The Effect of Water on Ionic Conductivity in Olivine

High‐temperature ionic conductivity in olivine single crystals has been measured in the [100], [010], and [001] crystallographic orientations as a function of pressure from 2 to 10 GPa, temperature from 1450 to 2180 K, and H2O content from 20 to 580 wt. ppm using multianvil presses with in situ impedance analyses. The experimental results yield an activation energy, activation volume, and H2O content exponent of 250–405 kJ/mol, 3.2–5.3 cm3/mol, and 1.3 ± 0.2, respectively, for the high‐temperature ionic conduction regime. Olivine ionic conductivity has negative pressure and positive temperature dependences and is significantly enhanced by H2O incorporation. The [001] direction is more conductive than the [100] and [010] directions. The H2O‐enhanced ionic conductivity may contribute significantly to the electrical conductivity profile in the asthenosphere, especially in the regions under relatively high‐temperature and low‐pressure conditions.

To understand the electrical conductivity profiles in the upper mantle, a series of experimental studies have been performed to measure the proton and small polaron conductivities in olivine (e.g., Du Frane et al., 2005;Dai & Karato, 2014a, 2014bPoe et al., 2010;Wang et al., 2006;Xu et al., 1998;Yang, 2012). Their results suggest that the proton conduction is significantly enhanced by water incorporation. It may account for the magnetotellurically detected anomalously high and highly anisotropic electrical conductivity (10 −1 -10 −2 S/m) in the asthenosphere at 70-120 km depth beneath young plates near the East Pacific Rise (Baba et al., 2006;Evans et al., 2005), which cannot be explained by small polaron conductivity in dry olivine. However, this idea was later refuted (e.g., Gardés et al., , 2015Yoshino et al., 2006Yoshino et al., , 2009) because newer experimental results show that proton conductivity even in H 2 O-saturated olivine is insufficient to explain the highly conductive asthenosphere.
The ionic conduction mechanism, in contrast, has received only minimal attention because its contribution to olivine bulk conductivity is considered to be significant only at temperatures above 1750 K (e.g., Constable et al., 1992), which is unrealistically high for the majority of asthenosphere. However, this conclusion is based on dry olivine experiments. Incorporation of H 2 O produces additional point defects on Mg (Fe) sites (Demouchy & Mackwell, 2006;Kohlstedt & Mackwell, 1998) and enhances the exchange of Mg (Fe) ions between regular and vacant sites (Fei et al., 2018a(Fei et al., , 2018b, which is expected to raise the ionic conductivity. Therefore, although the contribution of ionic conductivity is negligible in dry olivine at asthenospheric temperatures (<1750 K), it may become significant by considering small amounts of H 2 O in the asthenosphere (Fei et al., 2018a). To evaluate this hypothesis, knowledge about the H 2 O-content dependence of olivine ionic conductivity is required. However, such experimental results have not been reported because olivine dehydration occurs at high temperatures (Yoshino et al., 2009), and the temperature range of previous H 2 O-effect related studies was therefore limited to~1400 K (e.g., Dai & Karato, 2014a;Wang et al., 2006;Yang, 2012), which is insufficient for observing ionic conduction.
In this study, we measured the conductivity of olivine single crystals at pressures of 2 to 10 GPa, temperatures of 1400 to 2180 K, and H 2 O contents of~20 to 580 wt. ppm along the [100], [010], and [001] crystallographic axes. Our results demonstrate that olivine ionic conductivity is enhanced by H 2 O incorporation and may contribute significantly to the bulk conductivity of olivine under asthenospheric conditions.

Starting Material
Three pieces of handpicked natural olivine single crystals from Pakistan with grain sizes of~15 mm were used as the starting material. The initial H 2 O content of the crystals was about 50 wt. ppm from infrared analysis, and the Fe/(Mg + Fe) atomic ratios were 9.0-9.5% by electron microprobe measurements. Trace element contents were reported in Gose et al. (2010). After orientation to the [100], [010], and [001] crystallographic directions using a single-crystal X-ray diffractometer, inclusion-free disks with a 1.0-mm diameter and 0.3-mm thickness were cored from the single crystals along crystallographic directions and used for the following conductivity measurements.

