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 Presence of graphite is one of the mechanisms to explain enhanced electrical conductivity. Because the conductivity of graphite is highly anisotropic and the connectivity of graphite depends strongly on the geometry of the crystals, the key issue is the geometry of graphite in a rock including their crystallographic orientation and the shape of graphite crystals. We explored the role of graphite on electrical conductivity in olivine-rich aggregates. To obtain well-defined results, we conducted an experimental study at high pressure and temperature conditions. Olivine aggregates containing diamonds were annealed to transform diamond to graphite with nearly equilibrium morphology. Graphite formed by the transformation from diamond has thin disk-shape morphology, the plane being the highly conductive (0001) plane. When the concentration of graphite exceeds the percolation threshold (~ 1 wt%), electrical conductivity is significantly enhanced. Some of the observed high conductivity regions may represent regions of high concentration of graphite.
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 The regions of high electrical conductivity in Earth have attracted much attention because they may correspond to regions of anomalous compositions including the presence of fluids or melts [Shankland and Ander, 1983; Gaillard et al., 2008], high hydrogen content [Karato, 1990; Wang et al., 2006; 2008; Yoshino et al., 2006; 2009; Poe et al., 2010], and high carbon content as graphite [Duba and Shankland, 1982; Glover and Vine, 1992]. Carbon and hydrogen are the two important volatile elements in Earth's interior. They occur roughly the same amount in the mantle [Wood et al., 1996; Dasgupta and Hirschmann, 2010], and both elements promote melting [Kushiro, 2001; Gaillard et al., 2008; Green et al., 2010; Dasgupta and Hirschmann, 2006; 2007] and control the nature of Earth's atmosphere [Kasting and Catling, 2003], and therefore the evolution of Earth including its surface conditions such as the habitability [Kasting and Catling, 2003]. A large number of studies have been performed to infer hydrogen distribution in Earth's interior [Karato, 2003; Dixon et al., 2002; Karato, 2011]. In addition to direct, petrological (or geochemical) approach [Dixon et al., 2002], remote sensing of hydrogen is possible because of the sensitivity of electrical conductivity to hydrogen content [Wang et al., 2006; Yoshino et al., 2009; Karato, 2011; Yang et al., 2012].
 In contrast, remote sensing of carbon is more challenging because the solubility of carbon in many minerals is low [Shcheka et al., 2006], and the influence of carbon on physical properties is in most cases minor. The low solubility of carbon in mantle minerals means that carbon occurs in isolated carbon-bearing phases in most cases. The stable carbon-bearing species in the mantle depends on the pressure, temperature, and oxygen fugacity [Frost and Wood, 1997; Kennedy and Kennedy, 1976]. At relatively low pressure and low oxygen fugacity conditions, carbon occurs as graphite and because graphite has high and anisotropic electrical conductivity (conductivity in the (0001) plane is higher than conductivity in the direction normal to this plane by a factor of ~104) [Dutta, 1953], the presence of graphite could be detectable through electrical conductivity if there is enough graphite with appropriate crystallographic orientations.
 However, previous studies on the influence of graphite on electrical conductivity were limited for several reasons. First, there was little direct experimental study where the electrical conductivity of graphite-bearing rock was measured under the upper mantle conditions. Most of previous studies were conducted under the crustal conditions [Glover and Vine, 1992; Duba et al., 1988], and the geometry of graphite is likely out of equilibrium. Watson et al.  conducted an experimental study under the upper mantle conditions, but they did not observe appreciable effects of graphite presumably because of a small amount (~0.1 wt%) of graphite they added. Yoshino and Noritake  conducted an experimental study on the quartz-graphite system where higher temperature (to 1200 K) was used to study the morphology of graphite, but the relevance of their study to the upper mantle conductivity is questionable because the morphology of a secondary phase depends on the interfacial energy that depends on the host mineral. Second, in many studies, the presence of amorphous graphite at grain boundaries was considered [Duba and Shankland, 1982; Glover and Vine, 1992], but amorphous graphite unlikely occurs under the (deep) upper mantle conditions. Electrical conductivity of single crystal of graphite is highly anisotropic [Dutta, 1953] and therefore the electrical conductivity of a rock containing graphite with equilibrium morphology needs to be studied to understand how graphite may enhance electrical conductivity.
