Influence of sulfur on the electrical resistivity of a crystallizing core in small terrestrial bodies

Earth and Planetary Science Letters 496 (2018) 37–46

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Influence of sulfur on the electrical resistivity of a crystallizing core in small terrestrial bodies Anne Pommier UC San Diego, Scripps Institution of Oceanography, Institute of Geophysics and Planetary Physics, La Jolla, CA, USA

a r t i c l e

i n f o

Article history: Received 3 January 2018 Received in revised form 30 April 2018 Accepted 20 May 2018 Available online xxxx Editor: B. Buffett Keywords: electrical resistivity planetary cores crystallization regimes iron alloys

a b s t r a c t Electrical experiments were performed on core analogues in the Fe–S system and on FeSi2 up to 8 GPa and 1850 ◦ C in the multi-anvil apparatus. Electrical resistivity was measured using the fourelectrode method. For all samples, resistivity increases with increasing temperature. The higher the S content, the higher the resistivity and the resistivity increase upon melting. At 4.5 GPa, liquid FeS is up to >10 times more resistive than Fe-5 wt.% S and twice more resistive than FeSi2 , suggesting a stronger influence of S than Si on liquid resistivity. Electrical results are used to develop crystallizationresistivity paths considering both equilibrium and fractional crystallization in the Fe–S system. At 4.5 GPa, equilibrium crystallization, as expected locally in thin snow zones during top-down core crystallization, presents electrical resistivity variations from about 300 to 190 microhm-cm for a core analogue made of Fe-5 wt.%S, depending on temperature. Fractional crystallization, which is relevant to core-scale cooling, leads to more important electrical resistivity variations, depending on S distribution across the core, temperature, and pressure. Estimates of the lower bound of thermal resistivity are calculated using the Wiedemann–Franz law. Comparison with previous works indicates that the thermal conductivity of a metallic core in small terrestrial bodies is more sensitive to the abundance of alloying agents than that of the Earth’s core. Application to Ganymede using core adiabat estimates from previous studies suggests important thermal resistivity variations with depth during cooling, with a lower bound value at the top of the core that can be as low as 3 W/m K. It is speculated that the generation and sustainability of a magnetic field in small terrestrial bodies might be favored in light element-depleted cores. © 2018 Published by Elsevier B.V.

1. Introduction In terrestrial bodies (e.g., Earth, Mars, Mercury, Ganymede), the generation of a global intrinsic magnetic field likely results from convection in a fully or partially liquid metallic core (Breuer et al., 2015 and references therein). The presence and intensity of this field highly varies among cores and this diversity possibly arises from different crystallization mechanisms that take place during planetary cooling. The cooling rate of a planetary body is affected by temperature and core chemistry. Light elements (such as sulfur, silicon, oxygen, or hydrogen) could have been added in significant amount to the metallic iron core of terrestrial bodies during differentiation (e.g., Li and Agee, 1996). In particular, meteorite geochemistry (e.g., Dreibus and Wänke, 1985) and solubility experiments (e.g., Tsuno et al., 2011) suggest that the presence of sulfur in metallic cores is possibly a general feature of terrestrial bodies due to their iron-loving properties observed over a wide pressure range. Sulfur is expected to be a major element in the core of

E-mail address: [email protected]. https://doi.org/10.1016/j.epsl.2018.05.032 0012-821X/© 2018 Published by Elsevier B.V.

small terrestrial bodies such as Mars, Mercury, and Ganymede (e.g., Dreibus and Wänke, 1985; Hauck et al., 2006; Stewart et al., 2007; Kimura et al., 2009). This contrasts with the Earth’s core, where sulfur might be less abundant than previously thought since a combination of light and/or other elements is required to explain the core’s density deficit (Alfè et al., 2002; Badro et al., 2015; O’Rourke and Stevenson, 2016; Hirose et al., 2017). The presence of sulfur – like any light element – in a cooling metallic core affects the onset of crystallization by lowering the liquidus temperature (e.g., Fei et al., 2000; Chen et al., 2008a; Stewart et al., 2007) and influences transport properties such as electrical resistivity (or its inverse, electrical conductivity) (Vostryakov et al., 1964; Suehiro et al., 2017), thermal resistivity (Suehiro et al., 2017), and density (Sanloup et al., 2000). Investigating how transport properties relate to core crystallization is required to increase our understanding of planetary evolution, as variations in mass and heat transport in the crystallizing fluid likely impact the convective and diffusive processes that govern core cooling and might contribute to generate a magnetic field (Schubert et al., 1996; Hauck et al.,

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A. Pommier / Earth and Planetary Science Letters 496 (2018) 37–46

2006; Dumberry and Rivoldini, 2015; Rückriemen et al., 2015; Davies and Pommier, 2018). Core crystallization in terrestrial bodies is initiated at the depth where adiabat and melting curve intersect (Breuer et al., 2015). Because the melting temperature does not evolve linearly with pressure in the Fe–S system, crystallization may take place at different depth and existing magnetic observations of terrestrial planets and satellites are compatible with top-down, middle, and/or bottom-up crystallization regimes (e.g., Hauck et al., 2006; Chen et al., 2008b; Rückriemen et al., 2015; Davies and Pommier, 2018). In particular, a top-down crystallization regime is thought to be relevant in the core of small terrestrial bodies (Breuer et al., 2015). Electrical resistivity being particularly sensitive to melting, temperature, and chemistry, it is a relevant probe of core crystallization processes. However, the effect of sulfur abundance and crystallizationinduced distribution of S across the core on electrical resistivity is not presently understood. The current experimental database of the electrical properties of iron and iron alloys comes mostly from experiments conducted at very high pressure to mimic Earth’s core conditions (e.g., Seagle et al., 2013; Gomi and Hirose, 2015; Ohta et al., 2016), or at very low temperature (e.g., Kobayashi et al., 2005). The existing electrical experimental or computed data on Fe and its alloys at pressure and temperature conditions relevant to small bodies remain meager (Deng et al., 2013; Kiarasi and Secco, 2015; Suehiro et al., 2017) and did not investigate systematically the effect of the abundance of the alloying agent on the bulk electrical resistivity. Electrical resistivity can be related to thermal conductivity and magnetic field evolution, though these relationships are debated at planetary core conditions (e.g., Christensen, 2010; Secco, 2017). Here the results of laboratory experiments at pressures up to 8 GPa and temperatures up to 1850 ◦ C are reported for iron and iron-sulfur samples. One additional experiment was performed on iron disilicide to compare the effect of S and Si on bulk electrical resistivity. These experiments were designed to investigate the electrical properties of core analogues, in order to develop an electrical model of core cooling in small terrestrial bodies (such as Ganymede) containing different amounts of alloying agents and to estimate the effect of core chemistry on electrical and thermal conductivity upon cooling. The effect of alloying agents on the generation of a magnetic field is also discussed.

