JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 94, NO. B10, PAGES 13,975-13,996, OCTOBER 10, 1989

Effect of Water on the Rheology of Experimentally Deformed Quartzite

PHILIP S. KOCH, 1 JOHN M. CHRISTIE, ALISON ORD, 2 AND RICHARD P. GEORGE, JR. 1

Department of Earth and Space Sciences, University of California, Los Angeles

Empirical flow laws have been determined for Simpson quartzite samples deformed to mechanical steady state in the a-quartz stability field using Griggs-Blacic solid-medium deformation apparatus. Experiments were conducted on samples both as received ("dry") and with water added via the dehydra- tion of a talc confining medium ("wet"). Best fits of the power law type yield a stress exponent of 2.72 + 0.19, an activation enthalpy of 134 + 32 kJ mol-•, and a preexponential constant of 1.16 [+1.15, -0.58] x 10 -7 MPa -2.72 s -• for the dry quartzite law; and are 2.61 + 0.15, 145 + 17 kJ mol 4, and 5.05 [+ 5.00] x 10 -6 MPa -2.61 s -1 for the wet quartzite. The enhanced hydrolytic weakening of the wet experiments appears to affect the flow laws mostly in the preexponential constants, possibly as a defect concentration term that is higher in the wet than in the dry law. Over the range of experimental conditions (750ø-900øC, 10 -7 to 10 -4 s -1, and 1.0-1.25 GPa confining pressure), dry specimens are 1.5- 2.5 times stronger than wet samples deformed at the same conditions. The microstinctures produced are analogous to those observed in many natural quartz tectonites. Recrystallization is well developed in the wet but not the dry specimens. At flow stresses below 500 MPa, microstructures indicative of re- covery are well developed. A comparison of our creep activation enthalpies with those determined from diffusion experiments are consistent with deformation of wet Simpson quartzite that is limited by oxygen self-diffusion. Inconsistencies between the present study and previous studies are probably the result of differences in sample material, sample treatment, and sample assemblies (chemical environ- ment).

INTRODUCTION

Although by the late nineteenth century some quartz tec- tonires were postulated to originate by ductile flow [Miigge, 1896, pp. 769-771], quartz crystals and aggregates proved exceedingly refractory in the laboratory until the early 1960s [Carter et al., 1961, 1964; Christie et al., 1961, 1964]. Despite the poor stress resolution in these early experiments, calculations extrapolating the experimental data to the conditions of crustal deformation suggested that huge crustal deviatoric stresses (hundreds of megapascals) would be required to form quartz tectonites. This was not consistent with the ample geologic evidence for quartz ductility or with then extant estimates of deviatoric stress in the crust (cf. calculation of Griggs and Blacic [1964, p. 103] and values quoted by Jeffreys [1959, p. 202, 203, and 206- 207]). In subsequent experiments, Griggs and Blacic [ 1964, p. 102] observed that trace amounts of water would greatly facilitate the flow of quartz single crystals. As water, both connate and generated by dehydration reactions, is known to abound during prograde metamorphism, the phenomenon of "hydrolyric weakening" provided a strong qualitative link between natural and experimental observations.

Much subsequent research has been devoted to investigat- ing the ductile rheology of quartz single and polycrystals as well as the nature of hydrolyric weakening. (See, for exam- ple, reviews of Carter [1976, pp. 316-329], Tullis [1979, pp. 1138-1139], Kirby [1983, pp. 1474-1479], Kirby and

•Now at Exxon Production Research Company, Houston, Texas. 2Now at Division of Geomechanics, Commonwealth Scientific and

Industrial Research Organization, Mount Waverly, Victoria, Australia.

Copyright 1989 by the American Geophysical Union

Paper number 89JB00675. 0148-0227 / 89/89JB-0067 5505.00

McCormick [1984, p. 145], Hobbs [1985], Kirby and Kronenberg [1987, pp. 1225-1228, 1234-1235, 1680- 1681], and Table 1.) When the present study was undertaken, rheological modeling of the crust was difficult due to the lack of well defined constitutive relations (flow laws) applicable to crustal materials, notably quartz aggregates. Our study was undertaken to provide such flow laws, to make qualitative observations of how water affects the rheology of ductile quartz aggregates, and also to generate a suite of experimentally deformed samples for microstructural observations.

EXPERIMENTAL METHODS

Starting Material and Sample Preparation

The starting material was a block of Simpson ortho- quartzite provided by H. C. Heard from the Sunray Cullen well of Oklahoma (section 34, T10N, R7W; well depth: 3949 m (12,959 ft); see also studies of Heard and Carter [1967, 1968], Tullis [1971], Tullis and Tullis [1972], Tullis et al. [1973], Tullis [1977], Mainprice [1981], and Mainprice and Paterson [1982, 1984]). Simpson orthoquartzite is a well-cemented quartz aggregate of mean grain size (1.5 times the mean intercept length) 0.21 + 0.01 mm. There is no detectable crystallographic preferred orientation [Tullis et al., 1973, p. 298], and mineralogical purity is high (over 99.75% quartz by volume as determined by lineal analysis, the principal impurity being magnetite). Room temperature infrared spectra integrated from wave numbers 4000 to 2300-cm '1 yield calculated hydrogen concentrations of 642 + 47 H / 106 Si, using "dry" crystal A-1 as the standard (B. D. Marshall, 1981, personal communication). This represents a hydrogen concentration larger than that of natural quartz single crystals and many synthetic single crystals as well [cf. Linker and Kirby, 1981, pp. 31-32; Blacic and Christie, 1984, pp. 4227 and 4229-4232; Mackwell and Paterson, 1985, p. 142 and Table

13,975

13,976 KOCH ET AL.: RIIEOLOGY OF EX?ERIMENTALLY DEFORMED QUARTZITE

TABLE 1. O -n Summary of Other Quartz Aggregate Ductile Flow Behavior $ = A 1 exp (-H/RT)

Source Constants Units "Wet" [Air] "Dry" [Vacuum] "Dry" Sample Material

Heard and Carter n

[1967, Table 3, H kJ mol-1 1968, p. 24]

A• MPa -n s -1

Parrish et al. [ 1976, n pp. 191-193]

A 1

Heard [ 1976, n

Table 1] H

A1

kJ mol- 1

MPa- n s- 1

kJ mol- 1

MPa- n s - •

Brace and Kohlstedt n

[1980, p. 6250] H kJ mol-1

A•' MPa -n s -•

Jaoul et al. [1981, n

p. 396] H kJ mol- •

A 1 MPa -n s-1

Shelton and Tu!!is n

[1981, p. 396] and H kJ mol- • Shelton [ 1981,

pp. 2-3, 36-42, A1 MPa-n s-1 and 111-112]

kJ mol- 1

MPa-n s-•

H kJ mol- •

Kronenberg [ 1983, n

pp. 3-14, 167, H and Table 2] and

Kronenberg and A • Tullis [1984, Table 2]

Jaoul et al. [1984, Table 1]

A• MPa-n s -1

11 Simpson quartzite

377

2.6 + 0.4 6.5 _+ 0.8 Canyon Creek

230 _+ 29 266 _+ 23 quartzite ("wet") Simpson quartzite

4.44x 10 -2+ 1.99x 10 -l 3 19x 10 -3 6.7x 10 -•2 +9.1 x 10 -10 - . - 2.3 x 10-14 ([air] "dry") 2.6 + 0.4 5.7 + 0.8

231 + 28 243 + 21

3.98x10 -2 +4.6x10 -1 3.7x10_ 2 7.94x 10 -•+6'23X 10-9 - -7.84x 10 -l•

1.2

153 _+ 21

3.74 x 10 -2

---1

--- 168

2.7 + 0.3

120 + 10

•-2.18x 10 -6+2'18X 10-6 - 1.45 x 10 -6

3

190

5x10 -6

153 + 21

1.26 x 10 -3

2.0

168

+ 1.9 x 10 -4 - 1.6 x 10 -4

2.8

153 + 21

1.59 x 104

2.9 + 0.3 -' 3.2 + 0.02 --4

170 + 20 -, 220 + 20 300 + 20

-5x10 -6 +2.6x10 -5 -4.0x 10 -6 -4x 10 -6+2'8X 10-7 -3.0x 10 -8

2.0 + 0.2 [.12%] 2.4 + 0.4 [NaC1] 2.8 + 0.2 [NaC1] 1.4 _+ 0.05 [.28%] 2.3 _+ 0.1 [CaCO3] 3.3 ___ 0.4 [CaCO3] 1.8 _+ 0.2 [.39%]

146 ___ 4 [.28%] 163 _+ 13 [NaC1] 184 + 6 [NaCI] 151 [.39%] 171 _+ 8 [CaCO3]

5.26 x 10 -3 [.28%] 9.98x 10 -6 [NaC1] 3.44 x 10 -6 [NaC1] 2.91 x 10 -3 [.39%] 3.11 x 10 -4 [CaCO3]

same as Parrish et

al. [1976]

Simpson quartzite

Heavitree quartzite

Heavitree quartzite

Heavitree quartzite

Heavitree quartzite

1, p. 146; Ord and Hobbs, 1986, p. 53; Kronenberg et al., 1986, pp. 12,724 and 12,727].

