Electrical conductivity model of Al-bearing bridgmanite with implications for the electrical structure of the Earth's lower mantle

Earth and Planetary Science Letters 434 (2016) 208–219

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Electrical conductivity model of Al-bearing bridgmanite with implications for the electrical structure of the Earth’s lower mantle Takashi Yoshino a,∗ , Seiji Kamada b,c , Chengcheng Zhao a , Eiji Ohtani b , Naohisa Hirao d a

Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193, Japan Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Miyagi, Sendai 980-8578, Japan c Department of Earth and Planetary Material Sciences, Tohoku University, Miyagi, Sendai 980-8578, Japan d Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 678-5198, Japan b

a r t i c l e

i n f o

Article history: Received 30 July 2015 Received in revised form 7 November 2015 Accepted 23 November 2015 Available online 9 December 2015 Editor: J. Brodholt Keywords: Al content bridgmanite electrical conductivity lower mantle small polaron synchrotron Mössbauer spectroscopy

a b s t r a c t Electrical conductivity measurements of bridgmanite with various Al contents and a constant Mg# of 90 were performed at temperatures ranging from room temperature up to 2000 K at pressures of 26–28 GPa in a Kawai-type multianvil apparatus by impedance spectroscopy analysis. The incorporation of Al into bridgmanite raises its electrical conductivity significantly, but it is a small conductivity variation with respect to the quantity of Al. Synchrotron Mössbauer spectroscopy of recovered samples showed significant amounts of ferric iron in aluminous bridgmanite. The mobility of the charge carriers in bridgmanite was calculated based on the conductivity and the Fe3+ / Fe ratio. The relationship between the logarithm of the electrical conductivity and the reciprocal temperature is consistent with Fe2+ –Fe3+ electron hopping (small polarons) as the dominant conduction mechanism at low temperatures (<1400 K) and ionic conduction at higher temperatures (>1600 K). By taking various conduction mechanisms into account, we develop an electrical conductivity model for aluminous bridgmanite as a function of the Al and Fe contents. The small polaron conduction model indicates that the electrical conductivity of aluminous bridgmanite has a maximum at around 0.06 Al atoms per formula unit, and any further increase in the Al content in bridgmanite reduces the conductivity. In contrast, the ionic conduction model indicates that the electrical conductivity simply increases with increasing Al content. The resulting conductivity of Al-bearing bridgmanite first increases up to 0.06 Al atoms per formula unit and then remains constant or increases with increasing Al content at higher temperatures. The increase in conductivity observed in the uppermost part of the lower mantle by electromagnetic studies can be explained by the gradual decomposition of majorite garnet. The deeper lower mantle conductivity would be controlled by small polaron conduction because of the large positive activation volume required for ionic conduction. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Electrical conductivity measurements provide a useful method for constraining temperature, structure and composition of Earth’s deep interior (e.g., see Yoshino, 2010; Yoshino and Katsura, 2013). Conductivity-depth profiles from Earth’s surface to the deep mantle have shown that conductivity increases with increasing depth up to 800–1000 km, and becomes constant at greater depths (e.g., Olsen, 1999a, 1999b; Tarits et al., 2004; Kuvshinov et al., 2005; Kuvshinov and Olsen, 2006; Velímský, 2010; Civet et al., 2015). This increase in conductivity in the uppermost lower mantle cannot be explained by a major pressure-induced phase transforma-

*

Corresponding author. E-mail address: [email protected] (T. Yoshino).

http://dx.doi.org/10.1016/j.epsl.2015.11.032 0012-821X/© 2015 Elsevier B.V. All rights reserved.

tion, because the post-spinel phase transition occurs at approximately 23.5 GPa, and is related to the 660-km seismic discontinuity (Ito and Takahashi, 1989). Bridgmanite is a dominant constituent mineral in the lower mantle. Thus, knowledge of the electric conduction mechanism for bridgmanite is essential to understand the conductivity profile of the lower mantle. Bridgmanite is thought to store much of the Al and Fe content in the lower mantle (Irifune, 1994; Wood and Rubie, 1996). One plausible hypothesis that accounts for the increased conductivity in the uppermost lower mantle is that the increase in the Al content of bridgmanite with increasing depth is associated with the continuous decomposition of majorite garnet to depths of approximately 800 km in pyrolitic composition (Irifune et al., 2010). We report here on a systematic study of the effect of the Al content on the electrical conductivity of bridgmanite to investigate this hypothesis.

T. Yoshino et al. / Earth and Planetary Science Letters 434 (2016) 208–219

Early studies involving electrical conductivity measurements of bridgmanite were performed using Fe-bearing and Al-free compositions at low temperatures (Peyronneau and Poirier, 1989; Shankland et al., 1993). This work indicated that small polaron conduction characterized by electron-hole hopping between the ferrous and ferric iron sites is a dominant conduction mechanism. Later, Katsura et al. (1998) measured the conductivity of Al-free bridgmanite at higher temperatures in a Kawai-type multi-anvil press, and found that ionic conduction with a strong temperature dependence is dominant at high temperatures rather than small polaron conduction. However, Xu et al. (1998) reported that Al incorporation in bridgmanite strongly enhances the small polaron conduction mechanism. There are large variations in the Al content of bridgmanite under lower mantle conditions. For example, the Al contents of bridgmanite in pyrolitic and mid-ocean ridge basalt (MORB) compositions are 3.5–6 and 15 wt%, respectively (Irifune et al., 2010; Ono et al., 2001). However, the electrical conductivity of aluminous bridgmanite has not previously been measured as a function of its Al content. In this study, impedance spectroscopy measurements were performed at 26 or 28 GPa and at temperatures up to 2000 K in a Kawai-type multi-anvil apparatus to investigate the effects of the Al content on the electrical conductivity of bridgmanite. To understand the role of the small polaron conduction mechanism, the ferric iron content of the bridgmanite was determined by synchrotron 57 Fe Mössbauer absorption spectroscopy. We then used the results of these measurements to construct a conductivity model of bridgmanite as a function of the Al and Fe contents. Finally, we will discuss the origin of the conductivity increments observed in the uppermost lower mantle and a conductivity-depth profile of the lower mantle based on the proposed conductivity model. 2. Experimental procedure The starting materials were synthetic orthopyroxene (Mg0.9 , Fe0.1 )SiO3 powders containing various amounts of aluminum (Al2 O3 = 0, 4, 7 and 11 wt.%). To measure its electrical conductivity, the sample powder was placed in an Al2 O3 sleeve with an inner diameter of 1.3 mm and a thickness of 1 mm. Molybdenum electrodes (1.3 mm-diameter) were then placed in contact with the sample; the measured conductivity included that of the electrodes in addition to that of the sample. The oxygen fugacity was controlled using a Mo/MoO2 buffer, which is close to or slightly higher than an iron-wüstite buffer (Xu et al., 1998). Two sets of WRe3 –WRe25 thermocouples were mechanically connected to each of the Mo electrode in contact with the sample, and were insulated from the LaCrO3 furnace using Al2 O3 and MgO insulators. The assembly consisted of a Cr2 O3 -bearing MgO pressure medium, a ZrO2 thermal insulator and a cylindrical LaCrO3 furnace. Tungsten carbide cubes with truncated edge lengths of 3 mm were used. The conductivity measurement cell design is described in detail elsewhere (Yoshino et al., 2008a). Xu et al. (1998) found that the iron loss from the sample to the electrodes during synthesis of the high-pressure phase prior to performing the conductivity measurements leads to abnormally low conductivity values, and thus emphasized the importance of pre-synthesis of the high-pressure phase in a separate run. Therefore, a sample (4 wt% Al2 O3 ) was synthesized before the conductivity measurements were performed. The orthopyroxene powder was placed in a molybdenum capsule. The synthesis experiments were conducted at 25 GPa and 1873 K in the Kawai-type multianvil apparatus for 4 h within the stability field of bridgmanite. The retrieved samples were polished to remove the iron-poor part that existed close to the buffer material (Mo foil). Phase identifications were then carried out using a micro-beam X-ray diffractometer in reflection geometry. Finally, the polished samples were

