The olivine samples were obtained from the Damaping area of Hebei Province, China. The olivine was handpicked and then ground into powder in agate. Then, the powder samples were baked in a 393-K baking oven for 24 h to completely eliminate the adsorbed water in the whole assemblage. The chemical composition of the sample was determined by energy dispersive spectrometry (Fig. A1 in Appendix A) and is listed in Table 1. Subsequently, Fourier-transform infrared spectroscopy (FTIR) was used to verify the anhydrous nature of the sample prior to the conductivity measurements. The FTIR spectrum of olivine is shown in Fig. A2 (in Appendix A). The olivine water content was < 1 ppm, which we refer to as “anhydrous” olivine.

Table 1.

Table 1.

Table 1. Major chemical compositions of olivine material. . Composition SiO2 AI2O3 FeO MgO CaO Na2O K2O Total Content/wt% 40.26 0.75 3.99 54.68 0.21 0.02 0.09 99.81

Table 1. Major chemical compositions of olivine material. .

The experiments under high pressures and temperatures were performed with the new DAC device as shown in Fig. 1(a). Two ceramic resistance-heating rings were used in the DAC. One was located inside the groove of the plate seat, and the other was located on the platform of the spherical seat. An external water cooling system was introduced to avoid pressure loss caused by heated DAC. The DAC was placed inside a vacuum chamber during the measurement. Figure 1(b) is the schematic diagram of the vacuum device. This vacuum system effectively suppresses the oxidation of the diamond anvil, and improves the temperature range of the experiment. At the same time, the vacuum environment minimizes the effect of thermal exchange and thermal convection of air, improves the effective utilization of heat, and reduces temperature measurement error. High pressure was generated by using a DAC with a 400-µm-diameter anvil culet. Pressure was measured by the ruby fluorescence method. No pressure-transmitting medium was used to avoid an additional error from the electrical measurements.

Fig. 1.

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	Fig. 1. (a) Section view of high pressure/high temperature DAC, and (b) schematic diagram of vacuum device.

To fabricate the microcircuit on the diamond anvil, we adapted the Gao et al.’s method^[35] A mixed film of Mo and MoO₂ was sputtered on the face of the diamond anvil to form electrodes. The sputtering power was 90 W and the chamber working gas pressure was 1.0 Pa. The flow ratio of Ar to O₂ was 1.6 : 30. The film was then integrated into a two-electrode configuration microcircuit through photolithography. After the preparation of the electrical circuit, an alumina layer (Al₂O₃) was deposited on the circuit. This acted as an electrical and heat insulator and surrounded the microcircuit. A detection window was made in the center of the culet by removing the covering alumina, which kept the film electrode contacting the sample. The anvil and electrode configuration are shown in Figs. 2(a) and 2(b).

Fig. 2.

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	Fig. 2. (a) Schematic diagram of film microcircuit on diamond anvil cell, (b) photograph of electrode corresponding to panel (a), (c) configuration of composite insulating gasket, (d) photograph of Pt electrode, (e) cross-section of DAC showing Mo + MoO2 film electrode, and (f) cross-section of DAC showing Pt electrode.

We developed a complex gasket, which is a metal gasket with an oxygen fugacity buffering ring and insulating gasket material as shown in Fig. 2(c). An Re tablet was used as the gasket. The gasket was pre-indented to 50 µm in depth. A hole with a diameter of 250 µm was drilled into the middle of the indentation. High-purity Mo and MoO₂ powders were packed into the hole and mixed uniformly according to the weight rate given from buffering equilibrium equation (i.e., 86-wt% Mo+14-wt% MoO₂). After being firmly pressed, a new hole that is 150 µm in diameter was obtained in the center of the mixed powder. This cylinder of mixed Mo and MoO₂ powder forms a sealed atmospheric environment that controls the partial oxygen pressure in the sample chamber. In order to insulate the gasket from the electrodes on the anvils, BN powder was placed in the hole and compacted into a hole-shaped piece, which a smaller hole with 100 µm in diameter was then drilled into, resulting in a sample chamber. Figure 2(c) shows a cross-sectional view of the DAC. After measuring the electrical conductivity, the buffer was analyzed by x-ray diffraction (Fig. 3) to check whether Mo and MoO₂ are existent, and the results show that the oxygen fugacity in the sample chamber was fully controlled. We used Pt as a test electrode for a comparative experiment without oxygen fugacity control. Figures 2(d) and 2(f) show a photograph and schematic of the anvil with a Pt electrode, respectively.

Fig. 3.

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	Fig. 3. X-ray diffraction pattern confirming Mo and MoO2 buffer existing after conductivity has been measured.

A Solartron-1260 impedance/gain-phase analyzer was used to record the impedance spectrum. This was operated with a signal voltage of 1 V at frequency ranging from 10⁻¹ Hz to 10⁷ Hz. Temperature was varied in steps of 50 K, with the electrical conductivity being measured at each step. For the sample thickness measurements it was assumed that the diamond deformation was elastic and so was it during loading and unloading. If the gasket undergoes entirely plastic deformation, then the thickness of the sample (t) at each pressure during compression is

where L_m is the sample thickness at maximum pressure and δ_P is the difference in thickness between loading and unloading for each pressure.^[36,37]

Electrical conductivity increases with temperature increasing (Fig. 5). As is the case for dielectric medium isolators, the olivine charge carriers move by thermally excited hopping during conduction.^[38,39] With the increase of temperature, the carriers have higher energy and more carriers can cross the energy barrier. Electrical conductivity and carrier concentration are linked by the relationship described by the Nernst–Einstein equation

where σ is the conductivity, n is the charge carrier concentration, and q is the effective charge. Therefore, an increase in the carrier concentration leads to a higher sample conductivity.