2. Experimental and analytical methods 2.1. Starting materials Five starting compositions were considered: pure iron, Fe-5 wt.%S (5.69 mol.%), Fe-20 wt.%S (22.8 mol.%), Fe-36.5 wt.%S (FeS, 41.5 mol.%), and Fe-50.1 wt.%Si (FeSi2 , 44.7 mol.%) (Table 1). These samples were made from high purity Fe rod or of mixtures of high purity (>99%) Fe, FeS, and FeSi2 powders. To avoid oxidation and contamination, all starting materials were stored in sealed glass containers within a glass desiccator. Nickel was not added to the core analogues as it was observed that its effect on the melting properties of Fe–S is insignificant (e.g., Stewart et al., 2007; Martorell et al., 2013) or only minor when observed (Zhang and Fei, 2008). Among the starting compositions, Fe, FeS and FeSi2 correspond to a single phase. Fe-5 wt.%S and Fe-20 wt.%S starting samples are not alloys, meaning that these two materials below the melting temperature correspond to Fe coexisting with S, instead of a Fe–S single phase. As shown below, comparison of the electrical data for all five materials suggests that the difference in bulk resistivity between these two materials (Fe-5 wt.%S and Fe-20 wt.%S) and single-phase samples (Fe, FeS and FeSi2 ) is not significant at the considered experimental conditions. However, the interpretation of the electrical results will focus on data collected at temperatures above the eutectic temperature, i.e. when the samples are partially or fully molten and correspond to Fe–S alloys. Experiments on pure Fe were conducted on Fe powder and on an Fe rod in order to estimate the potential effect of electron scattering due to a granular (powder) sample on the bulk electrical resistivity. 2.2. Multi-anvil cell assembly All electrical experiments were performed up to 8 GPa in a multi-anvil apparatus in the Planetary and Experimental Petrology Laboratory at UCSD-SIO, using tungsten carbide cubes with a corner-truncation edge length of 8 mm and mullite octahedral pressure media with an edge length of 14 mm. Rhenium heaters were used, placed inside an outer zirconia sleeve that provided thermal insulation. Experimental samples were 2 mm in diameter and 0.8–1.5 mm in length and were placed at the center of the cylindrical heater inside an MgO sleeve (Fig. 1). Two molybdenum squares (1.5 mm in edge) or two iron disks (outer diameter 2 mm)

Table 1 Summary of electrical experiments. Run #

System

wt.% S or Si

mol.% S or Si

Electrode composition

Pressure (GPa)

Temp. range (K)

Dwell time (hr)

Relative error on resistivity (%)b

BB86 BB129 BB62 BB83 BB135 BB119

Fea Fe Fe–S Fe–S Fe–S Fe–S

– – 5.00 5.00 5.00 5.00

– – 8.4 8.4 8.4 8.4

Mo Fe Mo Mo Fe Mo

4.5 4.5 3.2 4.5 4.5 8.0

1420–2129 720–1973 867–1773 1123–1970 628–1891 471–1506

– – 2.5 2 3.5 2

4.8–5.7 3.7–4.9 9.1–12.6 8.1–11.9 1.8–2.5 4.7–9.9

BB120 BB133

Fe–S Fe–S

20.0 20.0

30.3 30.3

Mo Fe

4.5 4.5

478–1743 728–1558

2 6

3.8–10.3 3.5–4.6

BB60 BB76 BB131 BB97 BB122

Fe–S Fe–S Fe–S Fe–S Fe–S

36.5 36.5 36.5 36.5 36.5

50 50 50 50 50

Mo Mo Fe Mo Mo

3.2 4.5 4.5 8.0 8.0

670–1385 980–1767 1253–1403 923–1628 1120–1590

2 2.5 3.5 2 3

1.5–6.3 5.6–10.8 3.7–6.4 2.7–5.3 3.7–7.3

BB140

Fe–Si (FeSi2 )

50.1

66

Fe

4.5

1500–1803

3.5

5.6–6.0

a

Starting composition

(FeS) (FeS) (FeS) (FeS) (FeS)

Starting material is an iron disk. Samples in all other experiments are powders. b Error on resistivity (ρ ) derived from Eq. (1). In the case of Fe disk electrodes, ρ = |Π r 2 /l| ×  R + |2Π Rr /l| × r + | − Π Rr 2 /l2 | × l. In the case of Mo square electrodes, ρ = |r 2 /l| ×  R + |2Rr /l| × r + | − Rr 2 /l2 | × l with R the electrical resistance (corrected from the electrode foils), r the radius of the electrode disk in contact with the sample, l the thickness of the sample.

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FeSi2 samples because the high amount of alloying agent makes these samples behave more like semi-conductors than conductors. Since the two foils form a series circuit with the sample, their contribution to the bulk resistance was subtracted from the measured (bulk) resistance in order to get access to the sample’s resistance value. 2.4. Analytical techniques

Fig. 1. Four-electrode cell for the 14/8 multi-anvil assembly. Two electrodes are used for the current circuit (one at the top of the sample, one at the bottom), while the other two electrodes are used to measure the voltage (V1 high and V1 low). The two wires in contact at the top and bottom of the sample also serve as thermocouples. The presence of a Mo or Fe foil between the TC wires and the sample contributes to the distribution of lines of current throughout the whole sample whole, limiting the values of the spreading resistance.

were in contact with the sample, serving as electrodes. The temperature was monitored with a W95 Re5 –W74 Re26 (C-type) thermocouple inserted within an MgO sleeve with the junction in contact with the top of one of the metal disks. A second C-type thermocouple was connected to the other disk (Pommier and Leinenweber, 2018). All MgO parts were fired at 1400 ◦ C and 1 atm for 1 hr, and then stored in a sealed desiccator until used for the experiments. The multi-anvil apparatus was calibrated in pressure using phase transitions in bismuth, SiO2 (quartz–coesite–stishovite), carbon (graphite–diamond), and lawsonite, and temperature calibration was performed using gold melting experiments over the pressure range 2–7 GPa (Zhang and Pommier, 2017). 2.3. Electrical measurements and data processing Electrical measurements were performed during heating using the four-electrode method and resistance was measured using an impedance-meter (1260 Solartron Impedance/Gain-Phase Analyzer). The electrode system consists of two wires for voltage drop measurement (V 1 low and V 1 high, Fig. 1) and two wires for current measurement (Generator output and Current Input, Fig. 1). Electrical measurements were collected by imposing a current with a controlled voltage (DC potential of 1V and AC amplitude of 1000 mV). Electrical resistance is directly collected over a frequency range and the average value corresponds to R at the defined P , T conditions with an uncertainty  R. Examples of electrical data are presented in Supplementary Fig. 1. The reproducibility of electrical measurements was validated by performing a few measurements during cooling and second heating. A manual switch was used to shift from temperature reading to electrical measurements. The electrical resistivity was calculated for each sample using the measured electrical resistance and sample geometric factor G

ρ = R × G with G = A /l

(1)

