Electrical conductivity of orthopyroxene: implications for the water content of the asthenosphere.

Electrical conductivity of minerals is sensitive to water content and hence can be used to infer the water content in the mantle. However, previous studies to infer the water content in the upper mantle were based on pure olivine model of the upper mantle. Influence of other minerals particularly that of orthopyroxene needs to be included to obtain a better estimate of water content in view of the high water solubility in this mineral. Here we report new results of electrical conductivity measurements on orthopyroxene, and apply these results to estimate the water content of the upper mantle of Earth. We found that the electrical conductivity of orthopyroxene is enhanced by the addition of water in a similar way as other minerals such as olivine and pyrope garnet. Using these new results, we calculate the electrical conductivity of pyrolite mantle as a function of water content and temperature incorporating the temperature and water fugacity-dependent hydrogen partitioning. Reported values of asthenosphere conductivity of 4x10(-2)-10(-1) S/m corresponds to the water content of 0.01-0.04 wt%, a result in good agreement with the petrological model of the upper mantle.

Introduction

It was proposed that water (hydrogen) may enhance electrical conductivity of minerals[1)]. If it is the case, then much of the electrical conductivity in Earth’s mantle is due to proton (hydrogen) but not by “polaron” (ferric iron to ferrous iron hopping) as previously considered[2)–4)] and electrical conductivity might be used to infer the water content in Earth’s interior. Consequently, a large number of experimental studies have been conducted to study the influence of water (hydrogen) on the electrical conductivity of mantle minerals[5)–10)]. For example, Wang et al.[10)] determined the influence of water on conductivity of olivine and inferred the water content of Earth’s upper mantle. A similar study was conducted by Yoshino et al.[5)] who obtained different conclusions on the influence of water from those by Wang et al.[10)]. Karato and Dai[11)] and Dai and Karato[8)] showed that the discrepancies between the results from these two laboratories are due to the technical problems in the approach by Yoshino et al.[5)] (see also references[6),12)]), and after the correction of technical problems in Yoshino et al.[5)], most of the published results agree each other.

However, even though these technical problems have been resolved[11)], the previous studies are incomplete because they considered olivine only in estimating the water content of the upper mantle. The recent study by Mierdel et al.[13)] showed that orthopyroxene can dissolve a significantly higher amount of water than olivine under the shallow upper mantle conditions, implying that orthopyroxene might have important effects on electrical conductivity of the upper mantle. However, until now, no data have been reported on the conductivity of hydrous pyroxene, which constitutes about 20–40% of the minerals in the upper mantle. Another issue is the water content measurements. In most cases, water content in minerals is measured either by FT-IR (Fourier-transformed infrared spectroscopy) or SIMS (secondary ion mass spectrometry), but SIMS gives a factor of ∼3 higher water content than FT-IR for olivine (there is no difference for orthopyroxene)[14),15)]. In both Wang et al.[10)] and Yoshino et al.[5)], water content in the upper mantle was inferred using FT-IR based water content calibration. When the estimates of water content based on different methods are used, the influence of the used method needs to be evaluated. The purpose of this paper is to report the results of conductivity measurements of hydrous and anhydrous orthopyroxene and revise the estimate of the water content of the upper mantle where the influence of different methods of water content measurements is evaluated.

Experimental

Samples

We used two orthopyroxene single-crystals from the Stuttgart region in Germany (sample A) and the Han Nuoba region in eastern China (sample B). The surface of the sample was fresh and had good crystal form without any evidence of major alteration. The chemical composition of the sample is shown in Table 1. The iron content of these orthopyroxene samples (Fe/(Fe+Mg+Ca) = 0.14 and 0.18) is higher than a typical upper mantle orthopyroxene, but aluminium content (0.4 and 0.8 wt%) is in the lower end of typical upper mantle peridotites[16)] (a correction will be made on the influence of iron content, when we apply the present results to the upper mantle). The crystallographic orientation was determined using electron-backscattered diffraction with an error less than 1°. Samples of single-crystal orthopyroxene with different crystal axes ([001], [010] and [100]) were cut into a disc of ϕ1.6 mm × 0.4 mm with an ultrasonic drill and diamond slice; then, the samples were cleaned with acetone, alcohol and deionized-distilled water in turn. The samples were baked for 48 h in a 473 K vacuum drying furnace to remove the adsorbed water on the surface of the samples.