209

Table 1 Chemical composition of run products. 5K1478a n=6

5K2629 n = 15

5K1485 n=7

5K1488 n=6

SiO2 Al2 O3 FeOb MgO CaO Na2 O Total

57.40(98) 4.06(20) 7.11(11) 36.24(81) 0.37(11) 0.04(3) 105.24(112)

56.31(81) 4.07(48) 7.09(62) 36.20(63) 0.25(15) 0.03(3) 104.63(32)

58.20(139) 6.48(58) 6.15(44) 34.05(228) 0.30(14) 0.06(4) 105.20(278)

51.62(112) 10.45(66) 7.07(89) 31.41(116) 0.31(12) 0.11(5) 100.11(160)

O=3 Si Al Fe Mg Ca Na Total

0.94(1) 0.08(0) 0.10(0) 0.89(2) 0.01(0) 0.001(0) 2.02(1)

0.95(1) 0.13(1) 0.08(1) 0.83(4) 0.01(0) 0.002(1) 1.99(2)

0.89(1) 0.21(1) 0.09(1) 0.81(3) 0.01(0) 0.003(1) 2.01(1)

Mg#

90.1(1)

0.94(1) 0.08(1) 0.10(1) 0.90(1) 0.00(0) 0.001(1) 2.02(4) 90.1(8)

90.8(1)

90.0(1)

The chemical compositions of melt were measured by an electron probe microanalyzer under the operating condition of 15 kV and 12 nA. a This run failed in the conductivity measurement by breakage of lead wire. Albearing bridgmanite was synthesized at 1900 K and 26 GPa, and was used for synchrotron Mössbauer spectroscopy. b

FeO is assumed that all Fe is ferrous iron.

prepared in the form of disks for use in the conductivity measurements. Impedance spectroscopic measurements were carried out using a Solartron 1260 impedance gain-phase analyzer combined with a Solartron 1296 interface, which makes it possible to measure the properties of very high impedance materials (up to 1014 ). Complex impedances were obtained at frequencies ranging from 1 MHz down to 0.1 Hz. The fundamental applied voltage is 1 V. The impedance spectra of Al-bearing bridgmanite measured at various temperatures generally showed a semicircular arc characteristic at low temperatures, suggesting that the equivalent circuit of the material is a sample resistance and capacitance in parallel (Supplementary Fig. 1). The sample resistance was calculated by fitting of the experimental data under the assumption that the equivalent circuit is a resistance–capacitance parallel circuit. At higher temperatures, the first arc disappeared and the induction component derived from the lead wire appeared. The conductivity values were computed from impedance values ( Z  ) that were measured at the frequency where the phase shift is closest to zero. In the case where orthopyroxene was used as the starting material, during heating to 1500 K, the nominal conductivity generally increased with increasing temperature and exceeded 1 S/m. During continuous heating to more than 1800 K, and following annealing at this temperature, the conductivity decreased until the orthopyroxene was completely transformed into bridgmanite, and then became nearly constant. After annealing for 1 h, heating and cooling cycles were repeated over a temperature range from 500 to 2000 K. During each cycle, the temperature was changed in 50–100 K increments and the electrical conductivity was measured at each temperature. Subsequent heating and cooling cycles were conducted until the reversibility of the conductivity behavior was confirmed. After the conductivity measurements, the presence of bridgmanite was confirmed by micro-focused X-ray diffraction in all the samples. The samples were then polished to observe their microstructure by scanning electron microscopy and to determine their chemical compositions using electron microprobe analysis (EPMA), which was performed under operating conditions of 15 kV, 12 nA, a point beam and a 10-s counting time. The measured chemical compositions are summarized in Table 1. Finally, the samples were prepared in the form of doubly-polished thin

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T. Yoshino et al. / Earth and Planetary Science Letters 434 (2016) 208–219

Table 2 Summary of runs. Run no. d

Al pfu

H2 O (ppm.wt)a

P (GPa)

T (K)

log σ0 (S/m)b

Hσ

log μ0 (m2 V−1 s−1 )c

Eh

350–1100 1750–2000 400–1800 500–1500 1600–1800 310–1400 1700–2000 small polaron

3.72 5.75 5.14 4.69 6.65 5.05 6.02

0.46 0.90 0.57 0.48 1.17 0.47 0.79

−4.25

0.42

−6.67 −3.64

0.57 0.55

−3.71

0.52

−3.91

0.49

5K906

0

n.d.

