Physics and Chemistry of Minerals

, Volume 37, Issue 6, pp 353–359 | Cite as

Melting of iron–silicon alloy up to the core–mantle boundary pressure: implications to the thermal structure of the Earth’s core

  • Hidetoshi Asanuma
  • Eiji Ohtani
  • Takeshi Sakai
  • Hidenori Terasaki
  • Seiji Kamada
  • Tadashi Kondo
  • Takumi Kikegawa
Original Paper

Abstract

The melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell experiments. We have also investigated the subsolidus phase relations of Fe–18 wt% Si alloy by the in-situ X-ray diffraction method and confirmed that the bcc phase is stable at least up to 57 GPa and high temperature. The melting curve of the alloy was fitted by the Simon’s equation, P(GPa)/a = (Tm(K)/T0)c, with parameters, T0 = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. The melting temperature of bcc Fe–18 wt% Si alloy is comparable with that of pure iron in the pressure range of this work. The melting temperature of Fe–18 wt% Si alloy is estimated to be 3,300–3,500 K at 135 GPa, and 4,000–4,200 K at around 330 GPa, which may provide the lower bound of the temperatures at the core–mantle boundary and the inner core–outer core boundary if the light element in the core is silicon.

Keywords

FeSi alloy Core High pressure Melting 

Introduction

The thermal structure of the Earth’s core can be constrained at the core–mantle boundary (CMB) and the inner core–outer core boundary (ICB) by the melting temperature of the core material. Therefore, the melting relation of iron alloy at high pressure is indispensable to estimate the thermal structure of the Earth. Iron is the most abundant element in the Earth’s core. However, seismic data show that the Earth’s core is about 10% less dense than pure metallic iron at the core pressure and temperature (Birch 1952). This density deficit suggests the presence of light elements, such as H, C, O, S, and Si, in the outer core. Silicon is one of the major candidates for the light element because it is one of the most abundant elements in the Earth (Birch 1964; Ringwood 1959). The Earth’s mantle is depleted in silicon relative to C1 chondritic material, which suggests that the dominant light element in the core might be silicon (MacDonald and Knopoff 1958; Ringwood 1959; Wänke 1981; Allègre et al. 1995). Solubility of silicon into metallic iron increases with increasing pressure together with temperature (Takafuji et al. 2005; Sakai et al. 2006). The amount of silicon in the outer core (assuming the light element is only Si) has been estimated to be 14–20 wt% Si (Ringwood 1959; Balchan and Cowan 1966; Poirier 1994).

In this study, the melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell (DAC) experiments. Although Fe–18 wt% Si alloy is a binary system and the solidus and liquidus temperatures can be defined in the phase relation, the melting relations of Fe–Si alloy at an ambient pressure (Schurmann and Hensgen 1980), 5.5 GPa (Yang and Secco 1999), and 21 GPa (Kuwayama and Hirose 2004) indicate that the solidus and liquidus temperatures in Fe–18 wt% Si alloy are very close with a narrow binary loop. Therefore, we used the term of melting temperature instead of the solidus and liquidus temperatures in this paper. We have also investigated the subsolidus phase of Fe–18 wt% Si alloy using in-situ X-ray diffraction at high pressure and temperature.

Experimental method

The Fe–18 wt% Si powder (Goodfellow Co. Ltd.) was used for the starting material. Homogeneity of the starting alloy powder was checked by the electron microprobe analysis. The result showed that the powder was homogeneous and the iron alloy contains 17.7 ± 0.4 wt% Si.

High pressure was generated by a Mao–Bell-type DAC with type-I diamond as anvils. The anvils with a culet size of 0.35 mm in diameter without bevels were used for the runs to 68 GPa, whereas the beveled anvils with a 0.15 mm culet for the runs to 119 GPa. The rhenium or SUS301 gaskets were pre-indented to about 20 GPa. A thin foil of Fe–18 wt% Si alloy embedded in powdered Al2O3 or powdered MgO pressure medium was loaded into the hole of the gasket for the experiments to determine the melting temperature by heating efficiency and by the textural observation for melting. A small piece of ruby crystal with a few micrometers in grain size was placed between the pressure medium and diamond anvil surface for the pressure measurement. Pressures generated at 300 K before heating, after annealing, and after heating are given in Table 1. The thin foil of the alloy was embedded in powdered NaCl pressure medium, and the NaCl-B2 pressure scale by Fei et al. (2007) was applied for determination of the pressure for the in-situ X-ray diffraction runs.
Table 1

Pressures at 300 K measured before heating, after annealing, and after heating

Run no.