Multianvil Cell Assembly
Each olivine disk was sandwiched by two Mo electrodes, each of which consisted of one or two layers of Mo disks with a 1.0-mm diameter and 0.025 mm thickness. The sample was insulated by an MgO single-crystal sleeve and shielded by a Mo foil, which prevented the migration of conductive materials from the graphite furnace into the MgO insulator at high temperature. In Runs H4721 and H4745 ( was connected to one electrode to measure the sample temperature, and another W 97 Re 3 wire was connected to the other electrode for impedance analyses ( Figure 1).

High P-T Experiments
After assembly, each cell was dried in a vacuum oven at 420 K for 24 hr, then loaded into a multianvil press and compressed to 2 or 4 GPa at room temperature using eight tungsten carbide cubes with edge lengths of 32 mm and truncated edge lengths of 11 mm. From test experiments, it was found that even with drying in the vacuum oven, some moisture remains in the pressure medium. The assembly was therefore heated to 1300 or 1500 K and maintained for a few hours until no decrease in apparent sample conductivity with time was observed. The pressure was then increased to the desired values of 2 to 10 GPa, and two to five heating-cooling cycles up to 2180 K were performed with a step of 30-100 K in each pressure stage. In each step, the sample was heated/cooled to the target temperature at a rate of~100 K/min, followed by impedance analysis, which took 1-3 min. The duration of each heating-cooling cycle was 1-2 hr depending upon the temperature range. The assembly was quenched to room temperature by switching off the heating power and decompressed to ambient pressure over 10 hr.
As mentioned in section 1, olivine dehydration has prevented the investigation of H 2 O dependence of conductivity at very high temperatures (Yoshino et al., 2009). Dehydration was also observed in this study: H 2 O content (C H2O ) decreases from 50 to 20 wt. ppm after heating above 1700 K. Therefore, although the low-C H2O runs (~20 wt. ppm) (I471, I511, and H4674) were preformed up to 2200 K; the temperature was limited to 1700 K for higher-C H2O runs (H4694, H4721, and H4745) ( Table 1). To clearly observe ionic conductivity at relatively low temperatures, measurements were performed in the [010] and [001] directions, along which small polaron conductivity and ionic conductivity are the lowest and highest, respectively (Constable et al., 1992). is substantially lower than in other runs; therefore, the small polaron conduction is probably masked by other mechanisms (e.g., proton conduction) as explained in the main text.

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In Situ Impedance Analysis
In situ impedance analysis was performed using a Solartron 1260 Impedance/Gain Phase analyzer. In each measurement, an alternating voltage (1 V) with a frequency swept from 10 7 to 10 2 -1 Hz with 20 steps per decade was applied to the electrodes, and the complex impedance was recorded at each frequency ( Figure 2). The sample resistance R was obtained by fitting the impedance spectrum to an equivalent parallel circuit with a resistor and constant phase element using the impedance analysis software, Z-View. Conductivity (σ) under given pressure and temperature conditions was calculated from the formula σ = 4 L/(πd 2 R), where L and d are the thickness (0.3 mm) and cross-sectional diameter (1.0 mm) of the sample, respectively .
The L and d had no distinct change (less than 5% shortening) before and after the high-pressure experiments. The background conductivity of the cell assembly was examined by Fe-free forsterite samples, whose conductivity is more than 1 order of magnitude lower than those in the olivine samples. The fitting of impedance spectrum causes negligible error on σ (<1%). Additionally, the variation of Fe% (from 6.6% to 8.7% in Table 1) may affect the ionic conductivity in dry olivine by a maximum of~30% in dry olivine (section 3.2). Therefore, the total uncertainty of σ is by a maximum of 50%. This maximum uncertainty is also confirmed by the variation of data points in different heating-cooling cycles ( Figure 3).