Samples for deformation were right circular cylinders 6.35 mm (0.250 in.) in diameter and 12.7 mm (0.500 in.) long, cored from sawn slabs using a water-cooled diamond coring drill. All samples were cored perpendicular to bedding, and the perpendicularity of the base with respect to the cylinder axis was adjusted by grinding with a V-block on a lap (tolerance: 0.039 mm (0.001 in.)). Samples for both nomi- nal wetnesses (see below) were air-dried under room condi- tions prior to use.

Sample Assemblies

All experiments were conducted in compression by means of the Griggs-Blacic solid-medium deformation apparatus. (See Griggs [1967, pp. 22-23] and Blacic [1972, pp. 109-

110] for general description of this apparatus and Koch [1983, pp. 22-28 and 336-380] for details concerning this apparatus and its manipulation.) In "dry" experiments, cop- per was the confining medium; talc, which dehydrated prior to and during sample deformation, was the confining medium in "wet" experiments. Temperature distribution was smoothed by making four modifications to preexisting assemblies [Post , 1973, pp. 37-40, 1977, pp. 78; George and Christie, 1979]: a good thermal conductor surrounds the sample, which is then capped with ceramic endpieces (to re- duce the large temperature gradients at the sample's ends); stepped furnaces were employed; and thermocouples were placed in stable regions away from the sample. Measured longitudinal temperature differences were 20øC for a sample of central temperature 1000øC (Figure 1), and resultant sam- ple strains are much more uniform than in the past (Figure 2).

KOCH ET AL.: RHEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,977

A

TEMPERATURE PROFILES' DRY SAMPLE ASSEMBLY No. 2 I I

•, x; I A •b• [!7p '"-•'•- ,

•', •,, I',

I 0.5 •n. I

o o

o

i•1•

o o

o

i

i I

i I

i I

i I

i

i I

i I

I i

TEMPERATURE PROFILES-WET ASSEMBLY No. 4

p-

P

P P A P

I; I 0.5 in I

03 03 0 0 0 0 0 0 0 0 0 0 0 0

& I i i , I , i , , , i , , , i

i i I

\' \l \• \, \ I

i i I

i i r-

I I I 03

' z I I I I

/ ' /t /, /, /,

i • , i i , , , i , , , i , , , i

Fig. 1. Temperature profiles for (a) "dry", and (b) "wet" assemblies (ICULI IIA and ICUTA IV, respectively). Dashed curves represent the temperature sensed by the fixed thermocouples; correlative solid curves are for the moving thermo- couple (profiled through the center of a hollow sample; thermocouple attached to a micrometer head). Optimal position for 12.7-mm-long (0.500 in.) samples shown for present assemblies.

Experimental Conditions and Measurement Errors

The experimental conditions are listed in Tables 2 and 3, and shown graphically in Figure 3. All samples used in flow law calculations were deformed in the a-quartz stability field allowing for changes in temperature and deviatoric stress (Coe and Paterson [1969, pp. 4929-4934] and Figure 3). Confining pressure varied from approximately 1.0 GPa at

750øC to 1.25 GPa at 900øC. Shortening strain rates in these constant displacement rate tests varied between approximately 10 '7 s '1 and 10 '4 s '1. Multiple data were obtained in certain experiments by performing temperature or strain rate steps. Whenever possible, these steps were made to higher differential stress (i.e., lower temperature or faster strain rate) after "hitting" the sample anew. Differential stresses at mechanical steady state occurred in

13,978 KOCH ET AL.: RHEOLOGY OF EXPEREMENTALLY DEFORMED QUARTZITE

Fig. 2. Macroscopic homogeneity of strain in "dry" Simpson quartzite. All specimens were deformed in "dry" assembly ICULI IIA, and the copper jackets were removed by dissolution in acid; note the lack of barreling even at high macroscopic strains.

the range 0.14-2.4 GPa and in most tests were below 600 MPa. As the activation volume is unknown for creep of quartz (S. H. Kirby, 1982, personal communication), the effect of our confining pressure changes on flow stress is uncertain. By analogy to estimates for olivine [Ross et al., 1979, p. 262; Kohlstedt et al., 1980, p. 3127; Karato and Ogawa, 1982, p. 109; Green and Hobbs, 1984; Green and Borch, 1986; Chen and Green, 1987], however, the effect on our data is expected to be small.

The chemical environment of the deforming samples is not well characterized as the system is not closed (in the chemical sense) and the fugacities of volatiles are not known. We expect the fo2 to be bracketed between the C(graphite)/CO2 and Cu/Cu20 buffers and the fH20 to approach the confining pressure during the wet experiments. Chemical species present certainly include H20, 02, H2, CO2, and possibly CH4 [French, 1966, pp. 225-231]. By performing experiments with and without dehydrating talc, it was our intent to appraise the qualitative effect of varying the amount of water in the deforming sample. We are certain that the wet experiments contain more water than do the dry

as long as talc remains available for dehydration (confirmed by X ray diffractometry). The dry experiments, however, are not strictly anhydrous as some water is available in the starting material's grains and on grain boundaries (see starting material section, above). Infrared analyses as yet have not been done on deformed samples; hence we cannot compare the differences in uptake of water related species in the dry versus the wet deformation experiments.

Errors in the physical measurements vary with the details of the experiment. Reported temperatures are correct to within 5øC of actual at the centers of the samples. Additional errors occur due to temperature differences between the center and ends of the samples. In the range of tempera- tures in our experiments, the volume averaged geometric mean temperature is at most 10øC less than reported, and usually about 7øC. Strain and strain rate are corrected for ap- paratus distortion but not for porosity closure; the resulting errors are less than 8%. Petrological experiments in simpler assemblies of the same general materials [Kim, 1974; Johannes, 1978] indicate that reported confining pressure (minimum principal compressive stress) may exceed the ac-

KOCH ET AL.' RItEOLOGY OF EXPER]ME•AI LY DEFORMED QUARTZITE 13,979

6

/ /

•tishovite -- /'

c•- Quar

750 8(•0 850 900 95t

\ /

,, Coesite ,,' \ // - \

\ /

\\\ ///

- "•- Q u a r•,,,,•,,•.. •u a r t z - ,,,,,• .... •,'

?:'" • /Tridymite. .......... I 18/' I

0 250 500 750 •000 •250 500 •750

5O

50

•o

Fig. 3. Phase diagram for SiO2 with continental crustal geotherm for cool granitic crust. Inserted block brackets the conditions of our experiments; the minimum and maximum displacements of the quartz/13-quartz transition due to deviatoric stresses also are shown in the insert for 1.0 and 1.2 GPa confining pressure. Data sources: 1, Ehlers [1972, p. 157] after Ostrovsky [1967, p. 327]; 2, Bohlen and Boettcher [1982, pp. 7075-7076]; 3, Coe and Paterson [1969, pp. 4933-4943]; 4, Cohen and Klement [1967, pp. 4346-4248]; 5, Tuttle and England [1955, p. 150] and Tuttle and Bowen [1958, p. 29] ;6, Kennedy et al. [1962, p. 503]; 7, Ostrovsky [1966, pp. 130-133]; 8, Kracek and Clark [1966, pp. 304-305]; and 9, Sosman [1965, p. 154].

tual pressure in the vicinity of the sample by between 50 and 75 MPa. The load (maximum principal compressive) stress is corrected for changes in sample cross sectional area; however, errors occur due to frictional losses within the sample assembly. These have been estimated in two manners. Based upon published experimental data of Bridgman [1935, pp. 845, 846], Garofalo [1965, pp. 52, 82], and Getting [1979, p. 838], extrapolation of the data from Edmond and Paterson [1971, p. 143, 146, 152], and unpublished experimental data of S. M. Schmid (~1975) and P.S. Koch (1982), errors in the load are at most 75 MPa in the dry assembly and 180 MPa in the wet assembly (if one assumes our highest stress case, 750øC and 10 -4 s-l). We also tested ceramic samples (A1203/ll%TiO2 and ZrO2) known to deform elastically at the temperatures of our experiments and of known elastic constants. Frictional

losses in the load at 750øC and 10 -4 s -1 (our highest differential stress experiments) were approximately 50 and 90 MPa in the dry and wet assemblies, respectively.

