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Unstable graphite films on grain boundaries in crustal rocks
Earth and Planetary Science Letters 306 (2011) 186–192
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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l
Unstable graphite films on grain boundaries in crustal rocks Takashi Yoshino a,⁎, Fumiya Noritake b a b
Institute for Study of the Earth's Interior, Okayama University, Misasa, Tottori 682-0193, Japan Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan
a r t i c l e
i n f o
Article history: Received 11 January 2011 Received in revised form 28 March 2011 Accepted 5 April 2011 Available online 30 April 2011 Editor: L. Stixrude Keywords: electrical conductivity interfacial energy graphite quartz lower crust
a b s t r a c t The origin of high electrical conductive anomalies in the lower crust is a long-standing and controversial problem. Although it has been proposed that saturated saline water or partial melt increases electrical conductivity, graphite film has also been recognized as a potential cause of high conductivity since the discovery of fine graphite films on the grain boundaries of high-grade metamorphic rocks. To investigate the stability of graphite film on grain boundary of silicate minerals under lower crustal conditions, electrical conductivity of graphite film on synthetic grain boundaries of quartz bicrystals was measured by means of impedance spectroscopy at 1 GPa and up to 1200 K in a multianvil apparatus. At first heating, the electrical conductivity of the thin graphite film with thickness less than 100 nm was initially very high but decreased with time during annealing. Under high temperature conditions (N1000 K), the conductivity of a thin carbon film rapidly decreases and approaches the quartz conductivity. This indicates that graphite film on a grain boundary between two quartz crystals is not stable at high temperatures. Optical microscopic observation of the run products suggested a disconnected feature of graphite on a quartz grain boundary. Disconnection of graphite film can be caused by higher interfacial energy between graphite and silicate minerals than that of the grain boundary energy. Therefore, a thin graphite film is not a likely candidate to account for high conductivity anomalies in the middle and lower continental crust. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The origin of high electrical conductive anomalies in the lower crust is a long-standing and controversial problem. It has been known from laboratory conductivity measurements that dry rocks have very low conductivity (~10−4 S/m) at lower crustal temperatures and pressures (e.g., Brace, 1971; Fuji-ta et al., 2004, 2007; Kariya and Shankland, 1983), which is significantly lower than the electrical conductivity (~10−1 S/m) of the lower crust observed in many parts of the world (Shankland and Ander, 1983). Thus the presence of a conductive phase is needed to account for the high electrical conductivity of the lower crust. It has been proposed that saturated saline water or partial melt increases electrical conductivity (e.g., Hyndman and Hyndman, 1968; Hyndman and Shearer, 1989). A carbon film on the grain boundaries of crustal minerals has been also considered as a possible cause of middle and lower crustal high electrical conductivity anomalies detected by magnetotelluric surveys (e.g., Duba and Shankland, 1982; Monteiro Santos et al., 2002; Shankland and Ander, 1983). This hypothesis has been supported by the observation of grain boundary graphite films in lower crustal rocks (Frost et al., 1989; Mareschal et al., 1992) and by graphite or amorphous carbon precipitation in shear zones or fractures
⁎ Corresponding author. E-mail address: [email protected] (T. Yoshino). 0012-821X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2011.04.003
at mid-crustal depths (Bigalke et al., 2003; ELEKTB et al., 1997; Mathez et al., 2008; Roberts et al., 1999). These types of carbon may originate from the precipitation of C–O–H fluids generated by mantle-derived magma or the metamorphism of carbonate rocks and organic-rich sediments. Duba and Shankland (1982) calculated the absolute amount of highly conductive and well-interconnected carbon required based on the upper bound formula (Waff, 1974), and found that a volume fraction of only 5x10−6 vol.% of carbon was necessary to enhance the electrical conductivity of dry rocks to values typical for conductive zones at lower crustal conditions (0.1 S/m). Although an interconnection of such thin graphite films or layers is required to explain high conductivity anomalies, impedance studies on graphite-bearing metamorphic rocks have only shown a slight increase of conductivity values (Frost et al., 1989; Glover and Vine, 1992; Mathez et al., 1995; Shankland et al., 1997). It has been postulated that rupturing these films during decompression could irreversibly reduce the electrical conductivity of rocks (Frost et al., 1989; Katsube and Mareschal, 1993; Shankland et al., 1997). On the other hand, the stability of graphite in lower crustal rocks has also been discussed from the aspect of petrology (Frost and Bucher, 1994; Yardley and Valley, 1997). However, the interfacial energetic stability of grain-boundary graphite films on crustal silicate minerals under lower-crustal pressure conditions has not been studied. The purpose of this study is to determine whether graphite film on grain boundaries of silicate minerals forming the lower crust is stable from the viewpoint of interfacial energy. Measurements of electrical
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conductivity are very sensitive to the connectivity of very small amounts of conductor (Watson et al., 2010; Yoshino et al., 2003) when the difference between the electrical conductivity of insulator and conductor is extremely large. Thus, the stability of a graphite film on grain boundaries can be detected by means of in situ electrical conductivity measurements. We performed in situ impedance spectroscopic measurements at 1 GPa on quartz bicrystals coated with carbon on their grain boundaries using a cubic-type and a Kawaitype multi-anvil apparatus to investigate the stability of the grain boundary carbon film under lower crustal conditions. Electrical conductivity measurements of a polycrystalline graphite rod and quartz single crystal were also performed at 1 GPa to constrain the end member conductivities. Our results suggest that the graphite film is not stable on grain boundaries of silicate minerals. 2. Experimental methods The starting materials were prepared from a single synthetic quartz crystal with an initial water content less than 1 ppm in weight. Disks with a diameter of 2 mm and 1 mm thickness were cored from the single quartz crystal parallel to the c-axis. The cored disks were cut into two halves with faces parallel to the cylinder axis, the c-axis as shown in Fig. 1a, so that both pieces have a semi-circular shape. The cut plane for the semi-circular piece was polished by diamond paste with 1 μm diameter. To avoid the mechanical destruction of the interconnected carbon film to graphite or the molybdenum electrode at the corner during compression, the corner was reshaped to a
Fig. 1. (a) Schematic cartoon of carbon-coated quartz bicrystals. Note that the corners consisting of two flat planes parallel and perpendicular to the cylindrical axis of disk were reshaped to a smoothly curved surface. (b) Schematic cross-section of highpressure cell assembly for conductivity measurements. Experiments in a Kawai-type multi anvil press were carried out in 25-mm Cr-bearing MgO octahedral assemblies with 15-mm truncation edge length of tungsten carbide cube. Experiments in a cubic multi anvil press were carried out in 20-mm pyrophyllite cubic assemblies with 15-mm truncation edge length of tungsten carbide cube.