25

5K2629 5K1485

0.08 0.13

0e 17(2)

26 26

5K1488

0.21

92(12)

28

Average a

(eV)b

(eV)c

Water content in bridgmanite was calculated from subtraction of a sharp peak at 3100 cm−1 derived from stishovite based on an empirical equation proposed by Paterson

(1982). b c d e

Values are derived from fitting σ = σ0 exp(− H σ /kT ) to the experimental conductivity data. Values are derived from fitting μ T = μ0 exp(− E h /kT ). Reference from Yoshino et al. (2008b). Sample (5K1478) synthesized at the conductivity measurement condition same as 5K2629.

sections with a thickness of less than 200 μm to determine their ferric iron concentrations by synchrotron Mössbauer spectroscopy and their H2 O content by Fourier transformation infrared (FTIR) spectroscopy. Synchrotron Mössbauer spectroscopy (SMS) measurements at room temperature were performed to clarify Fe3+ / Fe ratios of the samples. Energy-domain SMS measurements using a nuclear Bragg monochromator were performed at beamline BL10XU at SPring-8 in Japan. The 14.4-keV single-line 57 Fe-Mössbauer radiation obtained from broadband synchrotron radiation (SR) is filtered via the electronically forbidden pure nuclear Bragg (333) reflection of a single 57 FeBO3 crystal near the Néel temperature in the external magnetic field. The source Doppler shift is produced by oscillating the crystal, which is mounted on a velocity transducer, parallel to the reflection plane. The energy of the X-rays used in the Mössbauer spectroscopy experiments was 14.4125 keV, which was gained using a double-crystal pre-monochromator. The bandwidth of the incident X-rays was then set at around 4 meV using a high-resolution monochromator. The final energy-bandwidth product of the X-ray beam is thus set to be around 15 neV. The typical data collection time was 4 h for the spectra of doublets. The Mössbauer data were obtained using a sinusoidal acceleration spectrometer fitted with 1024 channels. The isomer shift was referenced to a standard metallic iron foil under ambient conditions, and the Doppler velocity was also calibrated with respect to the same standard. The MossA software package (Prescher et al., 2012) was used for the computational analysis and the spectra were fitted using a Lorentzian model. The results are shown in Table 2. Because Al-bearing bridgmanite can contain considerable amounts of water (e.g., Murakami et al., 2002; Litasov et al., 2003), proton conduction may be dominant in the lower temperature range. The presence of water in the samples was evaluated by non-polarized FT-IR spectroscopy after the conductivity measurements. The IR beam with dimensions of ∼50 × 50 μm was directed onto the sample. Background corrections for the absorbance spectra were performed via a spline fit of the baseline. At least four measurements were performed for each sample. The Paterson calibration was used to calculate the water contents of the bridgmanite aggregates from their FTIR spectra (Paterson, 1982). These results are also given in Table 2. 3. Experimental results The samples that were recovered after the conductivity measurements were composed of bridgmanite with tiny amounts of stishovite, and showed an equigranular texture with a grain size of a few micrometers. The electron microprobe data for the bridgmanite samples are reported in Table 1. The Fe and Al contents of

the bridgmanite were similar to those of the starting materials, and the Mo content of the bridgmanite phase was below the detection limit, indicating that the Mo electrodes had not caused any contamination. However, some of the samples with high Al content also contained significant amounts of Na. These samples showed uniform compositions in the electron microprobe data. Also, while Frost et al. (2004) proposed that Al-bearing bridgmanite should coexist with metallic iron, the presence of metallic iron was not confirmed by field emission scanning electron microscopy observations. An example of the conductivity measurement of the presynthesized Al-bearing bridgmanite is shown in Fig. 1. The nominal conductivity increased with increasing temperature. The electrical conductivity (σ ) for the ionic and small polaron conduction mechanisms, which are generally considered to be the dominant conduction mechanisms of nominally anhydrous mantle minerals, can be expressed as follows:

σ=

σ0 T

 exp −

H kT

 ,

(1)

where σ0 is the conductivity at an infinitely high temperature,  H is the activation enthalpy for conduction, and k is the Boltzmann constant. The relationship between log σ and the reciprocal temperature cannot be fitted using a straight line (Fig. 1a), whereas the plot of log σ T vs 1000/ T can be fitted well by a straight line (Fig. 1b). Therefore, the conduction mechanism of the pre-synthesized sample can be considered as a single conduction mechanism of either ionic or small polaron conduction. Fig. 2 shows the electrical conductivity data for Al-free and Al-bearing bridgmanite samples. The electrical conductivity of the Al-bearing bridgmanite is distinctly higher than that of the Alfree sample. However, the variation in the electrical conductivity is small and shows no systematic change with the Al content. At temperatures below 1400 K, the activation enthalpies of all samples are approximately 0.5 eV. At higher temperatures (i.e., >1800 K), corresponding to the temperature conditions of the uppermost lower mantle, the conductivities of the samples tend to increase with increasing temperature, with the exception of bridgmanite with only intermediate amounts of Al. The activation enthalpy is occasionally more than 1 eV for Al-free bridgmanite at high temperatures (see Table 2). The Mössbauer spectra show a significant Fe3+ presence in the Al-bearing bridgmanite, and are similar to spectra that were reported by McCammon (1997, 1998) and Lauterbach et al. (2000). The Fe3+ / Fe ratio of the Al-free sample is nearly 0%, whereas those of Al-bearing samples are estimated to be more than 40% or even 60%, when it is assumed that all Fe is substituted into site A (Fig. 3), or that Fe3+ is incorporated at both sites A and B (Supple-

T. Yoshino et al. / Earth and Planetary Science Letters 434 (2016) 208–219

211

Fig. 1. Electrical conductivity variation as a function of reciprocal temperature for a Mg# of 90 bridgmanite with Al pfu = 0.08, which is a pre-synthesized sample before conductivity measurement. (a) Electrical conductivity versus reciprocal temperature. Note that data follow an upward concave curve; a solid straight line is provided as a reference. (b) Electrical conductivity time temperature versus reciprocal temperature. The solid line indicates a fitting result corresponding to Eq. (1).

sults from the model where all Fe occupies site A in the following discussion for the small polaron conduction mechanism. The FTIR spectra of some of the samples exhibit absorption over a wide range of wavenumbers from 3800 to 3000 cm−1 , with an asymmetric peak occurring at around 3450 cm−1 (Supplementary Fig. 3), which is consistent with the results of previous studies (Litasov et al., 2003). In addition, the IR spectra show a sharp absorption band at 3110 cm−1 , which is derived from hydrous stishovite (Panero et al., 2003). The results presented here indicate that if the system has a significant aluminum content, the water preferentially partitions into aluminous stishovite. The estimated H2 O content in Al-bearing bridgmanite is less than 100 ppm by weight. 4. Discussion 4.1. Conduction mechanism of Al-bearing bridgmanite