RHEOI•GICAL RESULTS

Stress-Strain Curves

Representative stress-strain curves for both "dry" and "wet" quartzite experiments appear in Figure 4 for 900øC. All of the experiments discussed reached steady state in the mechanical sense that deviatoric stress and strain rate remain

constant with time (and strain) after yield. In many "wet" experiments, however, an upper yield point is observed (Figure 5). Subsequently, one of two sets of behavior oc- curs: either (1) differential stress decreases to a lower level of differential stress (e.g., GB907) or (2) differential stress decreases to a lower yield point and subsequently recovers to levels near that of the upper yield point (e.g., GB939). Microstructural observations (see below) suggest that these yield points may correspond to beginnings of cycles of dy- namic recrystallization as is observed in other materials [Jonas et al., 1969, pp. 4 and 11-14; Jonas and Muller, 1969] including flint deformed in the It-quartz field [Mainprice, 1981, pp. 90-91] and novaculite deformed in the a-quartz field [Koch, 1983, pp. 44-45].

Curve Fitting

An experiment was excluded from the fitting of a constitu- tive relation: (1) if the sample deformed brittly (as inferred by a rapid decrease in the load and the presence of a throughgoing fault in the deformed specimen); (2) if the sample was deformed in the [5-quartz stability field (four ex- periments; see Table 2); (3) if strain exceeded 35% before mechanical steady state flow was achieved; and (4) in most cases, if an experiment stepped downward in stress (i.e., to higher temperature or lower strain rate). All other experi- ments in the a-quartz field were included and are listed in Tables 2 and 3. Twenty-four samples, yielding 39 data points, were deformed with water added; 19 samples, provid- ing 23 data points, were deformed as received. Eight data were taken from Heard and Carter's [1967, 1968] gas-confin- ing medium experiments where differential stress measure- ment was more sensitive. The close agreement within our "dry" data at 800øC (Figure 6a) is encouraging.

Empirical constitutive relations of several functional forms were fitted to these data. (For details of the possible forms, including micromechanical laws, see reviews of Garofalo [1965, pp. 46-101 and 156-201], Sherby and Burke [1968, pp. 325-368], Jonas et al. [1969, pp. 1-4], Ashby [1972, pp. 888-889], Kirby and Raleigh [1973, pp. 166- 178], Takeuchi and Argon [1976, pp. 1542-1546], and Tsenn and Carter [1987, pp. 2-5].) All of these flow laws assume an Arrhenius relationship between strain rate and temperature, whereas the stress dependence assumes several related forms [Garofalo, 1965, p. 51]. The general form has a hyperbolic sine dependence of strain rate • upon differential stress o:

k = A3 [sinh (Co)] n exp (-H/RT) (1)

which degenerates to an exponential dependence at high stress (Co > 1.2):

k = A2 exp (Bo)exp (-H/œT) (2)

and to the common "power law" dependence at low stress (C o < 0.8):

k = A• o n exp (-H/RT) (3)

where R is the universal gas constant, T the absolute tem- perature, and A1,A2, A3, B, C, n (the stress exponent), and H (the activation enthalpy) are all empirically determined constants.

Empirical flow laws traditionally have been fit to data us-

13,980 KOCH ET AL.: RHEOLOGY OF EXPERIMF_2qTALLY DEFORMED QUARTZITE

TABLE 2. "Dry" Simpson Quartzite Rheological Data

GB

Deformation Conditions Preheating Conditions

Pc, GPa T, øC •, s-1 0.1- 0'3, MPa E;, ø7o t, Pc, GPa T, øC Notes hours

880 A

883

885

887

888 A

B

*C

889

892

893

894'A

B

C

896

898 D

900 B

D

1.09 800 1.37 x 10 -7 276 9 12.3 1.12 800 1.17 900 1.60x 10 -7 139 11 73.0 1.11 900 1.09 800 1.66x 10 -5 1852 29 40.5 1.13 800 1.07 800 1.85 x 10 -6 941 60 10.6 1.01 800 S 1.17 800 1.30 x 10- 5 1448 15 3.0 1.20 800 1.17 900 2.07 x 10 -5 688 16 1.24 1000 2.02x 10 -5 321 33 /3 1.12 900 1.74x 10 -6 461 23 3.8 1.12 900 S then H 1.13 800 1.69x 10 -7 328 12 6.1 1.24 800 1.17 900 2.01 x 10- 6 480 40 2.4 1.18 900 1.12 1000 1.59x 10 -5 528 14 2.7 1.03 1000 /3 1.12 900 1.57 x 10-5 1274 22 S (minor) 1.06 800 1.64 x 10- 5 1867 29 S 1.13 800 1.62 X 10 -4 2912 20 1.9 1.15 800 S; P (at end) 1.07 900 1.80 X 10 -4 2760 29 [ 1.5 1.10 1000 ] R (at end) 1.12 900 1.94x 10 -4 2338 32 [ 2.1 1.17 850 ] 1.13 900 2.00x 10 -4 2070 53

Data From Heard and Carter [1968, Table 2, pp. 20-21]

622 0.80 800 3.7 x 10- 5 1220 - 8 653 0.80 800 5.9x 10 -7 600 -5 L 10 -5 -• 10-6s -1 659 0.80 800 3.0x 10 -5 1300 660 0.80 800 3.0 x 10- 5 1340 - 7 662 0.80 800 3.4x 10 -6 950 -7 L 10 -5 s -1 677 1.00 800 3.9x 10 -6 780 -8 L 10 -5 s -l 679* 0.80 1000 - 3.6 x 10 -4 1040 - 15 /3 680* 0.80 1000 - 3 x 10 -5 480 -6 /3 681' 0.60 1000 -3x10 -6 240 -4 /3; L 10-5s -1 695 0.60 800 3.7 X 10 -6 810 -- 11 L 10-5 s-1 729* 1.00 1000 -3x 10 -6 210 -4 /3; L 10 -5 s -1 734 0.80 800 2.5 x 10 -6 840 L 10 -5 s- 1

Strains quoted are final strains (at the end of each step in multiple step experiments) and not necessarily the strains at which mechanical steady state behavior is achieved. The following abbreviations and symbols are used: C, "creep" experiment; H, strain hardening; L, initially loaded at strain rate of; P, run at constant power; R, rehit; S, strain softening; T, manual temperature control,/3, deformed in the/3-quartz stability field. Values in brackets are preheating occurred at an earlier, unquoted step.

*Omitted from flow law fitting.

ing multiple linear regression analysis. Two earlier studies employed nonlinear fitting procedures in their data analyses [Blacic, 1971, pp. 156-162; Parrish and Gangi, 1977, 1981]. Whenever numerical stability and convergence can be maintained, we believe nonlinear regression preferable to multiple linear regression as the latter always overempha- sizes the low stress data (where stress resolution is invari- ably the worst) and calculates errors that are difficult to in- terpret due to covariance of the fit parameters. In the present study, nonlinear regressions were attempted using the Gauss-Newton method, modified from Jennrich [1981], to minimize the nonlinear least squares residual on k to 10 -9 s -1. Our results were confirmed using nonlinear fitting procedures within the Statistical Analysis System (SAS).

Flow Laws

Preliminary versions of these results calculated by multiple linear regression analysis were given by Christie et al. [1979], Koch et al. [1980], Christie and Koch [1981], and Kirby and McCormick [1984, p. 262]; the final

calculated constants (Figure 6 and Table 4) include many more recent experiments. For the "dry" flow law, data were only available at two temperatures, and as the data scatter is large, the nonlinear solutions proved unstable and failed to meet the criterion for convergence. Multiple linear regression of the standard power law (3) was performed (Figure 6a), but the standard deviations of the flow law constants are large, as expected. A stress exponent of 2.72 + 0.19 was obtained while the activation enthalpy H and preexponential constant (A1) were 134 + 32 kJ tool -1 and 1.16 [+1.15, -0.58] x 10 -7 MPa -2'72 s -1, respectively.

