Some New Progress in the Experimental Measurements on Electrical Property of Main Minerals in the Upper Mantle at High Temperatures and High Pressures

Abstract

In this chapter, we present the recent progress in the experimental studies of the electrical conductivity of dominant nominally anhydrous minerals in the upper mantle of the deep Earth interior, namely, olivine, pyroxene, and garnet. The influences from pressure, oxygen partial pressure, and anisotropic orientation on hydrous and anhydrous electrical conductivities of minerals and rocks have been already explored detailedly. There are two main electric conduction mechanisms in Fe-bearing mantle minerals, for example, small proton and proton hopping conditions, which are well distinguished by the magnitude of activation enthalpy at high temperature and high pressure. Likewise, the conduction mechanisms are efficiently characterized by these obtained positive and negative effects from the oxygen fugacity on electrical conductivities of corresponding dry and wet Fe-bearing silicate minerals at the regions of the upper mantle under conditions of different oxygen partial pressures. On the base of high-pressure laboratory-based conductivity measurements for these nominally anhydrous minerals (e.g., olivine, pyroxene, and garnet), the water content will be estimated within the depth range of the upper mantle. In comprehensive considerations of filed geophysical magnetotelluric results, the electrical conductivity measurements of dominant upper-mantle minerals can thoroughly disclose the distribution, storage state, and migration conduction in the deep Earth interior.

1. Introduction

Global and regional field magnetotelluric (MT) and geomagnetic deep sounding (GDS) results revealed that there existed many high electrical conductivity layers (HCL) in various geotectonic units in the deep Earth’s interior (the magnitude of electrical conductivity range is 10⁻²–10⁰ S/m) [1, 2]. To investigate the cause of all of these available high conductivity layers, it is crucial to measure the electric transport properties of minerals and rocks at certain high-temperature and high-pressure conditions. As one of the crucial physical parameters of minerals, electrical conductivity (EC) is highly sensitive to temperature, pressure, and depth, which is strongly dependent on the physical and chemical environments in the deep Earth and other planetary interiors [3, 4, 5]. In particular, EC is dependent on several factors such as diffusion coefficients of alkali ion [6, 7], trace elemental contents [8], the spin transition of the electron [9, 10], anisotropic crystal orientation [11, 12, 13, 14, 15], contents of water and other volatile elements [16, 17, 18], partial melting [19, 20, 21], dehydration (or dehydrogenation) effects of minerals [22, 23, 24], impurity of high-conductivity phase [25, 26], salinity-bearing (or water-bearing) fluids [27, 28], and structural phase transformation (amorphization or metallization) [29, 30, 31, 32, 33, 34].

In the recent 20 years, with the development of measuring techniques and experimental methods of electrical conductivity in the AC electrical impedance spectroscopy (EIS) technique and multi-anvil high-pressure apparatus, there is a large number of research results on the electrical properties of minerals and rocks to be reported in the upper-mantle and mantle transition zone. Some international famous research administrations have successfully set up the experimental platform and measurement system of minerals and rocks at high temperatures and high pressures, such as the Key Laboratory of High-temperature and High-pressure Study of the Earth’s Interior (HTHPSEI), Institute of Geochemistry, Chinese Academy of Sciences, the People’s Republic of China; the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States; the Laboratoire Magmas et Volcans, Université Clermont Auvergne, French National Centre for Scientific Research, France; the Scripps Institution of Oceanography, University of California San Diego, United States; University of Bayreuth, Germany; and Okayama University, Japan.

As we know, previously available classic “Pyrolite” mineralogical models have already confirmed that the nominally anhydrous minerals (NAMs, e.g., olivine, pyroxene, and garnet) are dominant mineralogical composition in the upper mantle of the deep Earth interior. In light of the FTIR result, these NAMs can contain a certain amount of structural water rather than absolutely “dry.” Whereas, it is general that the trace structural water in NAMs stably exists as a form of hydroxyl point defect of the crystalline site in these minerals. Due to the presence of trace structural water in NAMs, many physical and chemical properties of NAMs have been thoroughly changed accordingly, such as electrical conductivity [3, 8, 13, 14, 15, 16, 17, 18, 35], diffusivity [36, 37], plastic deformation [38, 39], seismic wave attenuation [40, 41], grain growth [42, 43], and kinetic recrystallization [44, 45]. In the world, by virtue of the theoretical calculations of Nernst-Einstein equation between the electrical conductivity and coefficient in mineral, Professor Shun-ichiro Karato from the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States firstly brought forward the viewpoint that the trace structural water in hydrous olivine can enhance several orders of magnitude in the EC of upper-mantle mineral, which can be used to reasonably explain the observed high conductivity anomaly in the region of asthenosphere [46]. In the following 20 years, as a research hotpoint in the field of solid Earth science, a large amount of research work of electrical conductivity of minerals and rocks from the laboratory high-pressure experiments and theoretical calculations investigated have been conducted to focus on this hypothesis of water for the NAMS in the upper-mantle zone (olivine: [8, 13, 14, 15, 47, 48, 49, 50], pyroxene: [51], and garnet [52, 53, 54]). In the year 1998, it is first that Xu Yousheng from the Bayerisches Geoinstitut, University of Bayreuth, Germany fetched in AC electrical impedance spectroscopy (EIS) technique and applied it to report a series of electrical conductivity of minerals, such as olivine, orthopyroxene, and garnet of the upper mantle; wadsleyite of mantle transition zone; as well as the silicate perovskite of the lower mantle under conditions of high temperatures and high pressures in the multi-anvil high-pressure apparatus [55, 56, 57, 58, 59, 60]. Generally, to explore the effect of water on the electrical conductivity, we need to obtain a series of starting materials of hydrous either hot-pressure sintering synthetic or natural hydrous samples. Then, at a fixed temperature and pressure condition, we can measure the electrical conductivity of hydrous minerals. Further, the functional relationship between the EC and water content can be established at HP and HT conditions, thereby providing constraints of the water content in the deep Earth’s and planetary interiors.