ρ is the electrical resistivity (in units of ohm-m), R is the electrical resistance (ohms), A is the area of one electrode (Fe or Mo foil) (m2 ), and l is the thickness of the sample (m). Relative errors on values of ρ were calculated on the basis of errors on A and L as well as propagated errors on each measured value of resistance R (Table 1). Errors due to thermal expansion and compressibility of the samples are smaller than the uncertainties in length measurement (Silber et al., 2017) but are included in the bulk uncertainty calculations. The Mo or Fe foils located on both sides of the sample were used to enhance current distribution across the entire sample volume (Kennedy, 1960), which is especially relevant for S-rich or

The recovered run products were mounted in epoxy resin and then ground and polished for analytical characterization. Scanning electron microscope (SEM) imaging were performed at UCSD – Nanoengineering Department using a FEI Quanta 600 SEM to characterize the texture and bulk chemistry of the samples. Composition of the starting materials and of phases in quenched samples was analyzed using Energy Dispersive X-ray Spectrometry (EDS). 2.5. Experimental strategy Experiments were conducted under quasi-hydrostatic conditions in the multi-anvil apparatus during heating after a dwell of several hours (Table 1) at temperature of 400 or 500 ◦ C, i.e. below the eutectic temperature. A few measurements were then collected during cooling (at T < T melting ) and second heating above the melting temperature. The sample was left at each temperature until electrical equilibrium was reached. Each experiment was quenched at the highest temperature by shutting off power to the heater. Two types of electrodes were used: iron and molybdenum electrodes. The melting point of molybdenum being higher than the one of iron, it allows measurements at higher temperature than iron. However, as discussed below, molybdenum being highly siderophile and chalcophile (Walker and Li, 2007), molten samples at high temperature correspond to a Fe–S–Mo alloy. 3. Results Electrical conductivity data for all compositions are presented in Fig. 2. 3.1. Sample-cell parts interactions Experiments at 4.5 GPa using Fe or Mo electrodes yield comparable resistivity values for all Fe–S samples (Fig. 2), suggesting that the effect of Mo on the bulk resistivity of the Fe–S (partially) molten samples is limited over the considered temperature range. Molybdenum contamination of the sample is significant when the sample is highly molten, i.e., above about 1650 K, consistent with previous works (Pommier et al., 2015; Zhang and Pommier, 2017). The composition of retrieved samples using EDS analyses is listed in Table 2. For experiments using Mo electrodes, the high amount of Mo in the quenched sample is consistent with the high temperatures reached before the experiment was quenched (T quench > 1506 K). Since the presence of molybdenum acts as an alloying agent, it restricts the flow of the charge carriers and thus high-temperature measurements using Mo electrodes yield an upper bound on Fe–S resistivity. For experiments using Fe electrodes (BB131, Table 2), a higher Fe amount is measured in the quenched sample than in the starting composition, highlighting sample contamination by the Fe electrodes at high temperature. Although the effect of molybdenum on the bulk electrical resistivity of the samples appears to be small, high-temperature data from experiments using Fe electrodes were preferentially used as part of the electrical modeling presented below. A thin layer of ferropericlase (< about 100 microns thick) at the interface between the sample and the MgO sleeve was observed in all quenched samples, resulting from the interactions

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Fig. 2. Electrical resistivity of iron and iron alloys up to 8 GPa as a function of temperature. A) Pure iron; S. and S.: Secco and Schloessin (1989), D. et al.: Deng et al. (2013). B) Fe-5 wt.%S. Data for Fe-2.9 wt.%Si from Kiarasi and Secco (2015) (K. and S.). C) Fe-20 wt.%S; Estimates at 20–40 GPa for Fe-14 wt.%S from Suehiro et al. (2017) (S. et al.). D) FeS (red) and FeSi2 (purple); A. et al.: Argyriades et al. (1959). Arrows indicate the eutectic and liquidus temperatures, based on previous works (Brett and Bell, 1969; Chen et al., 2008a; Fischer et al., 2013). (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.) Table 2 EDS bulk map analyses on retrieved samples quenched at high temperature (in wt.% normalized to 100). Run #

Quenching T (K)

Fe

S

Mo

W

Re

Mg

BB62 BB119 BB120 BB76 BB131 BB97

1773 1506 1743 1767 1403 1628

65.63 62.38 52.22 37.08 71.07 50.49

4.44 6.69 15.99 23.90 28.39 29.04

15.86 30.26 29.58 35.85 – 19.96

9.16 0.12 1.70 2.87 0.05 0.01

4.78 0.28 0.45 0.26 0.06 0.42

0.11 0.28 0.06 0.03 0.42 0.07

between iron from the sample and the sleeve (Fig. 3). The sample and ferropericlase arrangement corresponds to a parallel model and the contribution of the (Mg,Fe)O layer to the measured electrical response can be calculated using the resistivity of ferropericlase (Yoshino et al., 2011) and the following equation (e.g., Glover et al., 2000)

1 R bulk

=

X fp R fp

+

1 − X fp R sample

(2)

where R bulk is the bulk (sample and ferropericlase) electrical resistance (ohm), X f p the volume fraction of ferropericlase, R f p the resistance of ferropericlase (ohm) from Yoshino et al. (2011), and R sample the resistance of the sample (ohm). The electrical resistivity is obtained using Eq. (1). Application of Eqs. (1) and (2) to the experiment on Fe-20 wt.%S (Fig. 3), considering a ferropericlase layer thickness of about 80 microns (corresponding to a volume fraction of about 0.202), suggests that the sample resistivity represents >99.99% of the measured bulk resistivity. This is explained by the huge difference in resistance between the Fe–S sample and ferropericlase (more than 9 orders of magnitude), highlighting the negligible contribution of ferropericlase on the bulk electrical response. 3.2. Electrical resistivity of iron and iron alloys Experiments on metal iron at 4.5 GPa were conducted on a high-purity Fe disk and on high-purity iron powder (BB86 and BB129, respectively, Table 1). As illustrated in Fig. 2a, both experiments yield similar resistivity values over the entire temperature range, suggesting that at the P, T conditions and timescale of the

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Fig. 4. Effect of Fe–FeS mixing on the bulk electrical resistivity for several temperatures. The large resistivity variations (resistivity jumps) correspond to the interconnectivity of the melt phase between the two electrodes. See text for details. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

Fig. 3. Scanning-Electron Microscopy images of retrieved samples. A) Presence of a thin ferropericlase layer at the sample-MgO sleeve interface. The contribution of this layer on the measured bulk resistance is negligible (see text for details). Melt is also present in thin veins between the MgO sleeves, highlighting melt escape from the cell at temperatures where melt viscosity is very low (experiment BB120). B) Example of electrode (Mo) contamination at high temperature. The quenched sample corresponds to a Fe–S–Mo alloy as the electrode became consumed by the metallic melt (experiment BB120). C) Retrieved sample not fully molten. Quenched Fe–S crystals (representing the melt phase, right) are coexisting with iron crystals (left) (experiment BB119). The qualitative chemistry of the different phases was verified using SEM-EDS analyses.