Fig. 2. Electrical conductivity of Al, Fe-bearing bridgmanite (blue: Al pfu = 0.08; green: Al pfu = 0.13; red: Al pfu = 0.21) as a function of reciprocal temperature. Black symbol indicates previous result for Al-free Mg#90 bridgmanite (Yoshino et al., 2008b). Light green line represents a result of Al-free Mg#93 bridgmanite (Katsura et al., 1998). Blue and orange solid lines denote Al-free and Al-bearing bridgmanite, respectively (Xu et al., 1998). A thick pink line represents majorite garnet with pyrolite minus olivine composition (Yoshino et al., 2008a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

mentary Fig. 2), respectively (Table 3). The proportion of Fe3+ at site A tends to increase with increasing Al content, suggesting that a considerable Fe3+ content caused by the Al incorporation into bridgmanite can induce enhanced conductivity by small polaron conduction. Under the conditions of the uppermost lower mantle, a single crystal X-ray diffraction study indicated that Fe (including both Fe2+ and Fe3+ ) does not occupy the octahedral site (B) for combined substitution of Al and Fe into the perovskite structure (Vanpetegham et al., 2006). Therefore, we basically use fitted re-

In ionic crystals, the interaction of the electrons with the lattice is too strong for general band theory to be applied (Poirier, 1999), so the electric charges (i.e., electrons or holes) then move via thermally activated jumps from one site to another. The presence of the electric charge induces deformation of the surrounding lattice by attractive and repulsive forces, and the charge then becomes self-trapped, forming a small polaron. This type of conduction has been observed in oxides, including transition metal oxides, when the metallic ions have different valence states. The mobility of the small polaron is controlled by the amount of Fe3+ content as a result of the oxidation state. For example, magnetite, which has equivalent numbers of Fe2+ and Fe3+ ions, has very low  H (nearly 0 eV) because it has almost no lattice strain, whereas olivine and its high-pressure polymorphs, which contain low amounts of Fe3+ , have high  H (more than 1.3 eV) due to high lattice strain (Yoshino et al., 2012). A systematic study of small polaron conduction in ferropericlase also shows a strong dependence of the Fe content on  H (Dobson and Brodholt, 2000; Yoshino et al., 2011). We demonstrate that at temperatures below approximately 1400 K,  H is very low (of the order of 0.5 eV), which is consistent with the values reported by Peyronneau and Poirier (1989) and Shankland et al. (1993), who measured the conductivity of quenched perovskites. This low  H results in a relatively high Fe3+ / Fe ratio in Al-bearing bridgman-

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Fig. 3. Room temperature synchrotron Mössbauer spectra of bridgmanite with various Al contents and the Al contents indicated. Red line indicates a fitting result. The doublets are assigned as follows: green (Fe2+ ), blue (Fe3+ ). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 3 Hyperfine parameters for bridgmanite from Mössbauer spectra recorded at 300 K. (QS quadrupole shift, FWHM full width at half maximum, IS isomer shift, A relative area.) Run #

5K906 5K1478 5K2629 5K1485 5K1488

Fe2+ A

Fe3+ A

Fe3+ B

χ 2 /dof

QS

FWHM

IS

A

QS

FWHM

IS

A

QS

FWHM

IS

A

1.62(5) 1.91(14) 2.00(11) 2.05(14) 2.32(15) 2.17(29) 2.35(11) 2.35(10)

1.05(9) 0.78(21) 0.55(17) 0.74(26) 0.52(31) 0.43(34) 0.33(23) 0.28(20)

1.14(3) 0.99(8) 1.01(6) 0.93(7) 0.89(8) 1.04(16) 0.96(7) 0.99(5)

54(29) 40(6) 36(14) 28(15) 22(7) 28(29) 24(5)

0.99(24) 0.76(6) 0.63(9) 0.98(13) 0.86(8) 1.00(29) 0.84(3)

0.15(29) 0.43(12) 0.85(30) 0.16(16) 0.41(10) 0.12(24) 0.29(6) 0

0.54(4) 0.57(3) 0.65(5) 0.53(3) 0.51(4) 0.55(2) 0.55(2)

31(30) 60(6) 64(12) 53(22) 78(7) 49(50) 76(5)

0.33(35)

0.10(82)

0.54(6)

15(30)

0.37(26)

0.10(58)

0.47(6)

19(25)

0.46(62)

0.10(73)

0.56(5)

22(56)

1.060 2.083 2.109 1.038 1.037 1.049 0.965 0.969

ite when compared with that of other mantle minerals. Pro-

1700 K, the hydrogen self-diffusion coefficient in bridgmanite

ton conduction is the other dominant conduction mechanism in

based on the Nernst–Einstein relation (10−7 m2 /s) is estimated

nominally anhydrous minerals (NAMs) at low temperatures. At

to be slightly higher than the same coefficients in other NAMs

T. Yoshino et al. / Earth and Planetary Science Letters 434 (2016) 208–219

(less than 10−8 m2 /s) (see e.g., Demouchy and Mackwell, 2006; Sun et al., 2015). While proton conduction in NAMs also has low  H (e.g., Yoshino and Katsura, 2013), the  H (>0.8 eV) for proton conduction in NAMs with low H2 O content (less than 100 ppm by weight) is distinctly higher than 0.5 eV determined by this study. In addition, there is no systematic relationship between the H2 O content in bridgmanite and the measured conductivity. Therefore, small polaron conduction should be considered the dominant conduction mechanism of Al-bearing bridgmanite at relatively low temperatures. At temperatures higher than 1600 K, our conductivity values deviate from the extrapolated values of small polaron conduction with the lower  H at lower temperatures, except in the case of bridgmanite with relatively low Al content. Katsura et al. (1998) reported a high  H (0.92 eV) obtained at temperatures ranging from 1600 to 2000 K, and concluded that the dominant conduction mechanism changes in that temperature range from small polaron to ionic conduction. Later, Xu and McCammon (2002) reported that in Al-bearing bridgmanite with Mg# of 92, ionic conduction characterized by a high  H (1.43 eV) becomes significant at temperatures above 1700 K. This conduction process with the higher activation enthalpy was interpreted in terms of the presence of oxygen vacancies, which chargebalance the substitution of Al and Fe3+ onto site B (Brodholt, 2000; Lauterbach et al., 2000). Thus high  H obtained at high temperatures in this study would thus imply a significant ionic conduction contribution because of the considerable numbers of the oxygen vacancies. 4.2. Conductivity model of Al-bearing bridgmanite The electrical conductivity of a material consists of the sum of the contributions from the various conduction mechanisms, i.e.