Using the nonlinear fitting routine, the "wet" quartzite data were fitted by expressions (1), (2), and (3) (Figure 7). The exponential law yielded the largest sum of squares of the residuals and the hyperbolic sine law the smallest (as should be expected with an additional degree of freedom). In the common range of experimental conditions, "dry" quartzite samples are approximately 1.5-2.5 times as strong as "wet" samples deformed at the same temperature and strain rate. For the multiple nonlinear regression fit to the power law (Figure 7a), the calculated "wet" stress exponent is lower

KOCH ET AL.: RItEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,981

TABLE 3. "Wet" Simpson quartzite Rheological Data

Deformation Conditions Preheating Conditions

GB Pc,GPa T,øC •,s-1 ol-o 3 ,MPa $,O7o t, Pc,GPa T,øC hours

Notes

874 0.95 800 1.52 x 10 -6 582 8 875 A 1.05 770 1.52 x 10 -6 445 6

B 1.03 770 1.75 x 10 -5 1166 22 C 1.04 770 2.11 x 10 -7 176 30 D 1.03 770 1.99 x 10 -6 356 35

903 0.91 850 1.81 x 10 -6 338 47 904 A 1.03 850 1.61 x 10 -5 595 12

B 1.04 850 2.05 x 10 -7 155 16 905 1.07 850 1.83 x 10 -6 230 28 906 1.15 850 1.59x 10 -4 2150 25 907 1.25 850 1.44 X 10 -4 1942 26 908 1.27 875 2.20 x 10- 5 500 51 909 1.16 900 1.51 x 10- 6 224 6

910 1.16 900 2.19x 10 -6 251 40

911 1.14 900 1.59 x 10 -4 871 14 912 A 1.20 900 1.48x 10 -7 87 10

C 1.21 850 1.63 x 10 -6 291 16 D 1.20 850 2.17 x 10 -7 155 20

919 A 0.94 750 1.64 x 10 -6 421 17 B 0.91 750 1.87 x 10 -7 212 23

922 A 1.05 800 1.64 x 10 -6 326 8 B 1.07 800 1.25 x 10 -7 117 11 C 1.07 800 1.86x 10 -5 1138 26

923 1.18 900 1.82x 10 -5 472 22

924 1.20 800 1.90 x 10- 5 927 32 929 A 1.20 900 1.73 x 10- 6 200 22

B 1.20 900 2.46 x 10 -7 56 23 C 1.20 900 1.90 x 10- 5 505 34

932 A 1.25 900 1.44 X 10 -4 800 13

B 1.25 800 1.64 X 10 -4 1326 14 933 A 1.15 750 1.65 x 10 -6 530 9

23.8 1.00 800

28.5 1.12 770

18.3 1.03 850

119.2 1.05 850

2.5 1.16 850

17.6 1.20 850

0.9 1.25 850

20.1 1.27 875

14.0 1.16 850

9.5 1.16 900

17.2 1.12 850

6.0 1.21 900

6.2 1.14 900

19.4 1.20 900

17.0 0.95 750

6.6 1.12 850

7.2 1.12 850

1.6 1.18 900

10.8 1.05 850

18.9 1.22 800

15.5 1.20 850

1.3 1.25 900

15.5 1.06 850

9.9 1.16 750

S

S

S then H

S then H

P

B 1.15 750 1.57 x 10 -7 225 13 C 1.13 750 1.64 x 10 -5 1315 23 D 1.11 750 1.35 X 10 -4 2400 31

934 1.20 900 1.80x 10 -6 180 21 14.3 1.12 850 9.8 1.12 900

936 1.24 850 1.69 x 10- 5 485 21 21.3 1.14 850 S then H 938 1.17 900 1.74 x 10 -5 416 26 19.2 1.05 850

2.2 1.05 900

939 1.15 850 2.32 x 10- 5 680 55 23.5 1.05 850 S then H 1021 1.23 800 1.84 x 10 -5 1575 32 19.1 1.15 850

2.1 1.18 800

R; S then H R

P

P

S (minor)

Strains quoted are final strains (at the end of each step in multiple-step experiments) and not necessarily the strains at which mechanical steady state behavior is achieved. Abbreviations and symbols are as for Table 2.

(2.61 + 0.15), whereas both the activation enthalpy H (145 _+ 17 kJ tool '•) and preexponential constant A1 (5.05 [_+ 5.00] x 10 '6 MPa -2.61 s -1) are higher than those in the "dry" flow law. Considering that the "dry" quartzite results have larger data scatter and larger error associated with the calculated value of H than do the "wet" quartzite data, the difference in activation enthalpy between the "wet" and "dry" quartzite laws is not considered significant.

For purposes of comparison, the power laws from the pre-

sent and previous studies (Table 1) have been plotted at 500øC in the range of differential stresses and strain rates pertinent to geological processes and with errors in the fit parameters, when these are reported (Figure 8). For such ex- trapolations to have any geological validity, the same de- formation mechanism(s) must operate in our experiments and in nature. (For a more general discussion, see Paterson [1987] and Carter and Tsenn [1987, p. 46].) Comparison of micro structure from natural quartz tectonites and these exper-

13,982 KOCH ET AL.' RIlEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE

3.0- • "DRY" QUARTZITE _

_ A •_, 9oooc GB900B, 10-4s -•

2,0-

.-. 900 D, 10-4s -•

• GB894B, 10-5s -• 1.o-

/ • GB888B, 10-5s -• • • -- G B889, 10-•s -•

I• GB893, 10-6s -• I/ • GBSS3, 10-7s -1

10 20 30 40 50 œ(%)

2.0

1.6

"WET" QUARTZITE

a 5oooc

•0' GB911, 10-4s -•

o.s - /

I I I I B, 10-•s-• ' I I I I I 0'00 10 20 30 40 50

œ(%)

Fig. 4. Representative stress-strain curves 900øC in the ct-quartz field for Simpson quartzite deformed (a)"dry" and (b) "wet." Curves not beginning at the origin are steps in multiple temperature step experiments.

imentally deformed samples supports this assumption (see below).

There exist four other complete flow laws for "dry" quartzites (Table 1) in the studies of Parrish et al. [1976], Heard [1976], Shelton [1981], Shelton and Tullis [1981], and Jaoul et al. [1984]. When compared with the present "dry" flow law, the stresses predicted by the laws of Parrish et al. [1976] and Heard [1976] are higher by one or two orders of magnitude at 500øC in the range of strain rates considered here (Figure 8a). This disparity is due principally to the much larger activation enthalpies in the laws of these other studies which fitted data of Heard and Carter [1967,

1968] from Heard gas apparatus [Heard and Carter, 1968, pp. 3-5]. Those data were gathered over a very large range of temperature with some of the samples deformed brittly (as determined by sharp drops in the stress-strain curves and microstructural observations) and several of them in the I•-

quartz stability field. Subsequent studies have shown that for synthetic single crystals [Kirby, 1976, 1977, pp. 97-98; Kirby et al., 1977; Kirby and McCormick, 1979, pp. 129, 136-137; Linker and Kirby, 1981, Table 3] and natural aggregates [Ross et al., 1983; Kronenberg and Tullis, 1984, p. 42] the activation enthalpy is appreciably lower in the I•- quartz than the a-quartz field. The present results and those of Shelton [1981], Shelton and Tullis [1981], and Jaoul et al. [1984] show reasonable consistency over the extrapolated range of strain rates at a temperature of 500øC. The relative position of Shelton's curve with that of the present study, however, is uncertain due to a systematic error in Shelton's analysis of flow stress (J. A. Tullis, personal communication, 1982). Differences increase between our results and those of these other studies if we extrapolate to temperatures lower than 500øC.

The only other complete "wet" quartzite laws are those of

KOCH ET AL.: RI•OLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,983

2.0

1.6

1.2

0.8

0.4

UPPER YIELD POINTS

"WET" QUARTZITE G B907, 850øC, 10-•s -•

GB936, 850øC, 10-Ss •

GB912C, 850øC, 10-Ss -•

GB939, 850øC 10 Ss •

GB908, 875øC, 10 Ss -•

G B910, 900øC, 10-Ss -•

0.0 0 10 20 30 40 50 œ(%)

Fig. 5. Stress-strain curves with upper yield points, "wet" Simpson quartzite.

Parrish et al. [1976] and Jaoul et al. [1984] (Table 1). The results of Parrish et al. [1976] predict flow stresses approximately 5 times as large as does the present "wet" quartzite law when extrapolated to 500øC and the range of strain rate considered here (Figure 8b). The Parrish et al. [1976] flow law has a much higher activation enthalpy, and this is responsible for the large difference in our respective extrapolated curves; our extrapolations do overlap somewhat if one considers the range determined by the errors in our respective flow laws. The results of Parrish et al. [1976] are problematical because samples were not isothermal and all of the fitted rheological data were collected in the It-quartz stablility field. The "water-added" quartzite flow law of Jaoul et al. [1984] predicts flow stresses that are approximately fivefold smaller than the present "wet" quartzite law.

The additional study of Kronenberg [1983] and Kronenberg and Tullis [1984] did not provide exact values for the preexponential constant A1. Comparisons to the flow law constants of the present study are restricted to the constants n and H as shown in Table 1. The study of Kronenberg finds that with increasing nominal water content, both the stress exponent and activation enthalpy decrease. In the present study, a decrease in stress exponent with increase in water content is also observed, similar in magnitude to that of the Kronenberg study; however, no significant change in activa- tion enthalpy was detected in our "dry" and "wet" quartzite flow laws.

