Tracking slab surface temperatures with electrical conductivity of glaucophane

Slab surface temperature is one of the key parameters that incur first-order changes in subduction dynamics. However, the current thermal models are based on empirical thermal parameters and do not accurately capture the complex pressure–temperature paths of the subducting slab, prompting significant uncertainties on slab temperature estimations. In this study, we investigate whether the dehydration-melting of glaucophane can be used to benchmark the temperature in the slab. We observe that dehydration and melting of glaucophane occur at relatively low temperatures compared to the principal hydrous phases in the slab and produce highly conductive Na-rich melt. The electrical properties of glaucophane and its dehydration products are notably different from the hydrous minerals and silicate melts. Hence, we conclude that the thermodynamic instability of glaucophane in the slab provides a unique petrological criterion for tracking temperature in the present-day subduction systems through magnetotelluric profiles.

(> 9 GPa) and high temperature up to 1300 K means that the lawsonite potentially remains stable to depths of more than 200 km 22,23 . In contrast, glaucophane is thermodynamically stable at lower P-T conditions and its dehydration marks the onset of the transition of hydrous oceanic crust to the dense anhydrous eclogite 10 . Notably, it has been observed that amphibole stability can be enhanced beyond 5 GPa by the substitution of fluorine for amphibole hydroxyl sites. Hence, depending on F contents, the blueschist-eclogite transition may shift to depths beyond 75 km 28,29 .
It is well established that the electrical conductivity of fluids or melts can be enhanced by the highly mobile Na + as a charge carrier 30 . Because glaucophane is one of the principal hosts of Na in subducting slabs, we focus on understanding whether the dehydration-melting of glaucophane can generate distinct geophysically detectable electrical anomalies, standing out from the hydrous minerals, fluid, and melts in subduction zones. We investigate the electrical conductivity of glaucophane in situ under high pressure and high temperature up to 6 GPa and 1258 K. We show that the dehydration melting of glaucophane produces highly conductive Na-rich fluids and melt that can serve as geophysical indicators for accurately benchmarking the slab temperatures.

Results
The electrical conductivity of glaucophane increases discontinuously with increasing temperature (Fig. 1). At 1.5 GPa, two electrical conductivity discontinuities define three distinct conduction mechanisms in glaucophane corresponding to (i) the solid-state sample prior to dehydration (0.92 ± 0.08 eV), (ii) sample and aqueous fluid following dehydration (0.87 ± 0.08 eV), and (iii) partially molten sample (0.33 ± 0.16 eV) (Fig. 1a). The first discontinuous increase of conductivity to 0.1 S/m occurs at 830 K, which may correspond to glaucophane dehydration and the release of aqueous fluids. The second increase is observed at around 1000 K, possibly due to the melting of glaucophane and the production of a Na-rich melt. The sample exhibits electrical conductivity of 97 S/m at 1258 K. The electrical conductivity of glaucophane at 6 GPa exhibits a sharp increase of conductivity at around 895 K, which corresponds to the breakdown of glaucophane and the release of aqueous fluids in the sample. At 950 K, the sample exhibits electrical conductivity of 1 S/m (Fig. 1b). The impedance spectra of the samples display spectral features that are characteristic of dehydration and melting of a hydrous mineral 7,26 (Fig. 2).
The observed conductivity variations correspond to textural and chemical changes of the sample, which confirms the dehydration and melting of glaucophane (Fig. 3). The chemical analyses of the sample after the   Figure 1. The electrical conductivity of glaucophane as a function of reciprocal temperature. (a) At 1.5 GPa, electrical conductivity is characterized by three stages, separated by discontinuous increases of conductivity at ~ 825 K and 1000 K. (b) Electrical conductivity of glaucophane at 6 GPa. The dehydration of the sample occurs at 895 K. The activation enthalpies corresponding to the dominant conduction mechanism at each stage are shown next to the fitting lines. The experimental uncertainty can arise from the estimation of temperature, geometrical parameters. Fitting errors are estimated to be less than 5% and are smaller than the symbol size.    Supplementary Table S1. Previous studies find that the dehydration of glaucophane at high temperature and high pressure follows the reactions: (1) glaucophane = jadeite + enstatite + nyböite + H 2 O 31 or (2) glaucophane = jadeite + enstatite + quartz + H 2 O 32 . However, the chemical analyses of our sample after the electrical conductivity measurements at 1.5 GPa indicate enstatite, olivine, plagioclase, and melt ( Fig. 3a). This disparity can be explained by the dissolution of quartz in the melt and olivine crystallization in consequence via reaction, enstatite = olivine + SiO 2 (in melt) 33 . The plagioclase found in our sample appears to crystallize from the melt during the cooling of the sample. To preserve the mineral assemblages after the dehydration, in our experiment at 6 GPa, we limit the maximum temperature to 950 K. The breakdown of starting glaucophane sample results in jadeite, enstatite, coesite, and secondary amphiboles (cummingtonite and barroisite) (Supplementary Table S2). Omphacite has been observed surrounding jadeite grains (Fig. 3b).

