiles at 667øC and 82 MPa P(H20). While a significant an_isotropy was observed for

transport

•ic,

and-k(1010),

Table 4 and

Figure 5, the absolutevalues of Doxare between 10• to 104 x faster than recorded by this study. Giletti and Yund[ this issue] have indicated potential

systematic errors

in the nuclear activat-

ion method to account for

addition,

significant

the discrepancy.

solution/reprecipation

In

in

700øC[Andersonand Burnham,1965]. The possible

the chargesused by Choudhury et al. [1965] can-

importance

not

of solution

effects

in basal plane

sections run at 100 MPa total pressure and 700eC

TABLE3.

be

ruled

out.

Only two determinations of Dox have been made

Preexponential Factors, Do, and Activation Enthalpies, AH, for the Empirical

Arrhenius

Relation,

Orientation

Do, m2 s-1

!!c

2ß09-+18'27 1 84x 10-1! -

_k(1010)

2.00

Data from the beta quartz field procedure.

The uncertainties

(7)

AH, kJ mo1-1

0

3'86+ 0 93x 10-1 --

Equation

138.54 + 19.1

203.72 + 2.28

only were used in the least

squares fitting

are expressed at the 95% confidence

level.

Dennis: Oxygen Diffusion

in Quartz

4053

under dry gas conditions, both at a near ambient oxygen fugacity (0.21 MPa). Haul and DUmbgen

[1962] monitoredthe changewith time of the isotopic composition of the gas phase during diffusion annealing with a crushed quartz powder between 1010ø and 1212øC. For the analysis a plate

diffusion model[Crank, 1975] wasassumed using the specific surface area, determined by gas adsorption, as a measure of the sample geometry. This gave an activation enthalpy for diffusion of

230 kJ mo1-1. The tracer diffusivity was also found to be independent of the A1, Li, Na, and H content of the crystals used. Schachtner and Soc-

kel [1977] monitoredthe total amountof 180 tracer

that

entered a single

crystal

during an

exchangeanneal (870ø-1280oc), using the nuclear

reaction 180(p, n)18F. The results are in reasonable agreement with

those of Haul and DHmbgen

[ 1962] with an activation enthalpyof 195 kJ mo1-1, Figure 5. No diffusion anisotropy was

oo

ooo

o

%

observed.

The absolute rates of transport in these water-free systems appears to be considerably slower than the extrapolated high temperature hydrothermal data would predict, Figure 5. It is difficult, however, to make a precise comparison due to the large potential systematic errors inherent in the bulk exchange technique. These include the use of the specific surface area of the crushed

%

powderas a measureof the samplegeometry[Haul

andDUmbgert, 1962] andthe assumption of fast gas/solid

•o oo

interface

isotope exchange kinetics

1962] indicate that their results should be corfSchachtner an dSockel, 1977 ].Haul and DHmbgen

rected, taking account of the "roughness factor", to yield true tracer diffusion coefficients. The roughness factor is defined as the ratio of the specific surface area measured by gas adsorption to the geometric surface area. Applying this cor-

rection, Dox is found to be approximately a factor

of

10 faster

than

indicated

Figure 5. The activation

ied. It

is unlikely

in

Table

4 and

enthalpy is not modif-

that these systematic errors

canaccountcompletelyfor the difference in oxy0 m•

o

=•

0

0

I•

o

--•

=

.•

o

o

=H

o

0

o

=

-•

m•

gen transport

rates between the hydrothermal and

dry gas exchange experiments. Theprobability is still that a significant enhancement in oxygen

diffusivity occurs under hydrous conditions, though the mechanism is not understood. A comp-

lete discussion will haveto wait until the tran-

8oOO o

00

sport rates under dry gas and low water activity conditions are more precisely characterized.

Defectchemistry anddiffusionmechanisms.

