Electrical conductivity of fluid-bearing quartzite under lower crustal conditions

Physics of the Earth and Planetary Interiors 198–199 (2012) 1–8

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Electrical conductivity of fluid-bearing quartzite under lower crustal conditions Akira Shimojuku a,⇑, Takashi Yoshino a, Daisuke Yamazaki a, Takamoto Okudaira b a b

Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193, Japan Department of Geosciences, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

a r t i c l e

i n f o

Article history: Received 8 August 2011 Received in revised form 23 February 2012 Accepted 6 March 2012 Available online 16 March 2012 Edited by Kei Hirose Keywords: Electrical conductivity Quartz Fluid Crust

a b s t r a c t The electrical conductivity of fluid-bearing quartzite was determined as function of temperature and fluid fraction at 1 GPa in order to assess the origin of the high conductivity anomalies observed in the middle to lower crustal levels. Dihedral angles of quartz-fluid-quartz determined from recovered samples were below 60°, suggesting that fluid forms an interconnected network through the quartz aggregate. The electrical conductivity of quartzite increases with increasing temperature, which can be approximately expressed by Arrhenius equation. The apparent activation enthalpy decreases from 0.70 to 0.25 eV with increasing fluid fraction in volume from 0.00043 to 0.32. The electrical conductivity (r) of the fluid-bearing quartzite increased with fluid fraction (/) proportionally to a power law (r / /0.56–0.71) within the temperature range of 900–1000 K. The electrical conductivity of the aqueous fluid-bearing quartzite with the maximum fluid fraction (0.32) was found to be about three orders of magnitude higher than that of dry quartzite at 1000 K. However, its electrical conductivity was definitely lower than the geophysically observed values of high-conductivity anomalies, even if the quartzite contained large fluid fractions (0.32). The present results suggest that fluid-bearing quartzite is unable to account for the high-conductivity anomalies in terms of fluid fraction. A significant amount of other ionic species, such as Na, Cl, and Al in aqueous fluid, in addition to silica phases dissolved in fluid, is required to increase conductivity. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Magnetotelluric surveys have revealed that the high-conductivity anomalies exist in the middle to lower crust (e.g., Shankland and Ander, 1983; Marquis and Hyndman, 1992). According to a compilation of worldwide field data on crustal electrical conductivity by Shankland and Ander (1983), the high-conductivity anomalies are present both tectonically active and stable regions over the depth range of about 6–50 km, and its values are ranging from 2.8  10–2 to 6.7  10–1 S/m. In addition, recent high-quality surveys on two-dimensional electrical conductivity structures obtained in Tohoku areas, Japan (Ogawa et al., 2001) and New Zealand (Wannamaker et al., 2009) have also shown that the high conductivity anomalies (>10–2 S/m) are distributed, and are closely related to active faults. Electrical conductivity measurements have been extensively conducted on dry crustal rocks such as granite, gabbro, and granulite (e.g., Olhoeft, 1981; Kariya and Shankland, 1983; Fuji-ta et al., 2004). These results have shown that the conductivity of the dry crustal rocks is much lower than the high-conductivity anomalies. Thus dry crustal rocks cannot account for the observed high-conductivity anomalies. This discrepancy suggests the existence of ⇑ Corresponding author. Tel.: +81 858 43 3754; fax: +81 858 43 3755. E-mail address: [email protected] (A. Shimojuku). 0031-9201/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.pepi.2012.03.007

conductive material in the crustal rocks that are stable only within the middle to lower crustal conditions. It has been proposed that the possible agencies for the conductive material are interconnected graphite films on grain boundaries (e.g., Frost et al., 1989; Glover, 1996), partial melts (e.g., Hermance, 1979; Roberts and Tyburczy, 1999; ten Grotenhuis et al., 2005), and aqueous fluid (e.g., Hyndman and Shearer, 1989; Glover et al., 1990; Glover and Vine, 1994). The graphite films on the grain boundaries of crustal minerals have been observed in high-grade metamorphic terranes (Frost et al., 1989; Mareschal et al., 1992). However, the graphite films on grain boundaries between crustal minerals, such as quartz and plagioclase, may not be stable due to high interfacial energies (Yoshino and Noritake, 2011). Thus interconnected networks of graphite are not likely to persist over geological time scales. Because the presence of partial melts is limited to tectonically-active regions with high geotherm, it is difficult to consider this process as the cause of the high-conductivity anomalies observed in low geotherm regions, such as South Island, New Zealand. Thus aqueous fluid seems to be the most likely candidates to explain the high-conductivity anomalies (e.g., Shankland and Ander, 1983; Marquis and Hyndman, 1992; Glover and Vine, 1994). Glover and Vine (1994) measured electrical conductivity of rocks saturated with saline fluid at 0.2 GPa, and concluded that fluid containing 0.5 mol% NaCl accounted for the high-conductivity anomalies. However, the electrical conductivity of fluid-bearing

