**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<sup>2</sup> –10<sup>0</sup> 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 [3–5]. 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 [11–15], contents of water and other volatile elements [16–18], partial melting [19–21], dehydration (or dehydrogenation) effects of minerals [22–24], impurity of high-conductivity phase [25, 26], salinity-bearing (or water-bearing) fluids [27, 28], and structural phase transformation (amorphization or metallization) [29–34].

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, 13–18, 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

*Some New Progress in the Experimental Measurements on Electrical Property of Main… DOI: http://dx.doi.org/10.5772/intechopen.101876*

water for the NAMS in the upper-mantle zone (olivine: [8, 13–15, 47–50], pyroxene: [51], and garnet [52–54]). 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 multianvil high-pressure apparatus [55–60]. 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 [61–64]. 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,

$$|\mathbf{Z\_r} = |\mathbf{Z}| \cos \varphi \tag{1}$$

$$\mathbf{Z}\_{\mathbf{i}} = |\mathbf{Z}| \sin \phi \tag{2}$$

Here, Zr stands for the real part of complex impedance spectroscopy, Zi 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*�*<sup>1</sup> –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.) [65–68]. After that, the electrical conductivity of the sample was obtained by the sample resistance, the calculating formula is expressed as,

$$
\sigma = \frac{1}{\rho} = \frac{L}{(\mathbb{R} \times \mathbb{S})} \tag{3}
$$

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 crosssectional area (m2 ). At a given pressure condition, it is usual that the electrical conductivity of sample and temperature satisfies with an Arrhenius relation, namely,

$$
\sigma = \sigma\_0 \exp\left(-\frac{\Delta H}{\text{kT}}\right) \tag{4}
$$

In here, *σ*<sup>0</sup> stands for the pre-exponential factor (S/m), Δ*H* 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

*Some New Progress in the Experimental Measurements on Electrical Property of Main… DOI: http://dx.doi.org/10.5772/intechopen.101876*

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 Hightemperature 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*, multifrequency 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 [69–87]. Dai Lidong and his collaborator [88–91] 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

### **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 multianvil 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<sup>4</sup> Hz–10<sup>7</sup> Hz; (c) the vertex-70v vacuum Fourier-transform infrared spectroscopy (FT-IR) analyzer to check the water content of sample.*

Solartron-1260 and Solarton-1296 interface impedance spectroscopy analyzer operating in the two-electrodes configuration for complex EIS measurements in the frequency range 10<sup>4</sup> Hz–10<sup>7</sup> 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.

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. [92–100]. 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.