In this chapter, we reviewed some recent progress in the electrical conductivity of the main NAMs in the region of the upper mantle, that is, olivine, pyroxene, and garnet at conditions of high temperatures and high pressures. Then, some experimental methods, measurement techniques, and electrical transport conductions on the electrical conductivity of minerals are summarized in the multi-anvil high-pressure apparatus. The newest progress in the recently reported conductivity measurements is outlined in detail. Finally, some comprehensive remarks on the mineral electrical conductivity are discussed.

2. Electrical conductivity of upper-mantle minerals

The electrochemical AC impedance spectroscopy is the most efficient method to measure the electrical conductivity of minerals and rocks at HT and/or HP conditions [61, 62, 63, 64]. The AC signal voltage and scanning frequency need to be designated before the sample resistance is measured. As usual, for a special mineral single specimen, the electrochemical AC impedance spectroscopy of samples consists of grain boundary impedance arc, and as well as the interface impedance between sample and electrode. However, for a special polycrystalline aggregate or rock, the electrochemical AC impedance spectroscopy of samples consists of grain boundary impedance arc, grain boundary impedance, and the interface impedance between sample and electrode. For each individual complex impedance spectroscopy, there are four parameters to be obtained at the same time, for example, real part, imaginary part, magnitude, and phase angle at the same time. The relation can be expressed as,

$${\mathrm{Z}}_{\mathrm{r}}=\mid \mathrm{Z}\mid cos\phi$$E1

$${\mathrm{Z}}_{\mathrm{i}}=\mid \mathrm{Z}\mid sin\phi$$E2

Here, Z_r stands for the real part of complex impedance spectroscopy, Z_i stands for the imaginary part of complex impedance spectroscopy, |Z| stands for the magnitude of complex impedance spectroscopy, and φ stands for the phase angle of complex impedance spectroscopy. Representative complex impedance spectra for natural eclogite from the Dabie-Sulu ultrahigh-pressure metamorphic belt of eastern China are shown in Figure 1.

Figure 1.

Representative complex impedance spectra for natural eclogite from Dabie-Sulu ultrahigh-pressure metamorphic belt of eastern China at conditions of 3.0 GPa, 873 K–1173 K and frequency range of 10⁻¹–10⁶ Hz (reproduced with permission from Dai et al., Geochem. Geophys. Geosyst.; published by American Geophysical Union, 2016 [4]).

Detailed description of measurement theory and experimental method of impedance spectroscopy are given in our previous review chapter [9]. The equivalent electric circuit was selected to fit the impedance spectroscopy of the sample, which is composed of some fundamental electronic elements (e.g., resistor, capacitor, inductor, constant phase element (CPE), Gerischer element, Warburg element, etc.) [65, 66, 67, 68]. After that, the electrical conductivity of the sample was obtained by the sample resistance, the calculating formula is expressed as,

$$\sigma =\frac{1}{\rho }=\frac{L}{\left(\mathrm{R}\times S\right)}$$E3

In here, σ stands for the electrical conductivity (S/m), ρ stands for the electrical resistivity (m/S), L stands for the sample height (m), and S stands for the cross-sectional area (m²). At a given pressure condition, it is usual that the electrical conductivity of sample and temperature satisfies with an Arrhenius relation, namely,

$$\sigma ={\sigma }_{0}exp\left(-\frac{\mathrm{\Delta }H}{\mathrm{k}T}\right)$$E4

In here, σ₀ stands for the pre-exponential factor (S/m), ΔH stands for the activation enthalpy (eV), k stands for the Boltzmann constant and T stands for temperature (K).

3. High-pressure apparatuses for conductivity measurements

In the recent several years, many researchers developed the high-pressure electrical property experiments of minerals and rocks by virtue of various high-pressure experimental apparatuses. From lower to higher pressure conditions, some typical high-pressure apparatuses on the laboratory-based electrical conductivity measurements are mainly included autoclave, piston-cylinder, multi-anvil press, and diamond anvil cell. In this counterpart, we focus on two types of multi-anvil apparatuses—(i) YJ-3000 t multi-anvil press is equipped in the Key Laboratory of High-temperature and High-pressure Study of the Earth’s Interior (HTHPSEI), Institute of Geochemistry, Chinese Academy of Sciences, the People’s Republic of China and (ii) Kawai-1000 t multi-anvil Press is equipped in the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States.