The differences between our results and those of

Kronenberg and of Jaoul have several possible causes: (1) differences in measurement errors for differential stress (we use constant displacement rate tests which have constant stress corrections for the "hit points" unlike the creep tests of the Kronenberg study); (2) differences in data selection (all of our data come from the a-quartz field, whereas the study of Kronenberg included a few [5-quartz data points in the determination of n and H); (3) differences in the methods of determining flow law constants (we analyzed all data

together; they analyzed experiments singly to determine the n and/or H appropriate to an experiment and then averaged these constants); and (4) differences in sample material, sample treatment, and sample assemblies (hence thermodynamic environment and sample buffering). This fourth point is, we believe, most important. In both the studies of Kronenberg [1983] and of Jaoul et al. [1984], deformation assemblies of different composition from our own were employed, and the chemical environment of deformation is expected to have been different. Also, Heavitree quartzite was deformed, whereas Simpson quartzite was deformed in the present study. Mainprice and Paterson [1984, Figure 1] (see also Mainprice [1981, p. 62]) have shown that Heavitree quartzite contains a larger concentration of the "gel-type" hydroxyl (now known to be molecular water) than does the Simpson quartzite deformed by them; by analogy to single crystal data, this should affect the degree of water weakening in these two aggregates (see discussion section). Observations made by Mainprice [1981, pp. 77-78 and 81-82] and P. J. Vaughan (personal communication, 1983) during TEM of experimentally deformed Heavitree quartzite have shown that impurities along grain boundaries cause local melting in both the sam- ples deformed at confining pressures of 0.3 GPa by Mainprice [1981] and 1.5 GPa by Jaoul et al. [1984]. If melting was sufficiently abundant, deformation of the aggre- gate might be controlled by diffusion through the melt film, which would in turn reduce the stress exponent, and possibly the activation enthalpy, below values obtained during in- tracrystalline flow (see, for example, Coble [1963] and Raj [1982]). As already noted, melting was never observed in the samples of the present study. An analogous decrease of activation enthalpy with the addition of water was also ob-- served by Chopra and Paterson [1981, pp. 467-470, 1984, Table 3] in deformation experiments performed on dunires at 0.3 GPa confining pressure. In those tests, grain boundary melting was also present.

13,984 KOCH ET AL.' RI•OLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE

-4

-6

-7

A

3 4

"DRY" QUARTZITE

i•[-QUARTZ FIELD)

In(o•-03) (MPa) 5 6 7 I I I

• = 1.16E-7\_5.78E_ 80 exp RT 888B {

,•85 894C

888A

662

734

Z•887

•653

© 900øC

a, 800øC (THIS STUDY)

• 800øC (HEARD AND CARTER, 1968)

8830 •892 880A

i i i

Iog•o(O•-O:•) (MPa)

Fig. 6. Power flow law, multiple linear regression (MLR) fit. for (a) "dry" Simpson quartzite (data from Table 2) and (b) "wet" Simpson quartzite (data from Table 3). Bold solid lines are MLR fit; bold dashed lines are single temperature linear regression fits with derived stress exponents and linear correlation coefficients (r) in parentheses. Faint solid line in Figure 6a is 1000øC extrapolated from MLR fit.

-8

-9

-10

-11

1

-13

-14

-15

-16

MICROSTRUCTURAL OBSERVATIONS

Methods of Examination

The following methods of microstructural examination were employed in this study: (1) standard petrographic exam- ination in transmitted light (standard thin sections, 30 gm thick, on flat and universal stages mounted on a photomicro- scope); (2) optical microscopy in reflected light (doubly pol- ished thin sections as well as polished and etched slabs us- ing standard flat stage); and 3) transmission electron mi- croscopy (TEM; foils of the central regions of samples, bright field illumination in a JEOL Company JEM-200 mi- croscope with a stage permitting 30 ø tilt and 360 ø preces- sion).

Observations From Optical Microscopy

Recrystallized grains are always observed in "wet" experi- ments, and they occur in all but the fastest (10 -5 s -1, 10 -4 s -1) low-temperature (800øC) "dry" quartzite experiments (GB885 and GB896). Small quartz grains rim the original grains (Figure 9) and occasionally appear within relict grains although the presence within the relict grains may be an artifact of the sectioning (i.e., rims of recrystallized grains above or below the central position of the thin section).

The spatial distribution of the recrystallized grains is nearly homogenous; however, the total volume recrystallized is generally much smaller in "dry" than in "wet" samples, perhaps due to differences in water content.

In addition to recrystallized grains, Dauphin6 twins, undu- latory extinction, kink bands, deformation lamellae, and subgrains are detectable optically (Figures 10 and 11). Dauphin6 twinnning is ubiquitous whereas undulatory extinc- tion and kink bands occur only in "dry" quartzite samples, ox "wet" quartzite samples deformed at flow stresses in excess of approximately 500 MPa (Figures 10 and lib). Although not strictly mutually exclusive, deformation lamellae and elongate subgrains appear to grade into one another (cf. Figures 11 a and 1 lb).

Observations From TEM

Foils thinned for TEM exhibited large residual distortions resulting from high strain and stored stresses. Numerous bending fringes and high dislocation densities were ob- served, especially in relict grains. Consequently, although observations of dislocation geometries could be made, we were unable to determine Burgers vectors in the deformed samples.

Dislocations are generally curved and non-parallel (Figures

KOCH ET AL.: Rt•OLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,985

-4

-6

-7

B

3 4

"WET" QUARTZITE

(•-QUARTZ FIELD)

In(o•-o=) (MPa) 5 6 i I

91 lt• 932A(D"'

= 1.2 x 10 [+1.0 x 10-'//3 2'48 +.11 (-168 + 19kJ'mol-') •,-0.6 x 10-"/'• exp RT

"08"/'

938

"875B"

021 133C

934•

910'

874A

"'875A"

(D929B "875C"

lB

•'933B

Iog•o(O•-o=) (MPa)

Fig. 6. (continued)

933D

900øC DATA

850øC DATA

800øC DATA

750øC DATA

-8

-9

-10

-11

-13

-14

-15

-16

12 and 13). Samples deformed at flow stresses greater than about 500 MPa contain tangled dislocation substructures and display very high dislocation densities (of the order of 5 x 109 cm '2) throughout relict grains (Figure 12a), whereas re- crystallized grains (Figures 12b and 12c) display lower dis- location densities (of the order of 2 x 109 cm '2) within their interiors and slightly higher densities near their boundaries. In sample GB907, with a high maximum differential stress of 2.0 GPa, dislocations in the relict grains are too dense and tangled to count. Tiny (1 I•m) equant recrystallized grains are present within such regions, and themselves contain dislocations with a density greater that about 5 x 109 cm '2. In contrast to such high stress specimens, those samples deformed at differential stresses less than 500 MPa (Figure 13) display lower dislocation densities (of the order of 1 x 109 cm -2) and contain elongate subgrain boundaries, dislocation triple nodes, and precipitated bubbles of water. There is no evidence for grain boundary melting in any of the samples examined in this study.

Summary and Geological Implications

There is good evidence for recovery (dislocation triple nodes, subgrains boundaries, cell walls, precipitated bubbles of water) in the substructure of quartzite samples deformed at differential stresses below approximately 500 MPa. Samples deformed at higher flow stress show fewer recovered struc-

tures, suggesting that, at these experimental conditions, lo- cal stress concentrations are predominantly relieved by re- crystallization, which is present in all of the specimens ob- served by TEM.

These optical and TEM microstructures are also observed in natural quartz tectonites and especially mylonites (e.g., overviews of Sander [1930, pp. 173-201], Turner and Weiss [1963, pp. 211-214], Vernon [1975, pp. 173-177 and 180- 182], and Hobbs et al. [1976, pp. 74-104] as well as studies of Christie [1960, pp. 87-89, 1963, pp. 397-399], White [1971, pp. 17-177], McLaren and Hobbs [1972, pp. 58-66], Bell and Etheridge [1973, pp. 339-345], White [1973a, b, p. 276], Wilson [1975, pp. 968-971], Jones [1975, pp. 430-431], Liddell et al. [1976, pp. 421-424], Ord [1981, pp. 43-53, 60-65, and 82-97], and Ord and Christie [1984, pp. 640-645]). By analogy to observations made in ductilely deformed metals and ceramics [Jonas et al., 1969, pp. 1 and 11; Christie, 1960, pp. 87-89, 1963, pp. 397- 399; White, 1971, pp. 175-177; McLaren and Hobbs, 1972, pp. 58-66; Bell and Etheridge, 1973, pp. 339-345; White, 1973a, b, p. 276; Wilson, 1975, pp. 968-971; Jones, 1975, pp. 430-431; Liddell et al., 1976, pp. 421-424; Kerrich et al., 1977, pp. 251-253], such microstructures suggest that intracrystalline deformation by slip (dislocation motion) accompanied by diffusion (climb) has occurred in these experimentally deformed quartz aggregates and in at least some natural quartz tectonites.