σ=



N jq jμ j,

(2)

j

where N j is the density of the j-th type of charge carrier, q j is the effective charge (q = ze), and μ j is its mobility. The activation energies for each conduction mechanism depend on the energies required for the charge mobility for that conduction mechanism. In addition, there is also temperature dependence of a defect concentration for many extrinsic (and all intrinsic) charge carriers (Poirier, 1999). The electrical conductivity for each conduction mechanism can be expressed based on the Nernst–Einstein equation

σ=

μ Nq2 kT

(3)

,

where μ denotes the temperature-dependent diffusion coefficient, k is the Boltzmann constant, and T is temperature. As shown in Fig. 3, the incorporation of Al in the perovskite structure is accompanied by the creation of a significant numbers of Fe3+ ions, independent of the oxygen fugacity (Lauterbach et al., 2000). Therefore, small polaron conduction should be considered to be one of dominant conduction processes in Al and Fe-bearing bridgmanite. Knowledge of the mobility of the small polaron is thus required to determine the electron hopping conductivity of bridgmanite at high temperatures under high pressure. The small polaron hopping mobility (μh ), when taking the Arrhenian form, is defined by

μh =

μ0h T

 exp −

Eh kT

 ,

(4)

213

Fig. 4. Mobility of charge carriers in bridgmanite. Solid symbols represent values calculated from the electrical conductivity data using Eqs. (3)–(5), whereas the line represents a fit to the small polaron model (Eq. (1)). Triangles denote values calculated from Al-free bridgmanite data from Yoshino et al. (2008b) assuming Fe3+ / Fe = 0.11 predicted from the fitting result of Eq. (9). Shaded lines are taken from Katsura et al. (1998) and Xu and McCammon (2002). The slight curvature is due to the 1/ T term in the mobility equation.

where μ0h is the pre-exponential factor. The charge carrier density is given by

N=

X Fe sN A V

(5)

,

where X Fe is the atomic fraction of total Fe per formula unit, s is the Fe3+ / Fe ratio, N A is the Avogadro constant, and V is the unit cell volume. Using the charge carrier concentrations for each sample, which were determined from the EPMA and Mössbauer data, we can calculate the charge carrier mobility from the electrical conductivity data that were obtained at low temperatures based on Eqs. (3)–(5). The temperature dependence of the charge carrier mobility for the small polaron model was fitted using Eq. (4). The variable fitting parameters are given in Table 2. Fig. 4 shows that the model fits the measured data well at low temperatures for Alfree bridgmanite. The charge carrier mobilities for all samples are quite consistent with each other. The calculated mobility range for bridgmanite is of the order of 10−9 m2 V s−1 and is slightly lower than that given by Xu and McCammon (2002). However, the activation enthalpy for small polaron conduction is consistent with the results of that earlier study. The electrical conductivity for small polaron conduction (σh ) is given by

σh =

N Fe cq2 μh kT

=

g N Fe c (1 − c )q2 a2 v kT

 exp −

Eh kT

 ,

(6)

where g is a geometric factor of the order of unity, N Fe is the density of the iron ions that involved in conduction, c is the fraction of these ions that are small polarons, (1 − c) is the corresponding fraction of the opposing valence, and which is therefore available for hopping, a is the jump distance, v is the lattice vibrational frequency responsible for hopping, and  E h is the hopping energy (Tuller and Nowick, 1977; Mason, 1987; Poirier, 1999). By defining μ0h = (1 − c ) A, where A is a constant that includes unknown

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T. Yoshino et al. / Earth and Planetary Science Letters 434 (2016) 208–219

parameters (g, a, v), the small polaron conductivity was finally calculated using the following equation:

σh =

N Fe c (1 − c )q2 A kT



Eh

exp −

kT

 .

(7)

For this calculation, the values of A and  E h that were obtained by fitting of our data are 10−6.92 and 0.49 eV, respectively. The relationship between Al, X Fe and the ferric iron contents (s) in Al-bearing bridgmanite was modeled based on the following assumptions. Assuming that this type of substitution (MgA 2+ + SiB 4+ ⇔ FeA 3+ + AlB 3+ ) occurs, X Fe can be expressed as a function of the Al content, the Fe3+ / Fe ratio and the Mg#:



X Fe =

1 − (1 − Mg#/100)s − X Al ) 2



1−

Mg# 100

 ,

(8)

where X Al is the atomic fraction of Al per formula unit. From a compilation of the available data for the relationship between X Al and the Fe3+ / Fe ratio (s) (Supplementary Fig. 4), we can express this relationship using the following empirical equation





s = a1 + b1 1 − exp(−c 1 X Al )

(9)

where a1 (0.12), b1 (0.75) and c 1 (−10.38) are the fitting parameters that are available over a limited range (0 < X Al < 0.25). Ionic conduction in bridgmanite has been considered to be caused by the migration of extrinsic oxygen vacancies by the substitution of impurities such as Na+ , Al3+ and Fe3+ in bridgmanite (Xu and McCammon, 2002; Dobson, 2003; Dobson et al., 2008). Because it is quite difficult to determine the extrinsic oxygen vacancy concentration X (Vo¨ ) accurately, in this study, three models of ionic conduction based on migration of extrinsic oxygen vacancies in Al-bearing bridgmanite were considered: 1) a fixed model, 2) the XM model, and 3) Fe3+ in the site B model based on the present SMS data. In the fixed model, the extrinsic oxygen vacancy concentration X (Vo¨ ) was assumed to be constant for the Al content in bridgmanite. We used values of 106.79 S/m and 1.43 eV for σ0 and  H , respectively, which were determined from Al and Febearing bridgmanite as reported by Xu and McCammon (2002). In the XM model, X (Vo¨ ) was estimated from the ideal stoichiometry [Fe3y+ (Fe2+ , Mg1− y ) Alz Si1−z O3−x , where X = ( z − y )/2]. The pre-exponential factor (σ0 ) for ionic conduction in Eq. (1) for the electrical conductivity was calculated from the ratio of Si4B+ between the calculated X value and the value of 0.015 that was obtained by Xu and McCammon (2002). Fe3+ may have substituted for Si4+ at site B and can be charge balanced by introducing a vacancy in the oxygen site: 2Si4B+ + O2− = 2Fe3B+ + Vo¨ , although both Fe2+ and Fe3+ are not favorable for site B (Vanpetegham et al., 2006). While we assume that Fe3+ is incorporated at both sites A and B, the fitting results from the Mössbauer spectrum indicate that the Fe3+ at site B tends to increase with increasing Al content. Based on the relationship between X Al and Fe3B+ (t ) (Supplementary Fig. 5), we can express this relationship using the following empirical equation