3.1 YJ-3000 t multi-anvil press

Early on half a century ago, Xie Hongsen and his coworkers successfully set up one multi-anvil press of the YJ-3000 t in the Key Laboratory of HTHPSEI, Chinese Academy of Sciences, People’s Republic of China. All of these available high-pressure measurement methods including the direct current, single frequency AC, multi-frequency electrical bridge, and electrochemical AC impedance spectroscopy are widely adopted in the past several years. In situ high-pressure EC results on minerals and rocks have been published by many previous researchers using this high-pressure apparatus [69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87]. Dai Lidong and his collaborator [88, 89, 90, 91] have developed the HP-HT electrical conductivity platform of minerals and rocks in HTHPSEI, as shown in Figure 2. It is composed of three main counterpart pieces of equipment, namely, (a) the pressure-generated apparatus of the YJ-3000 t multi-anvil press; (b) the Solartron-1260 and Solarton-1296 interface impedance spectroscopy analyzer operating in the two-electrodes configuration for complex EIS measurements in the frequency range 10⁻⁴ Hz–10⁷ Hz; and (c) the Vertex-70v vacuum Fourier-transform infrared spectroscopy (FT-IR) analyzer to check the water content of the sample. The influential ingredients include temperature, pressure, frequency, oxygen fugacity, water content, iron content, crystallographic anisotropy, grain boundary state, the content of alkali metallic elements, etc. on the electrical characterizations of minerals and rocks have already been explored using this high-pressure conductivity measurement platform in details.

Figure 2.

High-pressure conductivity measurement platform and experimental setup in the YJ-3000 t multi-anvil press is equipped in the Key Laboratory of High-temperature and High-pressure Study of the Earth’s interior (HTHPSEI), Institute of Geochemistry, Chinese Academy of Sciences, the People’s Republic of China. (a) The YJ-3000 t multi-anvil apparatus; (b) the Solartron-1260 and Solarton-1296 interface impedance spectroscopy analyzer operating in the two-electrodes configuration for complex EIS measurements in the frequency range 10⁻⁴ Hz–10⁷ Hz; (c) the vertex-70v vacuum Fourier-transform infrared spectroscopy (FT-IR) analyzer to check the water content of sample.

In addition to the in situ EC measurements, it has recently become possible to measure some other high pressure-dependent physical properties of minerals and rocks by using the YJ-3000 t multi-anvil press, such as the ultrasonic elastic wave velocity, thermal conductivity, thermal diffusivity, and kinetics of grain growth. [92, 93, 94, 95, 96, 97, 98, 99, 100]. Except for wide application in the field of high-pressure mineral physics, the YJ-3000 t multi-anvil press is one of the indispensable tools in some other aspects of high-pressure material science and high-pressure condensed physics.

3.2 Kawai-1000 t multi-anvil press

A representative high-pressure EC experimental assemblage in the Kawai-1000 t multi-anvil press installed in the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States [3, 8, 13, 14, 47, 48, 49, 51, 52] is displayed in Figure 3. Eight cubic WC anvils (it is corresponding to each edge length 26 × 26 × 26 mm³) with the 3–18 mm truncation was adopted to provide a high-temperature and high-pressure quasi-hydrostatic environment. Pressure calibrations were performed by pressure-induced structural phase transformations of some representative semiconducting materials (e.g., pure metallic bismuth, ZnTe, GaP, GaAs, etc.) at atmospheric pressure, the structural phase transformation between α-quartz, β-quartz, coesite, and stishovite, and as well as phase transitions between olivine, wadsleyite, ringwoodite, and bridgmanite. The pressure-transmitting medium is made of pure or Cr₂O₃-doped or Co-doped octahedral magnesium oxide. Two symmetric metallic discs are employed as electrodes of electrical conductivity measurement. A layer of metallic foil was installed to remove the signal disturbance of the measurement electric circuit and environmental noise. As usual, the ordinary heater, such as stainless steel slice, graphite, tantalum slice, and rhenium slice, is reasonably selected on the base of target temperature during a given electrical conductivity measurement. The temperature in the sample chamber is precisely measured by the B-type Pt_70%Rh_30%-Pt_94%Rh_6% thermocouple or K-type thermocouple. The experimental errors of pressure and temperature are not more than 0.5 GPa and 10 K, respectively.

Figure 3.

Sample assembly for the electrical conductivity measurement of minerals and rocks in the Kawai-1000 t multi-anvil press from Shun-ichiro Karato’s group from the Karato high-pressure laboratory, Department of Earth and Planetary Sciences, Yale University, United States: (1) metallic Mo ring; (2) MgO octahedral pressure medium with its edge length of 14 mm; (3) sample; (4) zirconia; (5) Al₂O₃ cement; (6) electric grounding; (7) lead wire of metallic electrode and Al₂O₃ insulation tube; (8) insulation tube made of four hole alumina; (9) heater of lanthanum chromite; (10) two symmetric buffer electrodes; (11) MgO insulation tube; (12) metallic shielding case made of Ni, Fe, Re or Mo foil; and (13) thermocouple and Al₂O₃ insulation tube.