Table 1

Chemical composition of the samples (wt%)

	Cr2O3	NiO	MnO	FeO	Na2O	K2O	Al2O3	CaO	MgO	TiO2	SiO2
Sample A	0.37	0.01	0.26	9.12	0.07	0.02	0.79	0.36	32.14	0.09	56.77
Sample B	0.92	0.08	0.34	11.73	0.01	0.03	0.42	0.51	30.48	0.05	55.43

The water content of the samples was determined using the Fourier-transform infrared (FT-IR) spectroscopy for double-polished samples with a thickness of ∼120 μm. FT-IR spectra were measure at several points in a sample and for each point, 256 scans were made, and the average of several points was used to calculate the water content. The infrared spectra of orthopyroxene along the direction of the [001] crystallographic axis are shown in Fig. 1. We used the Paterson calibration[17)] to determine the water content of the sample, where CW is the molar concentration of hydroxyl (ppm wt% H2O or H/106 Si), B is the density factor (2808 wt% or 3.11 × 104 cmH/106 Si), ξ is the orientation factor (1/2) and K(ν) is the absorption coefficient (cm−1) at the wavenumber of ν. For orthopyroxene, FT-IR (Paterson) calibration and the SIMS (secondary ion mass spectrometry) measurements give nearly identical results[14)]. The integration was performed for the wavenumber ranging from 3000 to 3700 cm−1. We obtained a water content of 4650 H/106 Si (0.042 wt%) and less than 8 H/106 Si (0.000072 wt%) for the orthopyroxene from the Stuttgart region in Germany and the Han Nuoba region in eastern China, respectively. Note that the latter value is close to the detection limit of water by FT-IR and should be considered as the upper limit. The water content was measured both before and after the conductivity measurements. The water loss during electrical conductivity measurement was less than 10%.

Fig. 1

FT-IR spectra of hydrous and dry orthopyroxene (beam parallel to [001]) for the wavenumber range from 3000 to 4000 cm−1. For a hydrous sample, well-defined absorption peaks are observed at 3064, 3415 and 3515 cm−1, and the total water content of the crystal is ∼4650 ppm H/Si (0.042 wt%) and the water content of an anhydrous sample is less than 8 ppm H/Si.

We also conducted Raman spectrum analysis before and after the electrical conductivity experiment. The results showed that there was no phase transition during the experiment.

Experimental methods

The experimental procedures are the same as those in the previous studies in our laboratory[7)–10)] and therefore only the essence is described here. We used a Kawai-type multianvil press and used the Solartron-1260 Impedance/Gain-Phase analyzer to determine the conductivity from the impedance spectroscopy. The pressure was determined based on the separate calibrations using the phase transformations of some standard materials such as olivine-wadsleyite[18)] and the phase transition of the coesite-stishovite transformation[19)]. The error in pressure estimate is ±0.5 GPa. Temperature was measured by a W95Re5-W74Re26 thermocouple. The error of the measured temperature was less than ±10 K. Both the MgO pressure medium and the zirconia tube were baked for 10 h in a 1273 K furnace to avoid the effects of adsorbed water on the experimental results of the conductivity measurements. To control the oxygen fugacity and to avoid electric noise in the sample cavity from the heater, a 0.025 mm thick Mo foil was placed between the samples and the MgO insulation. A disc-shaped sample (ϕ1.6 mm × 0.4 mm) was placed between two Mo electrodes (ϕ0.5 mm × 0.3 mm).

Pressure was first raised at a rate of 2.0 GPa/h to the predetermined value of 8.0 GPa. After the desired pressure was reached, temperature was raised at a rate of 95 K/min to the designated value. After pressure and temperature are at the desired values, we run the ZPlot software of the Solartron-1260 Impedance/Gain-Phase analyzer to obtain the impedance spectra of the samples. The frequency range and signal voltage were 10−2–106 Hz and 300 mV, respectively. Conductivity was measured at temperature from 873 to 1473 K. In order to evaluate the possible influence of non-equilibrium effects, we measured the impedance spectra both with increasing and with decreasing the temperature. We did not see any appreciable hysteresis and conclude that the measured impedance corresponds to the equilibrium value.