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rocks may increase at pressures relevant to the middle to lower crust even in no NaCl, since the solubility of silicate components in aqueous fluid increases with increasing pressure (e.g., Manning, 1994; Mibe et al., 2002). In addition, dihedral angles between silicate minerals and aqueous fluids decrease with increasing pressure and temperature (e.g., Mibe et al., 1998, 1999; Yoshino et al., 2007). Thus interconnected fluid phase may increase the conductivity even in small volumetric fluid fraction. To examine the effects of soluble ionic species in aqueous fluids and pore morphology on the bulk rock conductivity, we measured electrical conductivity of fluid-bearing quartzite—a model material for crustal rocks—as function of temperature and fluid fraction at 1 GPa. Based on the results, we discuss the origin of the high conductivity anomalies observed in the middle to lower crust. 2. Experimental methods Three kinds of starting materials were prepared to obtain various fluid fractions. (1) Reagent silicic acid with a stoichiometry of SiO20.5H2O (containing about 13 wt.% H2O). (2) Synthetic sintered quartzite from a mixture of powdered quartz and the silicic acid, which was sintered at 1 GPa and 1673 K in the piston-cylinder apparatus. The water content of the sintered quartzite was determined to be about 0.022 wt.% from the Fourier-transform infrared spectroscopy (FTIR). (3) Natural cherts from the Tanba Belt, Japan. Water content of cherts determined from FTIR showed a variation from 0.1 to 0.6 wt.%. High-pressure and high-temperature experiments were carried out using the DIA-type apparatus installed at the Institute for Study of the Earth’s Interior, Okayama University. Cubic pyrophyllite with edge length of 21 mm was adopted as pressure medium for the tungsten carbide anvils with top edge length of 15 mm. Cross section of the sample assembly is schematically shown in Fig. 1. The starting material was put in a cylindrical sleeve of single crystal quartz, bored along the c-axis, with an inner diameter of 1 mm and a length of 1 mm. The limited water content of quartz up to 10 ppm at 1–1.5 GPa and 1173–1273 K (Rovetta et al., 1986) effectively suppress water loss from the sample during electrical conductivity measurement. Both the sample and the sleeve were sandwiched between two Mo disc electrodes. Two W97Re3– W75Re25 thermocouples were set with Al2O3 insulating sleeves, whose junctions are in contact with the upper and lower Mo plates. The thermocouple wires are served as probes of the

four-wire resistance measurement as well. All these parts were put inside a graphite heater together with MgO sleeves. Electrical conductivity of the sample was obtained from impedance spectroscopic measurements which was conducted using Solartron 1260 impedance Gain-Phase analyzer combined with a Solartron 1296 interface. Complex impedance spectra were obtained over frequencies ranging from 1 MHz to 0.1 Hz. The amplitude of the applied voltage was 1.0 V. The electrical conductivity was calculated from an equation of the form r = l/SRs, where r is electrical conductivity (S/m), l is length of the sample (m), S is a cross-section area of the electrode (m2), and Rs is resistance of the sample (ohm). Experimental conditions are summarized in Table 1. Conductivity measurement was carried out at 1 GPa, and temperature ranging from 800 to 1100 K. We first measured the electrical conductivity from 300 K to the highest temperatures (1000 or 1100 K) at a 100 K interval and kept the sample at the temperature for at least 12 h until the conductivity reached a constant value to completely purge extra moisture adsorbed to the capsule and other specimen parts. After that, conductivity was measured at every 25 K interval down to 800 K. Then the sample was again heated to the desired highest temperature to check the reproducibility of the conductivity measurement. Then the sample was quenched. The recovered samples were made to polished sections parallel to the direction of the electrical conductivity measurement to observe the microstructures by employing the field-emission scanning electron microscope (FE-SEM; JEOL JSM-7001F). Volumetric fluid fraction of the quenched sample was determined by counting areal fraction of pores in the secondary electron image (SEI) following the method described in Yoshino et al. (2005). For the almost pore-free samples, the fluid fraction was determined from FTIR spectra collected on a double polished thin section of 400 lm by applying the equation proposed by Paterson (1982). The FTIR measurements were performed at six different points for each sample with unpolarized IR beam with an aperture size of 100 lm  100 lm. We adopted 1/3 as the orientation factor in the calibration of Paterson (1982), assuming that the quartz grains were randomly oriented. The calibration is based on an empirical correlation between OH stretching frequency and extinction coefficient. Background corrections of absorbance spectra were carried out by a linear fit of the baseline defined by points outside the OH species and H2O molecules. 3. Results 3.1. The fluid fraction

