Introduction

Carbonates can be transported into the Earth’s deep interior through subducting slabs, and thus have been proposed as host minerals for carbon in the Earth’s mantle. Therefore, revealing the behavior of carbonates at extreme conditions is a key to a better understanding of the deep carbon cycle. Siderite (FeCO3) forms a complete solid solution with magnesite (MgCO3), and its solid solution is the most likely carbonates candidate in the mantle (Boulard et al. 2012; Liu et al. 2015; Cerantola et al. 2017, 2019). Fe2+ in (Mg, Fe)CO3 is known to undergo a high-spin to low-spin transition under the pressure conditions of the lower mantle. The spin transition of Fe2+ in (Mg, Fe)CO3 has been identified by X-ray diffraction, Raman, infrared and Mössbauer spectroscopy in previous studies (Lavina et al. 2009, 2010; Nagai et al. 2010; Lin et al. 2012; Farfan et al. 2012; Spivak et al. 2014; Liu et al. 2014, 2015; Lobanov et al. 2015; Cerantola et al. 2015; Müller et al. 2017; Weis et al. 2017; Zhao et al. 2020; Hu et al. 2023). In Fe2+, the 3d electrons occupy different orbitals with the same electronic spin under ambient conditions in mantle minerals, which is the high-spin state with four unpaired electrons and two paired electrons. With increasing pressures, the crystal-field splitting energy increases, leading to the low-spin state with all the six 3d electrons paired in Fe2+ (e.g., Lin et al. 2013; Liu et al. 2020). The spin transition of iron affects physical properties of host phases such as density, electrical and thermal conductivities. Previous high-pressure studies on (Mg, Fe)CO3 observed the discontinuous change in compressibility (Lavina et al. 2009, 2010; Nagai et al. 2010; Lin et al. 2012; Farfan et al. 2012; Liu et al. 2014, 2015), thermal conductivity (Chao and Hsieh 2019), and sound velocities (Stekiel et al. 2017; Fu et al. 2017) due to the spin transition of Fe2+.

Electrical conductivity is a useful parameter to constrain thermal, chemical, and redox states of the Earth’s mantle. Recently, the resolution of the electrical conductivity structure in the lower mantle has been improved and lateral heterogeneities have been observed in the mid-lower mantle (Tarits and Mandéa 2010; Velímský and Knopp 2021). In addition to temperature and compositional changes, electrical conductivity varies depending on the spin transition of iron in mantle minerals. Previous studies on the dominant minerals forming the lower mantle, such as iron-bearing bridgmanite and ferropericlase, have reported the decreases in the electrical conductivities as a function of pressure, which is likely associated with spin transition from high-spin to intermediate/low-spin states due to the lower mobility of small polarons (electron-hole hopping between Fe2+ and Fe3+ ions) in intermediate/low-spin states (Lin et al. 2007a; Ohta et al. 2007; 2008; Yoshino et al. 2011). The electrical conductivities of iron-bearing bridgmanite and ferropericlase gradually increase by ~ 1 order of magnitude from ambient pressure to the pressure just below the pressure at which spin transition occurs, whereas they decrease by a factor of ~ 3 after the spin transition (Lin et al. 2007a; Ohta et al. 2007; 2008; Yoshino et al. 2011; Lin et al. 2013). In ferropericlase (Mg, Fe)O, the transition pressure gradually increases with increasing iron contents (Badro et al. 2003; Speziale et al. 2005; Lin et al. 2005, 2007b; Persson et al. 2006; Keppler et al. 2007; Fei et al. 2007; Crowhurst et al. 2008; Komabayashi et al. 2010; Mao et al. 2011; Glazyrin et al. 2016). On the other hand, there is no compositional effect on the transition pressure in (Mg, Fe)CO3 (Liu et al. 2020; Liu et al. 2014; Müller et al. 2017). In addition, the spin transition of (Mg, Fe)CO3 is sharper than that of (Mg, Fe)O under high-pressure and temperature conditions, which is likely because the localized FeO6 octahedra in (Mg, Fe)CO3 are more separated from other iron ions in the surrounding FeO6 octahedra (Lin et al. 2007b; Lavina et al. 2010; Liu et al. 2014; Müller et al. 2017). Therefore, the influence of spin transition of (Mg, Fe)CO3 on the electrical conductivity could be more detectable in the lower mantle. The electrical conductivity of (Mg, Fe)CO3 has been measured up to 3 GPa (Hu et al. 2022). However, the measured pressure range is far below the pressure at which spin transition occurs, which is expected at conditions of mid-lower lower mantle.