Results and discussions

Results and comparison to other minerals

The typical impedance spectra are shown in Fig. 2. Results from other crystallographic axes were similar to those that are illustrated. In the frequency range from 10−2 to 106 Hz, two impedance arcs were observed which correspond to two different conduction mechanisms: the circle at high frequencies corresponds to the grain interior conduction and the arc at lower frequencies corresponds to the polarization process at the sample and the electrode or at grain boundaries[20), 21)]. We determined the DC conductivity of a sample using high frequency part of spectra. The importance of using this part of spectra was discussed by previous papers[8),9),11)] and will not be repeated here.

Fig. 2

Impedance spectra along the [001] crystallographic axis of a hydrous orthopyroxene from 10−2 to 106 Hz (right to left), obtained under conditions of 8.0 GPa, 873–1273 K, Mo-MoO2 oxygen buffers and 0.042 wt% water content (Z’ and Z” stand for the real and imaginary parts of complex impedance, respectively).

We calculated the conductivity of the sample from the measured resistivity using the formula, , where σ is conductivity, L is sample thickness and S is the cross sectional area of the electrode. Figure 3 shows the relationship between electrical conductivity and temperature for these two samples. The data for each sample can be fitted to the following Arrhenius relation, where σ0 is the pre-exponential factor that is independent of the temperature and includes the water content’s influence on the electrical conductivity, R is the ideal gas constant, H* is the activation enthalpy and T is the absolute temperature. The Arrhenius fitting parameters for the hydrous and anhydrous electrical conductivity along the three different crystallographic axis directions are listed in Table 2. The anisotropy in conductivity is small.

Fig. 3

Temperature dependence of electrical conductivity of a hydrous orthopyroxene (∼4700 ppm H/Si) and an anhydrous (<10 ppm H/Si) orthopyroxene at pressure of 8 GPa.

Table 2

Parameters of Arrhenius equation, σ = σ0e− for the electrical conductivity of hydrous and anhydrous orthopyroxene under conditions of 8.0 GPa and Mo-MoO2 oxygen buffer

Run No.	orientation	T (K)	Water content (H/106 Si)		σ0 (S m−1)	H* (KJ mol−1)
			Before experiment	After experiment
K713	[001]	873–1273	4660	4540	181 ± 10	80 ± 2
K720	[100]	873–1273	4690	4600	162 ± 13	82 ± 3
K794	[010]	873–1273	4700	4640	153 ± 9	85 ± 2
K795	[001]	873–1473	<8	<7	531 ± 15	147 ± 6

For each sample (“dry” and “wet”), the electrical conductivity is well described by the Arrhenius relation with a single activation enthalpy for each, but the conductivity of a “wet” sample is much higher than that of a “dry” sample. This suggests that a single mechanism of conduction operates in each sample under these experimental conditions. However, the electrical conductivity of a sample with high water content is much higher than that of a water-poor (“dry”) sample, and the activation enthalpy is different. However, in order to evaluate the influence of water, it is necessary to compare the electrical conductivity with the same major element composition. Figure 4 shows a comparison of electrical conductivities of olivine, orthopyroxene and pyrope garnet for the same Mg#[7)–10)] at 8 GPa for the oxygen fugacity controlled by Mo-MoO2, and either for the water content of 0.042 wt% or water-free conditions. The electrical conductivities of these minerals are remarkably similar: under these normalized conditions they agree within an order of magnitude, and the activation enthalpies are also similar (the influence of aluminum content is small[22)]). Consequently, we consider that the mechanisms of electrical conduction in orthopyroxene is similar to those in other minerals, namely, “polaron” conduction (conduction by hopping of electron between ferric and ferrous iron) under “dry” conditions and proton conduction under “wet” conditions. We also note that the electrical conductivity of our “dry” sample is similar to the conductivity reported in some of the previous studies[23),24)]. However, our results on “dry” sample are considerably different from those by Duba et al.[25)] and by Hinze et al.[26)] Duba et al.[25)] reported a large hysteresis indicating the influence of non-equilibrium processes such as the influence of adsorbed water. Transformation of orthoenstatite to protoenstattite that occurs at low pressures may also be responsible for such a hysteresis. However, such a hysteresis was not observed in our studies presumably because all the parts were dried before each experiment and sample assembly was annealed before the measurement. Hinze et al.[26)] measured the conductivity at 1 GPa where orthoenstatite is stable. They reported considerably smaller activation enthalpy (and higher conductivity) for nominally “dry” orthopyroxene than the present results. Based on our experience[7),27)], we suspect that their samples contain a large amount of water. However, the water content of their samples was not measured and it is not possible to resolve the cause of discrepancy convincingly.