Prior to discussing the possible defect chemistry of quartz under the experimental conditions, it

must be madeclear that the conclusions herein

are basedonthe experimental resultsreportedin this study.Consequently, theyare constrained by the points raised in the preceeding discussion

and may require subsequent modification. The observed independence of Doxwithf(H20)

andf(02), Figures 2 and 3, is not consistent

with the suggestion that dissolved structural water in the lattice plays a role in the oxygen

transport mechanism [Donnayet al.,

1959; Dowty,

1980; Graham, 1981; Freer and Dennis, 1982;

Kirby, this issue]. Hobbs[1981; this issue] has reviewed several potential water incorporation mechanismsand their expected effect on oxygen self-diffusion

coefficients.

All

these

models

4054

Dennis: Oxygen Diffusion

TøC 1200

1018A1 cm -3) in the specimens,the f(02) indep-

800

•0

IIIIII

in Quartz

!

500

I

endence can be accounted for by assuming that

I

--

the

\

predominant defects are divalent vacancies of oxygen, which are created by incorporation of A1

/

incorporation

+

atoms

into

Si

lattice

sites.

For

this

case

the

of A1 is described by (using Kr•ger

-Vink notation [ Kr•ger, 1964]) 18

A1209 • 2Alsi' + 300*+ Vo'' The corresponding electroneutrality described by

• 20

23,.,

i

centrations.

i

!

t

1'0

i

i

,

Dox= y.a2.•.Nv

(11)

is the jump distance, • is the jump frequency,

andNV is the vacancyfraction (-- [Vo" ]/[Oo*]).

From equations

sources: 1, this study; 2, Giletti

and Yund [this issue]; 3, Freer and Dennis [1982]; 4, Choudhury et al. [1965]; 5, Haul and DUmbgen [1962];6, Schachtnerand Sockel [ 1977]. In the alpha field the open symbols and dashed-dotted

line

are from

Giletti andYund[this issue], and the closed

the

con-

Wherey is a geometric factor close to unity, a

Fig. 5. Compiled Arrhenius diagram of the available oxygen tracer diffusion data summarized in Table 4. The data are taken from the following

predict

mole fraction

1-•

1031TøK

symbols are from this

(10)

Shewmon, 1963

i

1'2

indicate

is

Assuming a vacancy mechanismfor

oxygen diffusion

0'8

condition

[Vo''] -- [Alsi']/2 where square brackets

,

(9)

study.

a strong dependence of Dox on f(H20) of

form

(10)

and (11) we can write

nox= ¾.a2.•.[A1si' ]

(12)

2[ Oo*]

At a constant[ Alsi' ] content,everytermon the right-hand side of (12) is independent of f(02), and so is Dox. Note that implicit in (12) is the assumption that there is no effect of impurities

on the jump frequency term •. It has been suggested that hydrogen defects can change the mobil-

Dox = f(H20)TM

(8)

ities of poinC..defects in silicates IS. H. Kirby, personal communication, 1983]. There is, however,

where the exponent, m, has values >+0.5 or <-0.5. This is clearly at variance with the results sum-

marized in Figure 2, at least to 100 MPa total pressure in the temperature range 6OOø-850øC. Further, as already indicated, it is not yet possible to make a valid comparison between the hydrothermal and water free systems in order to look for evidence of some form of hydroxyl cont-

little

experimental

evidence for this

present, though it must remain a potentially ortant

at

imp-

consideration.

Equation (12) can be written

in the standard

Arrhenius form [Kofstad, 1972]

Dox-- y.a2.v.[A1si '] .expASv TM .exp-AHv TM (13)

rolled diffusion. In this context, therefore, the

diffusion be•hviourof quartz departs significant

where the temperature

ly from that

Dox, is defined by the Boltzmann distribution

suggested as typical

of silicate

systemsunder hydrothermalconditions [Yund and Anderson,

1974,

1978; Giletti

et al.,

1978; Freer

and Dennis, 1982]. The results

material

are,

however, consistent

wtiose point defect structure

led by either

(1) intrinsic

with

a

is control-

(thermal) ionic dis-

order, or (2) an extrinsic, non-volatile, aliovalent impurity. Moreover, the transport system must involve a charged defect. Neutral defects are. characterised by a varying concentration with

10-3 mol % at •1000K.The crystals used in this work contain impurities to at least 10-2 mol %, and it is, therefore, probable that the defect concentrations are nonstoichiometric, depending on

the

trace

element

content.