In this study, we have conducted electrical conductivity and spectroscopic (Raman and Mössbauer) measurements of siderite using a diamond anvil cell (DAC) up to ~ 63 GPa at ambient temperature in order to better constrain the effect of spin transition on the electrical conductivity of siderite. Based on our experimental data, we discuss the heterogeneous electrical conductivity structure observed in the lower mantle.

Materials and methods

Electrical conductivity measurements

Natural siderite sample from Julcani Mine, Huancavelica, Peru with an average composition of (Fe0.76Mn0.19Mg0.03Ca0.02)CO3 has been characterized by energy-dispersive X-ray spectroscopy operating at a 15 kV accelerating voltage and a beam current of 10 nA and was used in the context of this study. The high-pressure behavior of siderite was investigated using diamond anvil cells (DACs) with 300 μm culets. Rhenium (Re) or tungsten (W) gaskets were pre-indented to about 45 μm thickness before laser drilling of sample holes with ~ 150 μm diameters, and then put Al2O3 powder into the holes and on the surface of the Re gaskets. After Al2O3 powder became transparent and was compressed to ~ 50 μm thick, ~ 100 μm diameter holes were drilled in the center of the Al2O3 layer. Two gold foils as electrodes were placed on the Al2O3 layer and then the sample was loaded into the hole (Fig. S1). The initial thickness and diameter of the sample pellet are about ~ 50 μm and ~ 100 μm. The gold foils were attached to the sample and connected to platinum electrodes outside the sample hole. The sample and electrodes were electrically insulated by the Al2O3 layer against the metal gasket.

To determine electrical conductivity of siderite, impedance spectroscopic measurements were performed using a Solartron 1260 impedance gain-phase analyzer combined with a Solartron 1296 interface at IPM. Complex impedances were obtained at frequencies ranging from 1 MHz down to 0.1 Hz using the two-wire terminal method with an alternating current signal and an amplitude of 1 V. The impedance spectra of samples measured at various pressures generally showed a characteristic semicircular arc at higher frequencies and long tails at lower frequencies, which is likely derived from electrodes reaction (Fig. 1). An equivalent electrical circuit consists of a sample resistance RS in series with parallel combination of double-layer capacitance Cdl and a Warburg impedance derived from diffusion of electric charge in the electrodes as shown in the insert in Fig. 1 (Yoshino and Katsura 2013). To determine the electrical conductivity from the sample resistance values obtained by the fitting of impedance spectra, we need information on sample dimension such as length, width, and thickness of the cross-sectional area. The length and width were determined by optical observation using a microscope. The thickness of the sample volume for which the electrical conductivity was measured should be the same as that of the sample chamber considering the current paths (Li and Jeanloz 1990) as shown in Fig. S1. The details of the estimation of sample thickness were described in Text S1 in supporting information (SI). The estimated sample thicknesses are in good agreement with the directly measured thicknesses of many common pressure-transmitting media (PTM) (Lobanov and Geballe 2022). We obtained the spectra with both increasing (compression) and decreasing (decompression) pressures.

Fig. 1
figure 1

Representative impedance spectrum of Real Z’ versus imaginary Z’’ components of impedance for siderite in this study at 38.1 GPa. The equivalent electrical circuit for fitting each spectrum is shown in the upper right

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Energy-domain synchrotron Mössbauer spectroscopic measurements

For synchrotron Mössbauer spectroscopic measurements, the powder samples were compressed into pellets, and then loaded into a DAC. We used KCl as the PTM. The sample pellet was sandwiched between two KCl layers and the initial thickness and diameter of the sample pellet are ~ 30 μm and ~ 80 μm. High-pressure energy-domain synchrotron 57Fe Mössbauer source (SMS) spectroscopic measurements were conducted at beamlines BL11XU of SPring-8 (Mitsui et al. 2009) at room temperature and pressures up to 60.1 GPa in order to confirm the spin transition of iron in siderite. SMS is based on a pure 57FeBO3 (111) monochromator, which via nuclear Bragg reflections provides neV energy resolution allowing the study of the Mössbauer effect on small specimen in a DAC. The Doppler velocity scales were calibrated using a 2 μm thick piece of α-57Fe foil under ambient conditions. Spectra were collected for ~ 1.5 h depending on the signal quality. The obtained Mössbauer spectra were fitted with pseudo-Voigt line-shape doublets using the MossA software package (Prescher et al. 2012).