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smoothly curved surface (Fig. 1a). The polished surfaces including smooth curved corner were coated with a carbon film by vapor deposition in vacuum using a carbon coater. The thickness of the carbon film ranged from a few to several tens of nanometers. Thus, the two half-moon shaped single crystals form a bicrystal containing a thin carbon film at the boundary (Fig. 1a). The starting material of graphite aggregate was prepared from a graphite rod, which was also used for the carbon coating. A cylindrical thin graphite rod loaded into a sintered MgO sleeve with inner diameters of 0.5 mm was used for the conductivity measurement to increase resistance of the sample because graphite has very high conductivity. The sample was sandwiched between two molybdenum disks that served as electrodes. Mo electrodes were used so that the oxygen fugacity would be close to the Mo-MoO2 buffer, which is lower than that of C–CO buffer. The starting material of quartz single crystal was also prepared from a synthetic quartz single crystal. A disk with a diameter of 2 mm and 1 mm thickness was cored from the single quartz crystal parallel to the c-axis. Two single crystals of quartz were used for most runs in a simplification of graphite films occurring in crustal silicate minerals. Because interfacial energy between crystals varies with crystal surface, the stability of the graphite film in mineral aggregates with variable grain boundary misorientations was also investigated. Anorthite (CaAl2Si2O8: an end-member of plagioclase solid solution) was used for this experiment, since plagioclase is thought to be the most abundant mineral in the lower crust. The starting material was synthetic anorthite prepared from a mixture of reagent-grade SiO2, Al2O3, and CaCO3. The mixture was heated for 1 h at 1073 K to remove carbon dioxide and then heated for 8 h at 1643 K to form seeds of anorthite. The retrieved sample was ground and sieved to produce uniform-sized crystals. The micrometer-sized powder was repeatedly coated by carbon. In order to cover all grain surfaces with carbon, the powder was shaken before each coating. These powdered starting materials were placed in MgO capsules. Molybdenum disks were used as electrode for conductivity measurement. Carbon-free anorthite aggregates were also measured to enable the identification of disconnected graphite films. Fig. 1b shows a design of the high-pressure cell assembly. The diskshaped sample made of two half-moon shaped single crystal was placed in a MgO capsule, and sandwiched between two electrodes made of either graphite or molybdenum. Two sets of W97Re3-W75Re25 thermocouples were mechanically connected to the two electrodes. Each thermocouple was insulated from the graphite heater by MgO sleeves. Electrodes with a diameter of 2 mm were placed in contact with the sample. The oxygen fugacity was controlled by the C–CO buffer or a Mo–MoO2 buffer. Both buffers yielded similar results. The recovered sample showed no significant deformation during the conductivity measurement runs. Sample conductivity and the thickness of the graphite film on the grain boundary were calculated from the minimum resistance at the maximum annealing temperature and the sample dimensions. Sample conductivities were measured by an impedance GainPhase Analyzer (combined with a Solartron 1296 interface if the sample resistance was higher than 1 MΩ). The amplitude of the applied voltage for alternating current was 1 V. A wide frequency range of 10−3–106 Hz was used to distinguish between grain boundary transport and electrode processes from the impedance spectrum. The impedance spectra were obtained from high to low frequencies. To determine sample resistance, the data were fitted to an expression for a simple RC parallel equivalent circuit. Electrical conductivity measurements were performed along the heatingcooling cycle. In the first cycle, the sample was heated to the desired temperatures (1000, 1073 and 1200 K). The coated carbon layer on the quartz grain boundary crystallized to graphite during first heating. The carbon phase on the grain boundary after conductivity measurement was identified to be graphite by micro-focused beam X-ray
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diffractometer. At the maximum temperature, the sample conductivity was monitored frequently to detect interconnections of the graphite film on the grain boundary as a function of time. Annealing time at the highest temperature was variable in a range from 3 to 71 h, and depended on a decreasing rate in electrical conductivity. After heating at the maximum temperature, heating and cooling were repeated to confirm repeatability. During each cycle, temperature was changed in 50 K interval, and electrical conductivity was measured at each temperature step. For several experiments, heating and cooling were performed in the process on the way of a decrease in the electrical conductivity at the highest temperature to evaluate the connectiveness of graphite film. Experimental conditions and results are shown in Table 1. 3. Experimental results Five electrical conductivity measurements were performed on quartz bicrystals with carbon-coated grain boundary. Clear evidence of fracturing and displacement along the grain boundary was not observed in any of the run products. The electrical conductivity of graphite aggregate and single crystal quartz parallel to the c-axis was also measured by one experiment of each at 1 GPa. Fig. 2 shows electrical conductivity of graphite aggregates and single crystal quartz parallel to c-axis as a function of reciprocal temperature. The electrical conductivity of graphite is nearly ten orders of magnitude higher than that of quartz single crystal at 1000 K. Both samples behave as a semiconductor. The absolute conductivity values increase with increasing temperature. Conductivity (σ)–temperature (T) relationships were expressed by the Arrhenian formula: ΔH σ = σ0 exp − kT
ð1Þ
where σ0 is pre-exponential factor, ΔH is activation enthalpy, k is the Boltzmann constant, and T is absolute temperature. The activation enthalpy of graphite is quite small (0.02 eV), whereas that of quartz is definitely larger (0.89 eV). This huge contrast is useful to detect the connectivity of very thin graphite film with thickness less than 100 nm. The details of the experimental conditions and some parameters fitted by Eq. (1) for each run are given in Table 1. An example of conductivity measurements is shown in Fig. 2. The conductivity values were initially high and slightly increased with temperature increasing up to the desired temperature. At the beginning of annealing at 1200 K, the sample conductivity was four orders of magnitude higher than the quartz conductivity. The conductivity decreased with time at the maximum temperature. The impedance spectra first showed a semicircular shape (Fig. 3a), suggesting that the conductive phase forms an electrical pathway in parallel with the solid matrix. Then an additional part with 0˚ phase angle appeared at low frequencies (Fig. 3b). This suggests that
Fig. 2. Electrical conductivity of carbon-coated quartz bicrystals as a function of reciprocal temperature (Run# AMA254). Open circles and closed diamonds indicate results of 1st and 2nd cooling-heating cycles, respectively. Thick line denotes electrical conductivity of graphite. Thick shaded line indicates electrical conductivity of single crystal synthetic quartz parallel to c axis.
resistance largely increased during the conductivity measurement because the impedance spectrum obtained at low frequencies requires a relatively longer time than that obtained at high frequencies. After heating at 1200 K for relatively short duration (a few hours), the conductivity values were nearly independent of temperature along the first cooling and second heating paths. This small temperature dependence (ΔH: 0.03 eV) is similar to that of the conductivity of graphite (ΔH: 0.02 eV). The activation enthalpy of conductivity of a bulk sample should correspond to that of a conductive phase if the conductive phase establishes interconnection in the resistive matrix (Yoshino et al., 2003, 2004). In addition, preservation of high conductivities after the temperature was reduced indicating that the carbon film was still interconnected on the quartz grain boundary. After heating at 1200 K for more than 15 h, the conductivity followed a different trend in the cooling path: the conductivity shows much larger temperature dependence than before. The temperature-conductivity path is essentially the same as the conductivity of quartz parallel to the c axis. In fact the activation enthalpies of conductivity of a bulk sample (1.06 eV) are close to that of quartz (0.89 eV). It is concluded that grain boundary graphite film was not interconnected. The impedance spectra showed a single arc with 45˚ of slope in the complex impedance plane below 10 Hz
Table 1 Summary of runs. Run no.a
Sample
Tmax (K)
Electrode
AMA125 AMA127 AMA128 AMA254
Quartz c// C-coated Graphite C-coated
1073 1073 1273 1200
Graphite Mo Mo Graphite
1K1199 1K1200 1K1204
C-coated C-coated C-coated
1000 1200 1200
Graphite Graphite Mo
Logσ0 (S/m)
ΔH (eV)
− 0.38 0.74 5.17 − 0.08 0.74 − 0.96 0.30 1.68
0.89 0.82 0.02 0.03 1.06 0.05 0.05 0.87
Duration (h)
b
δ (nm)
6
3
2.5 16 47 21 22
25
Remarks c
First cooling Second cooling
28 71 51
All experiments were conducted at 1 GPa. a The experimental run numbers which contain AMA and 1 K represent the experiment using a cubic press and a Kawai-type multi anvil press, respectively. b Annealing time (hours) at the maximum temperature. c Graphite film thickness was calculated from the maximum conductivity at the maximum annealing temperature based on the graphite conductivity data of AMA128.
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(Fig. 3c), suggesting an increase in the effect of polarization between the quartz and electrode. Fig. 4 shows the change in the electrical conductivity for all carbon-coated samples with time, while maintaining the maximum temperature. All samples finally showed a decrease of conductivity after a certain time passed. For the sample that annealed at the lowest temperature (1000 K), the conductivity slightly increased at the beginning of the annealing then became constant. After one day, the conductivity started to decrease due to the destruction of interconnectivity within the graphite film. However, a sample with a similar thickness of graphite film annealed at 1200 K, then showed a rapid decrease of the conductivity. For a sample with the thickest film annealed at 1200 K, the time required to start decreasing the sample conductivity was about half a day. After the conductivity maxima, the conductivity decrease rate defined by a slope in Fig. 4 gradually increased and finally approached to an asymptotic line. The rate seems to be constant at the same temperature, and increases with increasing temperature. The run products were observed by optical microscope across the quartz grain boundary to evaluate the distribution of the grain boundary graphite film. The samples, which were quenched before the decrease in conductivity was complete, contained a thin, dark film covering the interfaces (Fig. 5a). Although the shape of the graphite grains is becoming more rounded on the quartz grain boundary but they are smaller and likely to be interconnected. In contrast, run products that approached the quartz conductivity contained isolated
Fig. 3. A time change of impedance spectra of C-coated samples (1 K1204) during annealing at 1200 K. (a) An impedance spectrum at the beginning of heating at 1200 K. (b) Impedance spectra where the conductivity largely decreases. (c). An impedance spectra after the conductivity was identical to the quartz conductivity.