Considering the relatively of the major substitutional

high concentrations impurity

(2.5 x

and hence

factor exp (Asvm/R).exp (-AHvm/R.T) and the pre-

exponential constant for • is represented by v.

The free energy, AGv TM= AHv TM- TASv TM,is correlated with the energy change for an oxygen atom moving from a normal lattice site to the saddle position during doubly charged vacancy migration. The enthalpy

change involved

in the activated

process, AHVm,is directly equatedwith the empirical activation enthalpy, giving the following values for the vacancy migration enthalpy:

f(02) irrespective of the defect state [KrSger, 1964]. Hobbs[1981] estimatedthat the mostprobable intrinsic defect state is the Schottky defect with concentrations of approximately

dependence of •,

AHv TM(kJ mo1-1) •lc

138.54

-k(1OlO)

There is limited

203.72

supporting evidence for an

oxygen vacancy model for diffusion.

Both optical

and ESRdata indicate that oxygenvacancies are the dominantnative defects in quartz [Griscom,

1978]. Moreover,JonesandEmbree[1977] have identified

vacant oxygen species as the main

Dennis: Oxygen Diffusion

native

ionic

defect

in Quartz

4055

saddle •

in CO2 reduced silica

point [•c]I

(f(02) -- 8 x 10-12 Pa) at 9OOøC.These conditions closely ment

approximate

those of the present

•

experi-

s.

A key feature of the model is the ability to directly test the relationship given in (12),

where Dox is predicted to be linearly al

to the A1 content

of quartz.

proportion-

The extant

ects, thoughHobbs[1981] indicates that the Alsi'

saddle•

data,

however, do not cover a range of A1 contents in order to test this point. A major assumption is that of doubly charged oxygen vacancies. There is little direct evidence for the charge state of the mobile oxygen def-

acceptor level lies deeper in the band gap

than the VO' donor level. This implies that at

Fig.

6.

The structure

of idealized

beta quartz

projected onto (OOO1),after Deer et al. [1975]. Solid lines represent the upper edges and dotted lines the lower edges of tetrahedra. Projected

all but the highest temperatures, the divalent state will be stable. This suggestion while consistent with the data is not unique. For instance, a singly charged oxygen vacancy, VO', could well be the mobile defect species in a charge neutrality condition of the form

elementary diffusion paths are indicated by open arrows and saddle point positions by solid circles. The near.est neighbor lattice sites to the saddle points are indicated by A, B, and C (diffusion parallel to c), and 1, 2, and 3 (diffu•sion perpendicular to (1010). Note that site 3 is displaced from B by 1 unit cell edge in

[Vo' ] = [Alsi' ] . To resolve this problemthe

the

charge state of the defect can only be determined in experiments where the defect populations are dependent on the intensive thermodynamic parameters and not independent as in the present work.

The anisotropy in activation enthalpies for vacancy migration is not unexpected when.consid-

ering the hexagonalbeta quartz structure [ Deer et al', 1975]. Assumingthat vacancies can only jump along tetrahedral edges to adjacent oxygen sites, it is possible to outline potential diffusion paths. These are schemmtically illustrated

in Figure 6. The saddle point for the jumping ion is considered

oxygen lattice

to lie

mid-way between two regular

positions along a tetrahedral

edge. These are indicated by the solid circles in the center of jump paths (open arrows) on Figure 6.