Raman spectroscopic measurements

The high-pressure Raman spectroscopic measurements were performed at the Institute for Planetary Materials (IPM) and SPring-8 in order to determine the pressure conditions and confirm the pressure range of the spin transition in siderite. Pressure was determined using the Raman T2g mode of the diamond anvil (Akahama and Kawamura 2004) by measuring at the center of the culet and the pressure uncertainty was estimated from a separate experiment as described in Text S2. In all Raman measurements, the spot size was typically less than 5 μm. Raman spectra were collected between 200 and 1500 cm-1 frequency range with a green 532 nm diode-pumped solid-state laser for 5–30 s and 3–5 accumulations for the sample characterization and pressure determination. We conducted the Raman spectroscopic measurements simultaneously during both the electrical conductivity and Mössbauer spectroscopy measurements.

Results

We have conducted electrical conductivity measurements up to 63 GPa at 300 K with both increasing pressure (compression path) and decreasing pressure (decompression path). The pressure dependence of the resistance is shown in Fig. 2a. The resistance increases rapidly above 50 GPa. The uncertainties of the electrical conductivity are mainly derived from the errors of the sample thickness arise from the measuring methods as well as the non-isotropic compression and decompression. Therefore, we provided relatively large uncertainties for the electrical conductivity (± 50%). The results of resistance, thickness, and electrical conductivity at each pressure point are summarized in Table S1. Figure 2b shows the variation of the electrical conductivity of siderite as a function of pressure. The electrical conductivity is almost constant with increasing pressure up to 50 GPa, while drops above 50 GPa. All the 3d electrons of the low-spin Fe2+ in siderite are paired, whereas high-spin Fe2+ in siderite has four unpaired electrons (Liu et al. 2020). Therefore, the high- to low-spin transition results in the decrease of the electrical conductivity of siderite. A similar trend is also observed in (Mg, Fe)O ferropericlase between 25 and 80 GPa, which is likely associated with spin transition from high- to low-spin states of Fe2+ (Lin et al. 2007a; Ohta et al. 2007; Yoshino et al. 2011). The pressure range of the spin transition determined from both Mössbauer and Raman spectroscopic measurements is in good agreement with the pressure at which the electrical conductivity of siderite suddenly drops. Therefore, we can conclude with high certainty that the observed conductivity drop should be related to the high- to low-spin transition of Fe2+ in siderite.

Fig. 2
figure 2

Profiles of (a) resistance and (b) electrical conductivity of siderite in this study as a function of pressure at 300 K with both increasing pressure (compression path) and decreasing pressure (decompression path). We put large relative uncertainties of the electrical conductivity (± 50%)