13,986 KOCH ET AL.: KHEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE

TABLE 4a. Flow Laws for Simpson Quartzite: Multiple Linear Regression Fits for Power Law

•; = A 1 an exp (- H/R T) "Wet" [Air] "Dry"

n 2.48 + 0.11 2.72 + 0.19

H kJmo1-1 168 + 19 134 + 32

A 1 MPa-ns -1 1 20x10 -4+1'03X10-4 1 16x10 -? +l'15X10-? ß _5.55x10-5 ß _5.78x 10-8

DISCUSSION: ROLE OF WATER n• TKE

DEFORMATION OF QUARTZITE

Dilute Chemical Species and Silicate Weakening

Many researchers have observed that traces of chemical de- fects incorporated within certain silicates cause noticeable weakening of these crystals when compared to purer materi- als. Although the specific, causal point defects remain con- tested, this phenomenon has been described for CO2 in olivine [Green and Vaughan, 1982], Na in quartzite [Jaoul, 1984], and H20 in olivine, pyroxene, tourmaline, beryl, feldspar, and quartz (see, for example, Griggs and Blacic [1964, p. 102, 1965a, pp. 293-295, 1965b]; Griggs [1967, p. 29-30]; Tullis [1979, pp. 1141-1142]; Chopra and Paterson [1981, pp. 469-470, 1984]). Of these chemical substances, water has received the most attention, especially as it affects the theology of quartz. This is in part historical accident, as "hydrolytic weakening" was the first observed weakening behavior. Water is ubiquitous during prograde metamorphism and hydrolytic weakening is therefore antici- pated to be important during natural deformation. Modeling of quartzite deformation within the crust should then utilize constitutive relations involving water as a chemical defect. While deep crustal (granulite) conditions may be largely an- hydrous, the solubility of H20 is anticipated to increase with increasing metamorphic grade [Spear and Selverstone, 1983]. Water in grains at metamorphic conditions would have been incorporated from pore waters during compaction or from de- hydration reactions during lower-grade metamorphism. Thus hydrolyric weakening may occur even at the deepest crustal conditions.

The water-related defect (or defects) which results in a de- crease in flow stress and the mechanism by which this occurs are still in dispute. For crystals deforming by the motion of dislocations, however, there is a postulated reduction in the Peierls stress for glide and a promotion of climb and dislocation multiplication [Griggs, 1967, p. 29, 1974, pp. 1653 and 1654; Hobbs et al., 1972, pp. 50-53; Blacic and Christie, 1984, pp. 4228, 4233-4235; Ord and Hobbs, 1986, pp. 67-69], as well as a possible facilitation of the dissociation of dislocations into partials [Doukhan and Trepied, 1979, p. 143]. Because the fundamental nature of the "hydrolytic weakening" phenomenon is still obscure (see below), attempts to incorporate the hydroxyl concentration into theological constitutive relations [Blacic, 1971, pp. 164-184; Griggs, 1974, pp. 1654-1661; Kirby, 1975, pp. 70-72, 96-97, and 111; Ardell et al., 1976, p. 467; Blacic and Christie, 1984, pp. 4235-4236] must be viewed as speculative.

Phenomenology of Water Weakening in Quartz

Since the initial observations of Griggs and Blacic [1964], hydrolyric weakening in quartz has been described in a qualitative fashion based upon three sources of experimental data: quartz aggregates (e.g., Table 1), natural quartz single crystals [e.g., Griggs and Blacic, 1964, 1965a, b], and especially synthetic quartz single crystals [e.g., Griggs and Blacic, 1965a, b; Griggs, 1967; Bagta and Ashbee, 1967, 1969a, b; Kirby and McCormick, 1979; Linker and Kirby, 1981]. In synthetic crystals, yield strengths decrease systematically with increasing water concentrations and confining pressures (see reviews of Tullis [1979, pp. 1139 and 1142] and Kirby and McCormick [1984, p. 151]). Cryogenic absorption spectra at infrared and near-infrared frequencies suggest that hydrogen is present in these crystals either as interstitial hydrogen ions that do not correlate to weak crystals, or as the "gel-type" broad absorption [e.g., Kekulawala et al., 1981, pp. 52-53] due to clusters of water that do correlate with mechanically weak crystals [Aines et al., 1984, pp. 207-210].

The correlation between crystals that contain water clusters and that are weak during high-temperature deformation still does not identify the defect (or defects) responsible for the phenomenon of hydrolyric weakening. The results from infrared absorption spectroscopy do imply that the incorporation of defects for the hydrolytic weakening of initially dry single crystals is likely be limited by the diffusion into these crystals of either hydrogen or oxygen. Studies by Kronenberg et al. [1986] and Rovetta et al. [1986] have shown clearly that hydrogen cannot be the rate limiting species in the weakening of natural single crystals. This suggests, but does not prove, that oxygen diffusion may limit the incorporation of weakening defects in dry single crystals. The uptake of defects for hydrolyric weakening of initially dry quartz aggregates might be expected to show a similar dependence on oxygen diffusion unless the weakening phenomenon is

TABLE 4b. Nonlinear Least Squares Fits' "Wet"

Constants Units Values

Power Law: • = A• a n exp (-H/RT)

n 2.61 + 0.15

H kJ mo1-1 145 + 17

A t MPa-n s -• 5.05X10 -6 +5.00X 10 -6

Exponential Law: • = A 2 exp (Be0 exp (-H/RT)

B MPa -• 2.00x10 -3 + 1.73x 10 -4

H kJmo1-1 111 +21

A 2 s- • .542 + 1.44

Hyperbolic Sine Law: i• = A 3 [sinh (C(/)] n exp (-H/RT)

n 1.64 + 0.8

H kJmol-1 134+ 15

C MPa- 1 1.00 x 10- 3

A s s-1 61.68 + 102.34

KOCH ET AL.: RHEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,987

(OFO3) (kb) 0 10 20 30

•-F f///-•/'•-' "WET" SI•PSO• aU•TZITE NONLINEAR AND MULTIPLE LINEAR • / / EAR - • / / -- • 7 / REGRESSION POWER LAWS -13

_ / [J/ I // // NONLINE•••POWER) D 850øC DATA I / /

__ ,,,,,/,/ , I•l/I // • •s•,=• •-•5

-7 -16

0 1000 2000 3000

(0•-03) (MPa) A

0 10 (0:03) (kb) 20 30

/////o//•

ß • s )• "WET" SIMPSON QUARTZITE _• •/ / /

• • •///•/ NONLINEAR EXPONENTIAL AND - • .• • // MULTIPLE LINEAR REGRESSION -13

• • •• POWER LAWS ., '/ ./ / -6 // / / / O900øC DATA -14 I] j • / • EXPONENTIAL FIT • 850øC DATA

II/ / / -- MULTIPLE LINEAR FIT • 800øC DATA I1' / / (POWER) • 750øC DATA ,,/// / -15

ERRORS

-7 tJJ/ / , -16 o •ooo 2o•o 3doo

(o•- o•) (MPa) B

(O1-O 3 ) (kb) 0 10 20 30

• • / / / / / L/ / / /

E •//'//./// MULTIPLE LINEAR REGRESSION / - OW'ER L.WS 1

6 •/• / ----MULTIPLE LINEAR FIT •8•øC DATA ]- /// / •POWER) •0øC D•T• f// • •x,•u• ]-•5

r• • •..o.s / '/ 1-16 -7 / , 0 1000 2•00 30'00

(o•-o 3) (MPa) C

Fig. 7. "Wet" Simpson quartzite (data from Table 3). (a) Power flow law, MLR fit, compared to power flow law nonlinear fit.; (b) power flow law, MLR fit, compared to exponential flow law nonlinear fit.; (c) power flow law, MLR fit, compared to hyperbolic sine flow law nonlinear fit.

13,988 KOCH ET AL.' RHEO•GY OF EXPERIMENTALLY DEFORMED QUARTZITE

X 2

A

(3)

-15

/ //

-25

./

-2O

"DRY" FLOW LAWS

EXTRAPOLATED TO 500øC

'?

IOglO • (s '1)

! I i

4 o3 Q.

3

!