experiments, electron scattering due to the granularity of the samples does not affect significantly the electrical response. Electrical measurements were performed across a broad temperature range that involves crossing the eutectic temperature – and in most cases, the liquidus temperature – of the systems considered. Both eutectic and liquidus temperatures were determined using phase equilibria studies of the Fe, Fe–S, and Fe–Si systems (Brett and Bell, 1969; Chen et al., 2008a; Buono and Walker, 2011; Fischer et al., 2013). For all investigated compositions, electrical resistivity increases with increasing temperature and liquids are more resistive than solids (Fig. 2). As observed for metals and alloys (Deng et al., 2013; Kiarasi and Secco, 2015; Silber et al., 2017), the change in temperature-dependence of electrical resistivity at low temperature (< T melting ) is consistent with a magnetic transition. The effect of pressure on resistivity between 3.2–4.5 GPa and 8.0 GPa is significant for all samples: at low temperature (< T melting ), the resistivity at 8 GPa is up to about 5 times less than the resistivity at lower pressure. The electrical resistivity of iron alloys is higher than the one of pure iron at similar pressure and temperature conditions, in agreement with the increasing resistivity effect of alloying agents (S, Si, and at high temperature, Mo). The transition from a soliddominated to a liquid-dominated regime is accompanied by an increase in electrical resistivity (Fig. 2). This increase is sharp at low pressure and smooth at 8.0 GPa. At 4.5 GPa, the higher the amount of sulfur, the higher the resistivity jump upon melting,

with a jump in electrical resistivity corresponding to an increase of a factor of about 1.6 for Fe-5 wt.%S, 6.2 for Fe-20 wt.%S, and >5 for FeS, and 2 for FeSi2 . The temperature at which the transition to a liquid-dominated resistivity is observed corresponds to either a temperature slightly higher than the eutectic temperature or to the liquidus temperature and likely depends on melt distribution and interconnectivity throughout the electrical cell (Zhang and Pommier, 2017). The evolution of electrical resistivity with increasing sulfur content is presented in Fig. 4. For each temperature, increasing the amount of S increases bulk resistivity and a non-linear evolution is observed between Fe–FeS mixing and resistivity; this trend is affected at high temperature (>1400 ◦ C) by the resistivity jump. Constraints on melt fraction are precluded, as bulk resistivity in these experiments is more sensitive to melt distribution in the sample (causing the jump) than to the melt content. Comparison between FeS and FeSi2 indicates comparable electrical resistivity at T < T melting (Fig. 2d). Upon melting, a more significant resistivity increase is observed when the alloying agent is S than when it is Si (by a factor of about 2, Fig. 2d). In several cases, experiments were quenched before a plateau value was reached, in order to minimize loss of the liquid sample from the electrical cell. However, a few experiments were quenched after electrical resistivity starts decreasing, indicative of melt escape from the assembly when melt viscosity becomes too low to be contained in the electrical cell. 4. Discussion 4.1. Comparison with previous electrical studies of iron and iron alloys Electrical resistivity data for Fe are in agreement with previous studies performed at comparable pressure and temperature ranges (e.g., Deng et al., 2013; Secco and Schloessin, 1989; Fig. 2). Although previous electrical measurements in the Fe–S system are scarce, high resistivity values were also measured on FeS at 1 atm and 1473 K by Argyriades et al. (1959), as illustrated in Fig. 2d. Lower resistivity data (500 microhms.cm vs. 4000 microhm.cm in

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the present study) collected at 1873 K and 1 atm were obtained by Vostryakov et al. (1964). If Vostryakov et al. (1964) noticed such a discrepancy compared to Argyriades et al. (1959), the cause of the discrepancy remains unexplained and the absence of experimental details does not allow for comparing both setups. The pressure dependence of resistivity observed for all compositions is consistent with previous experimental observations and underlines a pressure saturation effect (e.g., Deng et al., 2013; Kiarasi and Secco, 2015). At P > 8 GPa, electrical resistivity is expected to decrease less significantly than over the 3.2–8 GPa range due to the saturation effect, as suggested by the small difference in iron resistivity at defined temperature between 7 and 15 GPa (Deng et al., 2013) and between 15, 26 and 51 GPa (Ohta et al., 2016). The comparison between data from the present study and the resistivity range recently calculated by Suehiro et al. (2017) for the Martian core (94–104 × 104 (ohm.m)−1 ) at 20–40 GPa assuming a homogeneous solid core chemistry containing 14.2 wt.% S (Fig. 2c) is also consistent with a small effect of pressure on resistivity between 4.5 and 20 GPa. Two observations can be made regarding the effect of S and Si on the electrical conductivity of iron: 1) at low temperature ( T < T eutectic ), data on Fe-2.9 wt.%Si from Kiarasi and Secco (2015) and on Fe-5 wt.%S indicate that a small amount of Si increases resistivity more than a small amount of S (Fig. 2b). This could highlight a smaller impurity resistivity of S than of Si, in agreement with Suehiro et al. (2017). However, a direct comparison of resistivity values is compromised by the fact that the starting samples in Kiarasi and Secco (2015) are Fe–Si alloys, whereas in the present study the Fe-5 wt.%S starting samples are not a single phase; 2) This dominant effect of Si on resistivity may not hold at high temperature when the sample is liquid: experiments on FeS and FeSi2 (corresponding to 50 mol.% S and 66 mol.% Si, respectively) point out a more important effect of S than Si on electrical resistivity upon melting (Fig. 2d). A different effect of S and Si has been observed on other physical properties of iron: increasing S decreases the bulk density of liquid iron significantly (e.g., Kuskov and Belashchenko, 2016) while increasing Si decreases bulk density only slightly (e.g., Tateyama et al., 2011). For instance, at 4 GPa and 1923 K, increasing the light element content from 1 to 30 mol.% decreases density by about 0.3 g/cc for Fe–Si and by about 1 g/cc for Fe–S (Shimoyama et al., 2013). Both elements have opposite effects on P-waves velocity and only S affects the compressibility of liquid iron (Sanloup et al., 2004), suggesting that the structure of molten iron alloys is more sensitive to the presence of S than to Si. In the solid state, high-pressure studies at 300 K observed that both S and Si decrease the bulk density of solid iron and increase P-waves velocity (e.g., Mao et al., 2012 and references therein). 4.2. Electrical models of Fe–S core crystallization Fig. 5 presents different crystallization scenarios based on experimental results at 4.5 GPa. The phase diagram at 4.5 GPa in Fig. 5a has been estimated using Brett and Bell (1969) and Chen et al. (2008a) and is in general agreement with the phase diagrams from Buono and Walker (2011) at 3 and 6 GPa. Scenarios A, B, C, and E correspond to equilibrium crystallization for different sulfur contents, i.e., in these cases, chemical equilibrium exists between the phases during cooling. Though this type of scenario is unlikely to occur at the scale of a core due to the large pressure and temperature ranges, it may be present locally, i.e., over narrow depth ranges. For instance, the thin snow layer that characterizes potentially top-down crystallization in the Martian core is considered to behave at first approximation as a closed system (Davies and Pommier, 2018). Fig. 5 indicates that electrical resistivity during equilibrium crystallization strongly depends on the amount of sul-