Before heating (GPa)

After annealing (GPa)

After heating (GPa)

FESI16

24.3

22.5

21.5

FESI04

35.9

28.1

27.2

FESI05

46.5

40.8

28.3

FESI06

55.1

48.4

50.1

FESI12

58.5

57.0

59.3

FESI09

75.7

66.3

69.9

FESI14

102.5

104.1

103.8

FESI15

119.4

118.6

120.1

Before heating to a target temperature at high pressure, the sample was annealed by laser scanning over the whole sample areas at about 1,800 K for 15 minutes in order to minimize the deviatoric stress in the samples. The samples were heated by the double-sided laser heating method using a high-power multimode Nd:YAG laser (λ = 1.064 µm, LEE LASER8100MQ) with the laser spot size of around 50 µm. Temperatures were measured by both side, and determined by fitting the emission spectra from the heated sample to the gray body formula. The emission spectra were measured by using the spectrometer (SpectraPro300i, Acton Research Co., Ltd.). The temperature fluctuations during the heating experiments were around ±50 ~ 100 K at a constant laser power. The error bars in temperatures shown in Table 2 were the temperature fluctuations during about one minute heating at a constant laser power in both sides of the sample.
Table 2

Experimental conditions and results

Run no.

Pressure (GPa)

Maximum temperature (K)

Melting temperature (K)

Pressure medium

Notes

FESI16

22 (1)

2,330 (50)

2,210 (50)

Al2O3

Quenched textures were observed.

FESI04

28 (1)

2,570 (50)

2,290 (50)

Al2O3

Quenched textures were observed.

FESI05

34 (6)

2,820 (50)

2,610 (50)

Al2O3

Quenched textures were observed.

FESI06

49 (1)

2,890 (50)

2,730 (100)

Al2O3

Quenched textures were observed.

FESI12

58 (1)

3,070 (100)

2,800 (100)

MgO

Quenched textures were observed.

FESI09

68 (2)

2,990 (50)

2,880 (50)

Al2O3

Quenched textures were observed.

FESI14

104 (1)

3,200 (100)

3,060 (100)

Al2O3

Textures were not observed.

FESI15

119 (1)

3,470 (100)

3,240 (100)

Al2O3

Quenched textures were observed.

FESI17

22a

2,000 (100)

No melting

NaCl

bcc phase observed by X-ray diffraction

FESI20

57a

1,600 (50)

No melting

NaCl

bcc phase observed by X-ray diffraction

FESI21

96a

2,000 (50)

No melting

NaCl

bcc phase observed by X-ray diffractionb

aPressure was determined at high temperature using the equation of state of B2-type NaCl (Fei et al. 2007)

bX-ray diffraction was taken at 96 GPa and 300 K. The error bars in temperatures are the temperature fluctuations during heating at a constant laser power in both sides of the sample

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. Experimental pressure was measured at 300 K by the ruby pressure scale based on pressure dependence of the ruby fluorescence (Mao et al. 1978) and the average value between the pressure after annealing and that after heating was adopted as the pressure value of the experiment. Thermal pressure corrections were not made to the pressures at high temperatures. The pressure increase at high temperatures determined by separate runs was about 3 GPa to 2,700 K at 50 GPa and about 4 GPa to 3,000 K at 100 GPa, which are comparable with the pressure uncertainties in the present experiments.

In order to clarify the subsolidus phase at high pressure and temperature, in-situ X-ray diffraction experiments at high pressure and temperature were carried out using the synchrotron X-ray at the BL13A beamline, KEK-PF in Tsukuba, Japan. The incident white X-ray beam was monochromatized to the wavelength of 0.4267 or 0.4266 Å, collimated to a 30 × 30 µm, and introduced to the sample through the diamond. The diffraction data captured by the imaging plate (IP) (RAXIS-IV, Rigaku Co Ltd.) were integrated to make one-dimensional patterns. The exposure time for taking diffraction was 15 min for high-temperature runs, whereas it was 15–60 min for the room temperature runs. Each diffraction pattern was analyzed using the PIP program for Windows (programmed by Y. Fujihisa) and PD Indexer (programmed by Y. Seto). However, it was not possible to detect melting of the sample precisely by the in-situ X-ray diffraction method due to the temperature and pressure gradients in the samples, i.e., relatively a large X-ray beam diameter compared to the hot spot size of the laser in this experiment.