Pyrophyllite Graphite W97Re3

W75Re25 Al2O3

Mo Quartz single crystal

Sample MgO

W97Re3

W75Re25 ZrO2

10 mm Fig. 1. Schematic cross-section of the cell assembly for the conductivity measurements in the DIA-type high-pressure apparatus.

Representative SEIs of the recovered samples are shown in Fig. 2. The fluid portions were recognized as pores filled with epoxy in samples with high fluid fraction (Fig. 2a–c). The pores are found along grain boundaries or at grain corners. The distribution of fluid pores and grain size were generally uniform (no segregation) in all the recovered samples, although the fluid was found in mainly triple junctions and occasionally large pores at grain corner as pool. The recovered single crystal quartz sleeve had cracks in all the runs. If cracks had created during pressurization or heating, fluid would easily escape through the cracks because of its high mobility. As a result, we would not observe fluid phases in the recovered samples. However, it was clear that fluid was present in all the recovered samples (Fig. 2). This suggests that the cracks had created during not pressurization or heating but decompression, otherwise the cracks healed during the conductivity measurement, because the dehydrated water during heating was retained in the capsule. For the sample utilized silicic acid powder as starting material (Run A2310), the SEI showed the presence of a great amount of

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A. Shimojuku et al. / Physics of the Earth and Planetary Interiors 198–199 (2012) 1–8 Table 1 Experimental conditions and results on electrical conductivity of fluid-bearing quartzite at 1 GPa. Run A2302 A2300 A2311 A2303 A2310

T (K) 850–1100 800–1000 800–1100 800–1100 850–1100

Sample Sintered quarzite Chert Chert Chert Silicic acid

Fluid fractiona 0.00043 (22) 0.0025 (5) 0.022 (4) 0.048 (20) 0.32 (2)

b

Log r0 (S/m)

H⁄ (eV)

0.16 (7) 0.94 (5) 0.02 (3) 0.03 (2) –0.56 (1)

0.70 0.77 0.51 0.48 0.25

(1) (1) (0) (0) (0)

Numbers in parentheses represent the uncertainties. a Fluid fraction is determined from the recovered sample quenched at the highest temperature in each experiment. b Fluid fraction is estimated from the water content determined using FTIR.

Fig. 2. SEM images of the recovered samples after conductivity measurements. Typical fluid positions are indicated by the white arrows. The staring materials were silicic acid in (a), chert in (b and c), and sintered quartzite in (d), respectively. The column crystals found in (b and c) are accessory minerals, such as spinel and titanium oxide.

fluid (Fig. 2a). This is because the silicic acid initially contained about 13 wt.% H2O. The fluid fraction of Run A2310 was determined to be 0.32 by counting areal fraction of pores in SEI image. In runs using natural chert as starting material (Run A2300, A2303, and A2311), the fluid phase was also observed as pore (Fig. 2b and c). The fluid fraction of these samples showed great variations (0.0025–0.048), which were determined by counting areal fraction of pores in SEI image. As shown in Fig. 2b and c, some accessory minerals, such as spinel and titanium oxide which were found by energy dispersive X-ray spectrometry equipped with SEM, were present in the samples of chert. The SEM observation suggested that the volume fraction of these minerals did not change significantly before and after the conductivity measurement. Thus these minerals did not preferentially dissolve into aqueous fluid during the conductivity measurement. In fact, solubility of titanium oxide in H2O was determined to be quite low at low temperatures (Tropper and Manning, 2005). In addition, the conductivity data obtained on the samples using natural chert are systematically plotted between data obtained from samples with the highest and lowest water contents (see Fig. 7). Therefore,