Fig. 4

A comparison of electrical conductivity of orthopyroxene with those of olivine[10),50)] and pyrope-rich garnet[9)] that are obtained at 8.0 GPa, 873–1473 K, Mo-MoO2 oxygen buffer and the same iron content (XFe = Fe/(Fe+Mg+ Ca) = 0.10). The results by Wang et al.[10)] were corrected for Mo-MoO2 buffer based on the results by Dai and Karato[8)]. The water content is measured using FT-IR. A correction is needed if the water content is measured by SIMS[14)] (see text).

Huebner et al.[22)] investigated the influence of trivalent cations (Cr3+ or Al3+) on electrical conductivity of orthopyroxene. The magnitude of this effect is, however, much smaller than the effects of water (hydrogen). Therefore we believe that a small difference in these cation concentration between the two samples studied here has relatively minor effects.

Water content of the upper mantle

Given the new data on electrical conductivity of orthopyroxene, and the similarities in conduction behavior between orthopyroxene and other minerals, we propose that the electrical conductivity of orthopyroxene follows the same trend as other minerals, viz., where the first term corresponds to the conductivity under “dry” (water-free) conditions, whereas the second term represents the conductivity under “wet” (water-rich) conditions. A1,2 is corresponding pre-exponential term, activation enthalpy, C is the water content, and r is a non-dimensional constant. Although we did not determine, r, for orthopyroxene, using the analogy with other minerals, we assume r = 0.62, a value the same as olivine. Given the value of r, electrical conductivity of orthopyroxene is completely characterized. The parameters in such a relation for olivine, orthopyroxene and pyrope garnet are summarized in Table 3.

Table 3

Electrical conductivity of upper mantle minerals (major element compositions are close to the typical upper mantle (Fe/(Fe+Mg+Ca) = 0.10 for olivine and orthopyroxene, = 0.15 for pyrope garnet). Parameters for the relation are shown corresponding to the Mo-MoO2 buffer. The influence of Fe content is corrected by adjusting the pre-exponential factor (this effect may also be included as a variation in activation enthalpy). The results shown are from 4–8 GPa but pressure effects are small (less than ∼30% in this pressure range). For olivine and pyrope garnet, the results are for isotropic polycrystalline aggregates. For orthopyroxene, the results are the average of single crystal data shown in Table 2. The results published by Wang et al.[10)] are for the Ni-NiO buffer and are corrected for the Mo-MoO2 buffer. Water content in these equations is for FT-IR based measurements. For olivine and garnet, a correction is needed if water content based on SIMS calibration is used (see text for detail)

	A1(S/m)	H1* (kJ/mol)	A2(S/m)	r	H1* (kJ/mol)
olivine	102.1	154	103.1	0.62	87
orthopyroxene	102.4	147	102.6	0.62	82
pyrope garnet	102.5	128	102.9	0.63	70

We use these relationships to estimate the water content of the asthenosphere by comparison of geophysically inferred conductivity values with mineral physics results on the influence of water on electrical conductivity. We assume that the asthenosphere has the pyrolite composition[28)], olivine : orthopyroxene : pyrope garnet = 60 : 25 : 15 (with Mg/(Mg+Fe) = 0.88) and calculate the electrical conductivity of pyrolite as a function of water content for a plausible range of asthenosphere temperature (1600±100 K[29)]). We consider a pressure of 5 GPa, but within the depth range of the asthenosphere (50–200 km), the influence of pressure on electrical conductivity for a given chemical composition (Fe content, water content) is negligibly small[9),30)].