4. Electrical conductivity of major minerals in the upper mantle

As one crucial cycling of deep Earth interior at the depth range from 80 km to 410 km, the upper mantle mainly contains three main dominant rock-forming minerals, that is olivine, pyroxene, and garnet. Previous available high-pressure experimental results have already confirmed that the electrical conductivity of upper-mantle minerals is highly sensitive to all of these influence ingredients, such as high temperature, high pressure, oxygen partial pressure, trace structural water, iron-bearing content, grain boundary state, graphite layer of grain boundary, magnetite-bearing impurity, titanium-bearing content, chromite-bearing content, sulfur-bearing content, the orientation of crystallographic axis, and partial melting, which is most concerned in the recent several years. Because the crucial effect of water content on EC of minerals and rocks in these representative regions of upper-mantle and mantle transition was neglected by other research groups, in the following paragraph, we mainly pay attention to some related results from Dai Lidong’s group from the high-pressure conductivity results from the Key Laboratory of High-temperature and High-pressure Study of the Earth’s Interior (HTHPSEI), Institute of Geochemistry, Chinese Academy of Sciences, the People’s Republic of China, and as well as Shun-ichiro Karato’s group from the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States.

4.1 Electrical conductivity of olivine

As a major rock-forming silicate mineral and nominally anhydrous mineral, olivine occupies ∼60% of the volume proportion of upper-mantle minerals. Therefore, most of the previously available profile between the electrical conductivity and depth was successfully constructed by the laboratory-based electrical conductivity of olivine data at high-temperature and high-pressure conditions. Electrical conductivities on those of natural olivine single crystal, polycrystalline olivine aggregates, and hot-pressed sintered synthetic olivine have already been performed, especially considering the effects of pressure, oxygen partial pressure, iron-bearing content, and orientation of crystallographic axis on the EC of hydrous olivine.

In an early 1990 year, Roberts and Tyburczy [62] reported the room-pressure electrical conductivity of polycrystalline olivine aggregates using impedance electrochemical impedance spectroscopy (EIS) method under conditions of frequency of 10⁻⁴–10⁴ Hz and 1073 K–1673 K. They discussed the influence of anisotropic thermal expansion-induced porosity and microfracture on the high-temperature electrical conductivity of polycrystalline olivine aggregates. At their measured olivine aggregates with the volume percentage of 2–8% inter- and intra-granular porosity and microfracturing, its effect becomes very feeble for the total electrical conductivity of olivine. In light of their findings, subsequent investigations on the electrical properties of upper-mantle polycrystalline samples do not need to consider the effects of porosity and microcracking. The previous investigation of pressure influence on the EC of olivine single crystal was reported by Xu et al. [55] using the EIS method in the Kawai-1000 t multi-anvil press. Detailed experimental conditions are controlled by pressures of 4–10 GPa, temperatures of 1273–1673 K, frequencies of 10⁻¹–10⁶ Hz, and as well as the solid oxygen buffer of molybdenum and molybdenum dioxide. The acquired pre-exponential factor (σ₀) of ∼200 S/m, the activation energy (ΔΕ) of 144.7 kJ/mol and the activation volume (ΔV) of 0.6 cm³/mole are well characterized by fitting Arrhenius relation at upper-mantle temperatures and pressures [60]. A negative pressure-dependent EC of olivine single crystal was also observed, and the electrical conduction mechanism of small polaron hopping between the ferrous and ferric irons of crystalline position was proposed. However, unfortunately, in all of those published results on the EC of olivine and its correspondent high-pressure polymorph in the regions of the upper mantle, mantle transition zone, and lower mantle, Xu et al., did not provide any available information on the water content of the selected experimental samples [55, 56, 57, 58, 59, 60].

The first research work for the effect of water on the EC of upper-mantle olivine was found by Karato [46] on the basis of the theoretical calculating of Nernst-Einstein equation, who brought forward that the trace structural water of nominally hydrous minerals plays a vital role in the EC of olivine in the upper mantle. To check this theoretical calculating hypothesis, the EC of hydrous synthetic polycrystalline olivine compacts was firstly conducted by Wang et al. [17] in Shun-ichiro Karato’s group from the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, the United States at conditions of a pressure of 4.0 GPa, temperature ranges from 873 K to 1273 K and water content ranges from 100 ppm wt% to 800 ppm wt%, using the Kawai-1000 t multi-anvil press and the Solarton-1260 EIS analyzer (Schlumberger, Houston, TX, USA). It is the first time that the ionized reaction model in hydrous synthetic polycrystalline olivine compacts is originated from the free proton-dominated conduction mechanism, as follows,

$${\left(2\mathrm{H}\right)}_M^{\times }={\mathrm{H}}_M^{\prime }+{\mathrm{H}}^{•}$$E5

where, in the Kröger-Vink notation, ${\left(2\mathrm{H}\right)}_M^{\times }$ represents two hydrogens of crystalline lattice in the position of metallic iron or magnesium, ${\mathrm{H}}_M^{\prime }$ represents the hydrogen vacancy in the position of metallic iron or magnesium, and ${\mathrm{H}}^{•}$ represents the free proton.