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The Mössbauer spectra of siderite at room temperature up to pressures of 60.1 GPa are shown in Fig. 3. The spectra can be fitted by one doublet up to 44.9 GPa. The spectra at 48.4 and 54.2 GPa can be analyzed into two components: one doublet and one singlet. The area ratio of the singlet increases whereas that of the doublet decreases with increasing pressure above 44.9 GPa. At the highest pressure, 60.1 GPa, the spectrum can be fitted by one singlet. The pressure variations of the obtained Mössbauer parameters, center shift (CS), quadrupole splitting (QS), and area ratio are shown in Fig. 4. According to a previous Mossbauer study (Cerantola et al. 2015), the doublet and singlet correspond to high- and low-spin states of Fe2+ in siderite, respectively. The Mössbauer results indicate that the high- to low-spin transition occurs at around 48–54 GPa. The CS and QS parameters of the polycrystalline sample measured in this study are in good agreement with values reported earlier (Cerantola et al. 2015) for powder samples. The Raman spectroscopic measurements were also conducted under the same conditions as the Mössbauer measurements. The pressure evolution of the Raman shift also shows the evidence of spin transition as shown in Fig. 5. We observed two lattice vibration peaks: one is a transitional mode Eg (T) and the other is a librational mode Eg (L) (Fig. 6). We also observed peaks of internal vibrations of the CO32- groups: the A1g symmetric stretch (ν1) and the Eg vibration (ν4). The Raman shifts of the modes generally increased with increasing pressure. The peaks of the ν1-mode have the highest intensity. Above 48.4 GPa, the new mode which is assigned to the ν1-mode of the low-spin state (ν1’) appears at lower wavenumbers and the intensity of the new ν1-mode (ν1’) becomes higher with increasing pressure, similar to previous Raman studies on siderite (Spivak et al. 2014; Cerantola et al. 2015; Müller et al. 2017; Zhao et al. 2020). The compositional dependences of Raman peaks position and the spin transition pressures of (Mg, Fe)CO3 are small (Liu et al. 2014; Spivak et al. 2014; Cerantola et al. 2015; Müller et al. 2017; Zhao et al. 2020).The Raman peaks position of this study almost agree with those reported in previous studies (Farfan et al. 2012; Spivak et al. 2014; Zhao et al. 2020) within the uncertainties, but there are some variations in the pressure conditions of emergence of the ν1-mode of the low-spin state (ν1’) among this study and the previous ones. This may be due to the presence or absence of a PTM and the different types of PTM used, i.e. He, Ne, Ar, KCl. The transition pressure estimated from the Raman shift is also between 48 and 54 GPa and is consistent with the Mössbauer results.

Fig. 3
figure 3

Representative high-pressure Mössbauer spectra at 19.9, 44.9, 48.4, 54.2 and 60.1 GPa. The solid green curves represent the overall fit to the data from the sum of subcomponent(s)

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Fig. 4
figure 4

Pressure dependence of (a) center shift (CS) and quadrupole splitting (QS), and (b) area ratio together with the previous study (Cerantola et al. 2015). Blue circles, triangles and diamonds represent the CS, QS and area ratio of the doublet and orange squares and diamonds represent the CS and area ratio of the singlet in this study. Symbols from Cerantola et al. (2015) are: open circles = doublet CS, lab, single crystal; open triangles = singlet CS, lab, single crystal; gay circles = doublet CS, lab, powder; gray triangles = singlet CS, lab, powder; solid circles = doublet CS synchrotron, single crystal; solid triangles = single CS, synchrotron, single crystal; open squares = doublet QS, lab, single crystal; gray squares = doublet QS, lab, powder; solid squares = doublet QS, synchrotron, single crystal

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Fig. 5
figure 5

Pressure dependence of the Raman shift of the ν1-mode of siderite together with those of previous studies on siderite near the Fe-endmember (Farfan et al. 2012; Spivak et al. 2014; Zhao et al. 2020). At around 50 GPa, the spin transition is indicated by the emergence of the ν1-mode at lower wavenumbers (ν1’). Green, blue and light blue circles represent the ν1-mode of high-spin state of siderite under the same condition as Mössbauer and electrical conductivity (EC) measurements in this study. Orange, red and yellow circles represent the ν1-mode of low-spin state of siderite (ν1’) under the same condition as Mössbauer and electrical conductivity (EC) measurements in this study. Symbols from previous studies are: open triangles = ν1, HS, (Fe0.76Mn0.15Mg0.09Ca0.01)CO3 (Farfan et al. 2012); solid triangles = ν1’, LS, (Fe0.76Mn0.15Mg0.09Ca0.01)CO3 (Farfan et al. 2012); open circles = ν1, HS, FeCO3 (Spivak et al. 2014); solid circles = ν1’, LS, FeCO3 (Spivak et al. 2014); open squares = ν1, HS, Fe0.998Mn0.002CO3 (Zhao et al. 2020); solid squares = ν1’, LS, Fe0.998Mn0.002CO3 (Zhao et al. 2020)

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Fig. 6
figure 6

Representative high-pressure Raman spectra of siderite in this study. Blue and red dotted lines represent the peak positions of the ν1-mode of the high-spin and low-spin states, respectively