it is concluded that the dissolved ionic species from accessory minerals could have a minimal effect on the bulk conductivity. For the sample using sintered quartzite as starting material, it is not so clear where fluid is present (Fig. 2d), because the initial water content of the sintered quartzite was low (0.022 wt.%). The fluid fraction was estimated based on the water contents from by the FTIR measurements. The obtained FTIR spectra before and after the conductivity measurement of Run A2302 are shown in Fig. 3. The broad band at around 3400 cm–1 and two smaller bands at 3596 cm–1 and 3360 cm–1 were observed in the sample before conductivity measurement. The broad band around 3400 cm–1 is attributed to the molecular water (H2O), whereas the smaller band at 3596 cm–1 is the OH species in the quartz crystal structure (e.g., Kronenberg and Wolf, 1990). The peak at 3360 cm–1 is possibly attributed to the OH species, because this peak was relatively sharp. After the conductivity measurement, there remained a broad peak around 3400 cm–1, and the absorbance intensities of two smaller bands were distinctly lower than those before the measurements. This indicates that a certain amount of OH species in the quartz crystal was dehydrated during the conductivity

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1.00

Temperature (K) 1200 1100 1000

900

800

700

600

-1.0

0.80

heating path cooling path

3360

0.60

(S/m)

3596

0.40

-2.0

log

Absorbance (/mm)

-1.5

-2.5 before experiment

0.20 -3.0 after experiment

0.00

8.0

10.0

12.0

14.0

4

4000

3800

3600

3400

3200

3000

16.0

18.0

-1

10 /Temperature (K )

2800

-1

Wavenumber (cm ) Fig. 3. FTIR spectra of quartzite (Run A2302) before and after the conductivity measurement. The broad band at 3400 cm–1 is attributed to H2O, and a smaller band at 3596 cm–1 is probably OH species (e.g., Kronenberg and Wolf, 1990). The peak at 3360 cm–1 is possibly due to OH species.

measurement. The remaining broad band at 3400 cm–1 indicates that fluid exists during the conductivity measurement. The water contents before and after conductivity measurements were 0.022 wt.% (0.00058 in volume fraction) and 0.010 wt.% (0.00027 in volume fraction), respectively. Thus the half of fluid was probably somewhat lost during the conductivity measurement or polishing of the recovered sample. We tentatively adopted 0.00043 as fluid fraction of Run A2302, which is determined from median value of 0.00027 and 0.00058. The determined fluid fractions are summarized in Table 1. The apparent dihedral angle measurements on the SEI were carried out for the samples with fluid fractions of 0.022 and 0.048. The median dihedral angles were 41°, and 46° in the sample with a fluid fraction of 0.022, and 0.048, respectively. Because the experiments were conducted at the same P–T conditions, the dihedral

Fig. 5. Electrical conductivity of fluid-bearing quartzite as a function of reciprocal temperature obtained in Run A2303. Open and black symbols indicate conductivity values for heating and cooling paths, respectively.

angles are likely to be similar even in changing fluid fraction. The determined dihedral angles are significantly lower than the critical value of 60° for interconnection. Thus fluids should have formed interconnected networks along grain edges in the quartz aggregates under the present experimental conditions. This result is consistent with those of Holness (1993) in which the dihedral angle in quartz and fluid was shown to be less than 60° at 1 GPa and below about 1273 K. 3.2. Impedance spectroscopy Representative Cole–Cole plots with fluid fractions of 0.0025 (Run A2300) and 0.32 (Run A2310) are shown in Fig. 4a and b, respectively. With increasing temperature the radius of the impedance arc decreased in all experiments. All the arcs seem to be composed of one semicircle at high frequencies and an additional tail at low frequencies. The impedance spectra of the quartz plus

(a) Run A2300, Fluid fraction=0.0025

(b) Run A2310, Fluid fraction=0.32

5000

70 Fluid

Fluid

60

4000

Electrode

Electrode

50 Grain interior

ohm )

ohm)

Grain interior

3000

900K

1100K 30

1000K

2000

1000K

40

20

1000 10

0

0

0

1000

2000

3000

Z' (kohm)

4000

5000

0

10

20

30

40

50

60

70

Z' (kohm)

Fig. 4. Representative impedance spectra of (a) Run A2300 with a fluid fraction of 0.0025, and (b) Run A2310 with a fluid fraction of 0.32. The expected electrical circuits are also shown. The straight lines indicate the fitted to the data points.