t = a2 1 − exp(−b2 X Al ) ,

(10)

where a2 (0.23) and b2 (13.0) are the fitting parameters that are available over a limited range (0 < X Al < 0.25). X (Vo¨ ) was calculated from t /2, and the pre-exponential factor (σ0 ) required for ionic conduction in Eq. (1) for the electrical conductivity was calculated from the X (Vo¨ ) ratio between the calculated X value and 0.015. Dobson (2003) reported a similar  H (1.4 ± 0.2 eV) value for the electrical conductivity of Na-doped Fe-free bridgmanite at lower temperatures, i.e., below 1800 K. The observation that the pre-exponential factor is proportional to the Na content was also

supported by extrinsic oxygen ionic conduction. Na incorporation in the perovskite structure is a substitution coupled with an oxygen vacancy, which can be expressed using the Kröger–Vink notation (Dobson, 2003);

Na2 O + 2MgMe + OO → 2NaMe + VO¨ + 2MgO.

(11)

If bridgmanite with its natural composition contains significant numbers of extrinsic oxygen vacancies derived from the substitution of Na, this type of extrinsic oxygen ionic conduction might be dominant in the lower mantle. Finally, the bulk conductivity of Albridgmanite was calculated as a summation of the small polaron conduction and each oxygen ionic conduction mechanism using Eq. (2). Fig. 5 shows the conductivity variation of Al-bearing bridgmanite with the Mg# of 90 as a function of the Al content at various temperatures, and these results are also comparable with our experimental data. The small polaron model (dotted line) indicates that the conductivity initially increases and then gradually decreases with increasing Al content. The maximum conductivity occurs when Al per formula unit (pfu) = 0.06, which corresponds to Fe3+ / Fe = 0.5. The Al content of bridgmanite (0.1 pfu) in the pyrolitic mantle composition is slightly lower than that at the conductivity maximum. The ionic conduction contribution to the bridgmanite bulk conductivity increases with increasing temperature. In the models that consider the creation of oxygen vacancies due to Al substitution into bridgmanite, ionic conduction (thin lines) increases monotonically with increasing Al content. The resulting bulk conductivity abruptly increases once with Al content of up to 0.06 pfu, and then decreases slightly with further increases in Al. In the XM model (Fig. 5b), the bulk conductivity increases continuously with increasing Al content at high temperatures (e.g., 2000 K) because of the large ionic conduction contribution. Fig. 6 shows the conductivity variation as a function of the Mg# with constant Al content (0.1 pfu). At high temperatures, the electrical conduction in bridgmanite with a very high Mg# is mostly controlled by ionic conduction. As the total Fe content increases, the conductivity increases monotonically because of an increase in the number of charge carriers that leads to small polaron conduction. In the XM model, the conductivity difference caused by differences in Mg# tends to become smaller at higher temperatures (Fig. 6b). The small polaron conduction contribution is dominant with decreasing Mg#, even at high temperatures, which suggests that the electrical conductivity of bridgmanite with significant Fe content originating from the subducted slab with the MORB composition could be governed by the small polaron conduction. The measured conductivity data for bridgmanite are consistent with the values calculated from the model. However, the higher conductivity values that were obtained from a sample with the highest Al content cannot be explained by any model that considers ionic conduction. The samples with the high Al contents contained significant levels of Na at site A (Table 1). The highest Na2 O content in bridgmanite measured in the present study is equivalent to that reported by Dobson (2003). Assuming that the concentration of oxygen vacancies caused by Na substitution is defined by the reaction in (11), the calculated conductivity value approaches the value in the present experimental data (Fig. 6d). Therefore, the distinctly higher conductivity of the sample with the highest Al content is possibly caused by the ionic conduction of the extrinsic oxygen vacancies created by the small quantity of Na. However, Na substitution in Al-bearing bridgmanite would differ from the reaction in (11), and the extrinsic oxygen vacancy concentration may be much smaller because of charge-coupled substitutions with Al3+ or Fe3+ . The other possible reason that would explain the discrepancy for the highest Al-bearing sample is proton conduction.

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Fig. 5. Electrical conductivity of bridgmanite with a Mg# of 90 as a function of Al content at 1500, 1700 and 2000 K. (a) Small polaron + ionic conduction using fixed model. (b) Small polaron + ionic conduction using XM model. (c) Small polaron + ionic conduction using Fe3+ in site B model. (d) Small polaron + ionic conduction using XM model + Na incorporation. Symbols indicate the measured conductivity data at 1500 and 1700 K. Dotted and thin solid lines represent small polaron and ionic conduction, respectively. Thick solid lines denote the bulk conductivity of bridgmanite.

The sample with the highest Al content also had significant water content. The near 100 ppm level of water can contribute to the bulk electrical conductivity of Al-bridgmanite by proton conduction. 4.3. Implications for the electrical structure of the lower mantle Bridgmanite is a key mineral that controls the electrical conductivity in the lower mantle with pyrolitic or perovskitic compositions because the relatively small amount of ferropericlase, which has higher conductivity than bridgmanite, cannot establish a 3D interconnected network in a bridgmanite matrix (Yoshino et al., 2008b), apart from very fine-grained postspinel aggregate that was transformed from ringwoodite at very low temperatures (Yamazaki et al., 2014). Because the bridgmanite with the coexisting pyrolitic composition contains a 3–6 wt% Al2 O3 component that corresponds to a Fe3+ / Fe ratio = 0.5, small polaron conduction is likely to be the dominant conduction mechanism at appropriate temperatures for the uppermost lower mantle (i.e., up to 2000 K). Some uncertainties are involved with the extrapolation of our conductivity model to the deeper lower mantle. First, it is nec-