Furthermore, a series of hydrous electrical conductivity measurements on single-crystal olivine with different crystallographic orientations, synthetic polycrystalline olivine compacts, and synthetic hot-pressed polycrystalline olivine aggregates have been extensively studied by virtue of Kawai-1000 t multi-anvil press and the EIS methods in recent several years [8, 13, 14, 47, 48, 49]. Figure 4 shows the influences of temperature, pressure, oxygen fugacity, iron-bearing content and water-bearing content on hydrous synthetic polycrystalline olivine compacts, and hydrous hot-pressed synthetic polycrystalline olivine aggregates at the temperature ranges from 873 K to 1273 K and pressure ranges from 4.0 GPa to 10.0 GPa.

Figure 4.

The effects of (a) water content on the EC of X_Fe (Fe/(Fe + Mg)) = 41.2% hydrous hot-pressed synthetic polycrystalline olivine aggregates, (b) pressure on the EC of hydrous synthetic polycrystalline olivine compacts, (c) oxygen fugacity on the EC of hydrous synthetic polycrystalline olivine compacts, and (d) water-bearing content and temperature on the EC of X_Fe (Fe/(Fe + Mg)) = 41.2% hydrous hot-pressed synthetic polycrystalline olivine aggregates at the temperature ranges from 873 K to 1273 K and pressure ranges from 4.0 GPa to 10.0 GPa. Three oxygen buffers including Ni-NiO, Mo-MoO_2, and Re-ReO₂ were selected to oxygen fugacity during the process of high-pressure electrical conductivity measurements (reproduced with permission from Dai and Karato, Phys. Earth Planet. Inter.; published by Elsevier, 2009 [47, 48, 49]).

For hydrous hot-pressed synthetic polycrystalline olivine aggregates with fixed iron-bearing content, X_Fe (= (Fe/(Fe + Mg))) = 41.2% (molar ratio percentage), the electrical conductivity of the sample increases with the rise of water contents from 45 ppm wt% to 620 ppm wt%, and one relatively a fixed activation enthalpy (ΔH = 80 kJ/mole) is observed under conditions of different water contents and temperatures (refer to Figure 4a and d). The activation enthalpy for hydrous hot-pressed synthetic polycrystalline olivine aggregates is lower than that of the ΔH of dry sample (136 kJ/mole) with the fixed iron content [47]. The influence of pressure on the EC of hydrous synthetic polycrystalline olivine compacts at conditions of 873–1273 K and the oxygen buffer of Ni-NiO controlled oxygen fugacity is displayed in Figure 4b. It makes clear that the EC of hydrous synthetic polycrystalline olivine compacts decreases with the pressure increasing from 4.0 GPa to 10.0 GPa, and at the same time, the activation enthalpy and pre-exponential factor of the sample also reduce, accordingly [49]. Figure 4c displays the influence of oxygen fugacity on the EC of hydrous synthetic polycrystalline olivine compacts under conditions of 4.0 GPa, temperatures range from 873 K to 1273 K and fixed water content of 280 ppm wt%. Three oxygen buffers including Ni-NiO, Mo-MoO₂, and Re-ReO₂ were selected to oxygen fugacity during the process of high-pressure electrical conductivity measurements. An available negative electrical conductivity of sample dependence on the oxygen fugacity is observed at each given temperature point at 4.0 GPa, which is attributed to the hydrogen-related defects in hydrous synthetic polycrystalline olivine compacts at conditions of high temperature and high pressure [48]. In all these listed previous cases, the relationship between the logarithm of EC of hydrous (or dry) polycrystalline olivine and the inverse temperature follows a good Arrhenius relation, which is clearly suggesting only one single conduction mechanism controlling the electrical conductivity of hydrous (or dry) sample at high pressure. Furthermore, as pointed out by Dai and Karato [47, 48, 49], the dominant conduction mechanisms in the hydrous and anhydrous polycrystalline olivines are corresponding to the hydrogen-related defects (e.g., free proton) and iron-related defects (e.g., small polaron), respectively.

On the other hand, Dai and Karato [13, 14] also measured the EC of hydrous San Carlos single-crystal olivine along with [001, 010, 100] three different crystallographic orientations at conditions of 573–1373 K and 4.0 GPa, as illustrated in Figure 5 in details. It is clearly observed that at lower temperatures range from 573 K to 900 K, one relatively feeble anisotropic EC in hydrous San Carlos single-crystal olivine with a lower activation enthalpy value (ΔH = 74 kJ/mole) is obtained, which is consistent with previously published EC results [11, 101, 102, 103]. In contrast, at a higher temperature ranges from 900 K to 1373 K, the EC of hydrous San Carlos single-crystal olivine with a higher activation enthalpy value (ΔH = ∼130–150 kJ/mole) shows an obvious anisotropy along with [001, 010, 100] three different crystallographic orientations, which is good agreement with the theoretical calculating electrical conductivity results by virtue of high-temperature H–D inter-diffusion method in hydrous single-crystal olivine along with [001, 010, 100] three dominant crystallographic orientations at conditions [104].

Figure 5.