Infrared Analyses
The recovered cell assemblies were double-side polished and Fourier transform infrared (FTIR) spectroscopy analysis was performed along   The H 2 O contents were calculated by integration of the infrared absorptions from 3,000 to 4,000 cm −1 , where C H2O is the H 2 O content in wt. ppm, 0.119 is the calibration based on polarized FTIR from Withers et al. (2012), ζ is the correction factor for unpolarized light (ζ ≈ 1 to 1.25 listed in Table 1 upon maximum absorbance (Withers, 2013)), and A(ν) is the absorption coefficient at wavenumber ν after background subtraction and thickness normalization to 1 cm.
Polarized FTIR on oriented crystals may give more precise C H2O . In that case, however, the crystals should be polished along three crystallographic orientations, which is unfavorable here because the orientation and polishing process would damage the cross section of the assembly and prohibit any further observations. Therefore, only unpolarized FTIR spectra were measured on a single plane for each sample, which may introduce uncertainties in C H2O evaluation (see section 3.3). Additionally, different infrared calibrations yield different C H2O . If using the Bell et al. (2003) calibration, the absolute values of C H2O are higher by about 50%, although the C H2O -exponent for ionic conductivity reported in this study should remain the same.

Dehydration or H 2 O-Reabsorption During Conductivity Measurements
To investigate the C H2O dependence of olivine conductivity, it is necessary to know C H2O in the samples during conductivity measurements. However, C H2O is only measured by FTIR in the recovered samples after conductivity measurements. Because the actual C H2O during each impedance spectrum acquisition is unknown, we evaluate the dehydration during heating paths and H 2 O-reabsorption during cooling paths according to the conductivity variation. It is expected that if significant dehydration had occurred continuously, the conductivity should have continuously decreased upon repeating heating-cooling cycles because the ionic conductivity is C H2O -dependent as shown later. Nevertheless, Figure 3 shows that, although the conductivity decreases in the first (and second) heating-cooling paths, changes were negligible in the later paths. We therefore expect that olivine dehydration has occurred mostly in the first (and second) heating paths, but is insignificant in later heating-cooling paths. On the other hand, H 2 O reabsorption is also unlikely to occur; otherwise, conductivity should have increased, rather than obtaining repeatable values in different heating-cooling cycles.
The above evaluation of C H2O variation relies on the extent of C H2O that can produce measurable changes in conductivity. This is unknown because both conductivity and C H2O are variables, and therefore insignificant dehydration during heating and H 2 O-reaborption during cooling is still theoretically possible (Karato, 2019). In that case, the C H2O under higher-temperature conditions for the ionic conduction regime would be slightly underestimated; namely, the conductivity is enhanced by less H 2 O, which further supports our conclusion.

Microstructure and Composition of the Recovered Samples
Scanning electron microscopy (SEM) observations of recovered assemblies show that olivine and electrodes remain in a sandwiched structure (Figures 5a and 5b). Cracks are found within olivine crystals, which should be caused mechanically by compression and/or decompression. Nevertheless, even with cracks, the measured conductivity data still represent that for single crystal rather than polycrystalline because there is no recrystallization process, therefore, the crystallographic orientation should remain. This is confirmed by the experimental results which shows strong conductivity anisotropy. As expected, no melts or fluid phases are observed near the samples or within cracks for both brucite-bearing and brucite-free runs.
Electron microprobe analysis show lower Fe contents in the recovered samples (Table 1). The Fe/(Mg + Fe) ratio does not show any systematic variation along the axial cross section but clearly decreases near MgO along the radial cross section (Figures 6a and 6b). The decrease of bulk Fe content in olivine is therefore owing to Mg-Fe exchange between olivine and MgO, rather than absorption by Mo. Because the samples are radially surrounded by MgO, the vacancy concentration on Mg (Fe) site should remain constant by Mg-Fe exchange despite a slight decrease in the Fe/(Mg + Fe) ratio, and ionic conductivity should therefore be unaffected. In view of defect chemistry, the defect concentration on the Mg (Fe) site is related to Fe 3+ in dry olivine with a charge balance of (Kohlstedt, 2006;Stocker & Smyth, 1978). Under a given oxygen fugacity condition, the [Fe 3+ ]/ΣFe ratio should be fixed (Stocker & Smyth, 1978); thus, we have [V Mg ″] ∝ ΣFe. The variation of Fe% (Table 1) will have very limited effect on the ionic conductivity in dry olivine. For hydrous olivine, the [V Mg ″] is controlled by H 2 O content and independent of ΣFe (Kohlstedt, 2006;Kohlstedt & Mackwell, 1998).