Fig. 4. Electrical conductivity of the C-coated samples with various thicknesses of graphite films as a function of time at the maximum annealing temperature. Thick coated samples or samples which were held at lower temperature require a longer time to destroy the interconnection of graphite film on the quartz grain boundaries.
Fig. 5. Transmitted microscope images across the quartz grain boundary. The darker portion indicates graphite on the quartz grain boundary. (a) An image of a sample (1 K1199) showing high conductivity. Quartz grain boundary is mostly covered with graphite. Note that graphite film starts clustering. (b) An image of sample (AMA254) showing low conductivity similar to single crystal quartz. Note that the distribution of graphite is scattered and heterogeneous.
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Fig. 6. Electrical conductivity of carbon-coated anorthite aggregates as a function of reciprocal temperature. Squares and circles indicate results of 1st and 2nd coolingheating cycles, respectively. Diamonds denote results of 3rd heating. Thick lines denote electrical conductivity of graphite and anorthite.
opaque blebs that increased in density with increasing thickness of the initial film (Fig. 5b). Most of these dark grains exhibited a rounded or globular morphology. These textural observations are consistent with results expected from conductivity measurements. This evidence suggests that graphite films are not stable along quartz grain boundaries at high temperatures. A summary of conductivity measurements for anorthite aggregates is shown in Fig. 6. During first heating, the conductivity values slightly increased with temperature from 700 to 1273 K. The sample conductivity was three orders of magnitude higher than the anorthite conductivity. The conductivity decreased with time at 1273 K. After heating for relatively short duration (an hour), the conductivity values slightly decreased with decreasing temperature along the first cooling and second heating paths. This relatively small temperature dependence was not consistent with that of anorthite but close to that of the conductivity of graphite. The preservation of high conductivity at room temperature suggests that the graphite film was still interconnected on the grain surface. In the cooling path after heating at 1273 K for more than 15 h, the conductivity values largely decreased with decreasing temperature. The conductivity values were slightly higher than the carbon-free anorthite aggregate, but the activation enthalpy determined from the second cooling path was consistent with that of anorthite aggregates. This means that the interconnectivity of the graphite film on the anorthite grain boundaries was destroyed during heating at 1273 K. In some runs, the conductivity values of the bulk sample were slightly higher than the carbon-free sample. An area of the graphite layer covering the quartz grain boundary is still large even if the interconnection was lost. The bulk conductivity is controlled by quartz conductivity in the smaller area where graphite film was disconnected, because conductivity of graphite is extremely larger than that of quartz and anorthite. As a result, an equivalent circuit can be considered as a series R-C circuit composed of quartz and isolated graphite layers (Fig. 7), although the semicircular arc caused by isolated graphite layers is difficult to identify from the impedance spectra in the complex impedance plane due to the huge conductivity contrast between graphite and quartz. The conductivity enhancement is controlled by a ratio of the effective total length of the grain boundary formed by silicate minerals to the distance between two
Fig. 7. Schematic cartoon showing distribution of graphite on grain boundary and equivalent circuits. (a) A case that graphite film is interconnected on silicate grain boundary. The bulk conductivity is controlled by the conductive phase in a parallel RC circuit. (b) A case that graphite film is disconnected on silicate grain boundary. Note that the bulk conductivity is controlled by the resistive phase in a series RC circuit.
electrodes. Therefore, the conductivity enhancement caused by the presence of graphite on grain boundary does not mean partial interconnection of graphite between two electrodes.
4. Discussion 4.1. Driving force of disconnection Our results indicate that carbon film on a synthetic quartz grain boundary is not stable at the conditions of our experiments. Rounding and isolation of graphite on quartz grain boundaries are likely to be caused by high interfacial energy between graphite and quartz. The stability of graphite film covering grain boundaries requires a zero degree dihedral angle (θ) of quartz–graphite–quartz defined by the ratio of the quartz–quartz grain boundary energy (γgb) to the graphite–quartz interfacial energy (γg-q). A value for γgb determined from metamorphic rocks (270 ± 110 mJ/m2) has been published (Hiraga et al., 2002), however, the value of γg-q at the graphite/quartz interface has not been previously constrained. According to Li et al. (2009), γg-q between graphite (0001) surface and quartz is estimated to be around 500 mJ/m2. The predicted dihedral angle is more than 135°. Such a high dihedral angle would not allow the maintenance of a graphite film on quartz grain boundaries to reduce the total surface energy of the system. Our conductivity measurements of carbon-coated quartz bicrystals were only performed on samples with grain boundary parallel to caxis. A specific crystal surface might have high interfacial energy against graphite because the interfacial energy between minerals varies with crystallographic orientation. To evaluate the effect of the crystallographic orientation on disconnection of graphite film on the grain boundary, electrical conductivity of a randomly-oriented polycrystalline aggregate whose surface was coated by carbon was also measured. We obtained the same tendency from the conductivity measurement of anorthite aggregates coated by carbon at 1 GPa and 1000 K. In addition, Watson et al. (2010) reported that bulk electrical conductivity and impedance spectroscopy of polycrystalline olivine with carbon impurities (0.16 vol.%) on grain boundaries showed a series-type grain boundary impedance in the sample, suggesting the isolated distribution of graphite on olivine grain boundaries. Therefore it is concluded that graphite films are not stable on grain
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boundaries of typical silicate minerals forming the Earth's crust and uppermost mantle irrespective of the crystal anisotropy. 4.2. Disconnection kinetics The data presented above can be used to consider disconnection kinetics of graphite film on quartz grain boundaries at 1 GPa and temperatures ranging from 1000 to 1200 K. The required time for the disconnection of a graphite film on a quartz grain boundary can be roughly estimated from conductivity change in the samples. The required time (t) was defined by an interval between a starting time at the maximum temperature and a time at which the conductivity assumes a constant value close to that of quartz. Then the apparent disconnection rate of the graphite film (R) was defined by the following simple equation: R = W=t;
ð2Þ
where W is a thickness of the graphite film. For cases when the experiment finished before disconnection was confirmed by a conductivity change, the required time was estimated by a crossing point between the final conductivity-decreasing trend of the sample with time on an Arrhenius plot and expected quartz conductivity at the annealing temperature. Fig. 8 shows a relation of log R vs reciprocal temperature. In an Arrhenius plot, this kinetic process can be expressed by a linear trend, suggesting that this process is controlled by thermal activation. R = R0 expð−Q = kT Þ;
ð3Þ
where R0 is the pre-exponential factor, Q is the activation enthalpy for the apparent disconnection rate, k is the Boltzmann constant and T is the absolute temperature. All data were fitted by Eq. (3). The activation enthalpy for the apparent disconnection rate of a graphite film on quartz grain boundaries is around 150 kJ/mol, which is close to that for carbon self-diffusion of graphite (163 kJ/mol: Kanter, 1957). Therefore, the disconnection of the graphite film is likely to be controlled by atomic migration of carbon in the graphite crystal rather than Si diffusion in quartz (733 kJ/mol: Jaoul et al., 1995) and carbon grain boundary diffusion in MgO and olivine (70 kJ/mol: Hayden and Watson, 2008).
