Phase relations of Fe-Si alloy up to core conditions: Implications for the Earth inner core

Authors


Abstract

[1] X-ray diffraction experiments were conducted to 257 GPa and high temperature in situ on an iron-silicon alloy containing 3.4 wt% silicon, a candidate for the Earth's inner core forming material. The results revealed that fcc and hcp phases coexist up to 104 GPa. A single hcp phase is stable at higher pressures at least up to 3600 K at 242 GPa and to 2400 K at 257 GPa. Dissolution of silicon in the liquid outer core following reaction with the silicate mantle during core formation strongly suggests the existence of silicon in the solid inner core. Our results revealed that the iron-3.4 wt% silicon alloy in the inner core is likely to possess an hcp structure, which can explain the inner core anisotropy observed in seismology.

1. Introduction

[2] Geophysical evidence indicates that the density of the inner core is about 2–5 wt% lower than the density of pure iron (Fe) under the conditions of the inner core [e.g., Dubrovinsky et al., 2000], indicating the presence of light elements such as hydrogen, carbon, sulfur, oxygen (O), or silicon (Si) contained within it [Birch, 1964; Mao et al., 1990]. Si is a major candidate for the light element because it is one of the most abundant elements in the Earth [Birch, 1952; Ringwood, 1959]. The solubility of both Si and O in metallic iron increases with increasing pressure [Takafuji and Hirose, 2005; Sakai et al., 2006]. Assuming that the light element is only Si, its amount in the inner core has been estimated to be 2.3–8.5 wt% based on compressibility measurements at high pressure [Lin et al., 2003; Dobson et al., 2003; Hirao et al., 2004], high pressure sound velocity measurement [Badro et al., 2007] and ab initio calculation [Alfe et al., 2002].

[3] Recent studies report that a small amount of Si as an additional component can substantially affect the phase relations and thermodynamic properties of iron alloys [Lin et al., 2003; Dubrovinsky et al., 2003]. Lin et al. [2002] reported that an Fe-Si alloy containing 8 wt% Si has hexagonal closed-packed (hcp) + body-centered cubic (bcc) phases at 84 GPa and 2400 K, and a bcc phase is stabilized at higher pressure–temperature (P–T) conditions. Consequently, study of the Fe-rich portion of the Fe-Si system and a knowledge of the effect of Si on the crystal structure and the equation of state of metallic Fe under the core conditions are essential for understanding the nature of the inner core.

[4] The phase relations of Fe have been extensively studied. In situ X-ray diffraction studies to 161 GPa and 3000 K demonstrate that hcp-Fe has a wide stability field extending to core conditions [Shen et al., 1998; Hemley and Mao, 2001; Ma et al., 2004]. Herein we report on the phase relations of the Fe-3.4 wt% Si alloy, a candidate for the inner core whilst assuming Si to be the only the light element present there.

2. Experiment

[5] The starting material used for the experiments was Fe-3.4 wt% Si (Rare Metallic Co. Ltd.). Homogeneity of the starting alloy was checked by the electron microprobe analysis. The result showed that the alloy was homogeneous and the composition was 3.4 ± 0.1 wt% Si. The rhenium gasket was preindented to about 20–27 GPa. The sample was loaded into a rhenium gasket with 25∼100 μm diameter drilled by a Nd:YAG laser in a symmetric diamond anvil cell (DAC). High pressure was generated by a symmetric DAC with beveled type-I diamond anvils. The Fe-3.4 wt% Si alloy was compressed using the anvils with differing culet sizes depending on the pressure generated; i.e., we used beveled anvils with 0.15/0.30 mm and 0.1/0.3 mm culets, and double beveled anvils with 0.075/0.10/0.30 mm and 0.035/0.10/0.30 mm culets. A sample foil (5–10 μm in thickness and 10–80 μm in diameter) of Fe-3.4 wt% Si alloy was sandwiched in thin (5–10 μm) layers of NaCl, which worked as a thermal insulator, a pressure-transmitting medium, and an internal pressure standard.