Fig. 5. Electrical resistivity evolution during crystallization. A) Phase diagram at 4.5 GPa (using Brett and Bell (1969) and Chen et al. (2008a)) and at 3 and 6 GPa (Buono and Walker, 2011) and different crystallization paths. Scenarios A, B, C, E are examples of equilibrium crystallization, scenario D corresponds to a fractional crystallization path. B) Electrical response of each scenario over the considered temperature range. The electrical resistivity at each temperature of a crystallization path corresponds to the resistivity value measured at the same temperature and chemistry conditions. Computed electrical data below the eutectic temperature represent a first approximation due to the sample’s texture (consisting of Fe and S powder mixtures, not a single phase). See text for details.

fur: electrical resistivity varies from about 300 to 55 microhm-cm in the electrical response during cooling of materials containing a small amount of sulfur (Fe or Fe-5 wt.%S), while a decrease in resistivity from 5000 to 850 microhm-cm is estimated upon the cooling of an FeS core. The most significant drop in electrical resistivity occurs in the liquid state, before the onset of crystallization (Fig. 5b). Scenario D illustrates an example of fractional crystallization. This cooling scenario considers a bulk composition ranging from pure iron to the eutectic composition, consistent with most bulk S estimates in terrestrial cores. The solids that precipitate are progressively removed from the residual liquid by sinking, as solid Fe is denser than the residual S-bearing liquid (e.g., Huang et al., 2011). Chemical homogenization of the core through time due to vigorous convection is unlikely as it is expected to recrystallize solid iron (Hauck et al., 2006). Electrical resistivity during fractional crystallization from 1800 ◦ C down to the eutectic temperature as shown in scenario D varies from about 90 to 350 microhm-cm at constant pressure (Fig. 5b). Top-down crystallization, as suggested for several small terrestrial bodies (e.g., Dumberry and Rivoldini, 2015; Rückriemen et al., 2015; Davies and Pommier, 2018), is an example of fractional crystallization. The electrical evolution of a snowing core at the present experimental conditions is illustrated in Fig. 6, using electrical data in Fig. 2. The formation and removal of iron crystals due to density contrasts with the liquid phase leads to the enrichment of the residual liquid in sulfur. In the snowing core, the sinking solids

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Fig. 6. Example of top-down core crystallization and the evolution of the electrical response as chemistry and temperature change. Electrical resistivity values come from experiments shown in Fig. 2. In this example, pressure ranges from about 5 to 8 GPa, which is relevant to Ganymede’s core. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

possibly remelt at depth, resulting in 1) the enrichment of the outer core in sulfur through time and 2) an associated decrease in electrical resistivity with increasing depth. In the extreme case of a fully solidified core, this electrical gradient represents a factor of about 10 in resistivity (Fig. 6). The decrease in electrical resistivity with increasing depth is driven by sulfur distribution across the core (the depletion of S at depth decreases resistivity) and the pressure effect. The increase in temperature with increasing depth is not expected to counter-balance the resistivity gradient across the core as the effect of temperature on resistivity becomes less important as pressure increases (Fig. 2). One can notice that in a bottom-up crystallization regime, the formation of Fe grains (progressively forming a solid inner core) would also contribute to the enrichment of the outer core in sulfur through time. Therefore, electrical gradients across the core are expected in both top-down and bottom-up crystallization scenarios. Fig. 7. Lower bound estimates of thermal resistivity for the different systems at 4.5 and 8 GPa. Data at 7 GPa for iron from Deng et al. (2013). Estimates are calculated using the Wiedemann–Franz law. See text for details.

4.3. Implications for core cooling Electrical resistivity-crystallization paths (Fig. 5) provide insight regarding the cooling history of planetary cores. For instance, it has been suggested for the Earth that the low electrical resistivity of iron extrapolated to P, T conditions relevant to the core indicates a high thermal conductivity and a rapid core cooling (Ohta et al., 2016). The increase in thermal conductivity k as electrical resistivity ρ decreases is observed if the following Wiedemann–Franz law applies

L0 × T = k × ρ

(3)

with L 0 the Sommerfeld value of the Lorenz number and T the temperature (Wiedemann and Franz, 1853). Although the validity of the Wiedemann–Franz law has been observed for liquid iron (Nishi et al., 2003; Gomi et al., 2013; Ohta et al., 2016), it has also been challenged for both iron and its alloys, depending highly on the pressure dependence of L 0 (e.g., Secco, 2017; Suehiro et al., 2017). As a result, Eq. (3) only provides a lower bound of thermal conductivity (Konôpková et al., 2016). This is consistent with the computations by Pozzo et al. (2012) who indicate that during Earth’s core cooling, the increase in thermal resistivity is more important than the decrease in electrical resistivity, i.e. thermal conduction dominates over electrical conduction. The lower bound of thermal conductivity for core analogues at 4.5 and 8 GPa is presented in Fig. 7. A constant value of 2.445 × 10−8 WK−2 was taken for L 0 , in order to compare calculations with estimates by Deng et al., 2013. Therefore, the pressure dependence of L 0 (Secco, 2017) was not considered at a first approximation. Calculated lower bounds of thermal conductivity suggest that ρ strongly depends on S or Si contents, and similar to

electrical resistivity, the effect of melting on thermal conductivity is more dramatic for S-rich and Si-rich materials than for pure Fe. The higher the amount of alloying agent, the lower the thermal conductivity. At T eutectic and 4.5 GPa, increasing the S content from 0 (Fe) to 36.5 wt.% (FeS) decreases the thermal conductivity dramatically from about 53 to 3.8 W/m K, i.e., by about 97%. A decrease in thermal conductivity of 83% and 69% is obtained when 20 wt.%S and 5 wt.%S are added, respectively. At 8 GPa, these values become 95%, 91%, and 52% when 36.5, 20, and 5 wt.%S are respectively added to Fe, underlining a more important effect of pressure on thermal conductivity for S-poor than for S-rich materials. At Earth’s core pressure, it was predicted that the addition of 12 wt.%S to liquid iron reduces the thermal conductivity by about 25% (Gomi et al., 2013) and the addition of Si or O was also found to decrease thermal conductivity (deKoker et al., 2012). The present study indicates that at much lower pressure than the Earth’s core, the effect of the alloying agent on thermal conductivity can be dramatic and thus, this effect needs to be accounted for as part of core modeling of small terrestrial bodies. Fig. 7 suggests that the presence of S and Si (and possibly other light elements) possibly impacts significantly core cooling history, as a less thermally conductive outermost core can translate into an insulating layer that may affect the heat budget through time. 4.4. Core conductivity and magnetic field The generation and sustainability of a magnetic field in a metallic core depends on both convection and diffusion processes, as