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-1.2

Temperature (K) -1.0

1200

1100

1000

900

800

-1.6 -1.5 0.32

-2.0

0.022

(S/m)

-2.4

-3.0

log

-2.5

-3.5

-3.2

-4.0

-3.6

0.0025

log

0.00043

Quartz single crystal (Yoshino and Noritake, 2011)

-4.5 -5.0 8.0

n=0.56 (1000K)

0.048

(S/m)

-2.0

9.0

10.0 4

11.0

12.0

-2.8

n=0.71 (900K)

-4.0 -4.0

-3.0

-2.0

-1.0

0.0

log

13.0

-1

10 /Temperature (K ) Fig. 6. Arrhenius plots of electrical conductivity for fluid-bearing quartzite at 1 GPa. The numbers attached indicate fluid fractions determined at highest temperature (1000 or 1100 K). The fluid fraction is not exactly same as that at lower temperatures, because the lower solubility of silica in fluid at low temperature increases the portion of solid part. However, the variation of fluid fraction with temperature was estimated to be 15% (see text). The electrical conductivity of quartzite increases with increasing temperature and increasing fluid fraction. The electrical conductivity of a quartz single crystal, parallel to c-axis, at 1 GPa reported by Yoshino and Noritake (2011) is also shown for comparison.

fluid systems include grain interior, fluid at the grain boundaries, and electrode-sample interface effects. It is expected that the dominant conductivity paths depend on the geometrical distribution of fluid in quartzite. Roberts and Tyburczy (1999) measured the electrical conductivity in olivine plus basaltic melts, and suggested that the electrical circuit may be different in terms of connectivity of the basaltic melts. In the case of presence of an interconnected melt pathway, the circuit was composed of the response of the grain interior and basaltic melts in a parallel circuit. On the other hand, in the absence of an interconnected melt pathway, the circuit was composed of the response of the grain interior and the basaltic melt in a series circuit. As is the case in the fluid-bearing quartzite, electrical responses should be different depending on the fluid connectivity. It is inferred that for runs in which one semicircle was observed in the impedance spectroscopy (Fig. 4), fluid possibly formed an interconnected network during the conductivity measurement. This interpretation is supported by the observed low dihedral angle (below 60°). The semicircular shape of the impedance spectra is almost controlled by ionic conduction in interconnected fluids. The low-frequency tails appeared in all impedance spectroscopy may be due to electrode-sample interface effects (e.g., ten Grotenhuis et al., 2005). As shown in Fig. 4, a two-parallel R–C in-series circuit can be considered as the equivalent circuit of the samples. Because the resistance of grain interior is much higher than that of interconnected fluid phase, the impedance spectra were fitted by a single parallel R–C circuit to determine the bulk resistance of the fluid-bearing quartzite. The low-frequency tail was not included in the fitting. The errors in electrical conductivity for each measurement were estimated from the uncertainty arising from the fitting, and were within ±0.1 log units.

3.3. Conductivity equilibrium Fig. 5 shows an example of electrical conductivity of fluid-bearing quartzite (Run A2303) as a function of reciprocal temperature.

Fig. 7. Relationship between fluid fraction (/) and electrical conductivity (r) in a log–log plot for the ranges of / = 0.00043–0.32, and at T = 900, and 1000 K. The n values in Archie’s law were determined to be 0.71 for 900 K, and 0.56 for 1000 K.

Electrical conductivity was measured at every 100 K while heating from 300 to 1100 K. Conductivity in the first heating decreased by about one order of magnitude with temperature. Since the conductivity in the first heating usually affected by absorbed water in the specimen assembly (e.g., Yoshino, 2010), we did not use the conductivity data obtained in the first heating. During keeping the sample at 1100 K for several hours, the sample resistance was slightly decreased and finally reached a constant value. This indicates that the sample reached textural equilibrium where the interfacial energy of the system is the minimum with equilibrium amount of fluid in the sample. Acquisition of conductivity data was performed on decreasing temperature at every 25 K interval to 800 K. We adopted the electrical conductivity data obtained on the cooling path. 3.4. Electrical conductivity The present results showed a linear relationship in logarithmic conductivity versus reciprocal temperature. The temperature dependence of the electrical conductivity can be approximately expressed by the Arrhenius equation:



r ¼ r0 exp 

H RT

 ð1Þ

where r0 is the pre-exponential factor (S/m), H is the activation enthalpy (eV), R is the gas constant (J/mol/K), and T is the absolute temperature (K). The Arrhenius plots of electrical conductivity obtained in the present study are shown in Fig. 6 for various fluid fractions. The least square fitting of the data to Eq. (1) yielded the pre-exponential factor and the activation enthalpy summarized in Table 1. Uncertainties of the pre-exponential factor and activation enthalpy are estimated by propagating from those of the electrical conductivity. The sample with fluid fraction of 0.00043 (Run A2302) showed conductivity increased around 1000 K (Fig. 6). This may be a change in conduction mechanism. The possible conductivity paths of the sample are the grain interior and/or the interconnected fluids. Thus the conductivity paths could change from interconnected fluids to grain interior. However, the conductivity of grain interior in quartz is considerably lower (Fig. 6). Thus it is unlikely that there is a change of conductivity mechanism around 1000 K. In addition, impedance arcs of 4 data points above 1000 K did not

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show clear semicircle shapes, leading relatively large uncertainties of conductivity as shown in Fig. 6. Therefore, the data showing the nonlinear relationship in Arrhenius plot was not used for fitting. The fitted lines in Fig. 6 are not exact isopleths of fluid fraction, because the fluid fraction can change with temperature. The fluid fractions were determined from the samples quenched at 1100 K. The fluid fraction might slightly decrease at lower temperature due to lower silica solubility (e.g., Manning, 1994). From the experimental results by Manning (1994), the variation of fluid fraction over the temperatures between the highest and the lowest temperatures was estimated to be about 15%. This variation may not result in a serious change in the conductivity judged from weak dependence of the conductivity on fluid fraction demonstrated in Fig. 6. Electrical conductivity increases with increasing both fluid fraction and temperature. Conductivity of quartzite with the lowest fluid fraction (0.00043) is still about 1.5 orders of magnitude higher than that of a water-free quartz single crystal (Yoshino and Noritake, 2011) at 1000 K. This indicates that existence of tiny amount of fluid strongly increases the conductivity. 4. Discussion 4.1. Effect of fluid fraction on electrical conductivity Fig. 7 shows the relationship between the bulk electrical conductivity and fluid fraction at 900 and 1000 K on the logarithmic scale. The apparent linear relationship between logarithmic conductivity and logarithmic fluid fraction is consistent with Archie’s law (Archie, 1942; Watanabe and Kurita, 1993):

rbulk ¼ C/n rf

ð2Þ

where rbulk is the bulk conductivity, C and n are constants, / is the fluid fraction, and rf is the electrical conductivity of the fluid. This law is empirically derived and only applicable to the system with constant fluid conductivity. The modified Archie’s law has been proposed by Glover et al. (2000) to address the relationship between conductivity and volume fraction in two conducting phases. Although knowledge of rf value is needed to apply the modified Archie’s law, it was difficult to constrain rf values in this study. The other mixing model for the bulk conductivity such as Hashin and Shtrikman bounds also requires rf values. Therefore, the conventional Archie’s law was used in this study to evaluate the effect of fluid fraction on the bulk electrical conductivity. The n value is closely related to the connectivity of the fluid and usually is close to unity. In this study, the n values were determined to be 0.71 for 900 K, and 0.56 for 1000 K by a least squares fit to the data (Fig. 7). The small n value implies that the degree of connectivity of fluid in quartzite is high at low fluid fraction. With increasing temperature, the exponent n became smaller, which could imply higher connectivity of the fluid at higher temperatures. As shown in Fig. 6, the apparent activation enthalpy of fluidbearing quartzite appeared to decrease with increasing fluid fraction, although fluid-bearing quartzite with a fluid fraction of 0.0025 (Run A2300) had a slightly larger activation enthalpy compared with that with a fluid fraction of 0.00043 (Run A2302). If number density of the charge carrier in the fluid and its diffusivity are constant with fluid fraction, the apparent activation enthalpy (hereafter denote simply by activation enthalpy) should be same even in changing the fluid fraction. One possible reason to explain the decrease in activation enthalpy with fluid fraction is due to the change in connectivity with fluid fraction. As temperature decreased, the dissolved silica components would preferentially precipitate at a grain corner or junction. The precipitated silica reduced the connectivity of the fluid, in particular, when fluid