Discussion
The electrical conductivity of glaucophane before the dehydration is slightly lower than the electrical conductivity of naturally occurring Cl-and/or F-bearing amphiboles, and broadly comparable to the Na-rich plagioclase (albite) [34][35][36] . This signifies that crystal structure-bound Na + may not be as mobile as the defect-bound volatiles or halogens. Na occupies both the alkali (A) and (B) sites in the crystal structure of amphiboles. Previous studies have shown that the preferential incorporation of Na in the large A sites may enhance the electrical conduction in amphiboles 37 . It appears that Na in glaucophane preferentially occupies the B-sites (0.02 mols in the A-site, 1.91 mols in the B-site), thus exerting negligible influence on the conductivity before dehydration. The fluid released during the dehydration of glaucophane shows comparable electrical conductivity to that of aqueous fluids observed under subduction zone pressure and temperature conditions 26,[38][39][40][41] (Fig. 4). While Na + can be mobile in fluids, the compatible nature of Na to glaucophane may restrict the partition of Na to the fluid phase during the dehydration 42 , thus limiting the role of Na + as a charge carrier in the fluid phase. Compared to the electrical conductivity of the fluid at 1.5 GPa, the increase of electrical conductivity associated with dehydration of glaucophane at 6 GPa appears to be larger (Fig. 1). We attribute this observation to a higher fluid fraction in the sample or the higher ion concentrations, such as ionization of H 2 O in the supercritical fluid at the elevated pressure 26 .
Na appears to have a profound effect on the electrical conductivity of silicate melts. The melting of glaucophane increases the conductivity by a factor of ~ 100 compared to the conductivity of the aqueous fluid at 1.5 GPa (Fig. 1a). Our observation suggests that the electrical conduction in silicate melt, produced after dehydration of amphibole, is largely controlled by the mobility of Na + ions (Fig. 5). This observation agrees well with previous experimental results, which identified Na + as the principal charge carrier in basaltic and albite melts 30 . Compared to Na + , the effect of other major cations, such as Ca +2 , Al +3 , and Fe +2/+3 , on the electrical conductivity is found to be negligible 7 . It has also been shown that the presence of H 2 O promotes the mobility of Na + in silicate melts 30 . The Na-rich hydrous melt produced by the melting of glaucophane exhibits an electrical conductivity of 97 S/m at 1250 K. Extrapolation to high temperatures shows that the Na-rich melts occurring in the subduction zone settings are significantly more conductive than the silicate melts observed in other geological settings [43][44][45] (Fig. 4). In contrast, the hydrous silicate melts produced by melting of tremolite, actinolite, ferri-kaersutite, and hornblende amphibole compositions show a convergence of electrical conductivities around 1 S/m above 1250 K (Fig. 5). These values closely resemble the electrical conductivity values obtained for hydrous basalts that are commonly found in volcanic-arc settings 43,46 (Fig. 4). The stability of amphibole could be extended to a depth beyond 75 km by substituting OH with F in the amphibole crystal structure 28,29 . In our 6 GPa experiment, glaucophane goes through a dehydration reaction forming jadeite + enstatite + quartz. We also observe the formation of secondary F-bearing amphibole (Supplementary Table S2) attesting to the stability of the amphibole phase at this pressure condition. The crystallization of F-bearing amphiboles has also been demonstrated by other amphibole dehydration experiments conducted under subduction zone pressure and temperature conditions 7 .
Electrical conductivity of glaucophane as a geothermometer. The dehydration temperature we observed for glaucophane using the in situ electrical conductivity measurements appears to occur at lower temperatures compared to the decomposition of OH − and F − bearing amphiboles 28,29 (Fig. 6). We attribute this decrease in dehydration and melting temperature to the presence of Na. Albite, another principal host of Na in the slab, transforms to jadeite + quartz through a fluid absent reaction at high pressure and temperature 48,49 , thus, may not influence the electrical conductivity measurements. The low dehydration and melting temperature associated with the high electrical conductivity makes glaucophane an ideal indicator-mineral for tracking the slab surface temperature in subduction zones (Fig. 7). As a case study, we investigated the 2D magnetotelluric (MT) profile at the Sodo ridge, where the old and cold Pacific plate subducts beneath North-East Japan 50,51 . The MT profile of the Sodo ridge provides a case for the extreme scenario found in subduction systems, where the high electrical anomaly appears to occur at depths greater than 150 km. The conductivity-depth profile at the Sodo ridge displays an increase of electrical conductivity from 0.01 to 0.1 S/m at the slab surface at 150-170 km depths, which is the characteristic electrical conductivity for aqueous fluids 8,26 . This apparent dehydration event is followed by a further increase of conductivity to more than 1 S/m at the slab surface at a depth of 185 km 50 . Given that glaucophane breaks down at relatively low temperatures, and any other types of melting in the slab cannot occur before the melting of glaucophane, we consider that the extremely high conductivity displayed at 185 km depth may be related to the melting of F-bearing glaucophane and the subsequent release of Na-rich melt in the slab.