[6] Fe-3.4 wt% Si alloy was compressed and laser-heated in a diamond anvil cell at pressures up to 257 GPa and temperatures up to 3600 K. X-ray diffraction patterns were collected in situ using the powerful synchrotron X-ray of SPring-8. A double-sided TEM01-mode Nd:YLF laser λ = 1.047 μm, Lee Laser8100MQ system was used for heating the sample. Laser power differs by the heating temperatures with the maximum of 90 W in the present heating conditions. Temperatures were determined by fitting the emission spectra from the heated sample to the gray body formula. The emission spectra were measured using the spectrometer SpectraPro300i (Acton Research Co. Ltd.). The temperature fluctuations during the X-ray diffraction experiments were circa ±50–500 K and shown as error bars in Figure 2. A 15 μm size of the collimated X-ray beam was smaller than the size of the stable heating area with a flat temperature profile of approximately 20 μm in the laser heating spot. Using NaCl insulating layers minimized axial and radial temperature gradients. The outer cylinder of the DAC was cooled by circulating water to avoid a pressure change during heating and to protect the DAC from oxidation.

[7] In situ X-ray diffraction experiments at high pressure and temperature were carried out using the synchrotron X-ray at the BL10XU beam line, SPring-8 in Harima, Japan. The incident white X-ray beam was monochromated to a wavelength typically 0.4122(1) Å. The beam was collimated to a 15 μm square and introduced into the sample through the diamond. The diffraction data captured on a RAXIS-IV imaging plate detector (Rigaku Co. Ltd., Japan) were integrated to make one-dimensional patterns. The exposure time for observing diffraction was five minutes for runs made at both room and high temperatures. Each diffraction pattern was analyzed using a PIP program for Windows and PD Indexer software (programmed by Y. Seto).

[8] The pressures below circa 30 GPa were determined by the equation of state of B1-NaCl [Brown, 1999]. The pressures above 30 GPa were tentatively determined by the equation of state of B2-NaCl [Fei et al., 2007], which is based on the P–T scale by Dewaele et al. [2004], although the pressure scale is not yet established above 98 GPa. The highest pressure generated in the present experiment was 257 GPa based on this pressure scale, whereas it is 317 GPa based on the equation of state of B2-NaCl determined by Sata et al. [2002]. The experimental conditions and results with pressure values determined using different pressure scales are summarized in Table 1.

Table 1. Experimental Conditions of Fe-3.4 wt% Si Alloya
Run NumberPressure (GPa)Temperature (K)Solid Phase of Fe-3.4 wt% SiRun NumberPressure (GPa)Temperature (K)Solid Phase of Fe-3.4 wt% Si
Brown [1999]Fei et al. [2007]Sata et al. [2002]Fei et al. [2007]Sata et al. [2002]
FeSiI2_0010  300bccFeSiI11_0321671893100(±200)hcp
FeSiI1_0012  300bccFeSiI11_0381711962100(±200)hcp
FeSiI1_00212  300bccFeSiI11_0391731963300(±200)hcp
FeSiI1_00321  300bcc + hcpFeSiI11_0441752022000(±100)hcp
FeSiI2_00323  300hcpFeSiI11_0451772032600(±200)hcp
FeSiI5_003 54511800(±100)hcp + fccFeSiI11_0461782033400(±300)hcp
FeSiI5_004 55512200(±100)hcp + fccFeSiI11_0491802082100(±200)hcp
FeSiI5_005 55512500(±100)hcp + fccFeSiI11_0501832103400(±500)hcp
FeSiI5_002 55531800(±100)hcp + fccFeSiI13_0062002332500(±100)hcp
FeSiI9_006 79782200(±100)hcp + fccFeSiI13_0072012353050(±150)hcp
FeSiI9_005 80792100(±100)hcp + fccFeSiI13_0082022343600(±300)hcp
FeSiI9_004 80801750(±250)hcpFeSiI13_0122082452700(±100)hcp
FeSiI9_007 80783100(±300)hcp + fccFeSiI13_0132102473500(±200)hcp
FeSiI9_008 81743500(±300)hcp + fccFeSiI13_0162152562850(±150)hcp
FeSiI9_002 85861500(±100)hcpFeSiI13_0172172553500(±500)hcp
FeSiI3_003 1021071400(±100)hcpFeSiI13_0192212633500(±200)hcp
FeSiI3_004 1041081900(±100)hcpFeSiI13_0212292743300(±300)hcp
FeSiI3_006 1041082400(±200)hcp + fccFeSiI13_0252402912900(±100)hcp
FeSiI3_010 1131192200(±200)hcp + fccFeSiI13_0262422923600(±200)hcp
FeSiI4_004 1131183100(±200)hcp + fccFeSiI13_0292422933000(±200)hcp
FeSiI3_012 1141192600(±200)hcp + fccFeSiI10_1882503092100(±100)hcp
FeSiI4_003 1151193300(±200)hcp + fccFeSiI10_1902503082550(±150)hcp
FeSiI11_030 1651872200(±300)hcpFeSiI10_1912513082950(±250)hcp
FeSiI11_031 1661882600(±300)hcpFeSiI13_0312573172400(±200)hcp