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expressed in the induction equation for an electrically resistive fluid (Busse and Wicht, 1992)

∂B ρ 2 = ∇ × (v × B ) + ∇ B ∂t μ0

(4)

where B is the magnetic field, t is the time, v is the typical velocity, ρ is the electrical resistivity, and μ0 is the magnetic permeability. The first right-hand term represents the convective term, while the second right-hand term, which directly depends on electrical resistivity, represents the diffusive term. The ratio of the two corresponds to the magnetic Reynolds number. Taken alone, this equation suggests that the generation of a magnetic field is favored when the diffusive term is minimized, which occurs when both electrical resistivity and the resistivity gradient are small (Busse and Wicht, 1992). This situation would occur in cores that contain a small amount of S (and probably, Si) (Fig. 2). Reciprocally, it comes that metallic liquid cores containing high bulk S (or Si) amounts are not expected to favor the appearance of a magnetic field due to high resistivity values and resistivity jumps upon melting. Comparison of the resistivity between FeS and FeSi2 indicates that Si might be a better alloying agent than S at these experimental conditions to generate a magnetic field as its resistivity gradient is smaller than the one of FeS. However, three major limitations exist regarding the application of Eq. (4) to planetary cores. First, the total effect on the dynamo will be related to the size of regions of high electrical resistivity (C. Davies, personal communication). For example, the bulk magnetic field of a metallic core characterized by a low resistivity is unlikely to be affected significantly if a resistivity jump occurs in a thin, spatially limited region of the core. Second, the competition between the convective and diffusive terms only applies in the liquid and is thus not valid in cores containing a significant solid fraction. Convection in a fully (or almost fully) solid core is expected to be too slow to generate a magnetic field or to be responsible for the observed magnetic fields (Hauck et al., 2006; Breuer et al., 2015; Davies and Pommier, 2018), no matter how resistive the solid and liquid phases are. Third, if most scaling laws for planetary dynamos depend on electrical resistivity, some of them are not a function of the core’s electrical response (Christensen, 2010). The variety of these models suggest that the internal energy that generates the magnetic field in a planetary core depends on any transport property, not only electrical resistivity. It is presently unknown which scaling law applies to what terrestrial body, and new parameterized modeling studies of core crystallization that combine phase relationships with transport properties are required to evaluate the relative importance of the cooling rate and crystallization-induced chemical evolution of the core on the magnetic history of terrestrial bodies. 4.5. Application to Ganymede’s core The conditions of the experiments presented in Fig. 2 are relevant to Ganymede. The core of Jupiter’s satellite is estimated to contain up to about 13 wt.% S (e.g., Hauck et al., 2006; Rückriemen et al., 2015), though higher S contents have also been proposed (Kimura et al., 2009). This suggests a core chemical evolution in the Fe-rich side of the Fe–FeS phase diagram and implies that core cooling will lead to the formation of Fe crystals, and not lighter S-bearing solids. Ganymede’s core corresponds to a pressure range of about 6–10 GPa and estimates for its thermal structure range from 1250 to 1750 K (Breuer et al., 2015). Small amounts of hydrogen (Shibazaki et al., 2011) or oxygen (Pommier et al., 2018) may also be present in the core. Past missions have observed that Ganymede’s present-day state is characterized by a strong intrinsic magnetic field (Schubert et al., 1996; Kivelson et al., 1996). In terms of core chemistry, a strong magnetic

field suggests that the satellite’s core may contain a small amount of sulfur (Fig. 7). The core dynamics of the Galilean satellite remain poorly understood and both thermal and compositional dynamos have been proposed to explain the magnetic field and moment of inertia (Hauck et al., 2006; Bland et al., 2008; Kimura et al., 2009). An iron snow regime has been suggested for Ganymede’s core (Hauck et al., 2006; Christensen, 2015; Rückriemen et al., 2015), with the possibility that the snow zone encompasses the entire Fe–S core since early in its history (Rückriemen et al., 2015). This fractional crystallization mechanism will likely result in the progressive enrichment in S of the outermost core (Fig. 6). Considering the effect of sulfur on thermal conductivity (Fig. 7), a core-scale iron snow implies a progressive decrease in heat release efficiency at the top of the core, and the lower bound of thermal conductivity is expected to vary from 3 to 100 W/m K from the top to center of the core, respectively. Though these values only represent thermal resistivity lower bounds, they indicate significant variations in k across the core, depending on chemistry (S content), temperature, and pressure. As a result, core convection mechanisms in the snowing core should not solely be attributed to the remelting of Fe in the deeper, liquid core but rather to the progressive enrichment in S in the outer core that may act as an electrically and thermally insulating layer. These k values agree with the preferred k value of 40 W/m K for Ganymede’s core in Rückriemen et al. (2015), but it should be noted that k was considered constant across the core in their models. The potential electrical, thermal and chemical stratification at the top of the core that is caused by fractional crystallization processes might also enhance chemical heterogeneities driven by mantle–core interactions (e.g., Buffet and Seagle, 2010), potentially reducing the coupling between the core and the overlying mantle through time and affecting significantly mantle convection and dynamics. 5. Conclusions The electrical resistivity of Fe, Fe-5 wt.%S, Fe-20 wt.%S, FeS, and FeSi2 samples was measured from 3.2 to 8 GPa and at temperature up to 1850 ◦ C. For all compositions, electrical resistivity increases with temperature and decreases with pressure. The higher the S content, the higher the resistivity and the resistivity jump upon melting. The resistivity of FeS and FeSi2 at 4.5 GPa is comparable at temperature below the melting temperature, whereas FeS becomes more resistive than FeSi2 by a factor of 2 upon melting. Experimental results are used to develop crystallization-resistivity paths considering both equilibrium and fractional crystallization. Electrical resistivity decreases by a factor >5 during the cooling of an FeS core analogue during equilibrium crystallization. Fractional crystallization, as expected at core scale, can also lead to significant electrical resistivity variations, depending mostly on S distribution across the core. Estimates of the lower bound of thermal resistivity are calculated using the Wiedemann–Franz law. Application to Ganymede suggests important thermal resistivity variations with depth, with thermal resistivity increasing with pressure. This experimental investigation underlines the importance of crystallization-induced distribution of alloying agents across the core on the transport properties of cooling terrestrial bodies. Acknowledgements AP thanks Christopher Davies, Cathy Constable, and Kurt Leinenweber for fruitful scientific and technical discussions as well as lab manager Jake Perez and Jon Souders for their help with developing the electrical setup in the Planetary and Experimental Petrology Lab at SIO. This work was partially supported through access and