An important issue in calculating the electrical conductivity is the partitioning of elements among co-existing minerals. When several minerals co-exist, then various elements will be partitioned among them and this effect must be included in the calculation of influence of water on the electrical conductivity of a mixture of minerals. Important elements for electrical conductivity are iron (Fe) and hydrogen (H). For iron partitioning, we used the results by Irifune and Isshiki[31)] and made a small correction based on available experimental data[32)]. Such a correction is more important for hydrogen. For hydrogen, the partition coefficients are calculated from the measured hydrogen solubility assuming the following relationship, where is water content in mineral i, f is the fugacity of water, r is a constant that depends on the mechanisms of water dissolution, and are corresponding energy and volume change respectively. According to Mierdel et al.[13)] and Kohlstedt et al.[33)], the water solubility in orthopyroxene and olivine depends on water fugacity differently (r = 1 for olivine[33)], r = 0.5 for Al-bearing orthopyroxene[13)]), and consequently, the water partitioning between these two minerals depends on water fugacity as well as other thermodynamic parameter such as temperature. For pyrope garnet, there is no detailed experimental study on hydrogen solubility. We tentatively use the results by Mookherjee and Karato[34)] suggesting the similar dependence of hydrogen solubility on water fugacity as orthopyroxene. Mookherjee and Karato[34)] also show that water solubility in pyrope garnet is significantly smaller than that in Al-bearing orthopyroxene (by a factor of ∼3). Because of the small volume fraction, pyrope garnet will occur in a pyrolite as isolated minerals, so the uncertainties on garnet conductivity will have only small effects on the results of electrical conductivity calculation. We calculated the water partition between olivine and orthopyroxene as a function of temperature and total water content assuming that the water content of garnet is 1/3 of that of orthopyroxene. We first calculated the water fugacity for a given total water content at a given pressure and temperature. Then the water content of each mineral was calculated using the solubility relationships.

Figure 5 shows the water (hydrogen) partition coefficient between olivine and orthopyroxene as a function of total water content (water fugacity) at 5 GPa and for various temperatures. Because the solubility data from Kohlstedt et al.[33)] is based on FT-IR and there is a factor of ∼3 difference in water content measurements between FT-IR and SIMS (a factor of 3 larger water solubility than Kohlstedt et al.). Such a discrepancy is not observed for orthopyroxene[14)] and wadsleyite. The cause of this discrepancy is not well known but it may be due to the influence of small water-filled inclusions that may be mineral specific. In any case, this SIMS versus FT-IR discrepancy for olivine is well documented[14),15),35)], and we consider both cases. Water partitioning between olivine and orthopyroxene is strongly dependent on water content (water fugacity) and temperature because of the different dependence of water solubility on water fugacity and temperature for these minerals. A large fraction of water is dissolved in orthopyroxene for the low total water content and/or low temperature. The calculated results of partition coefficient depend on the method of water content measurement.

Fig. 5

Water (hydrogen) partitioning between olivine and orthopyroxene as a function of water content at 5 GPa.

is water content in olivine, orthopyroxene respectively and C is the total water content. The water partitioning depends strongly on the water content (water fugacity) and temperature. Water solubility data based on FT-IR and SIMS calibration are different for olivine leading to a difference in water partitioning.

The electrical conductivity of a pyrolite was calculated using a model of electrical conductivity of a mixture. At a given conditions (temperature, pressure and water content), hydrogen partitioning among coexisting minerals was calculated, and corresponding electrical conductivity of each mineral was calculated. Then the electrical conductivity of a mixture (pyrolite composition) is calculated. Several models for electrical conductivity of a mixture were proposed[36)], but we use the Hashin-Shtrikman bounds. The choice of a model does not make much difference because the conductivity contrast is small (Hashin-Shtrikman upper and lower bounds give only less than a few % difference in electrical conductivity if the conductivity contrast is less than 2). In this calculation, we adjusted olivine data on electrical conductivity[10)] for SIMS-based water content. Therefore the water content in this figure corresponds to water content determined by SIMS. If FT-IR based water content is used, then the water content estimated from electrical conductivity should be interpreted as FT-IR based water content, and hence a factor of ∼3 correction must be multiplied to olivine water content to convert it to SIMS-based water content. As far as such a conversion is made, water content inferred from electrical conductivity is not sensitive to the method of water content measurement.