3. Results and Discussion

[9] On compression at room temperature, the Fe-3.4 wt% Si alloy with an ambient bcc structure transformed into an assemblage of bcc and hcp phases at 21 GPa. The mixture of bcc and hcp phases completely transformed to a single hcp phase at 23 GPa. Our results indicate that dissolution of 3.4 wt% Si into Fe stabilizes the fcc structure and expands the stability field for the coexistence of fcc and hcp structures up to about 110 GPa. The hcp phase of Fe-3.4 wt% Si alloy is stable up to 257 GPa. A similar phase transformation is reported for Fe-8 wt% Si alloy at room temperature and high pressure [Lin et al., 2003; Hirao et al., 2004].

[10] We observed that the hcp phase was stable at 104 GPa and 1900 K in Fe-3.4 wt% Si alloy and it transformed to hcp + face-centered cubic (fcc) phases at 2400 K at the same pressure. The hcp + fcc phases were stable at 113 GPa and 3100 K, whereas these phases transformed to a single hcp phase at 167 GPa at the same temperature. The change of the diffraction pattern with increasing temperature at 104 GPa is shown in Figure 1a, and the detailed diffraction patterns are seen in Figure 1b. The change with increasing pressure at 3100 K is also shown in Figure 1c, and the detailed diffraction patterns are given in Figure 1d. We revealed that the hcp phase is stable at 252 GPa at room temperature, and it persists at least up to about 2400 K at 257 GPa measured using the B2-NaCl pressure scale [Fei et al., 2007] as shown in Figure 1e. The phase relations for the Fe-3.4 wt% Si alloy composition are summarized in Figure 2. The phase boundary from fcc + hcp to a pure hcp phase locates in the pressure interval of 110 and 160 GPa. Further experiments are needed in future to determine the boundary more precisely.

Figure 1.

Examples of X-ray diffraction patterns derived from experiments with Fe-3.4 wt% Si. (a) The hcp phase is stable at 104 GPa and 1900 (±100) K. It transforms to hcp + fcc phases at 2400 (±200) K at the same pressure. (b) Detailed diffraction patterns for Figure 1a. (c) The hcp + fcc phases are stable at 113 GPa and 3100 (±200) K, whereas these transform to a single hcp phase at 167 GPa at the same temperature. (d) Detailed diffraction patterns for Figure 1c. (e) The hcp phase is stable at 252 GPa and room temperature (the result is not shown in Table 1), and it persists at least up to circa 2400 (±200) K at 257 GPa.

Figure 2.

