Melting relations in the Fe–S–Si system at high pressure and temperature: implications for the planetary core

The Earth’s core is mainly composed of an iron alloy, with light elements also required in the core to account for the core density deficit (Birch 1964). Sulfur (S), silicon (Si), oxygen (O), carbon (C), and hydrogen (H) have been identified as the likely light elements (e.g., Poirier 1994; Terasaki 2015). Alloying with light elements significantly affects the physical properties of iron and depresses its melting temperature (e.g., Boehler 1996; Lin et al. 2002; Fischer et al. 2013). There are significant implications for the chemical composition and thermal structure of the Earth’s core as a corollary. The melting temperature of an iron alloy is important information for estimating the temperature at the inner–outer core boundary (ICB) of the terrestrial planets. An investigation of the high-pressure phases of iron alloys also helps us to understand the structure of the solid inner core. Among the candidate light elements in the core, sulfur and silicon are considered as major light element components based on geochemical models (e.g., Allégre et al. 1995; Javoy 1995; McDonough 2014) and high-pressure partitioning experiments (e.g., Hillgren et al. 2000; Sakai et al. 2006). Additionally, some geochemical studies and high-pressure experiments have predicted that sulfur and silicon could be present not only in the core of the Earth but also in the cores of other terrestrial planets such as Mars and Mercury (e.g., Bertka and Fei 1998; Malavergne et al. 2010).

Previous high-pressure studies revealed that sulfur and silicon have different effects on the properties of iron alloys. In the Fe–FeS system, Fe₃S₂, Fe₂S, and Fe₃S have been reported as intermediate phases (e.g., Fei et al. 1997, 2000; Li et al. 2001), and hcp-Fe and Fe₃S are stable as the subsolidus phases up to the core conditions. The eutectic temperature in the Fe–Fe₃S system was measured up to 180 GPa using a diamond anvil cell (DAC) (e.g., Kamada et al. 2010, 2012; Morard et al. 2008). It was revealed that the melting temperature of iron is significantly depressed by the effect of sulfur, and the hcp-Fe phase coexists with partial melts between the solidus and liquidus temperatures. The amount of sulfur in the solid iron increases with increasing pressure at the eutectic temperature (e.g., Kamada et al. 2010, 2012; Li et al. 2001). Fe₃S is the only stable phase up to 250 GPa (Ozawa et al. GRL 2013).

Silicon has a high solubility into iron and forms a solid solution with iron at high pressure (e.g., Kuwayama and Hirose 2004). The solubility of silicon into solid iron increases with increasing pressure and temperature. The high-pressure phase relations of the Fe–Si alloy have been studied by using a DAC, and it was found that the subsolidus phases of the Fe–Si alloy are related to the amount of silicon in the iron alloy (e.g., Asanuma et al. 2008; Fischer et al. 2013; Lin et al. 2002). There is a stability field of hcp + fcc phases in the alloy with Fe-3.4 wt% Si, whereas the B2 phase coexists with these phases for the alloy with Fe8.85 wt% Si (Fischer et al. 2013). The hcp phase Fe-9 wt% Si is stable to pressure and temperature conditions of the inner core (Tateno et al. 2015). The melting temperature of Fe–Si alloy was determined up to above 100 GPa by laser-heated DAC (LHDAC) experiments, and it was revealed that the effect of silicon on the melting temperature of iron alloy is smaller than that of sulfur (Asanuma et al. 2010; Fischer et al. 2013).

In spite of the importance of the effect of both sulfur and silicon on the physical properties of iron alloy, there are few studies about the melting relations of the Fe–S–Si ternary system. Although some previous studies on the closure of the Fe–S–Si liquid immiscibility gap have been reported by Sanloup and Fei (2004) and Morard and Katsura (2010), their experiments were carried out by using a multianvil apparatus at pressures below 25 GPa, and the details of higher pressure phase relations and melting temperatures in the system were not revealed. We have investigated the phase and melting relations in the Fe–S–Si system up to 60 GPa by using the LHDAC combined with an X-ray diffraction technique. Our results provide important clues for understanding the properties of the cores of Earth, Mars, and Mercury.

High pressure was generated by a symmetric-type DAC. The culet sizes of the diamond anvils were 300, 250, or 100 μm, depending on the desired experimental pressures. The starting material was composed of a powder mixture of Fe (99.9%; Wako Pure Chemical Industries, Ltd.), FeS (99.9% purity; Rare Metallic Co., Ltd.), and FeSi (99.9% purity; Rare Metallic Co., Ltd.), which was ground in an agate mortar to homogenize the starting material. The typical grain size of the starting mixture was 1–5 μm, which was confirmed by using a scanning electron microscope (SEM; JEOL JSM-5410). This powdered mixture was compressed to make discs by using cylindrical jigs. The sample compositions used in this study were determined by the EPMA analysis to be Fe_80.1S_12.7Si_7.2 (Fe-8wt.%S-4wt.%Si) and Fe_74.4S_18.5Si_7.1 (Fe-12wt.%S-4wt.%Si). These compositions might be close to the composition of Mercury’s core, which might contain several wt.% silicon in addition to sulfur, as was suggested by previous high-pressure experiments under reducing conditions (e.g., Malavergne et al. 2010). The two starting materials were used for determination of the subsolidus phases and the solidus temperature of the Fe–S–Si system, whereas the liquidus temperature was determined for the starting material with Fe_80.1S_12.7Si_7.2 in composition.