The influence of anisotropy on the EC of hydrous San Carlos single crystal olivine along [001, 010, 100] three different crystallographic orientations at conditions of 573–1373 K and 4.0 GPa. Three different average schemes of series (${\sigma }_S=\left({\sigma }_{\left[100\right]}+{\sigma }_{\left[010\right]}+{\sigma }_{\left[001\right]}\right)/3$), parallel (${\sigma }_P=3{\left(\frac{1}{{\sigma }_{\left[100\right]}}+\frac{1}{{\sigma }_{\left[010\right]}}+\frac{1}{{\sigma }_{\left[001\right]}}\right)}^{-1}$) and effective medium models ($⟨\sigma ⟩=\left[{\sigma }_S+{\sigma }_P+\sqrt{{\left({\sigma }_S+{\sigma }_P\right)}^2+32{\sigma }_S{\sigma }_P}\right]/8$) were applied. (Reproduced with permission from Dai and Karato, Earth Planet. Sci. Lett; published by Elsevier, 2014 [13]).

In comprehensive considerations of geophysical field observations and geochemical models, the acquired EC results revealed that the high and highly anisotropic EC at the corresponding asthenospheric temperature and pressure conditions is reasonably explained by the high-water content in the region of the asthenosphere (100 ppm). On the other hand, the influence of the interconnected high conductive impurity phases (graphite, magnetite, chromite, sulfide impurity, etc.) and saline fluids (e.g., Ol-NaCl-H₂O, Ol-KCl-H₂O, Ol-CaCl₂-H₂O, etc.) on the EC of olivine has been also explored in details [25, 26, 27, 28, 105, 106, 107].

Except for high-pressure experimental measurements on the electrical conductivity of hydrous olivine, some important progress from the first-principles calculations based on density functional theory (DFT) has already been performed in order to deeply explore the microscopic electrical transport conduction within an atomic scale in the deep Earth interior. Recently, He et al. [15] firstly designed several point defect models (e.g., ${\left(2H\right)}_{\mathit{Mg}}^{\times }$, ${\left(4H\right)}_{\mathit{Si}}^{\times }$, ${\left[{\left(\mathit{Fe}\right)}_{\mathit{Mg}}^{•}{\left(H\right)}_{\mathit{Mg}}^{\prime }\right]}^{\times }$, etc.) by using the ab-initio molecular dynamics (AIMD) method, and applied them to efficiently provide a robust constraint on different contributions of hydrogen and iron within a wide temperature range of 700–2000 K at 5.0 GPa. Some crucial findings were obtained—(i) the mobility of hydrogen associated with Mg vacancy and Fe³⁺ defects change significantly with temperature; (ii) at high temperature, hydrogen is able to escape from the associated defect to form “free proton,” which is able to diffuse freely in olivine lattice shown high proton conductivity; (iii) the diffusion of ionized protons is highly anisotropic with extraordinary high diffusion coefficient along with [100] direction, and (V) hydrogen associated with Si vacancy is stable even at 2000 K. It suggests that different kind of hydrogen defect present different mobility at high temperature with great influence on ionic conductivity of hydrous olivine. AIMD simulations on hydrous wadsleyite and ringwoodite also suggest a higher diffusion rate of hydrogen at Mg vacancy in comparison with hydrogen at Si vacancy [108]. The migration barrier enthalpies of hydrogen along different lattice directions were calculated by using the climbing image nudged elastic band (CINEB) method [109]. The calculation results support the anisotropic diffusion behavior of hydrogen in hydrous olivine. The activation enthalpies for proton migration along with [100] direction in different models is about 180–240 kJ/mole, which is similar to the experimental results obtained by conductivity (140 ± 6 kJ/mole) and diffusion coefficient (229 ± 18 kJ/mole) measurements [13, 37]. Based on all of these obtained calculation results, an ionization-hopping proton conduction mechanism is proposed and the conductivity is calculated, as shown in Figure 6. Obviously, an approximately 80–160 ppm wt water content (correlated with Mg/Fe defects) in olivine is sufficient to produce the high and highly anisotropic conductivity anomaly (∼10⁻¹ S/m). The results are consistent with previous experimental studies and provide a good constraint on the conduction mechanism within an atomic scale for hydrous olivine. It also suggests previous conductivity measurements at relatively low temperatures ignored the contribution of ionized hydrogen, thus the extrapolated data underestimates the proton conduction for the electrical conductivity of hydrous olivine at high temperatures of the asthenosphere.

Figure 6.

The extrapolated proton and total conductivities of Fe-bearing hydrous olivine as the function of inverse temperature and water content compared with experimental results [13, 15, 110]. In here, the vertical axis stands for the logarithic electrical conductivity (the corresponding unit is S/m) and the horizontal axis stands for the inverse temperature (the corresponding unit is Kelvin), respectively. The conductivities with 16, 80, 160, and 800 ppm wt water content associated with $V_{\mathit{Mg}}^{\prime \prime }$ or Fe³⁺. Thick-light curves are the total conductivities counting on the measured conductivities of dry olivine [111]. Light yellow and cyan areas show the conductivity range representing conductivity structures at the asthenosphere (Reproduced with permission from He et al., J. Geophys. Res. Solid Earth; published by American Geophysical Union, 2121 [15]).