2•

-4O

-(150)

-(100)

-(50)

!n •- (s -•) -35 •-. -30

I ",-.I

"WET"

FLOW LAWS EXTRAPOLATED

TO 500øC

-(lO)

-(5)

-25 -2O

(3) / ;/-.., 1 '1•'-, ' I I !

-15 -10

B IOglO • (s '1)

•

Fig. 8. Power flow laws of present study and earlier studies extrapolated to 500øC and geologic stresses and strain rates for (a) "dry" and (b) "wet" flow laws: 1, Parrish et al. [1976]; 2, Heard [1976]; 3, Shelton [1981], Shelton and Tullis [1981]; 4, Jaoul et al. [1984] (A: vacuum "dry" in NaC1; B: as-is "dry" in NaC1; C: as-is "dry" in CaCO3; D: "wet" in CaCO3; E: "wet "in NaC1). Each flow law containing reported errors in its fit parameters determines a swath about the "best fit" line. The bounds in uncertainty are shown graphically by lines connected but at right angles to the best fit lines. The distance from the best fit line to the arrowheads represents the maximal range in uncertainty allowed by the reported fit constants (assuming all are independent). The swath of the extrapolations is then bounded by connecting arrowheads as has been done for the results of the present study (other such lines have been omitted in the interest of clarity). Lines that continue in dashed form from arrowheads to question marks lack reported errors in at least one fit parameter; in each such case, the range in predicted results is expected to be larger than what is calculable from the reported constams. (The "dry" quartzite results of Shelton [1981] and Shelton and Tullis [1981] have no reported errors in the fit parameters.) While the swaths illustrate the accuracy of the extrapolations, the only statistically useful comparisons between these flow laws come from the best fit lines, especially in view of inconsistent methods of reporting errors in fit parameters.

KOCH ET AL.: RHEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,989

Q.:.U.A.R-TZ-ITE

Fig. 9. Comparative strain: "dry" and "wet" Simpson quartzite deformed at 900øC, 10 -6 s 'l and the differential stresses indicated. Optical photomicrographs taken in transmission with crossed Nichols; maximum principal compressive stress applied left to right as read. Images show (left to right) the entire sample and portions of this sample near the top, the center, and the bottom. Note that there is grain boundary recrystallization in both specimens but much more in "wet" sample GB926.

Fig. 10. Optical microstructures typical of deformed Simpson quartzite. Both taken in transmission with crossed Nichols; cracks are unloading fractures perpendicular to the maximum principal compressive stress. (a) GB924 ("wet" 800øC, 10 -• s -1, 927 MPa): note grain boundary recrystallization and extensive undulatory extinction and kink bands in relict grains. (b) GB903 ("wet" 850øC, 10 •6 s 'l, 349 MPa): note larger volume of recrystallized grains and fewer strain optical microstructures in relict grains. Bar represents 100 ixm.

B Fig. 11. Optical microstructures typical of deformed Simpson quartzite. (a) GB938 ("wet" 900øC, 10 -s s -1, 416 MPa): deformation lamellae seen in transmission (uncrossed Nichols). (b) GB903 ("wet" 850øC, 10 -6 s -1, 349 MPa): subgrains seen in reflected light on polished and etched surface; note morphological similarity to deformation lamellae; note also the Dauphin6 twin boundaries (e.g., "T"). Bar represents 100 gm.

Fig. 12. TEM microstructures, Simpson quartzite. GB887 ("dry" 800'C, 10 -6 s -1, 940 MPa): (a) Relict grain, (b) and (c) recrystallized grains. Note straight dislocations, dislocation loops (e.g., "L"), bubbles (e.g., "B"), and dislocation tangles at the relict grain boundaries. Bar represent 1 gin.

KOCH ET AL.: RHEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,991

Fig. 13. TEM microstinctures, Simpson quartzite. GB910 ("wet" 900øC, 10 -6 s -1, 251 MPa). Note subgrain boundaries (e.g., "S"), dislocation loops (e.g., "L"), curved dislocations, bubbles (e.g., "B"), and generally lower dislocation density than in Figure 12. Bar represents 1 gin.

fundamentally different in aggregates (e.g., if water somehow pp. 366-367 and Figure 4, 1984, pp. 4031-4032, 1985], affects grain boundary mobility). If the deformation of these and Dennis [1984, pp. 4054-4055]). Of the many suggested aggregates involves dislocation climb (as suggested by our point defects, two negatively charged defects (HHO microstructural observations), the deformation may also be interstitial and 3H substituting for Si), one neutrally charge limited by the diffusion of the species that limits the defect (4H substituting for Si), and one positively charged diffusion rate of the weakening defects into quartz (quite defect (H interstitial or equivalently OH substituting for O) possibly the same species that must be incorporated into the have received the most attention. Table 5 and Figure 14 dry crystals in the first place). As a concentration show each defect, the species that may limit its diffusion, dependence of the diffusivity is common in ceramics and how the defect might be detected (note that all are [Kingery et al., 1976, p. 227] and is inferred for the expected to depend on fo2). At given thermodynamic "hydrolytic weakening" defect(s) in quartz [Paterson and conditions, defects that could weaken hydrolytically might Kekulawala, 1979, p. 96; Kekulawala et al., 1981, p. 58; not do so for kinetic reasons or because they were in an McLaren et al., 1983, p. 93; Blacic and Christie, 1984, unsuitable structural or electronic state. For example, the pp. 4232-4236], the higher the concentrations of the observed correlation between the weakness of synthetic appropriate defect(s) in the quartz grains of an aggregate, the single crystals and confining pressure might be due to the greater its anticipated hydrolytic weakening. Since the enhancement of the solubility or diffusion kinetics of the strength of the polycrystalline samples of the present study defect(s) responsible for weakening these crystals. Similar is greater than that of comparably wet synthetic single behavior had been anticipated for natural single crystals crystals deforming on any slip system [B alderman, 1974, [e.g., Hobbs, 1985, pp. 161-167] and received experimental Table 1, p. 1648; Kirby, 1975, Table II; Hobbs et al., 1972, support [Ord and Hobbs, 1983, 1986, pp. 62-64; Mackwell Figures 2-10; McCormick, 1977, Table I; Kirby and and Paterson, 1985, pp. 144-150], although these results McCormick, 1979, Figures 9-11; Linker and Kirby, 1981, recently have been questioned [Rovetta et al., 1986, Table 1; Linker et al., 1984, Table 2], not all of the pp. 146-147; Kronenberg et al., 1986, pp. 12,724 and hydrogen in our quartzite samples is available for 12,731-12,733]. weakening. Of the four possible defects suggested, none is entirely

Possible Causal Defects satisfactory. The uncharged 4H and negatively charged 3H both substitute for Si and their mobility are thus expected to

A multitude of possible defects has been suggested for the be limited by Si diffusion. While these defects in clusters hydrolytic weakening phenomenon (see reviews of might appear as the water seen in the broad absorption band Mainprice [1981, pp. 86, 88, Figure 4.15], Hobbs [1981, [McLaren et al., 1983, p. 91], the limited data for silicon

13,992 KOCH ET AL.: RIlEOLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE

TABLE 5. Some Possible Hydroxyl Defects in Quartz

Defect Source

Deformation Limited by Possible Methods Diffusion of Following Species of Detection

(HHO)] Griggs [1967, pp. 28-29] O, H fo2 Hobbs [1981, p. 366 and

Figure 4, p. 346] Mainprice [ 1981, Figure 4.15] Hobbs [1985, pp. 161-163] Ord and Hobbs [1986, Table 5,

pp. 66 and 67]

(3H)/ Hobbs [1981, p. 366] Si Ap'fo 2 ß beam Hobbs [ 1985, pp. 163-165] damage rate ?