Phases observed in the laser heating diamond anvil cell experiment with the Fe-3.4 wt% Si alloy. The open symbols are the current results, whereas the solid symbols represent those obtained by Lin et al. [2003]. The solid curve shows the phase boundary from fcc + hcp to hcp. Phase boundaries and the melting curve of pure Fe after Ma et al. [2004] are also shown as the broken curves.

[11] Comparing the phase relations of iron [Ma et al., 2004] and those of the Fe-3.4 wt% Si alloy given in Figure 2, it is clear that the stability field of the fcc phase expands to higher P–T conditions by dissolution of 3.4 wt% Si into iron. This is a similar effect with dissolution of nickel (Ni) in Fe as observed in the phase relations of the Fe-10 wt% Ni system [Mao et al., 1990], although it is in contrast with the recent result by Dubrovinsky et al. [2007] reporting the existence of a bcc structured phase in Fe-10 at. % Ni alloy at 225 GPa and 3400 K.

[12] The formation of a Si-bearing liquid outer core is considered inevitable through reaction with the surrounding silicate mantle during the core formation of the Earth [Takafuji and Hirose, 2005; Sakai et al., 2006]. Therefore, a partitioning of Si between Si-bearing liquid outer and solid inner cores suggests that the inner core also contains Si as a light element.

[13] Lin et al. [2002] reported that Fe-Si alloy containing 8 wt% Si has hcp + bcc phases up to at least 84 GPa and high temperatures and a bcc phase is stabilized at higher pressure-temperature conditions. They also reported that Fe-4 wt% Si alloy, which has a composition close to this study, does not have a bcc phase at 16 GPa. Dubrovinsky et al. [2003] observed a bcc structure in Fe-Si alloy containing 4.3–9.6 wt% at least up to 160 GPa and 3500 K and reported Fe-Si alloy containing more than 4 wt% Si has hcp + bcc (B2) phases at the pressures more than 60 GPa and high temperatures. Vocadlo et al. [1999] made ab initio calculations and suggested an existence of CsCl structured phase in FeSi at pressures above 13 GPa. Although we could not observe the bcc phase in our experimental conditions, the discrepancy between these previous works and the present results can be explained by the difference of the Si content and therefore the present results are not inconsistent with the results of the previous studies.

[14] The cause of the seismic anisotropy has been a matter of great debates. The inner core phase responsible for the seismic anisotropy might be different depending on the Si content of the inner core. An hcp phase of iron has accounted for the anisotropy of the inner core [e.g., Song, 1997; Stixrude and Cohen, 1995; Antonangeli et al., 2004]. On the other hand, recent studies suggested that the bcc structured phase observed in FeSi alloy containing Si greater than 4.3 wt% can be responsible for the anisotropy of the inner core [Vocadlo et al., 1999; Belonoshko et al., 2008]. However, recent estimations of the Si content of the inner core based on the compressibility of Fe-Si alloy suggested that the inner core contains silicon lower than 4.3 wt% [e.g., Lin et al., 2003; Hirao et al., 2004]. Badro et al. [2007] showed that the Si content of the inner core is about 2.8 wt% based on the density and seismic velocity determined experimentally. Our results revealed that the Fe-3.4 wt% Si alloy retains an hcp structure at least up to the maximum temperature of 3600 K at 242 GPa, and up to 2400 K at the maximum pressure of 257 GPa on the B2-NaCl pressure scale. [Fei et al., 2007]. This corresponds to 293 GPa and 317 GPa on the pressure scale of Sata et al. [2002]. Therefore, it is likely that the Si-bearing inner core has an hcp structure, which can account for its seismic wave anisotropy. However, more precise estimation of the silicon content of the inner core is essential in future to identify the phase responsible for the seismic anisotropy of the inner core.

Acknowledgments

[15] This work was partially supported by grant-in-aids for scientific research donated by the Ministry of Education, Culture, Science, Sport, and Technology of the Japanese Government to E.O. (18104009 and 16075202). This work was conducted as a part of the 21st COE program Advanced Science and Technology Center for the Dynamic Earth at Tohoku University.

Ancillary

Advertisement