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utilization of the UC San Diego Dept. of NanoEngineering’s Materials Research Center (NE-MRC) and AP thanks Sabine Faulhaber for technical assistance with SEM and EDS analyses. AP acknowledges financial support from an NSF-COMPRES IV EOID subaward and from NSF-EAR (award #1551200). Use of the COMPRES Cell Assembly Project was supported by COMPRES under NSF Cooperative Agreement EAR 1661511. AP thanks two Reviewers for their insightful comments. Appendix A. Supplementary material Supplementary material related to this article can be found online at https://doi.org/10.1016/j.epsl.2018.05.032. References Alfè, D., Price, G.D., Gillan, M.J., 2002. Iron under Earth’s core conditions: liquid-state thermodynamics and high-pressure melting curve from ab initio calculations. Phys. Rev. B 65, 165118. Argyriades, D., Derge, G., Pound, G.M., 1959. Electrical conductivity of molten FeS. Trans. Metall. Soc. 215, 909–912. Badro, J., Brodholt, J.P., Pieta, H., Siebert, J., Ryerson, F.J., 2015. Core formation and core composition from coupled geochemical and geophysical constraints. Proc. Natl. Acad. Sci. https://doi.org/10.1073/pnas.1505672112. Bland, M.T., Showman, A.P., Tobie, G., 2008. The production of Ganymede’s magnetic field. Icarus 198, 384–399. Brett, R., Bell, P.M., 1969. Melting relations in the Fe-rich portion of the system Fe–FeS at 30 kb pressure. Earth Planet. Sci. Lett. 6, 479–482. Breuer, D., Rückriemen, T., Sphon, T., 2015. Iron snow, crystal floats, and inner-core growth: modes of core solidification and implications for dynamos in terrestrial planets and moons. Prog. Earth Planet. Sci. 2 (39). https://doi.org/10.1186/ s40645-015-0069-y. Buffett, B.A., Seagle, C.T., 2010. Stratification of the top of the core due to chemical interactions with the mantle. J. Geophys. Res. 115, B04407. Buono, A.S., Walker, D., 2011. The Fe-rich liquidus in the Fe–FeS system from 1 bar to 10 GPa. Geochim. Cosmochim. Acta 75, 2072–2087. Busse, F.H., Wicht, J., 1992. A simple dynamo caused by conductivity variations. Geophys. Astrophys. Fluid Dyn. 64 (1–4), 135–144. Chen, B., Gao, L., Leinenweber, K., Wang, Y., Sanehira, T., Li, J., 2008a. In situ investigation of high-pressure melting behavior in the Fe–S system using synchrotron X-ray radiography. High Press. Res. 28, 3,315–3,326. Chen, B., Li, J., Hauck II, S.A., 2008b. Non-ideal liquidus curve in the Fe–S system and Mercury’s snowing core. Geophys. Res. Lett. 35, L07201. https://doi.org/10. 1029/2008GL033311. Christensen, U.R., 2010. Dynamo scaling laws and applications to the planets. Space Sci. Rev. 152, 565–590. Christensen, U.R., 2015. Iron snow dynamo models for Ganymede. Icarus 247, 248–259. Davies, C.J., Pommier, A., 2018. Iron snow in the Martian core? Earth Planet. Sci. Lett. 481, 189–200. deKoker, N., Steinle-Neumann, G., Vlcek, V., 2012. Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth’s core. Proc. Natl. Acad. Sci. 109 (11), 4070–4073. Deng, L., Seagle, C., Fei, Y., Shahar, A., 2013. High pressure and temperature electrical resistivity of iron and implications for planetary cores. Geophys. Res. Lett. 40, 33–37. Dreibus, G., Wänke, H., 1985. Mars, a volatile rich planet. Meteoritics 20 (2), 367–381. Dumberry, M., Rivoldini, A., 2015. Mercury’s inner core size and core-crystallization regime. Icarus 248, 254–268. Fei, Y., Bertka, C.M., Prewitt, C.T., 2000. Structure type and bulk modulus of Fe3 S, a new iron–sulfur compound. Am. Mineral. 85, 1830–1833. Fischer, R.A., Campbell, A.J., Reaman, D.M., Miller, N.A., Heinz, D.L., Dera, P., Prakapenka, V.B., 2013. Phase relations in the Fe–FeSi system at high pressures and temperatures. Earth Planet. Sci. Lett. 373, 54–64. Glover, P.W.J., Pous, J., Queralt, P., Munoz, J.A., Liesa, M., Hole, M.J., 2000. Integrated two-dimensional lithospheric conductivity modelling in the Pyrenees using field-scale and laboratory measurements. Earth Planet. Sci. Lett. 178, 59–72. Gomi, H., Ohta, K., Hirose, K., Labrosse, S., Caracas, R., Verstraete, M.J., Hernlund, J.W., 2013. The high conductivity of iron and thermal evolution of the Earth’s core. Phys. Earth Planet. Inter. 224, 88–103. Gomi, H., Hirose, K., 2015. Electrical resistivity and thermal conductivity of hcp Fe– Ni alloys under high pressure: implications for thermal convection in the Earth’s core. Phys. Earth Planet. Inter. 247, 2–10. Hauck, S.A., Aurnou, J., Dombard, A., 2006. Sulfur’s impact on core evolution and magnetic field generation on Ganymede. J. Geophys. Res. 111, E09008.