P, T, C H2O , and Crystallographic Orientation Dependences of Ionic Conductivity
An example of the conductivity (σ) and temperature (T) relationship is shown in Figure 7. The slope of the σ-1/T curve increases with increasing temperature owing to the change of the dominant conduction mechanisms. The contribution of the proton conduction mechanism is difficult to quantify, as discussed in the supporting information. Because this study focuses on the ionic conductivity at asthenospheric temperatures, only data points at temperatures higher than 1400 K are plotted in Figure 8 and fitted to the Arrhenius equation with two terms, where σ 0 is the preexponential factor, P is the pressure, T is the absolute temperature, R is the ideal gas constant, E is the activation energy, and V is the activation volume. Subscripted "ionic" and "sp" denote ionic and small polaron conduction mechanisms, respectively. The fitted parameters are listed in Table 1.
The E ionic along the [010] axis in the high-and low-C H2O runs (H4745 and I511) are essentially identical, whereas the data fitting indicates that E ionic along [001] may be C H2O -dependent (Table 1). However, the low E ionic in Runs H4721 and H4694 is likely owing to the relatively high small polaron conductivity along [001] (Constable et al., 1992), which leads to large uncertainties in the E ionic determination when the experimental temperature is relatively low.
The second term in equation 2 is suggested to be small polaron conduction because E sp and V sp are about 120-160 kJ/mol (except for the high C H2O runs) and~0 cm 3 /mol, respectively, both of which are comparable with previously reported values (e.g., Constable et al., 1992;Yoshino et al., 2009Yoshino et al., , 2012 (Table 2). The E sp Figure 7. Two conduction mechanisms (high-and low-temperature regimes) with different temperature dependences. The high-temperature regime is assigned as ionic conduction, whereas low-temperature regime is assigned as small polarcon conduction (or other mechanisms in high-C H2O runs).

Figure 8.
Olivine conductivity under various pressure, temperature, C H2O , and crystallographic orientation conditions. The bending of the fitting lines at relatively low temperatures is owing to contributions of low-temperature mechanisms. Only repeatable data points from different heating-cooling cycles are shown.