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Discussion and conclusions

For the lower mantle materials, three conduction mechanisms are thought to contribute to electrical conductivity: ionic, small polaron (electron-hole hopping between Fe2+ and Fe3+ ions) and proton conductions. In the mantle minerals, small polaron and proton conductions influence the electrical conductivity mainly, although ionic conduction occasionally appears as a dominant conduction mechanism at relatively higher temperatures close to the melting point (e.g. Yoshino 2010). The previous study (Hu et al. 2022) suggested that the small polaron is the predominant conduction mechanism in siderite at ambient temperature with the characteristic of a relatively lower activation energy. This study has been conducted at ambient temperature under dry condition, so the small polaron is likely to be the predominant conduction mechanism in siderite in this study. Generally, the conductivity becomes higher with increasing pressure when the small polaron hopping conduction mechanism is dominant as is the case with ferropericlase (Lin et al. 2007a; Ohta et al. 2007; 2008; Yoshino et al. 2011), which is the major reason for the difference in electrical conductivity between this study conducted above 25 GPa and the previous study at 1–3 GPa (Hu et al. 2022). In addition, the compositional difference may affect the electrical conductivity difference. Fe and Mg contents of siderite in this study are lower and Mn and Ca contents are higher than those of siderites previously investigated by Hu et al. (2022). Mn, Mg, and Ca generally substitute in part for Fe. The substitutions of Mg and Ca reduce the electrical conductivity (Hu et al. 2022). Specifically, Mn concentration of siderite in this study is high. A previous study on MnxFe1−xCO3 under ambient pressure showed that Mn-doping enhances the conductivity (Zhang et al. 2017), although the behavior under high pressure is unknown. In addition, Fe3+/ΣFe may affect the electrical conductivity of siderite as is the case with ferropericlase (Dobson and Brodholt 2000). In principle, iron exists as Fe2+ in siderite but small amount of Fe3+ may exist in siderite. The detectable limit of amount of each component in Mössbauer spectra is ~ 5%, so siderite in this study may contain Fe3+ up to ~ 5%. Thus, the small polaron (electron-hole hopping between Fe2+ and Fe3+ ions) can be the dominant conduction mechanism. The Fe3+ concentration in siderite of Hu et al. (2022) and the effect of Fe3+ on the electrical conductivity of siderite are unknown, but this also might explain why the electrical conductivity of siderite in this study is higher than that of siderite previously measured at 1–3 GPa at 373 K (Hu et al. 2022) as shown in Fig. 7.

Fig. 7
figure 7

Pressure dependence of the electrical conductivity of siderite in this study (blue squares) compared with previous studies on the major lower mantle phases at 300 K and siderite at 373 K. The composition of siderite (Sd) is (Fe0.88Mn0.03Mg0.09)CO3 (open blue squares) (Hu et al. 2022). Symbols from previous studies on ferropericlase (Fp) are: purple circles = Fp, (Mg0.93Fe0.07)O; blue circles = Fp, (Mg0.90Fe0.10)O; light blue circles = Fp, (Mg0.87Fe0.13)O; green circles = FP, (Mg0.83Fe0.17)O; light green circles = Fp, (Mg0.76Fe0.24)O (Yoshino et al. 2011); blue open circles = Fp, (Mg0.81Fe0.19)O (Ohta et al. 2007); green open circles = Fp, (Mg0.75Fe0.15)O (Lin et al., 2007a). Symbols from previous studies on bridgmanite (Brg) are: blue triangles = Brg, (Mg0.89Fe0.11)2SiO4 (Peyronneau and Poirier 1989); yellow triangles = Brg, (Mg0.88Fe0.12)SiO3; orange triangles = Brg, (Mg0.88Fe0.12)3Al2Si3O12 (Li and Jeanloz 1990); purple triangles = Brg, (Mg0.84Fe0.16)2SiO4 (Shankland et al. 1993); purple open triangles = Brg, (Mg0.9Fe0.1)SiO3 (Ohta et al. 2008); open blue tringles = Brg, (Mg0.9Fe0.1)SiO3 (Ohta et al. 2010); open green triangles = Brg, Mg0.83Fe0.21Al0.06Si0.91O3 (Sinmyo et al. 2014)