essary to estimate the pressure dependence of the small polaron and ionic conductions. Small polaron conduction in mantle minerals is characterized by a small negative activation volume (olivine: Yoshino et al., 2012; bridgmanite: Shankland et al., 1993; Katsura et al., 2007; Sinmyo et al., 2014). Therefore, the small polaron conductivity increases with increasing pressure, even at constant temperature. The estimated activation volume for small polaron conduction ranges from −0.26 to −0.55 cm3 /mol. Second, the pressure-induced spin transition of iron can also affect the small polaron conduction of bridgmanite. The high-spin to low-spin crossover of iron can affect on the electrical conductivity of ferropericlase strongly (Lin et al., 2007; Yoshino et al., 2011). In addition, recent ab initio calculations indicated that low-spin ferropericlase shows semimetallic conduction characteristics at high temperatures (Holmström and Stixrude, 2015). Although the Fe2+ spin crossover in bridgmanite remains highly controversial, recent studies do agree that the Fe3+ at site A remains in the high-spin state up to at least 135 GPa, and the Fe3+ at site B undergoes a high-spin to low-spin crossover at pressures below 70 GPa (Catalli et al., 2011; Fujino et al., 2012; Mao et al., 2015). However, the occurrence of Fe3+ in the B site of Fe- and Al-bearing bridgmanite is also still being debated. Recent single crystal X-ray diffraction

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Fig. 6. Logarithm of electrical conductivity versus reciprocal temperature of bridgmanite with Al 0.1 pfu for the conductivity models as a function of Mg#. (a) Small polaron + ionic conduction with fixed value. (b) Small polaron + ionic conduction using XM model. (c) Small polaron + ionic conduction using Fe3+ in site B model. Orange hatched area indicates the conductivity range in the uppermost lower mantle observed by EM induction studies. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

studies indicated that both Fe2+ and Fe3+ occupy A site of the Feand Al-bearing magnesium silicate perovskites under high pressure and temperature conditions (Glazyrin et al., 2014). Electrical conductivity measurements of Al-free bridgmanite in a diamond anvil cell (DAC) showed a reduction in the conductivity at higher pressures (∼60 GPa) caused by the spin transition (Ohta et al., 2010a). In contrast, recent laser-heated DAC studies showed a continuous increase in the electrical conductivity of Al-bearing bridgmanite with increasing pressure up to 120 GPa (Potapkin et al., 2013; Sinmyo et al., 2014). This indicates that the incorporation of Fe in Al-bearing bridgmanite would not induce an electronic spin transition of Fe3+ because of the absence of Fe3+ at site B. If this is the case, our small polaron conduction model would then apply for the entire lower mantle.

Third, the contribution of ionic conduction to the conductivity of bridgmanite in the deep lower mantle remains unclear. To date, there have been no experimental studies on the pressure dependence of ionic conduction in bridgmanite. However, some ab initio simulation studies have yielded the migration enthalpies of magnesium, silicon and oxygen in MgSiO3 perovskites at various pressures throughout the Earth’s mantle (Wright and Price, 1993; Amman et al., 2009). The activation volume for the ionic conduction is positive, and decreases from 1.95 to 1.49 cm3 /mol with increasing pressure from 25 to 135 GPa, respectively (Amman et al., 2009). The relatively large positive activation volume implies that the contribution of the ionic conduction to the bulk conductivity of Al-bearing bridgmanite decreases abruptly at the depth range of the uppermost upper mantle. On the other hand, numerical simulations indicated that extrinsic oxygen vacancies

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Fig. 7. Electrical conductivity profile of lower mantle along an adiabatic geotherm (Katsura et al., 2010). (a) Solid thick lines indicate the conductivity values calculated from a model in consideration of only small polaron conduction assuming two different activation volumes (−0.3 and −0.6 cm3 /mol). We assumed that 0.06 Al pfu at top of the lower mantle linearly increases to 0.1 Al pfu at 800 km, and Mg# is constant (90) and gradually increases from 90 at 1000 km to 92 at 1200 km due to the change in the partitioning coefficient between bridgmanite and ferropericlase (Irifune et al., 2010). Squares: Al, Fe-bearing bridgmanite (Sinmyo et al., 2014); circles: pyrolite material (Ohta et al., 2010b). Thin solid lines show geomagnetic observations (references appears at the top of the figure). (b) Electrical conductivity profile in the uppermost lower mantle as a function of Al content in bridgmanite at the top of the lower mantle. Numbers following Al and Mg# denote compositional range used for calculation. A single number indicates that the value is assumed to be constant. Numbers following MJ represent a range of volume fraction of majority garnet for calculation.

are destroyed by high pressure conditions (Brodholt, 2000). Indeed, recent laser-heated DAC studies have not observed ionic conduction with high  H , but have observed small polaron conduction with low  H at up to 120 GPa (Ohta et al., 2010b; Sinmyo et al., 2014). Therefore, we conclude that the ionic conduction contribution to the bulk conductivity of bridgmanite would be negligibly small in the deep lower mantle. The 1D conductivity-depth profile obtained from electromagnetic (EM) induction studies performed ranging from over periods of months to years (Fig. 7a) shows a continuous increase of conductivity across the 660-km seismic discontinuity in the uppermost lower mantle (e.g., Olsen, 1999a; 1999b; Tarits et al., 2004; Kuvshinov et al., 2005; Kuvshinov and Olsen, 2006; Velímský, 2010; Civet and Tarits, 2013; Civet et al., 2015). To constrain the conductivity-depth profile of the lower mantle, we have assumed that the adiabatic geotherm of Katsura et al. (2010) applies. The bulk conductivity of bridgmanite was calculated using the XM model for ionic conduction. To realize the continuous increase in conductivity at the uppermost lower mantle, the compositional model was constructed as follows. First, we consider an increase in the Al content of bridgmanite in association with the decomposition of garnet in the uppermost lower mantle. If the Al content in bridgmanite just beneath the 660-km discontinuity is nearly zero, and then increases to 0.1 Al pfu at 800 km, the electrical conductivity can increase by half an order of magnitude at a constant Mg#90. Experimental studies have shown significant Al content in bridgmanite that is coexisting with pyrolitic compositions at 24 GPa (e.g., Hirose, 2002; Nishiyama and Yagi, 2003). When the Al pfu is 0.04 at the top of