2 Experimental Procedure
 We prepared a mixture (~10–15 µm) of olivine and ~5% wt diamond (+ ~1% wt orthopyroxene) and annealed them under the controlled oxygen fugacity at high pressure and temperature. The powdered staring materials were well mixed and loaded into a molybdenum or rhenium foil capsule which was used to buffer the oxygen fugacity. The annealing experiments were performed at T = 1673 K and P = 3, 4 GPa in a 1000-tonne multianvil apparatus (Table 1). The run duration varied from ~10 to ~20 h. In one set of experiment (annealing at low fO2), the conditions were chosen where diamond transformed to graphite, and in another set of experiments (annealing at high fO2), diamond transformed to magnesite (Figure 1). The volume fraction and morphology of graphite (and magnesite) were studied using scanning electron microscopy (SEM). Both energy-dispersive x-ray analysis and electron back-scatter diffraction were used to study the samples. In a sample annealed at high fO2, diamond nearly completely disappeared and some magnesites are observed at grain boundaries as expected from the stability field of diamond [Frost and Wood, 1997]. In samples annealed at low fO2, most of diamond transformed to graphite. In one sample (annealed for 11.5 h), the transformation was ~50 % whereas in another sample (annealed for 20 h), the transformation was nearly complete. In both cases, the graphite formed from the transformation of diamond occurred at grain boundaries and has well-defined plate-like morphology (Figure 2), the (0001) plane being the plane.
Table 1. Conditions of Annealing Experiments and the Observed Volume Fraction of Graphite, and its Morphology (c and w) and the Calculated Parameter p ()
c (μ m)
w (μ m)
Note: Ol, olivine; G, graphite; D, diamond; M, magnesite. Numbers in parentheses are the errors in the last digit (one standard deviation)
Ol + G + D
Ol + M + D
Ol + G
 Electrical conductivity of annealed samples (a disk-shape with 1.6 mm in the diameter and 0.4–0.7 mm in the thickness) was measured using the impedance spectroscopy at condition of T = 1173–1673 K and P = 4 GPa (Table 2). The procedure of conductivity measurements is the same as before [e.g., Wang et al., 2006]. The samples were then loaded between two Mo or Re electrodes that are insulated by the alumina rings. To minimize the noise coming from the heater, we used a shield. The shield, typically the same metal as that of the electrode, is located between the sample and MgO tube. The oxygen fugacity was buffered by the metal shield and electrodes. Complex impedance measurements were conducted using the Solartron 1260 frequency response analyzer operated at 0.1–1 V over the frequency range 1.0 Hz–1.0 MHz.
Table 2. The Experimental Conditions for Conductivity Measurements, and the Results of the Least-Square Fit Using the Formula
Log10 A (S/m)
Note: K1251 denotes results of the sample (K1242) annealed for 10 h at high fO2; K1231 and K1253 indicate the results of samples annealed at low fO2 at 11.5 h (K1221) and 20 h (K1245), respectively.
P: pressure, T: temperature.
Numbers in parentheses are the errors in the last digit (one standard deviation)
3 Results and Discussions
 Figure 3 shows the representative impedance spectra of magnesite-bearing sample (a) and graphite-bearing sample (b) in the form of complex plane plots (real part (Z′) versus imaginary part (Z″) of the impedance. In the magnesites-bearing sample, at given temperature, a complete arc due to grain interior conduction and an incomplete arc (or tail) corresponding to grain boundary conduction are observed. The impedance spectra of graphite-bearing sample show the negative Z″ at high frequency and the positive Z″ indicative of the presence of inductive component at low frequency. The inductive component is often seen when chemical reactions occur (e.g., [Macdonald, 1978; Bai and Conway, 1991]). In both cases, DC component of conductivity can be determined from the first half-circle using an appropriate model.
 The results of electrical conductivity measurements are summarized in Figure 4 where the electrical conductivity of graphite containing samples is compared with that of pure olivine (+ opx) and a sample with magnesite. The uncertainty associated with these conductivity measurements is smaller than the symbol size. The FTIR measurements show that all the samples are for nearly dry (less than ~10 ppm wt). Samples containing magnesite or diamond show conductivity slightly higher than that of olivine, whereas samples containing graphite show much higher conductivity. Conductivity of graphite-bearing samples is high and depends only weakly on temperature. This suggests that the conductivity in these samples is controlled largely by graphite.
 The activation enthalpies (Table 2) were calculated by fitting the electrical conductivities according to the following equation:
where A is the pre-exponential factor, H* is the activation enthalpy, and R is the gas constant.