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Former studies showed that siderite is stable up to at least ~ 110 GPa and ~ 1400 K, pressure conditions of the lowermost mantle (Boulard et al. 2012; Liu et al. 2015; Cerantola et al. 2017, 2019). High-spin siderite has demonstrated to be stable up to 2000 K at around 30 GPa and decomposes to iron oxides + C (diamond) at higher temperatures. Experiments show that above 30 GPa the temperature of decomposition between high-spin siderite and iron oxides + C tends to decrease with increasing pressure (i.e. Cerantola et al. 2017). The temperature stability of low-spin siderite is limited up to 1500 K at lower-mantle pressure conditions, which is well below the mantle geotherm. Therefore, in the shallow lower mantle siderite could be stable without decomposing only in cold subducting slab, although the condition of the decomposition temperature at greater depths, i.e. around 50–60 GPa, which corresponds to the pressure range of the spin transition in siderite, has not yet been well determined (Maeda et al. 2017; Cerantola et al. 2017, 2019). In nature, siderite is expected to form a solid solution with magnesite following the stoichiometry Mg1-xFexCO3, where x is the amount of iron atoms per formula units. Although the stability of carbonates depends on oxygen fugacity, with increasing magnesium content the stability fields of Mg1-xFexCO3 has shown to expand to higher temperatures thus the solid solution could potentially be stable under lower-mantle temperature conditions, even at temperatures along the mantle geotherm (Isshiki et al. 2004; Boulard et al. 2012; Cerantola et al. 2017, 2019; Li and Stackhouse 2020). In Fig. 7, we compare the electrical conductivity of siderite with major lower mantle minerals, ferropericlase and bridgmanite, at 300 K (Peyronneau and Poirier 1989; Shankland et al. 1993; Li and Jeanloz 1990; Lin et al. 2007a; Ohta et al. 2007; 2008; 2010; Yoshino et al. 2011; Sinmyo et al. 2014). The spin transition in siderite and ferropericlase reduces the electrical conductivity (Lin et al. 2007a; Ohta et al. 2007; Yoshino et al. 2011). Previous studies suggest that for ferromagnesite the pressure-temperature range of iron spin transition is sharper and not much influenced by the iron content as instead in the case of ferropericlase (Lin et al. 2007b; Liu et al. 2014; Müller et al. 2017), where the transition pressure gradually increases with increasing iron content and spreads over a wide pressure-temperature range, with the consequence of clearly affecting the physico-chemical properties of this material in the lower mantle (Yoshino et al. 2011; Liu et al. 2014, 2020; Zhao et al. 2020). Therefore, the effect of spin transition in ferromagnesite could be more visible, using the proper tools, under lower mantle conditions. Previous studies reported the existence of heterogeneous electrical conductivity structures observed mainly in the mid-lower mantle at around 900–1400 km depth (Tarits and Mandéa 2010; Velímský and Knopp 2021), which is approximately corresponding to pressures between 37 and 57 GPa. Although the influence of other predominant minerals on electrical conductivity may be large, the spin transition in ferromagnesite can contribute to the electrical conductivity heterogeneity. Further observational constraints on the lateral conductivity heterogeneity and experimental studies on the electrical conductivity of the other minerals that may exist in the lower mantle have important implications for its thermal and chemical structures.

In conclusion, we found a robust decrease in the electrical conductivity of siderite around 50 GPa at room temperature. This behavior is similar to previous experimental results of electrical conductivity of ferropericlase (Lin et al. 2007a; Ohta et al. 2007; Yoshino et al. 2011), which were addressed to the spin transition of iron atoms. The pressure range where the change in pressure dependence of electrical conductivity of siderite is observed, agrees with the high- to low-spin transition pressure confirmed by Raman and Mössbauer spectroscopic measurements performed in this and previous studies. It is reasonable to think that the electrical conductivity of low-spin state of siderite is lower than that of high-spin state because the small polaron mobility in the low-spin state would become lower than that of high-spin state. Therefore, the observed change in electrical conductivity of siderite can be attributed to the pressure-induced spin transition of iron. Although more experiments on the electrical conductivity of other lower mantle minerals under high-pressure and temperature conditions are necessary to constrain a more realistic lower mantle electrical conductivity model, the existence of magnesite–siderite solid solutions could contribute to the lateral heterogeneity of electrical conductivity observed in the mid-lower mantle (Tarits and Mandéa 2010).