4.2 Electrical conductivity of pyroxene

As a secondary rock-forming mineral in the upper mantle, the volume percentage of pyroxene is close to the average content of 20–40% in a typical upper-mantle region. Thus, high-pressure electrical conductivity measurement on pyroxene is crucial to deeply explore the high conductivity anomalies in the regions of the upper mantle and mantle asthenosphere. For anhydrous clinopyroxene, Dai et al. [111] measured EC of dry single-crystal diopside along with [001, 010, 100] three main crystallographic orientations at 1.0–4.0 GPa, 1073–1373 K, and Ni-NiO oxygen buffer-controlled oxygen fugacity in the YJ-3000 t multi-anvil apparatus and the Solartron-1260 impedance spectroscopy analyzer. A feeble influence of anisotropy on the electrical conductivity of dry single-crystal diopside was observed. Similarly, the influence of oxygen fugacity on the electrical conductivity of dry orthopyroxene single crystal by Dai et al. [112] was performed at 1.0–4.0 GPa, 1073–1423 K, and different oxygen fugacities. The oxygen fugacity in the sample chamber of EC measurements is controlled by four solid buffers of nickel and nickel oxide, iron and magnetite, and as well as molybdenum and molybdenum dioxide. A positive dependence of oxygen fugacity on the EC of orthopyroxene single crystal is observed at a given temperature range from 1073 K to 1423 K and 2.0 GPa, which is highly related to the conduction mechanism of small polaron hopping in the anhydrous iron-bearing silicate mineral at high pressure.

On the other hand, EC measurements of anhydrous and hydrous orthopyroxene single crystals along with three main crystallographic orientations were performed by Dai and Karato [51] at conditions of 8 GPa, temperatures of 873–1273 K, and as well as the oxygen fugacity controlled by the molybdenum and molybdenum dioxide using the Kawai-1000 t multi-anvil apparatus and the Solartron-1260 impedance spectroscopy analyzer. Detailed experimental results were illustrated in Figure 7. According to the FT-IR spectroscopy results, the hydrous orthopyroxene single crystals contain 420 ppm wt% water. They found that trace structural water can enhance several orders of magnitude in the EC of orthopyroxene single crystals. The effect from the anisotropy of hydrous orthopyroxene on the EC of the sample can be neglected, which is consistent with the above-mentioned dry single-crystal diopside. As two main conduction mechanisms, small polaron and free proton play a crucial role in the electrical conductivity of anhydrous and hydrous orthopyroxene single crystals at high-temperature and high-pressure conditions.

Figure 7.

The influence of anisotropy on the electrical conductivity of hydrous single-crystal orthopyroxene along [001, 010, 100] crystallographic orientations at conditions of 8 GPa, temperatures of 873–1273 K, and as well as the oxygen fugacity controlled by the molybdenum and molybdenum dioxide. The EC of dry single-crystal orthopyroxene is also included (modified from Dai and Karato [51]).

In the recent days, Sun et al. [27] performed electrical conductivities of the polycrystalline clinopyroxene aggregates + sodium chloride + water system under conditions of 1 GPa, 673–973 K, the various salinity degree of fluid (5, 10, 15, 20, and 25%), and the volume fraction of fluid (5, 10, 15, 20, and 25%) using the YJ-3000 t multi-anvil apparatus and the Solartron-1260 impedance spectroscopy analyzer. They found that the electrical conductivity of polycrystalline clinopyroxene aggregates containing the salinity-bearing fluid with a certain salinity degree and volume fraction of fluid can be applied to explain the unusually high conductivities in some regional geotectonic units, such as southern Tibetan plateau, Dabie orogen, Grenville province, and central New Zealand.

4.3 Electrical conductivity of garnet

As a type of important constituent silicate mineral, garnet can stably exist over a wide depth from lower crust Earth to the topmost lower mantle. With increasing temperature and pressure in the deep Earth interiors, the form of pyrope-rich garnet in the lower Earth crust gradually transforms into the high-pressure phase of majorite garnet in the mantle transition zone, which is of the complex chemical composition and stable crystalline structure. Furthermore, the mineralogical content of garnet in the deep Earth interiors will gradually increase with the rise of depth [113]. Therefore, when we try to construct the profile between electrical conductivity and depth in the deep mantle of Earth’s interior, it is indispensable to comprehensively assess the influence of electrical conductivity of garnet at high temperatures and high pressures.

Dai and Karato [52] conducted the EC measurements of anhydrous and water-rich single-crystal pyrope-rich garnet [its corresponding chemical composition is close to 73 mole% of pyrope (Py), 14 mole% of almandine (Alm), and 13 mole% of grossular (Gr)] at conditions of temperature range from 873 K to 1473 K, pressure ranges from 4 GPa to 16 GPa, frequency ranges from 10⁻² Hz to 10⁶ Hz and water-bearing content range from less than 10 H/10⁶Si to 7000 H/10⁶Si using the Kawai-1000 t multi-anvil press installed in the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States. Figure 8 shows the effect of pressure on the dry and water-bearing (160 ppm wt) single crystal pyrope-rich garnet at temperatures of 873–1473 K. In comparisons with water-free water of pyrope-rich garnet, the electrical conductivity of the hydrous sample is higher, and the activation enthalpy of pyrope-rich garnet (ΔH = ∼70 kJ/mole) is lower than that of the anhydrous sample (ΔH = ∼128 kJ/mole).