(4H)•i Hobbs [1981, p. 366] Si Ao'fo 2 ß ESR McLaren et al. [1983, p. 91] Hobbs [1985, p. 164] Ord and Hobbs [1986, Table 5,

pp. 66 and 67-69]

H7 or (OH)7 Hobbs [1981, p. 366 and O, H fo2 Figure 4, p. 346]

Hobbs [1985, pp. 161-163] Ord and Hobbs [1986, Table 5,

pp. 66 and 67-69]

Kr'bger-Vink point defect notation used (see, for example, Kingery et al. [1976, pp. 127-129] or Hobbs [1981, pp. 339-340] where superscripts denote the effective charge of the point defect relative to the host lattice (ø, positive; ', negative, *, neutral) and subscripts denote occupied lattice sites (i, interstitial). Schematic, two-dimensional quartz structure incorporates each of the four hydroxyl defects discussed: note that all produce silanol defects groups. Other authors have suggested possible means of defect detection which we abbreviate using the following symbols:/xo, density change with respect to pure crystals (if concentrations are sufficiently high); fo 2, strength of crystal dependent on the fugacity of oxygen (see, for example, Hobbs [1981, 1985]); ESR, electron spin resonance; beam damage rate, rate of damage to crystals under electron beam during TEM (to maintain charge neutrality requires the incorporation of positively charge defects that are potential electron captors and may be related to beam damage during TEM [McLaren and Phakey, 1965, p. 139]; crystals containing higher concentrations would damage faster. Mainprice [ 1981, p. 81 ] has observed a general relationship between total water content and electron beam damage rate; however, such a correspondence is disputed by J. M. Christie, who has observed no such correlation in the samples that he has examined by TEM).

diffusion suggests that it is a very slow process (Giletti et al. [1976]; see also Table 6). The negatively charged HHO interstitial may be limited by the diffusion of H (which, as we have seen, seems unlikely) or by the diffusion of O. On the basis of postulated IR signatures and spatial restrictions within crystalline quartz, however, McLaren et al. [1983, p. 91] have argued that interstitial defects containing large atoms such as oxygen will not be favored; this makes the HHO interstitial less attractive. The positively charged OH

substituting for O may be the most logical selection at the present time as its diffusion may be limited by that of O. If, on the other hand, the diffusion of this defect is limited by the diffusion of H (as also has been suggested), OH substitut- ing for O would be an unlikely cause of hydrolytic weaken- ing according to the results of Kronenberg et al. [1986] and Rovetta et at. [1986].

If the diffusion of oxygen might limit both the uptake of the weakening defects and the deformation of defect laden

S ILANOL I I

I I I I I I I I o o o o o o o o o

I i I i I I I

_o o I I I

o o o !•• o !i! o o o o ISi-OHH'ho-sil-- o --Isi- o - -o -ISil-- o - - o --sil-- o -Isi--o\ '"si -

o o o o o /o o o o

--O--Si--O Si--O--Si--O--Si--O Si--O--ISil--O--Si--O--Si--O--Si-- I I I I I I I

(HH0): (3H);, (4H)s: H, OR (0H) o

Fig. 14. Schematic two dimensional quartz structure incorporating each of the four hydroxyl defects described in Table 5. X and Y provide compensation for the charged hydroxyl defects. Note that all four defects produce silanol groups

KOCH ET AL.: RI•OLOGY OF EXPERIMENTALLY DEFORMED QUARTZITE 13,993

TABLE 6. Activation Energies QD From Diffusion Studies of Quartz Experimental QD

Species Source Range of T, øC kJ mol-•

•s O

30Si

Katset al. [1962, p.75] 700-1000 175

Kronenberg et al. 700-900 200 + 20//c [1986, p. 12,735] 210 + 87//and ñ c

Giletti and Yund 500-550 284 + 92//c

[1984, Table 4, p. 238 + 12//(10•0) 4043]

Dennis [1984, Tables 515-850 138.5 + 19.1//c

3 and 4, pp. 203.7 + 2.3//(10•0) 4051-4052]

Giletti et al. [1976, p. 912-1028 230 884]

crystals, two important questions arise concerning the results of the present study. First, is there sufficient time to diffuse the defects into the quartzite grains during the preheating stage of the wet experiments? If all pore throats are wetted by fluid soon after release from the talc (as is likely in a high permeability quartzite such as the Simpson), then for our preheat conditions, the dimensions of the grains, and the 180 diffusion data of Giletti and Yund [1984, pp. 4042-4044], oxygen should have penetrated between 1/3 and 2/3 of the way into the grains depending on the preheat duration and confining pressure. This represents between 70 and 96% of the volume of each grain during the preheat alone; nearly all experiments have time for complete O diffusion if the time and conditions of subsequent deformation are included. Undeformed sample GB937 (preheated 19 hours at 850øC at 1.16 GPa, "wet" assembly) also shows an eightfold increase in total hydroxyl concentration when its room temperature infrared spectrum is compared to that of the starting material, suggesting major uptake of some hydrogen species. In the absence of cryogenic infrared spectra, ascribing some of this hydrogen to the broad band absorption, while likely, is speculative.

The second question should be: Are the activation en- thalpies of the flow laws in reasonable agreement with the activation energies for self-diffusion reported for oxygen in quartz? (While not strictly analogous, these quantities should be comparable if activation volumes can be ignored, as we have already argued.) Comparing the activation ener- gies for oxygen self-diffusion (Table 6) to our flow law en- thalpies (Table 4) suggests that all are in the same range. Activation energies for H and Si both seem appreciably larger than our empirically determined enthalpies although the diffusion constants are known with low precision. Quartzite deformed both with water added and as-received may have the same rate limiting step, the diffusion of oxygen. Micromechanical flow laws incorporating defect chemistry and concentration usually include these terms as preexpo- nential constants in the empirical flow laws [e.g., Ricoult and Kohlstedt, 1985, p. 172; Ord and Hobbs, 1986, pp. 69- 70]. Variation in these specific preexponential constants may account for the differences between our dry and wet re- sults as well as for some of the discrepancies between our own and earlier studies.

Issues Outstanding

Several important i.•.e• reqnlro further study. First, cryo- genic infrared signatures are poorly known for the hydrogen species within the grains of quartz aggregates, largely be- cause of scattering effects at grain boundaries. Second, while studies such as the present one can demonstrate the qualitative effect of water on the rheology of quartz aggregates, detailed, quantitative understanding of the phenomenon will require more controlled chemical environments than were present in our experiments. Third, diffusion data for quartz are incomplete, especially for the diffusion of silicon. Fourth, and most significantly, the defects responsible for hydrolyric weakening remain as yet unidentified both for quartz single crystals and aggregates. Until these issues are resolved fully, the phenomenon of hydrolyric weakening will remain poorly understood.

CONCLUSIONS

1. Specimens deformed in "dry" experiments are consis- tently stronger (1.5-2.5 times) than specimens deformed in "wet" experiments at comparable conditions. 2. The constants (A l, n, H) for the power law [• = A 1 (•n exp (-H/RT)] used to describe this ductile defor- mation at 750-900øC, 0.91-1.52 GPa, and 1.25 x 10 -7 s -• to 2.53 x 10 '4 s 'l are 1.16 x 10 -7 [+1.15 x 10'7 ; -5.78 x 10 -8] (MPa-2.72s-•), 2.72 + 0.19, 134 + 32 (kJ mol -•) for "dry" quartzite and 5.05 [+ 5.00] x 10 -6 (MPa-2.6•s-•), 2.61 + 0.15, 145 + 17 (kJ mol -•) for "wet" quartzite, re- spectively .

3. The total volume of recrystallized grains is lower in "dry" than in "wet" samples deformed under comparable con- ditions.

4. Microstructures indicative of recovery and therefore of diffusion are better developed in "wet" than in "dry" samples and at flow stresses below about 500 MPa.

5. The microstructures of the deformed specimens are anal- ogous to those observed in many natural quartz tectonites. 6. Similar activation enthalpies from deformation experi- ments and from diffusion experiments are consistent with de- formation of "wet" Simpson quartzite that is limited by oxy- gen self-diffusion.

7. If oxygen is the rate limiting species, OH substituting for O is the most likely defect causing the weakening.

13,994 KOCH ET AL.: RIIEO•GY OF EXPERIME•AI I.Y DEFORMED QUARTZITE

8. The rate-limiting species is the same in the "wet" and "dry" (not strictly anhydrous) tests. 9. The dry and wet flow laws differ slightly in n and greatly in A1 (perhaps as an activity term related to hydrolytic weakening). 10. Inconsistencies between the present study and previous studies are most likely a result of sample material, sample treatment, and sample assemblies (hence chemical conditions of deformation).

Acknowledgements We wish to thank J. N. Boland, B. E. Hobbs, G. P. Price, and P. Koch for comments on various drafts of this manuscript and for the insightful suggestions of Associate Editor B. Evans, A. K. Kronenberg, and S. J. Mackwell. This study consti- tuted part of the dissertation research for one of us (P.S.K.) and was funded by National Science Foundation, Earth Science Section grants EAR77-23163 and EAR81-15683 to J. M. Christie and A. J. Ardell. P.S. Koch also thanks the Department of Earth and Space Sciences, UCLA for additional support in the form of scholarships, fellow- ships, and teaching assistantships while he was a graduate student.

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J. M. Christie, Department of Earth and Space Sciences, University of California, Los Angeles, CA. 90024.

R. P. George, Jr. and P.S. Koch, Exxon Production Research Company, P.O. Box 2189, Houston, TX. 77252-2189. A. Ord, CSIRO, Division of Geomechanics, P.O. Box 54, Mount

Waverly, Victoria, 3449, Australia.

(Received March 17, 1988; revised April 5, 1989;

accepted April 6, 1989.)