For transport •c the obvious diffusion step is a series of jumps spiralling around the hexad symmetryaxes. The three nearest neighbor oxygen ions to the saddle position are indicated at A,

B, and C being 0.2245, 0.3424, and 0.3638 nmdistant respectively. To relax the short saddle point- A distance to the minimumO-O distance in quartz (0.259 nm) the jumping ion may translate parallel to (OOO1)into the emptypolyhedra lying along the c axis channel, Figure 6. This reduces the B and C- saddle point distances to 0.3056 and 0.3579 nm, respectively. Diffusion•.(1OlO) must involve a step jumping between the c axis channels,• Fibre 6. Nearest

neighbor oxygen ions to the Saddle point are indicated at Sites 1, 2, and 3 being 0,2245, 0.309, and 0.386 nm distant, respectively. Relaxation of the minimum distance

placement •c,

to 0.259

nm results

in

dis c

reducing 2 and 3-saddle point dist-

ances to 0.287 and 0.348 nm, respectively.

A comparison between the nearest neighbor 0-O distances directions for

in the relaxed state for both transport indicates that the activation enthalpy

diffusion

increases

as the

volume

of

the

un-

occupied polyhedra (lying along c and a axes "channels") decreases. This model also qualitatively accounts for the increase in activation enthalpy

on passing from the beta to alpha phase field

re-

ported by Giletti and Yund[this issue]. The phase transition

is simply a polyhedral tilting"

c direction.

[Hazen and Finger, 1982] due to a decreasein the polyhedral volumeon cooling. Kirby [this issue] has useda similar modelin discussing interstitial transport mechanisms for oxygen or hydroxyl species. As indicated in this work, however, there is little evidence at present to support such a model. Conclusion

The observation that hydrogen does not play a role in controlling the point defect chemistry of quartz under hydrothermal conditions is controversial and directly conflicts with the results

of Giletti

and Yund [this issue]. While there is

excellent agreement between the data at 1OOMPa total pressure in the temperature range 500ø850øC, there is a significant discrepancy concerning the effect

of water fugacity.

Due to poss-

ible systematic experimental errors in the extant dry gas isotope exchange data, reference to other sets of results cannot resolve this problem. Consequently, further confirmation of the vacancy diffusion model presented in this work must await the results of several important experiments. It is necessary to reexamine oxygen self-diff-

usion under dry gas conditions using an ion microprobe [this study; Giletti and Yund, this iss-

ue] Or profiling nuclear activation [Jaou! et al.,

1983] technique, This will allow a valid

comparison between the present from water-free

results

and data

systems.

The present experiments also require

refine-

ment. First, to assess the accuracy of the results, it is necessary to determine the effect of

microscopic solution coefficients.

phenomenaon the diffusion

Second, to confirm

the observation

of f(H20)-independent oxygen tracer diffusivity, the range of f(H20) conditions examined must be considerably expanded. Finally, the vacancy diffusion and defect model can be readily tested by monitoring Dox as a function of the aliovalent, substitutional trace element (particularly A1) content of quartz (equation (12)). Acknowledgments. The author is indebted to the support of J. A. Kilner and B.C. H. Steele

4056

Dennis: Oxygen Diffusion

in providing ion microprobe facilities, without which the work would not have been possible. B. K. Atkinson, E. H. Rutter, V. Cheel, and S. M. Dennis have provided many hours of stimul-

ating discussion. Thoughtful reviews by S. H. Kirby, R. A. Yund and B. E. Hobbs are gratefully acknowledged. The research was supported by a Royal Dutch Shell Scholarship and latterly by Natural Environment Research Council contract GR3 4565. High P and T experiments were carried

out in the Rock Deformation Laboratory, College,

London. Re ferenc

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ity Sci.,

Imperial

G. M.,

es

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1965.

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of

Ni in the bulk and along dislocations in NiO single crystals, Philos. Mag. A, 39, 581-595, 1978

Blacic, J. D., and J. M. Christie, Plasticity of quartz and hydrolyric weakening, J. Geophys. Res., this issue. Burnham, C. W., Water and magmas: A mixing Geochim. Cosmochim. Acta, 39, 1077-1084, Choudhury, A., P. W. Palmer, G. Amsel, H. and P. Baruch, Study of oxygen diffusion

model, 1975. Curien, in

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P. F. Dennis, Department of Geology, Imperial College, London SW72BP, United Kingdom.

(Received October 20, 1982; revised September 9, 1983; accepted

September

22,

1983.)