We made a thin foil of starting materials by using a cold compression technique. Before loading the sample, we checked the homogeneity of the sample with a grain size less than 2 μm again by using a high-resolution reflection microscope and selected only homogeneous pieces of the mixture foil. For the in situ experiments, the sample foil was sandwiched between NaCl pellets, which worked as a pressure medium, thermal insulator, and pressure marker. These samples were loaded into a sample hole in a pre-compressed SUS304 or Re gasket, which was typically about 30–50 μm in thickness. On the other hand, the sample foil was embedded into an Al₂O₃ powder, which worked as a pressure medium, for the sample recovered experiments. When NaCl was used as a pressure medium, it was difficult to recover the sample because it flowed in the NaCl pressure medium towards the gasket during decompression.

The sample was heated by using the double-sided laser heating method (Shen et al. 1996) employing an Nd:YAG laser or fiber laser. Radiation from the heated sample was collected for time durations between 0.5 and 3 s for analyzing the temperature. The temperature measurements were performed for several tens of seconds during heating. The experimental temperature was determined as an average of the measured temperature over several tens of seconds. The temperature fluctuation during the experiments was approximately 50–100 K. The experimental pressure was determined based on the lattice parameters of NaCl using the equation of states (EOS) of the B1 phase (Brown 1999) and the B2 phase (Fei et al. 2007) of NaCl. The experimental pressure at high temperature was assumed to be P _HT = P _300 K + ΔP _th. P _300 K is a pressure at room temperature based on the third-order Birch–Murnaghan equation of state, and ΔP _th is a thermal pressure based on the Mie–Grüneisen relation: P _th = γ/V[E(T, θ _D ) − E(T ₀, θ _D )] where γ = γ ₀(V/V ₀) ^q and θ _D  = θ ₀(V/V ₀)^− γ . The parameters of the EOS of NaCl are summarized in Brown (1999) and Fei et al. (2007). Since NaCl has a temperature gradient from the ambient temperature to the sample temperature, the procedure by Campbell et al. (2007, 2009) was used to evaluate the thermal pressure. The EOS of iron was not used to calculate experimental pressure in this study because incorporation of silicon or sulfur into solid iron may expand the unit cell volume of iron (e.g., Hirao et al. 2004). The error in pressure was evaluated from the error in the volume of NaCl, and the error in temperature was determined based on the standard deviation of the fluctuation of the measured temperature.

In situ X-ray diffraction experiments were conducted at the BL10XU beamline of the SPring-8 facility (Ohishi et al. 2008). We used a monochromatic X-ray beam with a typical wavelength of 0.4136(3) Å collimated to a diameter of 15 μm. The beam size was smaller than the size of the laser heating area, which was approximately 30–40 μm across. We checked the X-ray position by the X-ray fluorescence of diamonds before heating. Therefore, the X-ray and heating areas are aligned well. The melting detection in this study was based on the disappearance of the X-ray diffraction peaks which were the same as those in previous melting studies (e.g., Kamada et al. 2010, 2012; Terasaki et al. 2011). An imaging plate (IP: Rigaku R-AXIS IV⁺⁺) or an X-ray charge-coupled device (CCD: Brucker AXS, SMART APEX) was used as X-ray detectors. The typical exposure time for taking diffraction patterns was 1 s for the CCD detector or 3 min for the IP detector for each run. At high temperatures, the sample diffraction patterns were collected by using the CCD detector because it is important to take a diffraction pattern within a short duration of time to detect melting of the sample. First, the sample was compressed to a target pressure at room temperature and then annealed at around 1500 K for about 10 min to synthesize solid phases and to reduce stress in the cell assemblages. The diffraction patterns of the sample were recorded at room temperature and in the temperature ranges between 1350 and 2270 K in 50–100 K steps at each pressure. The temperature fluctuations were almost the same as those at subsolidus conditions and after melting conditions. After we observed the disappearance of the X-ray diffraction peaks of Fe₃S, the laser power was shut down to quench the sample. The reappearance of X-ray diffraction peaks of Fe₃S in the quenched sample was confirmed to be reproducible and suggests the disappearance of Fe₃S peaks at high temperatures was caused by the sample melting and was not caused by migration of Fe₃S from the heating spot of the sample. The diffraction patterns were analyzed by the IPAnalyzer software package and the PDIndexer software package programmed by Seto et al. (2010).

The phase and melting relations in the Fe–S–Si system were studied up to 60 GPa by using a double-sided laser-heated diamond anvil cell combined with X-ray diffraction. We confirmed that hcp/fcc Fe–Si alloys and Fe₃S are stable phases under subsolidus conditions in the system. The liquidus phase changes from fcc to hcp at around 40 GPa. Both solidus and liquidus temperatures are significantly lower than the melting temperature of pure Fe and both increase with increasing pressure. The slope of the Fe–S–Si liquidus temperature determined here is 12 K/GPa, which is significantly smaller than the adiabatic temperature gradients of the liquid cores of Mercury and Mars, at around 18~27 K/GPa. Thus, crystallization of their cores started at the core–mantle boundary region even in the cores containing both silicon and sulfur as light elements. This crystallization start is consistent with the snowing-core model proposed by previous authors for the cores with the Fe–S systems (Chen et al. 2008; Stewart et al. 2007).