Assuming that incorporation of F stabilizes amphiboles below depths of 75 km and the high conductivity anomaly is caused by the melting of F-bearing glaucophane; we can estimate the depth where the blueschisteclogite transition happens in the slab. In the case of Sodo ridge, the blueschist-eclogite transition can be fixed at a depth of 160 km (~ 5.5 GPa) and a temperature of ~ 887 K (Fig. 8). By setting the solidus of glaucophane parallel to the dehydration curve, we could estimate the onset of melting at 185 km depth (~ 6.5 GPa) and 1070 K. Our calculations suggest a thermal gradient of 7.3 K/km along the slab surface for the North-East Japan subduction zone. We conclude that the precise temperature for slab surfaces can be derived from the phase relations of glaucophane. These estimates can benchmark the slab-surface temperatures and provide a temperature-fixed point for thermal models of subduction zones. Na-effect Figure 6. The stability of glaucophane at high-pressure and high-temperature. The solid red line indicates a linear fit through experimental data points obtained at 1.5 and 6 GPa. The red dashed line is drawn parallel to the dehydration curve through the melting temperature obtained at 1.5 GPa. The dark blue, light blue, and green lines are the dehydration and melting temperatures observed for F and Na-free amphibole 29 , Na-free amphibole with 0.43 mol F replacing (OH − ) 28 , and Na-free amphibole with 1 mol F 29 at the pressure range from 3.0 to 5.5 GPa, respectively. am amphibole; gln glaucophane.  Figure S1). Cylindrical sample specimens for electrical conductivity measurements were synthesized by hot pressing of amphibole power in rhenium (Re) capsule at 1.5 GPa and 700 K for 1 h. Pre-sintered cylindrical samples were placed in a polycrystalline MgO capsule, which electrically insulated the sample from the furnace during the measurements. Two Ni disks placed at the top and bottom of the sample served as electrodes for the electrical conductivity measurements. These Ni disks also served as an oxygen buffer, controlling the oxygen fugacity in the sample close to the Ni-NiO buffer. A W 95 Re 5 -W 74 Re 26 thermocouple junction was placed at one side of the sample, which monitored the temperature. One cable formed the thermocouple, and a separate W 95 Re 5 cable was placed at the opposite side of the sample, connected to the impedance spectroscopy for the electrical conductivity measurements. MgO ceramic sleeves insulated the electrode wires from the furnace. All ceramic assembly parts, including the pressure media, were baked at 1273 K for more than 12 h and stored at 400 K in high-vacuum furnaces (< 100 mTorr) before assembling. This step reduced the exposure of assembly components to atmospheric moisture and other impurities.
The electrical conductivity of glaucophane samples was determined at pressures of 1.5 and 6 GPa, based on the impedance spectroscopy method with a Modulab MTS Impedance gain-phase analyzer in the frequency range of 10 6 -10 1 Hz. Sample resistance was measured in 30-50 K temperature steps. The maximum temperatures attained were 1258 K at 1.5 GPa and 950 K at 6 GPa.
Polycrystalline samples can be characterized by a combination of resistor-capacitor (R-C) or resistor-constant phase element (R-CPE) circuits, and the resistance can be obtained by fitting the impedance spectra to appropriate equivalent circuits. Once the sample resistance has been determined, conductivity can be calculated using the sample diameter and length measured after each experiment, assuming the sample geometry remained unchanged during the experiment. The activation enthalpy ( H ) of each conduction mechanism can be obtained by fitting the data to the Arrhenius equation, σ = σ 0 exp(−�H|RT) , where σ is the electrical conductivity (S/m), T is the absolute temperature, σ 0 is the pre-exponential factor (S/m), and R is the gas constant (J/K/mol).
After an electrical conductivity experiment, cross-sections of the experimental run products were investigated using an electron probe micro analyzer and energy dispersive X-ray spectroscopy (EDS) chemical mapping with a JEOL JSM-5910LV scanning electron microscope, to identify mineral assemblages and the dehydration reaction products. The compositions of the fluid and melt phases were determined by mass-balance calculations based on the mineral proportions and their chemical compositions of recovered samples after the dehydration/ melting events 7 .

Data availability
All data generated or analyzed during this study are included in this article. The raw electrical conductivity data are available from the corresponding author on reasonable request.  Figure 8. Application of the glaucophane geothermometer to N-E Japan subduction zone. Two temperaturefixed points for the N-E Japan subduction slab are determined using the electrical conductivity model discussed in Fig. 6. The electrical conductivity structure of the subduction system is taken from Toh et al. 2006 50 . The green, blue, and red zones were determined based on the electrical conductivity of the wedge mantle adjacent to the slab surface. The areas marked by dashedlines indicate high conductivity regions in the mantle wedge.