A monotonic linear relationship exists between the logarithm of electrical conductivity and temperature, which suggests that only one olivine conduction mechanism exists at 573 K–873 K. The main mantle minerals (i.e., ferromagnesian silicates) typically have three conduction mechanisms, i.e., protons, small polarons, and ions.^[40] Different conduction mechanisms can be distinguished from the activation enthalpy and activation bulk volume.^[10,41,42] The activation enthalpy of the proton conduction mechanism in hydrous silicate is typicall y < 1.0 eV and is weakly dependent on temperature. The activation enthalpy and activation bulk volume in our experiments are relatively low (ΔH < 1.0 eV; Table 2); however, the FTIR spectra of our olivine sample show that it is essentially anhydrous, in addition, the measured electrical conductivity is strongly dependent on temperature. Moreover, the experimental temperature is not high enough to generate protons, meaning that the proton conduction is implausible. The ion conduction mechanism is not viable either, given that the activation energy for this mechanism is generally more than 2.0 eV.^[43] This mechanism would also only be likely to occur for experimental temperatures of > 1500 K. Therefore, small polarons are likely the main charge carriers in our experiments. The activation volumes (ΔV) are negative (Table 2), which supports the suggestion that olivine experienced small polaron hopping conduction. This conduction mechanism refers to the directional hopping of a bound hole along a directional electrical field. In our experiment, the activation enthalpy decreases with pressure increasing. A decrease in the average Fe³⁺–Fe²⁺ distance by compression facilitates electron hole hopping between Fe³⁺ and Fe²⁺. Thus, the activation enthalpy decreases with pressure increasing. It is also strong evidence of a small polaron conduction mechanism in our experiments.

The conductivities of olivine measured without oxygen fugacity buffering are clearly lower than those measured with buffering (Fig. 5). The Mo + MoO₂ film electrode provides a better oxygen atmosphere than when using a Pt electrode. According to the point defect oxidation–reduction reaction,^[39] the point defect reactions between O in the sample chamber and Fe²⁺ in the sample occur under certain temperature conditions. As such, the Fe²⁺ that occupies the Mg²⁺ site in the olivine structure is oxidized into a small polaron. Consequently, the electron (e′) and hole (h^•) are of the main defect types. With time going by, concentrations of and reach a buffered equilibrium. The small polaron conduction in olivine takes place by polaron hopping between holes in the lattice Fe²⁺ sites, and can be expressed as

where is the oxygen ion, O₂ is the oxygen in the sample chamber, is the oxygen vacancy, e′ is the electron, is the Fe²⁺ occupying the Mg²⁺ site in the lattice structure of the sample, h^• is the hole, and is the Fe³⁺ in the lattice Mg²⁺ site. The increase in oxygen fugacity leads to higher small polaron concentrations produced by point defect reactions, which increases the electrical conductivity. As is well known, iron in the sample will be lost to the Pt measuring electrode during the experiment,^[44] resulting in a decrease in carrier concentration and a decrease in the conductivity of olivine. Therefore, the conductivity values obtained with an oxygen fugacity buffer are higher than those measured without a buffer.

We compare our olivine conductivity data with the data from previous studies.^{[18,22,45,46]} The data obtained with an oxygen fugacity buffer are in better agreement with previous experiments than with those determined without a buffer (Fig. 6). The activation enthalpies (0.685 eV–0.704 eV) of olivine measured with oxygen fugacity buffers are similar to those published by Yoshino et al. and Sakamoto et al., i.e., 0.74 eV–0.98 eV for the low-temperature region and 0.29 eV–0.67 eV, respectively. However, activation enthalpies (0.411 eV–0.432 eV) determined for olivine without an oxygen fugacity buffer are obviously lower than those of all previous studies. The Fe content (X_Fe = Fe/(Fe + Mg) = 0.18) of olivine in our experiments is close to that of Yoshino et al. (X_Fe = 0.2). If we extrapolate the olivine conductivity to T > 873 K, then the conductivity obtained with an oxygen fugacity buffer is comparable to that reported by Yoshino et al. Their difference in Fe content, mineralogical composition, and redox condition of olivine show that our obtained conductivity value is than that reported by Sakamoto et al. The activation enthalpy of olivine measured with an oxygen fugacity buffer is lower than the values reported by Dai et al. and Xu et al., i.e., 143.77 kJ/mol–151.44 kJ/mol and 1.40 ± 0.5 eV, respectively, which we attribute to the different temperature conditions and mineralogical compositions used in the various studies. In summary, our values obtained with oxygen fugacity buffering are close to those of previous studies, but the results determined without buffering are discrepant. Therefore, the conductivity data obtained by using our oxygen fugacity control technique during DAC experiments are robust and as reliable as the data obtained in multi-anvil experiments.

Fig. 6.

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	Fig. 6. Comparison of our olivine electrical conductivity measurements with previous studies.