fractions were very low. Another reason is effect of faceting. Faceting at pore wall strongly affects the fluid distribution. Yoshino et al. (2006) reported that the morphology of quartz-water system shows moderately faceted, which leads to the heterogeneous fluid distribution characterized by development of large pores surrounded by faceted walls and complementary shrinkage of triple junction tube. As faceting is likely to develop at lower temperature, effective pathways for charge carrier would decrease by the relative reduction of triple junction tube volume. Thus it could be concluded that decrease in activation enthalpy with fluid fraction is attributed to a change of fluid connectivity by the changes of silica solubility and faceting. The fluid fraction can change with temperature, as the solubility of silica can change with temperature. We determined fluid fraction only at 1100 K. Thus there can be a difficulty to make an extrapolation to much higher and lower temperatures. In fact, the apparent r0 in Eq. (1) increases with decreasing fluid fraction (see Table 1), indicating that the conductivity with a smaller fluid fraction exceeds that with a larger fluid fraction at a certain high temperature. This means that the estimated r0 does not express the concentration of charge carrier in the fluid. Thus application of Archie’s law to our data may be limited to the temperature range in which we determined fluid fraction (1100 K). We selected the data at 900 and 1000 K in the discussion on Archie’s law (Fig. 7). Since these temperatures are relatively similar, the discussion based on Archie’s law could be valid in such a small temperature range.

4.2. Conduction mechanism in fluid-bearing quartzite Since the presence of a fluid phase in the samples was confirmed from microstructural observations, the charge carrier for the bulk conduction should have been ionic species dissolved in the fluid. The SiO2 solubility of water have been extensively examined (e.g., Weill and Fyfe, 1964; Walther and Orville, 1983; Manning, 1994), and it has been generally accepted that dissolution of SiO2 into water may be expressed by the reaction: xSiO2 + yH2O = xSiO2yH2O in the fluid phase. Although there are controversies regarding the x and y values, x and y often are taken to be 1 and 2, respectively (e.g., Wasserburg, 1958; Wood, 1958). Thus the above reaction was written to be SiO2 + 2H2O = Si(OH)4. The Nernst-Einstein equation is known to address the relationship between electrical conductivity and diffusivity of the migrating species:

r ¼ Dq2 c=kB T

ð3Þ

where D is the diffusivity of the migrating species, q is the charge of the species, c is the concentration of the carrier, and kB is the Boltzmann’s constant. Thus neutral hydroxide of Si(OH)4 cannot contribute to conduction. In other words, the other charged ions must be attributed to the conduction. It has been reported that Si(OH)4 dis2 sociates into charged species, such as Si2 O2 ðOHÞ 5 , Si2 O3 ðOHÞ4 , and  SiOðOHÞ3 depending on the pH (e.g., Applin, 1987). It is highly likely that these complex anions may be agents of electrical conduction of aqueous fluids in water–quartz system. According to Nesbitt (1993), electrical conductivity of KCl solutions (3.6–24.7 wt.%) was within the range of 10–100 S/m at 373– 773 K and 0.1–0.3 GPa. The conductivity is several orders of magnitude higher than that of quartzite with a fluid fraction of 0.32, suggesting that K+ and/or Cl– have much significant effects on the bulk conductivity compared to SiO2. This is caused by the great difference in dissociation constant of the charged carrier between KCl solution and Si(OH)4 in water. In addition, the mobility of charged species formed in the SiO2–H2O system is likely to be