The results of such calculations are shown in Fig. 6. For a plausible temperature of 1600 K for the asthenosphere[29)], we obtain 0.04 wt% for a conductivity of 10−1 S/m and 0.01 wt% for 4 × 10−2 S/m. This is in good agreement with the petrological inference of water content for the MORB (mid-ocean ridge basalt) source region[37)–39)] (0.01–0.02 wt%). However, there is a large regional variation in electrical conductivity of the asthenosphere exceeding more than a factor of 10[40)–42)]. If such a variation is attributed solely to the temperature variation, it would correspond to the variation in temperature of more than ∼500 K that is not plausible in the asthenosphere[43)]. Consequently, we conclude that a large fraction of the lateral variation in electrical conductivity of the asthenosphere is caused by the variation in water content. Note that if we were to use the results by Yoshino et al.[5)] using SIMS-based water content calibration for olivine together with the present results for orthopyroxene, we would need a water content of ∼0.1 wt% or more to explain the observed electrical conductivity. Such a value exceeds petrologically inferred water content (0.01–0.02 wt%). This is due to the inappropriate method used by Yoshino et al. including the use of a single, low frequency data at low temperatures as discussed by Karato and Dai[8),11)].

Fig. 6

Relationship between the electrical conductivity of a pyrolite upper mantle (olivine : orthopyroxene : garnet = 60 : 25 : 15, Mg# = 88) and the water content and temperature at 5 GPa.

SIMS-based water content is assumed. Different relationship will be obtained if FT-IR based water content is used. However, if the correction between FT-IR and SIMS-based water content (for olivine)[14)] is applied, the water content inferred from electrical conductivity will not be sensitive to the method of water content measurements. Orange region represents a typical range of electrical conductivity in the asthenosphere[40),41),47)], and the green region corresponds to a range of water content in the asthenosphere inferred from petrological (geochemical) studies[37)–39)].

What about partial melting? Partial melting is often invoked to explain geophysical anomalies of the asthenosphere[44)]. However, as discussed by Shankland et al.[44)] (see also Karato[1)]), it is difficult to attribute high electrical conductivity to partial melting because it would require a large volume of melt (∼10%) for a basaltic melt. It is impossible to maintain such a large fraction of melt in a broad region of the asthenosphere because of the efficient compaction (the compaction length at the asthenospheric conditions is ∼10–100 m[45)]). Recently, Gaillard et al.[46)] showed that carbonatite melts have much higher electrical conductivity than hydrous basaltic melt and suggested that a small amount of carbonatite melt might explain high electrical conductivity of the asthenosphere. The high electrical conductivity in their carbonatite melts is essentially due to the high alkali content. The presence of such a melt cannot be ruled out, but in order for such a melt to explain high electrical conductivity, there must be a broad region where connected melt films (or tubes) are present. It is not clear how one can keep connected melt in a broad region against gravity-induced compaction.

In contrast, the present analysis showed that the geophysically inferred conductivity values of the asthenosphere, 10−2–10−1 S/m, can be easily attributed to the solid-state mechanism by considering the role of water (hydrogen) in the asthenosphere with an amount that is consistent with the petrological model of the MORB source region. We conclude that partial melting is not required to explain high electrical conductivity of the asthenosphere. Note, however, that this does not imply that there is no partial melting in the asthenosphere. A small amount of partial melting could be present, but its effect is unlikely reffected in electrical conductivity.

One way to address the issue of partial melting versus water (hydrogen) explanation for the high conductivity of the asthenosphere is to investigate the regional variation of electrical conductivity. Partial melting hypothesis would imply higher conductivity in the asthenosphere of the central Pacific (near Hawaii) where hot materials are carried to the asthenosphere by a plume than in other typical oceanic asthenosphere. However, the published results show rather low electrical conductivity in the central Pacific (e.g., Utada et al.[47)]). Karato[48)] proposed that the low electrical conductivity (and other geophysical anomalies) in the central Pacific may be due to water depletion in solid components caused by deep partial melting due to hot (and damp) plume. However a limitation of this approach is the resolution of geophysical inference of electrical conductivity. Utada et al.[47)] used relative long-period signals and their model for the upper mantle is poorly constrained. A detailed regional conductivity mapping of the upper mantle similar to the work by Kelbert et al.[49)] will be helpful to resolve this issue.