Equation of state of Fe3S at room temperature up to 2 megabars
Introduction
One of the most convenient ways to discuss the density of the Earth’s core is an equation of state (EOS) of the core materials. One can estimate the density of a material at the core conditions and directly compare the density of the core and that of the material. Since the density of the Earth’s core is less than that of pure Fe at the core conditions, the Earth’s core has been considered to include light elements, such as H, C, O, Si, and S (e.g., Poirier, 1994). Sulfur, in particular, has been considered as one of the most plausible light elements and hence the phase relationships in the Fe–FeS system have been studied (e.g., Fei et al., 1997, Fei et al., 2000, Kamada et al., 2010, Kamada et al., 2012, Li et al., 2001, Morard et al., 2008, Seagle et al., 2006). In the Fe–FeS system, some intermediate compounds were found, such as Fe3S2, Fe2S, and Fe3S (e.g., Fei et al., 1997, Fei et al., 2000). FeS is stable as a subsolidus phase with Fe up to 10 GPa, Fe3S2 becomes a stable subsolidus phase coexisting with Fe above 14 GPa and Fe3S is a stable phase with Fe above 18 GPa and up to at least 200 GPa (e.g., Andrault et al., 2009, Kamada et al., 2010). This suggests that Fe3S could be a candidate of the inner core materials.
Fe3S, which has an AuCu3-type cubic structure, was first predicted by Sherman (1995). Its structure was later experimentally shown to be a tetragonal structure (Fei et al., 2000), which is isostructural with Fe3P. The stability of Fe3S has been investigated up to 200 GPa and it has not transformed into another structure or a new compound (e.g., Chen et al., 2007, Fei et al., 2000, Kamada et al., 2010, Seagle et al., 2006). Although magnetic transition between 20 and 25 GPa (e.g., Lin et al., 2004, Shen et al., 2003) and anomalous compression behavior of a and c axes between 20 and 30 GPa (Chen et al., 2007) have been reported, these behaviors did not affect the structure and P–V relationships of Fe3S. The EOS of Fe3S was investigated up to 80 GPa (Chen et al., 2007, Fei et al., 2000, Seagle et al., 2006) at room temperature and at high temperatures (Chen et al., 2007, Seagle et al., 2006). The K0 values reported by Fei et al. (2000) and Chen et al. (2007) are higher than those reported by Seagle et al. (2006). On the other hand, the K′ values reported by Fei et al. (2000) and Chen et al. (2007) were less than 4, while Seagle et al. (2006) reported K′ close to 4. An extrapolation of the EOS of Fe3S reported previously produces a large pressure difference for the same volume. Previous studies on the EOS of Fe3S are limited to 80 GPa. Therefore, more precise data on the EOS of Fe3S at higher pressures are essential for a reliable discussion of the density deficit of the core.
We therefore investigated the compression behavior of Fe3S up to the pressure equivalent to the core conditions by in situ X-ray diffraction (XRD) experiments in order to discuss the density deficit of the core and the amount of sulfur in the inner core.
Section snippets
Experimental procedure
A symmetrical diamond anvil cell with beveled diamond anvils was used to generate high pressures. The culet sizes of the diamond anvils were between 75 and 200 μm. A mixture of powdered Fe (99.9% purity) and FeS (99.9% purity) containing 13.2 at.% sulfur or synthesized Fe3S was used as the starting material. Fe3S was synthesized from the mixture of powdered Fe and FeS containing 23.5 at.% sulfur using a MA-8 Kawai-type multianvil apparatus driven by a 1000 ton press with a cubic guide block
Results and discussion
In situ XRD experiments were conducted in the pressure range of 24–197 GPa at room temperature. The experimental results are summarized in Table 1. Under the experimental pressures used, Fe3S did not transform into another structure or form other compounds. An example of XRD patterns taken at 67 GPa are shown in Fig. 1. Typical mirror indices used for volume calculations were observed between 6 and 20 degrees in 2θ. Fig. 2 shows the compression behavior of Fe3S recorded in this study together
Density deficit of the inner core
To explain the density deficit of the inner core, the densities of ε-Fe and Fe3S were estimated by their EOSs. It is important to note that there is some discrepancy between the EOSs of ε-Fe based on pressure scales. It is important to consider this discrepancy because an extrapolation of EOS would give a large pressure difference. Since we used Fei et al.’s NaCl scale, the EOS of ε-Fe used here was based on Dewaele et al. (2006) because both scales were obtained based on the new ruby pressure
Acknowledgments
The authors thank Dr. Przemyslaw Dera and Prof. Jay Bass for fruitful discussions. S.K. gratefully acknowledges the Japan Society for the Promotion of Science (JSPS) for providing a research fellowship. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Science, Sport and Technology of the Japanese Government (Nos 18104009 and 22000002) to E.O., and a Grant-in-Aid for Young Scientists (B) (No. 21740374) to T.S. This work was conducted as
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