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lower than K+ and Cl– because their sizes are much larger than K+ and Cl–. Brenan (1993) has investigated the diffusion coefficients for Cl– in fluid-bearing quartzite at 1 GPa and 1273 K. Diffusion rate of Cl– of / = 0.027 is about one order of magnitude faster than that with / = 0.01. Nernst-Einstein relation suggests that increase of the diffusivity by an order can produce one-order increase of the conductivity. Therefore, it is expected that the conductivity of fluidbearing quartzite with Cl– increases about one order of magnitude in a range of / = 0.01–0.027. On the other hand, we calculated the conductivity of quartzite plus fluid (without Cl–) with / = 0.027, and 0.01 using Archie’s law (Fig. 7) at 1100 K based on our data. The result shows that the conductivity of quartzite plus fluid increases only about 0.2 orders of magnitude for changing / from 0.027 to 0.01. This means that diffusivity of the charged species in the SiO2–H2O system does not increase significantly by fluid fraction. Thus Cl– dissolved in the fluid could be a good agent for increasing conductivity. 4.3. Geophysical implications Fig. 8 shows comparison between the conductivity values observed in the high-conductivity anomalies and the present experimental data in the form of Arrhenius plot. As representative observational data, we selected those compiled by Shankland and Ander (1983), because their data were taken from worldwide regions including both tectonically active and stable regions. As shown in Fig. 8, electrical conductivity of high-conductivity anomalies is about one order of magnitude higher than that of quartzite with a fluid fraction of 0.32. Therefore, fluid-bearing quartzite cannot account for the high-conductivity anomalies in the crust in terms of fluid content. It is necessary to consider other plausible agents for understanding the high-conductivity anomalies. As has already been discussed by several authors (e.g., Shankland and Ander, 1983; Marquis and Hyndman, 1992; Nesbitt, 1993; Glover and Vine,

Temperature (K) 0.0

1200 1100

1000

900

800

700

7

1994), saline fluid is one possible agent to raise the conductivity, because the Na+ and Cl– in the fluid become to form charge carriers. For another possible explanation, the other ionic species originated from other constituent minerals are soluble in the aqueous fluid, which can enhance the bulk conductivity. In fact, Glover and Vine (1994) demonstrated that electrical conductivity of fluid-bearing rocks containing 0.5 mol% NaCl depends on rock type, which suggests that electrical conductivity in fluid-bearing rocks depends on dissolved ionic species that originated from various minerals. Further experiments to investigate the effects of other ionic species on bulk conductivity are needed to reveal possible agents for the high-conductivity anomalies in the crust. 5. Conclusions (1) The electrical conductivity of fluid-bearing quartzite was measured at conditions of 1 GPa, 800–1100 K, and fluid fractions ranging from 0.00043 to 0.32 by using impedance spectroscopy. (2) Fluid in quartzite forms the interconnected network in present experimental conditions judged from the measured dihedral angles. (3) The electrical conductivity of fluid-bearing quartzite with fluid fraction of 0.00043 was found to be about 1.5 orders of magnitude higher than that of a water-free quartz single crystal at 1000 K. This indicates that existence of tiny amount of fluid strongly increases the conductivity. (4) The electrical conductivity of fluid-bearing quartzite is definitely lower than that of observed values of the high-conductivity anomalies in the middle to lower crust even if the quartzite contained large fluid fractions (0.32). Thus the high-conductivity anomalies cannot be accounted for fluid-bearing quartzite in terms of the fluid content. The reason for the relatively low conductivity in fluid-bearing quartzite is possibly due to the fact that soluble ionic species in fluid-bearing quartzite are mainly composed of neutral hydroxide of Si(OH)4. (5) The other ionic species such as Na, Cl, and Al dissolved in aqueous fluid are plausible agents to explain the high-conductivity anomalies.

High-conductivity anomalies (Shankland and Ander, 1983)

-1.0

Acknowledgments We acknowledge E. Ito, for correcting the manuscript, A. Yoneda, N. Tomioka, and T. Okuchi, for their helpful comments, X. Guo and S. Shan for their technical assistance with the highpressure experiments, S. Yamashita for his technical assistance with the FTIR measurements. We are also grateful to K. Mibe, and an anonymous reviewer for their insightful comments to improve manuscript. This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas (Research in a Proposed Research Area), ‘‘Geofluids: Nature and Dynamics of Fluids in Subduction Zones’’ from the Japan Society for Promotion of Science (No. 2109003).

log

(S/m)

0.32

-2.0

0.048 0.022

0.0025 -3.0 0.00043

-4.0

8

9

10

11 4

12

13

14

15

16

-1

10 /Temperature (K ) Fig. 8. Comparison between observational data and experimental data of fluidbearing quartzite. The solid lines represent electrical conductivity of fluid-bearing quartzite. The numbers attached indicate fluid fractions determined at highest temperature (1000 or 1100 K). The dashed line represents high-conductivity anomalies compiled by Shankland and Ander (1983), and the gray region indicates the ranges of 1r in the high-conductivity anomalies. Even in the quartzite with large fluid fraction (0.32), the electrical conductivity is lower than the observed values, suggesting that quartzite plus fluid are unable to account for observed highconductivity anomalies.

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