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4.3. Implications for conductivity anomaly of the lower crust Graphite film on the grain boundaries of silicate minerals forming the lower crust is generally accepted to have originated from the precipitation of carbon-rich fluids such as CO2 and CH4 through an oxy-exsolution reaction during cooling of high-grade metamorphic rocks (Frost et al., 1989; Frost and Bucher, 1994). In fact, carbon-rich fluids, especially CO2, are very common in high-grade metamorphic terranes, and are an important component of the volatiles released by magmatic processes. When a large amount of carbon-rich fluids are present, interconnected graphite films might develop along grain edges or boundaries, even if carbon-rich fluids are not able to efficiently wet the surfaces of silicate minerals (Watson and Brenan, 1987). Although interconnected graphite films were not confirmed by microscopic observations, some research has shown that a confining pressure increases the degree of interconnection of carbon-rich phases in rocks, causing an increase in measured rock conductivity (Glover and Vine, 1992; Katsube and Mareschal, 1993; Shankland et al., 1997). The development of fractures has been interpreted to destroy the continuity of graphite films during decompression. However, the present results suggest that the interconnection of graphite films on grain boundaries would actually be rapidly destroyed at high temperatures due to the rapid kinetics within the graphite film. If the formation of graphite films covering grain surfaces occurred throughout the cooling of the high-grade metamorphic rocks or the solidification of magma, then the graphite film is also likely to disconnect rapidly on the grain boundaries of silicate minerals under such high temperature conditions (N900 K). In other words, interconnected graphite films are unlikely to be maintained through geological time. If graphite precipitation occurred at less than 1000 K, the maximum residence times of the interconnected carbon film with initial thickness of 100 nm are ~ 200 and 20,000 years at 700 and 600 K, respectively, based on kinetic data. The presence of carbon films formed at lower temperatures may point to relatively sluggish kinetics for textural equilibrium, and therefore to the possibility that carbon films may be present as transient features in the crust. In particular, a carbon film developed along open fractures or shear zones at low temperatures (Mathez et al., 2008) may have a long residence time, and sustain interconnection on grain or fracture surfaces. Black shale containing relatively large amount of graphite has been considered as a candidate of high-conductivity anomalies caused by graphite in the mid- to lower continental crust (Jödicke et al., 2004; Mathez et al., 1995; Nover, 2005; Nover et al., 1998; Shankland et al., 1997). A well-interconnected thick graphite layer with millimeter-scale thickness might survive over geological time scale. However, Jödicke et al. (2007) reported that the natural graphite quartzite originated from the lower crust experienced high-grade metamorphism is highly resistive based on the impedance spectroscopy despite the high portion (12–15 vol.%) of graphite in its rock composition. They concluded that the spatial ordering of isolated graphite flakes in the rock matrix prevents the generation of throughgoing electrical pathways. At high temperatures, interconnection of graphite would be readily destroyed due to minimization of the interfacial energy. Therefore, we conclude that graphite is not a likely candidate to explain the high conductivity anomaly observed in the lower crust. 5. Conclusions
Fig. 8. An apparent disconnection rate vs reciplocal temperature on Arhenius plot. Note that all data were plotted on a linear trend.
In this study, the electrical properties of a carbon film on quartz grain boundary have been analyzed by means of complex impedance spectroscopic measurements at 1 GPa. The quartz grain boundary contains a graphite film with various thicknesses less than 100 nm, which is thought to be within a typical range of graphite film observed (Frost et al., 1989). For the first heating to the desired temperatures,
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the electrical conductivity was always high and showed little temperature dependence, suggesting connectivity of graphite film on grain boundary. During annealing at high temperatures (N1000 K), the conductivity decreases with time and finally approaches to the quartz conductivity. After annealing, the electrical conductivity largely decreases with decreasing temperature. The activation enthalpy estimated from the cooling path is definitely larger than that determined from the first heating path and is close to that of the quartz. Optical microscopic observation of the run products suggested an isolated feature of graphite on a quartz grain boundary. These lines of evidence indicate that graphite film on a grain boundary between two quartz crystals was disconnected at high temperatures. Disconnection of graphite film can be caused by higher interfacial energy between graphite and silicate minerals than that of the grain boundary energy. Therefore, a thin graphite film is unlikely to account for high conductivity anomalies in the middle and lower continental crust. Acknowledgments The authors are indebted to E. Ito, D. Yamazaki, N. Tomioka, Y. Ogawa, K. Fuji-ta, M. Ichiki, E. Takahashi for benefit discussions and C. Oka for technical assistance. This paper benefited from reviews by J. Roberts and two anonymous reviewers. This work was supported by Grant-in-Aids for Scientific Research on Innovative Areas (Research in a Proposed Research Area), “Geofluids: Nature and Dynamics of Fluids in Subduction Zone” from the Japan Society for Promotion of Science. References Bigalke, A., Junge, A., Zulauf, G., 2003. Electronically conducting brittle–ductile shear zones in the crystalline basement of Rittsteig (Bohemian Massif, Germany): evidence from self potential and hole-to-surface electrical measurements. Int. J. Earth Sci. 93, 44–51. Brace, W.F., 1971. Resistivity of saturated crustal rocks to 40 km based on laboratory measurements. In: Heacock, J.G. (Ed.), Structure and Physical Properties of the Earth's Crust: AGU Geophys. Monogra. Ser., 14, pp. 206–210. Duba, A., Shankland, T.J., 1982. Free carbon and electrical conductivity in the Earth's mantle. Geophys. Res. Lett. 9, 1271–1274. ELEKTB, Haak, V., Simpson, F., Bahr, K., Bigalke, J., Eisel, M., Harms, U., Hirschmann, G., Huenges, E., Jödicke, H., Kontny, A., Kück, J., Nover, G., Rauen, A., Stoll, J., Walther, J., Winter, H., Zulauf, G., 1997. KTB and the electrical conductivity of the crust.1997. KTB and the electrical conductivity of the crust. J. Geophys. Res. 102, 18289–18305. Frost, B.R., Bucher, K., 1994. Is water responsible for geophysical anomalies in the deep continental crust? A petrological perspective. Tectonophysics 231, 293–309. Frost, B.R., Fyfe, W.S., Tazaki, K., Chan, T., 1989. Grain-boundary graphite in rocks and implications for high electrical conductivity in the lower crust. Nature 340, 134–136. Fuji-ta, K., Katsura, T., Tainosho, Y., 2004. Electrical conductivity measurement of granulite under mid- to lower crustal pressure-temperature conditions. Geophys. J. Int. 157, 79–86. Fuji-ta, K., Katsura, T., Matsuzaki, T., Ichiki, M., Kobayashi, T., 2007. Electrical conductivity measurement of gneiss under mid- to lower crystal P-T conditions. Tectonophysics 434, 93–101. Glover, P.W.J., Vine, F.J., 1992. Electrical conductivity of carbon-bearing granulite at raised temperatures and pressures. Nature 360, 723–726.
Hayden, L.A., Watson, E.B., 2008. Grain boundary mobility of carbon in Earth's mantle: a possible carbon flux from the core. PNAS 105, 8537–8541. Hiraga, T., Nishikawa, O., Nagase, T., Akizuki, M., Kohlstedt, D.L., 2002. Interfacial energies for quartz and albite in pelitic schist. Contrib. Miner. Petrol. 143, 664–672. Hyndman, R.D., Hyndman, D.W., 1968. Water saturation and high electrical conductivity in the lower continental crust. Earth Planet. Sci. Lett. 4, 427–432. Hyndman, R.D., Shearer, P.M., 1989. Water in the lower continental crust: modelling magnetotelluric and seismic reflection results. Geophys. J. Int. 98, 343–365. Jaoul, O., Béjina, F., Érie, F., Abel, F., 1995. Silicon self-diffusion in quartz. Phys. Rev. Lett. 74, 2038–2041. Jödicke, H., Kruhl, J.H., Ballhaus, C., Giese, P., Untiedt, J., 2004. Syngenetic, thin graphiterich horizons in lower crustal rocks from the Serre San Bruno, Calabria (Italy), and implications for the nature of high-conducting deep crustal layers. Phys. Earth Planet. Inter. 141, 37–58. Jödicke, H., Nover, G., Kruhl, J.H., Markfort, R., 2007. Electrical properties of a graphiterich quartzite from a former lower continental crust exposed in the Serre San Bruno, Calabria (southern Italy). Phys. Earth Planet. Inter. 165, 56–67. Kanter, M.A., 1957. Diffusion of carbon atoms in natural graphite crystals. Phys. Rev. 107, 655–663. Kariya, K.A., Shankland, T.J., 1983. Electrical conductivity of dry lower crustal rocks. Geophysics 48, 52–61. Katsube, T.J., Mareschal, M., 1993. Petrophysical model of deep electrical conductors: graphite lining as a source and its disconnection due to uplift. J. Geophys. Res. 98, 8019–8030. Li, D., Windl, W., Padture, N.P., 2009. Toward site-specific stamping of graphene. Adv. Mater. 21, 1243–1246. Mareschal, M., Fyfe, W.S., Percival, J., Chan, T., 1992. Grain-boundary graphite in Kapuskasing gneisses and implications for lower-crustal conductivity. Nature 357, 674–676. Mathez, E.A., Duba, A.G., Peach, C.L., Léger, A., Shankland, T.J., Plafker, G., 1995. Electrical conductivity and carbon in metamorphic rocks of the Yukon-Tanana Terrane, Alaska. J. Geophys. Res. 100, 10187–10196. Mathez, E.A., Roberts, J.J., Duba, A.G., Kronenberg, A.K., Karner, S.L., 2008. Carbon deposition during brittle rock deformation: changes in electrical properties of fault zones and potential geoelectric phenomena during earthquakes. J. Geophys. Res. 113 (B12), B12201. Monteiro Santos, F.A., Mateus, A., Almeida, E.P., Pous, J., Mendes-Victor, M.A., 2002. Are some of the deep crustal conductive features found in SW Iberia caused by graphite? Earth Planet. Sci. Lett. 201, 353–367. Nover, G., 2005. Electrical properties of crustal and mantle rocks—a review of laboratory measurements and their explanations. Surv. Geophys. 