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Journal of Geophysical Research: Solid Earth obtained in Runs H4721, H4745, and H4694 are considerably lower (<115 kJ/mol) than others (Table 1). This might be because the temperature ranges for these runs were substantially smaller than others and the E sp determination therefore became less precise or because the small polaron mechanism is masked by other mechanisms (e.g., proton mechanism if it is valid).
Ionic conduction is found to be significantly anisotropic.  (Figure 8). This order is identical to that of Mg self-diffusivity Chakraborty et al., 1994), as well as to that of ionic conductivity at ambient pressure (Constable et al., 1992). Mg defects are primarily located on sites with e 1 symmetry (M1), and the migration distances of M1 defects are in the order of [001] ≪ [100] < ≈ [010] (longer distance means more difficult for migration, Ottonello et al., 1990;Brodholt, 1997). The anisotropy of both ionic conduction and self-diffusion can therefore be explained by the anisotropic hopping distances of defects on M1 sites (Brodholt, 1997;Constable et al., 1992).
Most importantly, olivine with~270-580 wt. ppm H 2 O has more than 1 order of magnitude higher conductivity than those with~20 wt. ppm H 2 O (Figure 8). On the basis of the simulation of the fitting parameters for the σ ionic term in Table 1, both σ ionic[010] and σ ionic[001] at 1700 K (average asthenospheric temperature beneath young plates, that is, about 1600 and 1800 K at 100 and 410 km depth, respectively, for a 5 My geotherm, Katsura et al., 2017;Turcotte & Schubert, 2002) show Note that the absolute bulk conductivity values obtained in different runs cannot be directly compared owing to the various contributions of the low-temperature mechanisms.
Because σ ionic has different temperature dependences in different runs, the C H2O exponent varies slightly with temperature during data fitting, but remain within uncertainty under the asthenospheric temperature range (i.e.,~1.5 at 1500 K and~1.2 at 1800 K). In any case, the C H2O exponent remains in the range of 1.0-1.7 even though the the C H2O based on unpolarized FTIR analysis may have uncertainties as large as a factor of 2. The large C H2O dependence of ionic conductivity has therefore been demonstrated by direct measurement following our previous prediction based on Mg self-diffusivity, which has a C H2O exponent of 1.2 ± 0.2 (Fei et al., 2018a). This large C H2O exponent is expected because defect migration on Mg (Fe) sites in hydrous olivine occurs by the exchange of species among V Me ″, (2H) Me × , and Me Me × , and the concentration of (2H) Me × is proportional to C H2O according to the hydration process of Mg sites, Mg × Mg þ H 2 O→ 2H ð Þ × Mg þ MgO (Kohlstedt, 2006;Kohlstedt & Mackwell, 1998). A C H2O exponent larger than 1.0 also suggests that defect concentration and mobility are both enhanced by hydration (Fei et al., 2018a).
The H 2 O dependence of σ ionic [100] is not determined in this study because it is masked by small polaron conduction at relatively low temperatures (<1700 K), whereas significant dehydration occurs at >1700 K. We assume that σ ionic[100] has the same C H2O dependence as other crystallographic orientations.  (Table 1). This might be caused by the contribution of other mechanisms and is therefore not assigned as small polaron conduction here).

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Theoretically, we cannot exclude the possibility of anisotropic C H2O dependence, but it is a reasonable assumption because H substitution is independent of orientation, whereas the weakening of Mg 2+ bonding by hydration along different directions is expected to be similar because the overall bond strength of Mg 2+ is weakened.

Ionic Conductivity of Olivine Under Asthenospheric Conditions
Using the pressure, temperature, C H2O , and crystallographic dependences determined in this study, the integrated models of anisotropic conductivity along [hkl] axis (σ ionic [hkl] and σ sp [hkl] for ionic and small polaron conductivities, respectively) and isotropic conductivity (σ ionic [iso] and σ sp [iso] , respectively) in hydrous olivine under asthenospheric conditions are given as The bulk conductivity of anisotropic and isotropic models are The fitting parameters of σ ionic,0 , E ionic , V ionic , σ sp,0 , E sp , and V sp are listed in  (Constable et al., 1992) is more than 1 order of magnitude lower than our experimental data with 20 wt. ppm H 2 O (Figure 8), the contribution of σ anhydrous ð Þ ionic hkl ½ is considered negligible in this study, as expressed in equation 4. The transition of ionic conduction from an anhydrous to hydrous mechanism should occur at C H2O much lower than 20 wt. ppm. The r is assumed to be 1.3 ± 0.2 for different crystallographic orientations and independent of temperature and pressure, whereas E ionic and V ionic are assumed to be independent from C H2O (Table 3). These assumptions are expected to have little effect on the simulated results because our conductivity data were obtained under asthenospheric P-T conditions, and the range of C H2O extrapolation is small owing to the relatively low (30-60 wt. ppm) H 2 O content of olivine in the depleted MORB mantle (Demouchy & Bolfan-Casanova, 2016;Katsura et al., 2017).
The simulated results of σ ionic for isotropic and anisotropic models under the topmost asthenospheric conditions (3 GPa) are plotted in Figures 9a and 9b, whereas the bulk conductivity, which is the summation of different mechanisms, are plotted in Figure 9c. The σ ionic in this study shows a comparable