the lower mantle, the conductivity is almost constant with depth. An increase in the Fe content (i.e., a decrease in the Mg#) in bridgmanite with depth may effectively increase the conductivity of the lower mantle material. However, the reduction of Mg# from 92 to 90 with depth that was predicted by Irifune et al. (2010) is still insufficient to be considered for the increase in conductivity by nearly half an order of magnitude at that depth. The most likely explanation for this increased conductivity is a gradual reduction of the garnet proportion down to a depth of 800 km, because the electrical conductivity of garnet with a composition of pyrolite minus olivine is more than one order of magnitude lower than that in the Al-bearing bridgmanite (Yoshino et al., 2008a). If the volume proportion of garnet decreases linearly with depth from 40 to 0 vol%, more than half an order of magnitude increase in conductivity in the uppermost lower mantle can be realized. In summary, the continuous increase in conductivity at the uppermost lower mantle requires a large change in the volume fraction of majorite garnet at that depth. Irifune et al. (2010) found a sudden reduction in the ironmagnesium partition coefficient (K D ) at approximately 40 GPa that can be explained by a spin transition in ferropericlase, and Fe depletion in bridgmanite that could be accompanied by a preferential partitioning of Fe in ferropericlase. Because the Fe3+ / Fe ratio in bridgmanite was almost constant in pyrolitic compositions across 40 GPa (Irifune et al., 2010; Sinmyo et al., 2011), the reduction of the total Fe content in bridgmanite caused by a change in the Fe– Mg partitioning at around 40 GPa would also induce a reduction in the conductivity at a depth of 1200 km. Electrical conductivity measurements of pyrolitic materials show a drop in conductivity

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at a depth of 1200 km (Ohta et al., 2010b), whereas the electrical conductivity of Al, Fe-bearing bridgmanite increases monotonically with depth, as observed by Sinmyo et al. (2014). If bridgmanite coexisting with pyrolitic composition has a less amount of Fe after the spin transition of ferropericlase, the K D change would contribute to the conductivity drop at around 40 GPa, even if the interconnection of ferropericlase is not established (Fig. 7a). Acknowledgements The authors would like to thank D. Yamazaki, A. Jephcoat and K. Baba for discussions. The synchrotron Mössbauer spectroscopy experiments were performed at BL10XU in SPring-8 (proposals 2014A0104, 2014B0104 and 2015A0104). This work was supported by a Grant-in-Aid for Scientific Research (No. 24244087) to TY from the Japan Society for the Promotion of Science. We thank two anonymous reviewers for helpful comments. Appendix A. Supplementary material Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.epsl.2015.11.032. References Amman, M.W., Brodholt, J.P., Dobson, D.P., 2009. DFT study of migration enthalpies in MgSiO3 perovskite. Phys. Chem. Miner. 36, 151–158. Brodholt, J.P., 2000. Pressure-induced changes in the compression mechanism of aluminous perovskite in the Earth’s mantle. Nature 407, 620–622. Catalli, K., Shim, S.-H., Dera, P., Prakapenka, V.B., Zhao, J., Sturhahn, W., Chow, P., Xiao, Y., Cynn, H., Evans, W.J., 2011. Effects of the Fe3+ spin transition on the properties of aluminous perovskite—new insights for lower-mantle seismic heterogeneities. Earth Planet. Sci. Lett. 310, 293–302. Civet, F., Tarits, P., 2013. Analysis of magnetic satellite data to infer the mantle electrical conductivity of telluric planets in the solar system. Planet. Space Sci. 84, 102–111. Civet, F., Thëbault, E., Verhoeven, O., Langlais, B., Saturnino, D., 2015. Electrical conductivity of the Earth’s mantle from the first Swarm magnetic field measurements. Geophys. Res. Lett. 42, 3338–3346. Demouchy, S., Mackwell, S., 2006. Mechanisms of hydrogen incorporation and diffusion in iron-bearing olivine. Phys. Chem. Miner. 33, 347–355. Dobson, D.P., 2003. Oxygen ionic conduction in MgSiO3 perovskite. Phys. Earth Planet. Inter. 139, 55–64. Dobson, D.P., Brodholt, J.P., 2000. The electrical conductivity of the lower mantle phase magnesiowüstite at high temperatures and pressures. J. Geophys. Res. 105, 531–538. Dobson, D.P., Dohmen, R., Weidenbeck, M., 2008. Self-diffusion of oxygen and silicon in MgSiO3 . Earth Planet. Sci. Lett. 270, 125–129. Frost, D.J., Liebske, C., Langenhorst, F., McCammon, C.A., Trønnes, R.G., Rubie, D.C., 2004. Experimental evidence for the existence of iron-rich metal in the Earth’s lower mantle. Nature 428, 409–411. Fujino, K., Nishio-Hamane, D., Seto, Y., Sata, N., Nagai, T., Shinmei, T., Irifune, T., Ishii, H., Hiraoka, N., Cai, Y.Q., Tsuei, K.-D., 2012. Spin transition of ferric iron in Al-bearing Mg-perovskite up to 200 GPa and its implication for the lower mantle. Earth Planet. Sci. Lett. 317–318, 407–412. Glazyrin, K., Boffa Ballaran, T., Frost, D.J., McCammon, C., Kantor, A., Merlini, M., Hanfland, M., Dubrovinsky, L., 2014. Magnesium silicate perovskite and effect of iron oxidation state on its bulk sound velocity at the conditions of the lower mantle. Earth Planet. Sci. Lett. 393, 182–186. Hirose, K., 2002. Phase transitions in pyrolitic mantle around 670-km depth: implications for upwelling of plumes from the lower mantle. J. Geophys. Res. 107 (B4), 2078. http://dx.doi.org/10.1029/2001JB000597. Holmström, E., Stixrude, L., 2015. Spin crossover in ferropericlase from firstprinciples molecular dynamics. Phys. Rev. Lett. 114, 117202. Irifune, T., 1994. Absence of an aluminous phase in the upper part of the Earth’s lower mantle. Nature 370, 131–133. Irifune, T., Shinmei, T., McCammon, C.A., Miyajima, N., Rubie, D.C., Frost, D.J., 2010. Iron partitioning and density changes of pyrolite in Earth’s lower mantle. Science 327, 193–195. Ito, E., Takahashi, E., 1989. Post-spinel transformations in the system Mg2 SiO4 –Fe2 SiO4 and some geophysical implications. J. Geophys. Res. 94, 10,637–10,646. Katsura, T., Sato, K., Ito, E., 1998. Electrical conductivity of silicate perovskite at lower-mantle conditions. Nature 395, 493–495.

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