 In order for graphite to contribute to conductivity of aggregate, graphite grains need to be connected and the electric current dominantly flow in the (0001) plane. As shown in Figure 2, graphite grains are planar and the plane is (0001) in which the conductivity is highest [Dutta, 1953]. Therefore, if graphite grains are connected at edges, they will serve high conductivity path. The electrical conductivity of olivine and graphite mixture is dominated by olivine at a small volume fraction of graphite, but because graphite has much higher conductivity than olivine, the conductivity of an aggregate increases substantially once graphite grains are interconnected. Such a behavior can be described by the theory of percolation [Gueguen and Dienes, 1989]. The contribution from the high conductivity inclusion is negligible below the percolation threshold, but increases above the threshold following the relation,
where σ is the conductivity of the aggregate, σ0 is the conductivity of a high conductivity inclusions (conductivity of graphite in the (0001) plane), σm is the electrical conductivity of the matrix (olivine), r is a nondimensional parameter, (c: diameter of a graphite disk, w: thickness of the graphite disk), φ is the volume fraction of the high conductivity inclusions (graphite), pc is the threshold value of p (percolation threshold) that depends on the geometry of conductor (graphite) [Stauffer and Aharony, 1994]. We determined the parameter p from the microstructural measurements (Table 1). We plotted the measured values of conductivity as a function of p (Figure 5). Fitting the experimental data to equation ((2)), we found that r ~ 10 and pc ≈ 0.3.
 Efficient enhancement of conductivity by the presence of graphite is largely due to the planar morphology () controlled by the anisotropy of the surface energy of graphite. The observed 10–20 is roughly consistent with the known anisotropy of surface energy of graphite that predicts ( [Abrahamson, 1973; Zaidi et al.,1995], a small deviation from the simple model may be caused by the strain energy or by the influence of some impurities, γc is the surface (interface) energy of disk plane ((0001) plane), and γa the surface (interface) energy of a plane normal to the disk plane). In Earth's mantle, the morphology of graphite is likely near equilibrium, and in such a case, we may use to estimate the percolation threshold to obtain 0.017 volume fraction (~1 wt%).
 A majority of the geophysical observations of electrical conductivity in the upper mantle may be attributed to the conduction in an olivine + orthopyroxene mixture with the help of hydrogen [Wang et al., 2006; Karato, 2011; Dai and Karato, 2009]. However, high conductivity regions in some of the continental upper mantle are difficult to explain by this mechanism because a majority of the continental lithosphere is depleted with water and relatively low temperatures [Carlson et al., 2005] and temperatures in the relatively shallow part (~100 km or shallower) is not high (<1300 K). Jones et al.  suggested that high conductivity regions (~0.1 S/m) at around the depth of ~100–120 km in the Western Canadian Shield may be produced by carbon, either as graphite or as carbon on grain boundary films. High conductivity (~0.1 S/m) at this depth (temperature ~ 1000–1300 K) is difficult to be attributed to the presence of hydrogen because more than ~0.1 wt% of water would be required [Wang et al., 2006] exceeding the solubility limit of water in olivine. Using our results, we suggest that such high conductivity may be attributed to a large concentration of graphite (~1 wt%).
 The ability for graphite to enhance electrical conductivity depends on its volume fraction and geometry. A previous study [Mathez, 1987] suggested that only ~ 0.01 wt% carbon in mantle-derived rock is needed to create a good conductor (~0.1 S/m). However, their argument was based on the assumption that all grain boundaries are covered by amorphous graphite. Watson et al.  showed that even up to 0.1 wt% carbon did not enhance the bulk conductivity of an olivine aggregate. Their observations are consistent with ours, but detailed interpretation cannot be made because they did not study the morphology of graphite.
 The critical fraction of graphite is different if graphite morphology is controlled by the surface energy. We report that graphite in olivine-rich matrix assumes highly anisotropic near equilibrium morphology under the upper mantle conditions. Such morphology promotes mutual connection of graphite grains along the orientations with high electrical conductivity (the (0001) plane). In such a case, ~1 wt% of graphite will be needed to enhance electrical conductivity in some regions.
 The amount of carbon in Earth's mantle is highly uncertain. The published results range from ~0.001 wt% to ~1 wt% suggesting high regional variation in carbon content including both lateral and radial variation [e.g., Dasgupta and Hirschmann, 2010; Deines, 2002; Wood et al.,1996]. Typical oxygen fugacity in the upper mantle is about 1 to 3 log unit less than the oxygen fugacity corresponding to the FMQ buffer [Frost and Mccammon, 2008; Frost and Wood, 1997] (see Figure 1). This corresponds roughly to the limit of the stability field of graphite [Frost and Wood, 1997]. Therefore, we conclude that high conductivity regions at ~100–150 km depth might correspond to regions of high carbon content with typical or somewhat lower than typical oxygen fugacity, e.g., upper mantle above some subduction zones with a large amount of subducted sediments.
 We are grateful to Z. Du, G. Amulele, K. Otsuka, R. Farla, and Y.Guo for technical support. R. Dasgupta provided a discussion on the carbon content in the mantle. We thank three anonymous reviewers for their useful comments. This study was supported by the NSF of USA (EAR-0911465) and by the National Science Foundation of China (NSFC, Nos.40774036 and 41074063).