26 (5), 593–651. Nover, G., Heikamp, S., Meurer, H.J., Freund, D., 1998. In-situ electrical conductivity and permeability of mid-crustal rocks from the KTB drilling: consequences for high conductivity layers in the earth crust. Surv. Geophys. 19, 73–85. Roberts, J.J., Duba, A.G., Mathez, E.A., Shankland, T.J., Kinzler, R., 1999. Carbon-enhanced electrical conductivity during fracture of rocks. J. Geophys. Res. 104, 737–747. Shankland, T.J., Ander, M.E., 1983. Electrical conductivity, temperatures, and fluids in the lower crust. J. Geophys. Res. 88, 9475–9484. Shankland, T.J., Duba, A.G., Mathez, E.A., Peach, C.L., 1997. Increase of electrical conductivity with pressure as an indicator of conduction through a solid phase in midcrustal rocks. J. Geophys. Res. 102, 14741–14750. Waff, H.S., 1974. Theoretical considerations of electrical conductivity in a partial molten mantle and implications for geothermometry. J. Geophys. Res. 79, 4003–4010. Watson, E.B., Brenan, J.M., 1987. Fluids in the lithosphere. 1. Experimentally determined wetting characteristics of CO2–H2O fluids and their implications for fluid transport, host-rock physical properties, and fluid inclusion formation. Earth Planet. Sci. Lett. 85, 496–515. Watson, H., Roberts, J.J., Tyburczy, J.A., 2010. Effect of conductive impurities on electrical conductivity in polycrystalline olivine. Geophys. Res. Lett. 37, L02302. Yardley, B.W.D., Valley, J.W., 1997. The petrologic case of a dry lower crust. J. Geophys. Res. 102, 12173–12185. Yoshino, T., Walter, M.J., Katsura, T., 2003. Core formation in planetesimals triggered by permeable flow. Nature 422, 154–157. Yoshino, T., Walter, M.J., Katsura, T., 2004. Connectivity of molten Fe alloy in peridotite based on in situ electrical conductivity measurements: implications for core formation in terrestrial planets. Earth Planet. Sci. Lett. 222, 625–643.
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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l
Unstable graphite films on grain boundaries in crustal rocks Takashi Yoshino a,⁎, Fumiya Noritake b a b
Institute for Study of the Earth's Interior, Okayama University, Misasa, Tottori 682-0193, Japan Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan
a r t i c l e
i n f o
Article history: Received 11 January 2011 Received in revised form 28 March 2011 Accepted 5 April 2011 Available online 30 April 2011 Editor: L. Stixrude Keywords: electrical conductivity interfacial energy graphite quartz lower crust
a b s t r a c t The origin of high electrical conductive anomalies in the lower crust is a long-standing and controversial problem. Although it has been proposed that saturated saline water or partial melt increases electrical conductivity, graphite film has also been recognized as a potential cause of high conductivity since the discovery of fine graphite films on the grain boundaries of high-grade metamorphic rocks. To investigate the stability of graphite film on grain boundary of silicate minerals under lower crustal conditions, electrical conductivity of graphite film on synthetic grain boundaries of quartz bicrystals was measured by means of impedance spectroscopy at 1 GPa and up to 1200 K in a multianvil apparatus. At first heating, the electrical conductivity of the thin graphite film with thickness less than 100 nm was initially very high but decreased with time during annealing. Under high temperature conditions (N1000 K), the conductivity of a thin carbon film rapidly decreases and approaches the quartz conductivity. This indicates that graphite film on a grain boundary between two quartz crystals is not stable at high temperatures. Optical microscopic observation of the run products suggested a disconnected feature of graphite on a quartz grain boundary. Disconnection of graphite film can be caused by higher interfacial energy between graphite and silicate minerals than that of the grain boundary energy. Therefore, a thin graphite film is not a likely candidate to account for high conductivity anomalies in the middle and lower continental crust. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The origin of high electrical conductive anomalies in the lower crust is a long-standing and controversial problem. It has been known from laboratory conductivity measurements that dry rocks have very low conductivity (~10−4 S/m) at lower crustal temperatures and pressures (e.g., Brace, 1971; Fuji-ta et al., 2004, 2007; Kariya and Shankland, 1983), which is significantly lower than the electrical conductivity (~10−1 S/m) of the lower crust observed in many parts of the world (Shankland and Ander, 1983). Thus the presence of a conductive phase is needed to account for the high electrical conductivity of the lower crust. It has been proposed that saturated saline water or partial melt increases electrical conductivity (e.g., Hyndman and Hyndman, 1968; Hyndman and Shearer, 1989). A carbon film on the grain boundaries of crustal minerals has been also considered as a possible cause of middle and lower crustal high electrical conductivity anomalies detected by magnetotelluric surveys (e.g., Duba and Shankland, 1982; Monteiro Santos et al., 2002; Shankland and Ander, 1983). This hypothesis has been supported by the observation of grain boundary graphite films in lower crustal rocks (Frost et al., 1989; Mareschal et al., 1992) and by graphite or amorphous carbon precipitation in shear zones or fractures
⁎ Corresponding author. E-mail address: [email protected] (T. Yoshino). 0012-821X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2011.04.003
at mid-crustal depths (Bigalke et al., 2003; ELEKTB et al., 1997; Mathez et al., 2008; Roberts et al., 1999). These types of carbon may originate from the precipitation of C–O–H fluids generated by mantle-derived magma or the metamorphism of carbonate rocks and organic-rich sediments. Duba and Shankland (1982) calculated the absolute amount of highly conductive and well-interconnected carbon required based on the upper bound formula (Waff, 1974), and found that a volume fraction of only 5x10−6 vol.% of carbon was necessary to enhance the electrical conductivity of dry rocks to values typical for conductive zones at lower crustal conditions (0.1 S/m). Although an interconnection of such thin graphite films or layers is required to explain high conductivity anomalies, impedance studies on graphite-bearing metamorphic rocks have only shown a slight increase of conductivity values (Frost et al., 1989; Glover and Vine, 1992; Mathez et al., 1995; Shankland et al., 1997). It has been postulated that rupturing these films during decompression could irreversibly reduce the electrical conductivity of rocks (Frost et al., 1989; Katsube and Mareschal, 1993; Shankland et al., 1997). On the other hand, the stability of graphite in lower crustal rocks has also been discussed from the aspect of petrology (Frost and Bucher, 1994; Yardley and Valley, 1997). However, the interfacial energetic stability of grain-boundary graphite films on crustal silicate minerals under lower-crustal pressure conditions has not been studied. The purpose of this study is to determine whether graphite film on grain boundaries of silicate minerals forming the lower crust is stable from the viewpoint of interfacial energy. Measurements of electrical
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conductivity are very sensitive to the connectivity of very small amounts of conductor (Watson et al., 2010; Yoshino et al., 2003) when the difference between the electrical conductivity of insulator and conductor is extremely large. Thus, the stability of a graphite film on grain boundaries can be detected by means of in situ electrical conductivity measurements. We performed in situ impedance spectroscopic measurements at 1 GPa on quartz bicrystals coated with carbon on their grain boundaries using a cubic-type and a Kawaitype multi-anvil apparatus to investigate the stability of the grain boundary carbon film under lower crustal conditions. Electrical conductivity measurements of a polycrystalline graphite rod and quartz single crystal were also performed at 1 GPa to constrain the end member conductivities. Our results suggest that the graphite film is not stable on grain boundaries of silicate minerals. 2. Experimental methods The starting materials were prepared from a single synthetic quartz crystal with an initial water content less than 1 ppm in weight. Disks with a diameter of 2 mm and 1 mm thickness were cored from the single quartz crystal parallel to the c-axis. The cored disks were cut into two halves with faces parallel to the cylinder axis, the c-axis as shown in Fig. 1a, so that both pieces have a semi-circular shape. The cut plane for the semi-circular piece was polished by diamond paste with 1 μm diameter. To avoid the mechanical destruction of the interconnected carbon film to graphite or the molybdenum electrode at the corner during compression, the corner was reshaped to a
Fig. 1. (a) Schematic cartoon of carbon-coated quartz bicrystals. Note that the corners consisting of two flat planes parallel and perpendicular to the cylindrical axis of disk were reshaped to a smoothly curved surface. (b) Schematic cross-section of highpressure cell assembly for conductivity measurements. Experiments in a Kawai-type multi anvil press were carried out in 25-mm Cr-bearing MgO octahedral assemblies with 15-mm truncation edge length of tungsten carbide cube. Experiments in a cubic multi anvil press were carried out in 20-mm pyrophyllite cubic assemblies with 15-mm truncation edge length of tungsten carbide cube.