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temperature dependence with the previously reported ionic conductivity data (e.g., Constable et al., 1992), indicating the same conduction mechanisms (Figures 9a and 9b). After adjusting to a C H2O of 1 wt. ppm, the isotropic σ ionic from this study is comparable with σ ionic reported in dry olivine at ambient pressure (Constable et al., 1992 (Constable et al., 1992) although the absolute values differ by more than 1 order of magnitude due to the H 2 O enhancement.
The isotropic σ ionic from our model at 10 GPa is within experimental uncertainty consistent with that reported by Yoshino et al. (2009) under similar conditions due to the negative pressure dependence (Figure 9a). The 3 GPa data are comparable with that estimated from hydrogen diffusivity as well by assuming a linear relationship between C H2O and hydrogen-related σ (Du Frane & Tyburczy, 2012;Novella et al., 2017), which is not surprising because hydrogen diffusion is the migration of protons into/out of cation sites and is therefore also controlled by Mg defects. Figure 9. Ionic conductivity in olivine with 60 wt. ppm H 2 O is higher than dry olivine conductivity and higher than small polaron and proton conductions as well.
The thick lines are simulations from this study based on equations 4-9 with all parameters given in Table 3 Constable et al. (1992). G14: . C06: Constable (2006). X98: Xu et al. (1998). Fei18: Fei et al. (2018a). Fei et al. (2018a) is based on conductivity data reported by Constable et al. (1992) with pressure and C H2O corrections using the activation energy and C H2O exponent for Mg diffusivity by assuming proportionality of C H2O 1.3 and σ ionic at C H2O ≥ 1 wt. ppm. Although a correction factor of 3 in equation 1) was not applied in Fei et al. (2018a), the absolute values of C H2O were not used for the simulation and therefore do not affect the σ ionic estimation.

Journal of Geophysical Research: Solid Earth
Owing to the H 2 O-enhancement of σ ionic , the bulk conductivity obtained in this study with 60 wt. ppm H 2 O is clearly higher than values reported under dry conditions (Constable, 2006;Constable et al., 1992;Xu et al., 1998) and comparable with that estimated from Mg diffusion by assuming an C H2O exponent of 1.3 (Fei et al., 2018a) (Figure 9c). However, although the absolute values of our bulk conductivity data are identical to Gardés et al.'s (2014) model at 1600-1700 K, the temperature dependences are completely different, indicating the dominance of different mechanisms. This inconsistency is likely caused by an overestimation of proton conductivity in previous studies (see discussion in the supporting information).
The comparison of σ ionic and σ sp (and proton conduction) shows a mechanism transition from small polaron to ionic conduction at 1600~1650 K (Figures 9a and 9b). This transition temperature, although pressure-and C H2O -dependent, is much lower than the previously estimated values (>1750 K, Yoshino et al., 2009) and comparable with the asthenospheric geotherm (Katsura et al., 2017;Turcotte & Schubert, 2002). Therefore, by H 2 O-enhancement, σ ionic of olivine is nonnegligible under asthenospheric conditions. It may contribute significantly, or dominate the bulk conductivity of olivine in the asthenosphere especially in the shallow region beneath young plates where the pressure is relatively low and temperature is relatively high.
Based on our model, the bulk conductivity of olivine with 60 wt. ppm H 2 O is >10 −2 S/m when the temperature is above 1600 K (Figure 9c), which is comparable with the high conductivity observed at the topmost asthenosphere beneath young plates (Baba et al., 2006). On the other hand, the asthenosphere is associated with low seismic velocity, which cannot be attributed to olivine hydrated with only tens of wt. ppm H 2 O (Cline et al., 2018). By considering the fact that the high conductivity is observed mostly beneath young plates (summarized in Katsura et al., 2017) whereas the low seismic velocity zone is detected nearly globally, the origins of these geophysical features could be different, although they occur at similar depths.