45

Hirose, K., Morard, G., Sinmyo, R., Umemoto, K., Hernlund, J., Helffrich, G., Labrosse, S., 2017. Crystallization of silicon dioxide and compositional evolution of the Earth’s core. Nature 543. https://doi.org/10.1038/nature21367. Huang, H., Fei, Y., Cai, L., Jing, F., Hu, X., Xie, H., Zhang, L., Gong, Z., 2011. Evidence for an oxygen-depleted liquid outer core of the Earth. Nature 479, 513–516. https://doi.org/10.1038/nature10621. Kennedy, D.P., 1960. Spreading resistance in cylindrical semiconductor devices. J. Appl. Phys. 31 (8), 1490–1495. Kiarasi, S., Secco, R.A., 2015. Pressure-induced electrical resistivity saturation of Fe17 Si. Phys. Status Solidi B, 1–9. Kimura, J., Nakagawa, T., Kurita, K., 2009. Size and compositional constraints of Ganymede’s metallic core for driving an active dynamo. Icarus 202, 216–224. Kivelson, M.G., Khurana, K.K., Russell, C.T., Walker, R.J., Warnecke, J., Coroniti, F.V., Polanskey, C., Southwood, D.J., Schubert, G., 1996. Discovery of Ganymede’s magnetic field by the Galileo spacecraft. Nature 384, 537–541. Kobayashi, H., Kamimura, T., Ohishi, Y., Takeshita, N., Môri, N., 2005. Structural and electrical properties of stoichiometric FeS compounds under high pressure at low temperature. Phys. Rev. B 71, 014110. Konôpková, Z., Williams, R.S., Gómez-Pérez, N., Goncharov, A.F., 2016. Direct measurement of thermal conductivity in solid iron at planetary core conditions. Nature 534. https://doi.org/10.1038/nature18009. Kuskov, O.L., Belashchenko, D.K., 2016. Molecular dynamics estimates for the thermodynamic properties of the Fe–S liquid cores of the Moon, Io, Europa, and Ganymede. Sol. Syst. Res. 50 (3), 165–183. Li, J., Agee, C.B., 1996. Geochemistry of mantle–core differentiation at high pressure. Nature 381, 686–698. Mao, Z., Lin, J.-F., Liu, J., nAlatas, A., Goa, L., Zhao, J., Mao, H.-K., 2012. Sound velocities of Fe and Fe–Si alloy in the Earth’s core. Proc. Natl. Acad. Sci. 109 (26), 10239–10244. Martorell, B., Brodholt, J., Wood, I.G., Vocadlo, L., 2013. The effect of nickel on the properties of iron at the conditions of Earth’s inner core: ab initio calculations of seismic wave velocities of Fe–Ni alloys. Earth Planet. Sci. Lett. 365, 143–151. Nishi, T., Shibata, H., Waseda, Y., Ohta, H., 2003. Thermal conductivities of molten iron, cobalt, and nickel by laser flash method. Metall. Mater. Trans. A 34, 2801–2807. Ohta, K., Kuwayama, Y., Hirose, K., Shimizu, K., Ohishi, Y., 2016. Experimental determination of the electrical resistivity of iron at Earth’s core conditions. Nature 534, 95–98. O’Rourke, J.G., Stevenson, D.J., 2016. Powering Earth’s dynamo with magnesium precipitation from the core. Nature 529, 387–389. Pommier, A., Leinenweber, K., Tasaka, M., 2015. Experimental investigation of the electrical behavior of olivine during partial melting under pressure and application to the lunar mantle. Earth Planet. Sci. Lett. 425, 242–255. Pommier, A., Laurenz, V., Davies, C., Frost, D., 2018. Melting phase relations in the Fe–S and Fe–S–O systems at core conditions in small terrestrial bodies. Icarus 306, 150–162. Pommier, A., Leinenweber, K., 2018. Electrical cell assembly for reproducible conductivity experiments in the multi-anvil. Am. Mineral. https://doi.org/10.2138/ am-2018-6448. In press. Pozzo, M., Davies, C., Gubbins, D., Alfè, D., 2012. Thermal and electrical conductivity of iron at Earth’s core conditions. Nature 485, 355–358. Rückriemen, T., Breuer, D., Spohn, T., 2015. The Fe snow regime in Ganymede’s core: a deep-seated dynamo below a stable snow zone. J. Geophys. Res., Planets 120, 1095–1118. https://doi.org/10.1002/2014JE004781. Sanloup, C., Guyot, F., Gillet, P., Fiquet, G., Mezouar, M., Martinez, I., 2000. Density measurements of liquid Fe–S alloys at high-pressure. Geophys. Res. Lett. 27, 811–814. Sanloup, C., Fiquet, G., Gregoryanz, E., Morard, G., Mezouar, M., 2004. Effect of Si on liquid Fe compressibility: implications for sound velocity in core materials. Geophys. Res. Lett. 31, L07604. https://doi.org/10.1029/2004GL019526. Schubert, G., Zhang, K., Kivelson, M.G., Anderson, J.D., 1996. The magnetic field and internal structure of Ganymede. Nature 384, 544–545. Seagle, C.T., Cottrell, E., Fei, Y., Hummer, D.R., Prakapenka, V.B., 2013. Electrical and thermal transport properties of iron and iron–silicon alloy at high pressure. Geophys. Res. Lett. 40 (20), 5377–5381. Secco, R.A., Schloessin, H.H., 1989. The electrical resistivity of solid and liquid Fe at pressures up to 7 GPa. J. Geophys. Res. 94 (B5), 5887–5894. Secco, R.A., 2017. Thermal conductivity and Seebeck coefficient of Fe and Fe–Si alloys: implications for variable Lorenz number. Phys. Earth Planet. Inter. 265, 23–34. Shibazaki, Y., Ohtani, E., Terasaki, H., Tateyama, R., Sakamaki, T., Tsuchiya, T., Funakoshi, K., 2011. Effect of hydrogen on the melting temperature of FeS at high pressure: implications for the core of Ganymede. Earth Planet. Sci. Lett. 301, 153–158. Shimoyama, Y., Terasaki, H., Ohtani, E., Urakawa, S., Takubo, Y., Nishida, K., Suzuki, A., Katayama, Y., 2013. Density of Fe-3.5 wt% C liquid at high pressure and temperature and the effect of carbon on the density of the molten iron. Phys. Earth Planet. Inter. 224, 77–82. Silber, R.E., Secco, R.A., Yong, W., 2017. Constant electrical resistivity of Ni along the melting boundary up to 9 GPa. J. Geophys. Res., Solid Earth 122, 5064–5081. https://doi.org/10.1002/2017JB014259.

46

A. Pommier / Earth and Planetary Science Letters 496 (2018) 37–46

Stewart, A.J., Schmidt, M.W., van Westrenen, W., Liebske, C., 2007. Mars: a new corecrystallization regime. Science 316, 1323–1325. Suehiro, S., Ohta, K., Hirose, K., Morard, G., Ohishi, Y., 2017. The influence of sulfur on the electrical resistivity of hcp iron: implications for the core conductivity of Mars and Earth. Geophys. Res. Lett. https://doi.org/10.1002/2017GL074021. Tateyama, R., Ohtani, E., Terasaki, H., Nishida, K., Shibazaki, Y., Suzuki, A., Kikegawa, T., 2011. Density measurements of liquid Fe–Si alloys at high pressure using the sink–float method. Phys. Chem. Miner. 38, 801–807. Tsuno, K., Frost, D.J., Rubie, D.C., 2011. The effects of nickel and sulphur on the core– mantle partitioning of oxygen in Earth and Mars. Phys. Earth Planet. Inter. 185, 1–12. Vostryakov, A.A., Vatolin, N.A., Yesin, O.A., 1964. Viscosity and electrical resistivity of molten alloys of iron with phosphorus and sulphur. Fiz. Metal. Metalloed. 18 (3), 476–477.

Walker, D., Li, J., 2007. Partitioning of molybdenum to 60 kbar along a warped Fe– FeS liquidus. Chem. Geol. 248, 166–173. Wiedemann, D., Franz, R., 1853. Ueber die Wärme-Leitungsfähigkeit der Metalle. Ann. Phys. Chem. 89, 497–531. Yoshino, T., Ito, E., Katsura, T., Yamazaki, D., Shan, S., Gui, X., Nishi, M., Higo, Y., Funakoshi, K-i., 2011. Effect of iron content on electrical conductivity of ferropericlase with implications for the spin transition pressure. J. Geophys. Res. 116, B04202. https://doi.org/10.1029/2010JB007801. Zhang, L., Fei, Y., 2008. Effect of Ni on Fe–FeS phase relations at high pressure and high temperature. Earth Planet. Sci. Lett. 268, 212–218. Zhang, Z., Pommier, A., 2017. Electrical investigation of metal–olivine systems and application to the deep interior of Mercury. J. Geophys. Res., Planets 122. https:// doi.org/10.1002/2017JE005390.