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smoothly curved surface (Fig. 1a). The polished surfaces including smooth curved corner were coated with a carbon film by vapor deposition in vacuum using a carbon coater. The thickness of the carbon film ranged from a few to several tens of nanometers. Thus, the two half-moon shaped single crystals form a bicrystal containing a thin carbon film at the boundary (Fig. 1a). The starting material of graphite aggregate was prepared from a graphite rod, which was also used for the carbon coating. A cylindrical thin graphite rod loaded into a sintered MgO sleeve with inner diameters of 0.5 mm was used for the conductivity measurement to increase resistance of the sample because graphite has very high conductivity. The sample was sandwiched between two molybdenum disks that served as electrodes. Mo electrodes were used so that the oxygen fugacity would be close to the Mo-MoO2 buffer, which is lower than that of C–CO buffer. The starting material of quartz single crystal was also prepared from a synthetic quartz single crystal. A disk with a diameter of 2 mm and 1 mm thickness was cored from the single quartz crystal parallel to the c-axis. Two single crystals of quartz were used for most runs in a simplification of graphite films occurring in crustal silicate minerals. Because interfacial energy between crystals varies with crystal surface, the stability of the graphite film in mineral aggregates with variable grain boundary misorientations was also investigated. Anorthite (CaAl2Si2O8: an end-member of plagioclase solid solution) was used for this experiment, since plagioclase is thought to be the most abundant mineral in the lower crust. The starting material was synthetic anorthite prepared from a mixture of reagent-grade SiO2, Al2O3, and CaCO3. The mixture was heated for 1 h at 1073 K to remove carbon dioxide and then heated for 8 h at 1643 K to form seeds of anorthite. The retrieved sample was ground and sieved to produce uniform-sized crystals. The micrometer-sized powder was repeatedly coated by carbon. In order to cover all grain surfaces with carbon, the powder was shaken before each coating. These powdered starting materials were placed in MgO capsules. Molybdenum disks were used as electrode for conductivity measurement. Carbon-free anorthite aggregates were also measured to enable the identification of disconnected graphite films. Fig. 1b shows a design of the high-pressure cell assembly. The diskshaped sample made of two half-moon shaped single crystal was placed in a MgO capsule, and sandwiched between two electrodes made of either graphite or molybdenum. Two sets of W97Re3-W75Re25 thermocouples were mechanically connected to the two electrodes. Each thermocouple was insulated from the graphite heater by MgO sleeves. Electrodes with a diameter of 2 mm were placed in contact with the sample. The oxygen fugacity was controlled by the C–CO buffer or a Mo–MoO2 buffer. Both buffers yielded similar results. The recovered sample showed no significant deformation during the conductivity measurement runs. Sample conductivity and the thickness of the graphite film on the grain boundary were calculated from the minimum resistance at the maximum annealing temperature and the sample dimensions. Sample conductivities were measured by an impedance GainPhase Analyzer (combined with a Solartron 1296 interface if the sample resistance was higher than 1 MΩ). The amplitude of the applied voltage for alternating current was 1 V. A wide frequency range of 10−3–106 Hz was used to distinguish between grain boundary transport and electrode processes from the impedance spectrum. The impedance spectra were obtained from high to low frequencies. To determine sample resistance, the data were fitted to an expression for a simple RC parallel equivalent circuit. Electrical conductivity measurements were performed along the heatingcooling cycle. In the first cycle, the sample was heated to the desired temperatures (1000, 1073 and 1200 K). The coated carbon layer on the quartz grain boundary crystallized to graphite during first heating. The carbon phase on the grain boundary after conductivity measurement was identified to be graphite by micro-focused beam X-ray
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diffractometer. At the maximum temperature, the sample conductivity was monitored frequently to detect interconnections of the graphite film on the grain boundary as a function of time. Annealing time at the highest temperature was variable in a range from 3 to 71 h, and depended on a decreasing rate in electrical conductivity. After heating at the maximum temperature, heating and cooling were repeated to confirm repeatability. During each cycle, temperature was changed in 50 K interval, and electrical conductivity was measured at each temperature step. For several experiments, heating and cooling were performed in the process on the way of a decrease in the electrical conductivity at the highest temperature to evaluate the connectiveness of graphite film. Experimental conditions and results are shown in Table 1. 3. Experimental results Five electrical conductivity measurements were performed on quartz bicrystals with carbon-coated grain boundary. Clear evidence of fracturing and displacement along the grain boundary was not observed in any of the run products. The electrical conductivity of graphite aggregate and single crystal quartz parallel to the c-axis was also measured by one experiment of each at 1 GPa. Fig. 2 shows electrical conductivity of graphite aggregates and single crystal quartz parallel to c-axis as a function of reciprocal temperature. The electrical conductivity of graphite is nearly ten orders of magnitude higher than that of quartz single crystal at 1000 K. Both samples behave as a semiconductor. The absolute conductivity values increase with increasing temperature. Conductivity (σ)–temperature (T) relationships were expressed by the Arrhenian formula: ΔH σ = σ0 exp − kT
ð1Þ
where σ0 is pre-exponential factor, ΔH is activation enthalpy, k is the Boltzmann constant, and T is absolute temperature. The activation enthalpy of graphite is quite small (0.02 eV), whereas that of quartz is definitely larger (0.89 eV). This huge contrast is useful to detect the connectivity of very thin graphite film with thickness less than 100 nm. The details of the experimental conditions and some parameters fitted by Eq. (1) for each run are given in Table 1. An example of conductivity measurements is shown in Fig. 2. The conductivity values were initially high and slightly increased with temperature increasing up to the desired temperature. At the beginning of annealing at 1200 K, the sample conductivity was four orders of magnitude higher than the quartz conductivity. The conductivity decreased with time at the maximum temperature. The impedance spectra first showed a semicircular shape (Fig. 3a), suggesting that the conductive phase forms an electrical pathway in parallel with the solid matrix. Then an additional part with 0˚ phase angle appeared at low frequencies (Fig. 3b). This suggests that
Fig. 2. Electrical conductivity of carbon-coated quartz bicrystals as a function of reciprocal temperature (Run# AMA254). Open circles and closed diamonds indicate results of 1st and 2nd cooling-heating cycles, respectively. Thick line denotes electrical conductivity of graphite. Thick shaded line indicates electrical conductivity of single crystal synthetic quartz parallel to c axis.
resistance largely increased during the conductivity measurement because the impedance spectrum obtained at low frequencies requires a relatively longer time than that obtained at high frequencies. After heating at 1200 K for relatively short duration (a few hours), the conductivity values were nearly independent of temperature along the first cooling and second heating paths. This small temperature dependence (ΔH: 0.03 eV) is similar to that of the conductivity of graphite (ΔH: 0.02 eV). The activation enthalpy of conductivity of a bulk sample should correspond to that of a conductive phase if the conductive phase establishes interconnection in the resistive matrix (Yoshino et al., 2003, 2004). In addition, preservation of high conductivities after the temperature was reduced indicating that the carbon film was still interconnected on the quartz grain boundary. After heating at 1200 K for more than 15 h, the conductivity followed a different trend in the cooling path: the conductivity shows much larger temperature dependence than before. The temperature-conductivity path is essentially the same as the conductivity of quartz parallel to the c axis. In fact the activation enthalpies of conductivity of a bulk sample (1.06 eV) are close to that of quartz (0.89 eV). It is concluded that grain boundary graphite film was not interconnected. The impedance spectra showed a single arc with 45˚ of slope in the complex impedance plane below 10 Hz
Table 1 Summary of runs. Run no.a
Sample
Tmax (K)
Electrode
AMA125 AMA127 AMA128 AMA254
Quartz c// C-coated Graphite C-coated
1073 1073 1273 1200
Graphite Mo Mo Graphite
1K1199 1K1200 1K1204
C-coated C-coated C-coated
1000 1200 1200
Graphite Graphite Mo
Logσ0 (S/m)
ΔH (eV)
− 0.38 0.74 5.17 − 0.08 0.74 − 0.96 0.30 1.68
0.89 0.82 0.02 0.03 1.06 0.05 0.05 0.87
Duration (h)
b
δ (nm)
6
3
2.5 16 47 21 22
25
Remarks c
First cooling Second cooling
28 71 51
All experiments were conducted at 1 GPa. a The experimental run numbers which contain AMA and 1 K represent the experiment using a cubic press and a Kawai-type multi anvil press, respectively. b Annealing time (hours) at the maximum temperature. c Graphite film thickness was calculated from the maximum conductivity at the maximum annealing temperature based on the graphite conductivity data of AMA128.