Figure 8.

The influence of pressure on the dry and water-bearing (160 ppm wt) single crystal pyrope-rich garnet at temperatures of 873–1473 K (reproduced with permission from Dai and Karato, Phys. Earth planet. Inter.; published by Elsevier, 2009 [52]).

In subsequent investigations, a series of EC experiments on garnet with different chemical compositions (Py₂₀Alm₇₆Grs₄, Py₃₀Alm₆₇Grs₃, Py₅₆Alm₄₃Grs₁, Py₇₃Alm₁₄Grs_13, and Alm₈₂Py₁₅Grs₃) were conducted by Dai et al. [53, 54] using the YJ-3000 t multi-anvil apparatus and the Solartron-1260 impedance spectroscopy analyzer to explore the influences of oxygen fugacity and mineralogical composition on the EC of garnet at 1.0–4.0 GPa and 873–1273 K. Five different solid buffers including Fe₃O₄-Fe₂O₃, Ni-NiO, Fe-Fe₃O₄, Fe-FeO, and Mo-MoO₂ were employed to control the oxygen fugacity of the high-pressure sample chamber. Based on these obtained experimental results, some absolutely new models of electrical conductivity of garnet series as functions of the variation of oxygen fugacity and chemical compositions have already been constructed, as illustrated in Figure 9(a) in detail. Furthermore, in conjunction with previously available electrical conductivity of clinopyroxene results, the average models of rock and as well as the regionally geothermal gradient, the profile between the electrical conductivity of eclogite and depth is established from the EC of garnet series at high temperatures and high pressures, as shown in Figure 9(b) in detail. All of these acquired laboratory-based electrical conductivity profiles can be widely applied to systematically disclose and deeply explore the cause of the observable high conductivity anomalies from global and regional field magnetotelluric and geomagnetic deep sounding results in those representatively geotectonic units, for example, stable mid-lower continental Earth crust, Dabie-Sulu ultrahigh-pressure metamorphic belt of eastern China, Tibet plateau, and North China craton.

Figure 9.

(a) The influence of volume percentage on the electrical conductivity of eclogite on the base on our obtained electrical conductivity results for single crystal pyrope-rich garnet at high temperatures and high pressures (modified from Dai et al. [53]), (b) the profile between the electrical conductivity of eclogite and depth in conjunction with previously available electrical conductivity of clinopyroxene results, the average models of rock and as well as the regionally geothermal gradient is established from the EC of garnet series at high temperatures and high pressures (reproduced with permission from Dai et al., Contrib. Mineral. Petrol.; published by Springer Nature, 2012 [53]).

5. Conclusions

High-pressure laboratory-based measurement results on electrical properties of several dominant minerals (olivine, orthopyroxene, clinopyroxene, garnet, etc.) in the upper mantle regions are highly sensitive to some influential factors including temperature, pressure, oxygen fugacity, water content, crystallographic orientation, trace element of titanium content and iron content. The proper determination of EC of upper-mantle minerals in a broad temperature and pressure range requires the utilization of complex electrical electrochemical impedance spectroscopy measurements. The iron-related hopping of small polaron and the hydrogen-related defects are possibly the two dominant conduction mechanisms in anhydrous and hydrous Fe-bearing silicate minerals within the depth range of the upper mantle. The trace structural water of mantle minerals plays a crucial role in explaining the high conductivity anomaly and the water distribution in the deep mantle. In comprehensive considerations of some newest results from high-pressure laboratory-based conductivity measurements, geophysical field observations, and first-principles theoretical calculations, high and highly anisotropic EC at the corresponding asthenospheric temperature and pressure conditions can be used to reasonably explain by the 100 ppm wt% of water content for the high conductivity anomaly in the asthenospheric region. In addition, the influence of the interconnected high conductive impurity phases (graphite, magnetite, chromite, sulfide impurity, etc.) and saline fluids (e.g., Ol-NaCl-H₂O, Ol-KCl-H₂O, Ol-CaCl₂-H₂O, etc.) on the EC of olivine also needed to be considered in a special geotectonic environment. With the development and advancement of measurement techniques and experimental methods, more and more laboratory-based high-pressure conductivity experimental results will be indispensable to systematically disclose the cycle discontinuity and high conductivity anomaly in the upper-mantle region.

Acknowledgments

Almost all listed original high-pressure electrical conductivity data have already been obtained by Lidong Dai and his collaborators in the Chinese Academy of Sciences and Yale University. In here, please accept my best honest thanks and greetings to Professor Heping Li in the Key Laboratory of High-temperature and High-pressure Study of the Earth’s Interior (HTHPSEI), Institute of Geochemistry, Chinese Academy of Sciences, the People’s Republic of China, and Professor Shun-ichiro Karato in the Karato High-pressure Laboratory, Department of Earth and Planetary Sciences, Yale University, United States. This work was financially supported by the National Natural Science Foundation of China (Grant numbers 42072055, 41774099, and 41772042), Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant number 2019390), Special Fund of the West Light Foundation of Chinese Academy of Sciences and as well as Special Fund from Shandong Provincial Key Laboratory of Water and Soil Conservation and Environmental Protection.