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(Fig. 3c), suggesting an increase in the effect of polarization between the quartz and electrode. Fig. 4 shows the change in the electrical conductivity for all carbon-coated samples with time, while maintaining the maximum temperature. All samples finally showed a decrease of conductivity after a certain time passed. For the sample that annealed at the lowest temperature (1000 K), the conductivity slightly increased at the beginning of the annealing then became constant. After one day, the conductivity started to decrease due to the destruction of interconnectivity within the graphite film. However, a sample with a similar thickness of graphite film annealed at 1200 K, then showed a rapid decrease of the conductivity. For a sample with the thickest film annealed at 1200 K, the time required to start decreasing the sample conductivity was about half a day. After the conductivity maxima, the conductivity decrease rate defined by a slope in Fig. 4 gradually increased and finally approached to an asymptotic line. The rate seems to be constant at the same temperature, and increases with increasing temperature. The run products were observed by optical microscope across the quartz grain boundary to evaluate the distribution of the grain boundary graphite film. The samples, which were quenched before the decrease in conductivity was complete, contained a thin, dark film covering the interfaces (Fig. 5a). Although the shape of the graphite grains is becoming more rounded on the quartz grain boundary but they are smaller and likely to be interconnected. In contrast, run products that approached the quartz conductivity contained isolated
Fig. 3. A time change of impedance spectra of C-coated samples (1 K1204) during annealing at 1200 K. (a) An impedance spectrum at the beginning of heating at 1200 K. (b) Impedance spectra where the conductivity largely decreases. (c). An impedance spectra after the conductivity was identical to the quartz conductivity.
Fig. 4. Electrical conductivity of the C-coated samples with various thicknesses of graphite films as a function of time at the maximum annealing temperature. Thick coated samples or samples which were held at lower temperature require a longer time to destroy the interconnection of graphite film on the quartz grain boundaries.
Fig. 5. Transmitted microscope images across the quartz grain boundary. The darker portion indicates graphite on the quartz grain boundary. (a) An image of a sample (1 K1199) showing high conductivity. Quartz grain boundary is mostly covered with graphite. Note that graphite film starts clustering. (b) An image of sample (AMA254) showing low conductivity similar to single crystal quartz. Note that the distribution of graphite is scattered and heterogeneous.
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Fig. 6. Electrical conductivity of carbon-coated anorthite aggregates as a function of reciprocal temperature. Squares and circles indicate results of 1st and 2nd coolingheating cycles, respectively. Diamonds denote results of 3rd heating. Thick lines denote electrical conductivity of graphite and anorthite.
opaque blebs that increased in density with increasing thickness of the initial film (Fig. 5b). Most of these dark grains exhibited a rounded or globular morphology. These textural observations are consistent with results expected from conductivity measurements. This evidence suggests that graphite films are not stable along quartz grain boundaries at high temperatures. A summary of conductivity measurements for anorthite aggregates is shown in Fig. 6. During first heating, the conductivity values slightly increased with temperature from 700 to 1273 K. The sample conductivity was three orders of magnitude higher than the anorthite conductivity. The conductivity decreased with time at 1273 K. After heating for relatively short duration (an hour), the conductivity values slightly decreased with decreasing temperature along the first cooling and second heating paths. This relatively small temperature dependence was not consistent with that of anorthite but close to that of the conductivity of graphite. The preservation of high conductivity at room temperature suggests that the graphite film was still interconnected on the grain surface. In the cooling path after heating at 1273 K for more than 15 h, the conductivity values largely decreased with decreasing temperature. The conductivity values were slightly higher than the carbon-free anorthite aggregate, but the activation enthalpy determined from the second cooling path was consistent with that of anorthite aggregates. This means that the interconnectivity of the graphite film on the anorthite grain boundaries was destroyed during heating at 1273 K. In some runs, the conductivity values of the bulk sample were slightly higher than the carbon-free sample. An area of the graphite layer covering the quartz grain boundary is still large even if the interconnection was lost. The bulk conductivity is controlled by quartz conductivity in the smaller area where graphite film was disconnected, because conductivity of graphite is extremely larger than that of quartz and anorthite. As a result, an equivalent circuit can be considered as a series R-C circuit composed of quartz and isolated graphite layers (Fig. 7), although the semicircular arc caused by isolated graphite layers is difficult to identify from the impedance spectra in the complex impedance plane due to the huge conductivity contrast between graphite and quartz. The conductivity enhancement is controlled by a ratio of the effective total length of the grain boundary formed by silicate minerals to the distance between two
Fig. 7. Schematic cartoon showing distribution of graphite on grain boundary and equivalent circuits. (a) A case that graphite film is interconnected on silicate grain boundary. The bulk conductivity is controlled by the conductive phase in a parallel RC circuit. (b) A case that graphite film is disconnected on silicate grain boundary. Note that the bulk conductivity is controlled by the resistive phase in a series RC circuit.
electrodes. Therefore, the conductivity enhancement caused by the presence of graphite on grain boundary does not mean partial interconnection of graphite between two electrodes.
4. Discussion 4.1. Driving force of disconnection Our results indicate that carbon film on a synthetic quartz grain boundary is not stable at the conditions of our experiments. Rounding and isolation of graphite on quartz grain boundaries are likely to be caused by high interfacial energy between graphite and quartz. The stability of graphite film covering grain boundaries requires a zero degree dihedral angle (θ) of quartz–graphite–quartz defined by the ratio of the quartz–quartz grain boundary energy (γgb) to the graphite–quartz interfacial energy (γg-q). A value for γgb determined from metamorphic rocks (270 ± 110 mJ/m2) has been published (Hiraga et al., 2002), however, the value of γg-q at the graphite/quartz interface has not been previously constrained. According to Li et al. (2009), γg-q between graphite (0001) surface and quartz is estimated to be around 500 mJ/m2. The predicted dihedral angle is more than 135°. Such a high dihedral angle would not allow the maintenance of a graphite film on quartz grain boundaries to reduce the total surface energy of the system. Our conductivity measurements of carbon-coated quartz bicrystals were only performed on samples with grain boundary parallel to caxis. A specific crystal surface might have high interfacial energy against graphite because the interfacial energy between minerals varies with crystallographic orientation. To evaluate the effect of the crystallographic orientation on disconnection of graphite film on the grain boundary, electrical conductivity of a randomly-oriented polycrystalline aggregate whose surface was coated by carbon was also measured. We obtained the same tendency from the conductivity measurement of anorthite aggregates coated by carbon at 1 GPa and 1000 K. In addition, Watson et al. (2010) reported that bulk electrical conductivity and impedance spectroscopy of polycrystalline olivine with carbon impurities (0.16 vol.%) on grain boundaries showed a series-type grain boundary impedance in the sample, suggesting the isolated distribution of graphite on olivine grain boundaries. Therefore it is concluded that graphite films are not stable on grain
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boundaries of typical silicate minerals forming the Earth's crust and uppermost mantle irrespective of the crystal anisotropy. 4.2. Disconnection kinetics The data presented above can be used to consider disconnection kinetics of graphite film on quartz grain boundaries at 1 GPa and temperatures ranging from 1000 to 1200 K. The required time for the disconnection of a graphite film on a quartz grain boundary can be roughly estimated from conductivity change in the samples. The required time (t) was defined by an interval between a starting time at the maximum temperature and a time at which the conductivity assumes a constant value close to that of quartz. Then the apparent disconnection rate of the graphite film (R) was defined by the following simple equation: R = W=t;
ð2Þ
where W is a thickness of the graphite film. For cases when the experiment finished before disconnection was confirmed by a conductivity change, the required time was estimated by a crossing point between the final conductivity-decreasing trend of the sample with time on an Arrhenius plot and expected quartz conductivity at the annealing temperature. Fig. 8 shows a relation of log R vs reciprocal temperature. In an Arrhenius plot, this kinetic process can be expressed by a linear trend, suggesting that this process is controlled by thermal activation. R = R0 expð−Q = kT Þ;
ð3Þ
where R0 is the pre-exponential factor, Q is the activation enthalpy for the apparent disconnection rate, k is the Boltzmann constant and T is the absolute temperature. All data were fitted by Eq. (3). The activation enthalpy for the apparent disconnection rate of a graphite film on quartz grain boundaries is around 150 kJ/mol, which is close to that for carbon self-diffusion of graphite (163 kJ/mol: Kanter, 1957). Therefore, the disconnection of the graphite film is likely to be controlled by atomic migration of carbon in the graphite crystal rather than Si diffusion in quartz (733 kJ/mol: Jaoul et al., 1995) and carbon grain boundary diffusion in MgO and olivine (70 kJ/mol: Hayden and Watson, 2008).
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4.3. Implications for conductivity anomaly of the lower crust Graphite film on the grain boundaries of silicate minerals forming the lower crust is generally accepted to have originated from the precipitation of carbon-rich fluids such as CO2 and CH4 through an oxy-exsolution reaction during cooling of high-grade metamorphic rocks (Frost et al., 1989; Frost and Bucher, 1994). In fact, carbon-rich fluids, especially CO2, are very common in high-grade metamorphic terranes, and are an important component of the volatiles released by magmatic processes. When a large amount of carbon-rich fluids are present, interconnected graphite films might develop along grain edges or boundaries, even if carbon-rich fluids are not able to efficiently wet the surfaces of silicate minerals (Watson and Brenan, 1987). Although interconnected graphite films were not confirmed by microscopic observations, some research has shown that a confining pressure increases the degree of interconnection of carbon-rich phases in rocks, causing an increase in measured rock conductivity (Glover and Vine, 1992; Katsube and Mareschal, 1993; Shankland et al., 1997). The development of fractures has been interpreted to destroy the continuity of graphite films during decompression. However, the present results suggest that the interconnection of graphite films on grain boundaries would actually be rapidly destroyed at high temperatures due to the rapid kinetics within the graphite film. If the formation of graphite films covering grain surfaces occurred throughout the cooling of the high-grade metamorphic rocks or the solidification of magma, then the graphite film is also likely to disconnect rapidly on the grain boundaries of silicate minerals under such high temperature conditions (N900 K). In other words, interconnected graphite films are unlikely to be maintained through geological time. If graphite precipitation occurred at less than 1000 K, the maximum residence times of the interconnected carbon film with initial thickness of 100 nm are ~ 200 and 20,000 years at 700 and 600 K, respectively, based on kinetic data. The presence of carbon films formed at lower temperatures may point to relatively sluggish kinetics for textural equilibrium, and therefore to the possibility that carbon films may be present as transient features in the crust. In particular, a carbon film developed along open fractures or shear zones at low temperatures (Mathez et al., 2008) may have a long residence time, and sustain interconnection on grain or fracture surfaces. Black shale containing relatively large amount of graphite has been considered as a candidate of high-conductivity anomalies caused by graphite in the mid- to lower continental crust (Jödicke et al., 2004; Mathez et al., 1995; Nover, 2005; Nover et al., 1998; Shankland et al., 1997). A well-interconnected thick graphite layer with millimeter-scale thickness might survive over geological time scale. However, Jödicke et al. (2007) reported that the natural graphite quartzite originated from the lower crust experienced high-grade metamorphism is highly resistive based on the impedance spectroscopy despite the high portion (12–15 vol.%) of graphite in its rock composition. They concluded that the spatial ordering of isolated graphite flakes in the rock matrix prevents the generation of throughgoing electrical pathways. At high temperatures, interconnection of graphite would be readily destroyed due to minimization of the interfacial energy. Therefore, we conclude that graphite is not a likely candidate to explain the high conductivity anomaly observed in the lower crust. 5. Conclusions
Fig. 8. An apparent disconnection rate vs reciplocal temperature on Arhenius plot. Note that all data were plotted on a linear trend.
In this study, the electrical properties of a carbon film on quartz grain boundary have been analyzed by means of complex impedance spectroscopic measurements at 1 GPa. The quartz grain boundary contains a graphite film with various thicknesses less than 100 nm, which is thought to be within a typical range of graphite film observed (Frost et al., 1989). For the first heating to the desired temperatures,
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the electrical conductivity was always high and showed little temperature dependence, suggesting connectivity of graphite film on grain boundary. During annealing at high temperatures (N1000 K), the conductivity decreases with time and finally approaches to the quartz conductivity. After annealing, the electrical conductivity largely decreases with decreasing temperature. The activation enthalpy estimated from the cooling path is definitely larger than that determined from the first heating path and is close to that of the quartz. Optical microscopic observation of the run products suggested an isolated feature of graphite on a quartz grain boundary. These lines of evidence indicate that graphite film on a grain boundary between two quartz crystals was disconnected at high temperatures. Disconnection of graphite film can be caused by higher interfacial energy between graphite and silicate minerals than that of the grain boundary energy. Therefore, a thin graphite film is unlikely to account for high conductivity anomalies in the middle and lower continental crust. Acknowledgments The authors are indebted to E. Ito, D. Yamazaki, N. Tomioka, Y. Ogawa, K. Fuji-ta, M. Ichiki, E. Takahashi for benefit discussions and C. Oka for technical assistance. This paper benefited from reviews by J. Roberts and two anonymous reviewers. This work was supported by Grant-in-Aids for Scientific Research on Innovative Areas (Research in a Proposed Research Area), “Geofluids: Nature and Dynamics of Fluids in Subduction Zone” from the Japan Society for Promotion of Science. References Bigalke, A., Junge, A., Zulauf, G., 2003. Electronically conducting brittle–ductile shear zones in the crystalline basement of Rittsteig (Bohemian Massif, Germany): evidence from self potential and hole-to-surface electrical measurements. Int. J. Earth Sci. 93, 44–51. Brace, W.F., 1971. Resistivity of saturated crustal rocks to 40 km based on laboratory measurements. In: Heacock, J.G. (Ed.), Structure and Physical Properties of the Earth's Crust: AGU Geophys. Monogra. Ser., 14, pp. 206–210. Duba, A., Shankland, T.J., 1982. Free carbon and electrical conductivity in the Earth's mantle. Geophys. Res. Lett. 9, 1271–1274. ELEKTB, Haak, V., Simpson, F., Bahr, K., Bigalke, J., Eisel, M., Harms, U., Hirschmann, G., Huenges, E., Jödicke, H., Kontny, A., Kück, J., Nover, G., Rauen, A., Stoll, J., Walther, J., Winter, H., Zulauf, G., 1997. KTB and the electrical conductivity of the crust.1997. KTB and the electrical conductivity of the crust. J. Geophys. Res. 102, 18289–18305. Frost, B.R., Bucher, K., 1994. Is water responsible for geophysical anomalies in the deep continental crust? A petrological perspective. Tectonophysics 231, 293–309. Frost, B.R., Fyfe, W.S., Tazaki, K., Chan, T., 1989. Grain-boundary graphite in rocks and implications for high electrical conductivity in the lower crust. Nature 340, 134–136. Fuji-ta, K., Katsura, T., Tainosho, Y., 2004. Electrical conductivity measurement of granulite under mid- to lower crustal pressure-temperature conditions. Geophys. J. Int. 157, 79–86. Fuji-ta, K., Katsura, T., Matsuzaki, T., Ichiki, M., Kobayashi, T., 2007. Electrical conductivity measurement of gneiss under mid- to lower crystal P-T conditions. Tectonophysics 434, 93–101. Glover, P.W.J., Vine, F.J., 1992. Electrical conductivity of carbon-bearing granulite at raised temperatures and pressures. Nature 360, 723–726.
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