Melting of the sample was determined based on a change of the heating efficiency and observation of quenched sample textures. The change of heating efficiency (E*) may be defined by the relation between the laser power (W) and the measured temperature (T); E* = dT/dW, where dT and dW are the temperature increase and the laser power increase, respectively. Change of the heating efficiency is caused by melting of the sample because the laser absorption substantially increases by change from solid to liquid (Boehler 1993, 2000). This phenomenon can be confirmed by measuring the melting of the material whose melting point is well known. In this study, we have used platinum to confirm the change of the laser absorption during melting. A Pt wire with a diameter of 0.2 mm was heated by the double-sided laser heating method at an ambient pressure. The result of melting experiment of Pt is shown in Fig. 1. The beginning of a rapid temperature increase, shown by a black arrow in Fig. 1, is consistent with the reported melting temperature of Pt in all six independent measurements. Thus, the temperature value at the beginning of a rapid temperature increase can be adopted as the melting temperature of Fe–18 wt% Si alloy.
Fig. 1

Detection of the melting temperature of platinum based on the temperature generation efficiency of the YAG laser at an ambient pressure. A drastic change of the absorption coefficient associated with melting can be used to detect melting as was reported by the previous authors (e.g., Boehler 1993, 1996)

Recovered samples were put on an epoxy resin and were polished for textural observation by the scanning electron microscope equipped with an energy-dispersive spectrometer (SEM/EDS) (JEOL-8800). Operating conditions were the accelerating voltage of 15 kV and the beam current of 10 nA.

Results and discussion

The experimental conditions and the results of melting experiments are summarized in Table 2. The spot size of the laser heating was about 50 µm in diameter, whereas we measured the average temperature of the area about 10 µm in diameter within the hot spot, where the flat temperature profile was observed. The temperature difference across the area of 10 µm in diameter was smaller than the temperature fluctuation during heating with a constant laser power (±50–100 K). We measured the temperature with 0.5–1 W interval with increasing laser power for each run, and we observed a change of the heating efficiency during heating. The changes in the heating efficiency in representative runs are given in Fig. 2a, b, which show the relations between the laser power and measured temperature of runs FESI16 and FESI04 in which the melting points at 22 and 28 GPa were determined to be 2,210 ± 50 and 2,290 ± 50 K, respectively, which correspond to the temperature of beginning of the abrupt temperature increase.
Fig. 2

a The relation between the laser power and temperature for the high-pressure experiment made at 21 GPa (Run FESI16). A jump in the laser power–temperature curve is observed at 2,210 K (a solid arrow) which is determined as the melting temperature. Similar jumps in temperature are observed at various pressures as shown in solid arrows, 2,290 K at 28 GPa (Run FESI04) (b), 2,610 K at 40 GPa (Run FESI05) (c), 2,800 K at 58 GPa (Run FESI12) (d), 3,060 K at 104 GPa (Run FESI14) (e), and 3,240 K at 119 GPa (Run FESI15) (f)

The changes in the heating efficiency in other representative runs are shown in Fig. 2c–f. Figure 2c, d represent the relation between the laser power and measured temperature of runs FESI05 and FESI12 in which the melting temperatures at 40 and 58 GPa were determined to be 2,610 ± 50 and 2,800 ± 100 K, respectively, which correspond to the temperature of beginning of the abrupt temperature increase. In the run made at 58 GPa with the MgO pressure medium (FESI12, Fig. 2d), we observed nearly a constant temperature at around 2,800 K with increasing laser power just below the melting point, which is in contrast with the other runs using the Al2O3 pressure medium. The difference in the temperature-power relation is not well explained, although it might be due to difference in mechanical properties of the different pressure medium. Figure 2e, f represent the relation of runs FESI14 and FESI15 with the melting points of 3,060 ± 100 K at 104 GPa and 3,240 ± 100 K at 119 GPa, respectively.

The experimental conditions and the results of the in-situ X-ray diffraction experiments are summarized in Table 2. Typical X-ray diffraction profiles are given in Fig. 3 showing that Fe–18 wt% Si has a bcc structure. We observed a stability of the bcc phase in the FeSi alloy clearly at high pressure and temperature at least up to 57 GPa. The bcc phase is likely to be stable at higher pressure up to 96 GPa, since we observed the bcc phase after temperature quenching from 2,000 K at 96 GPa. This result is consistent with Lin et al. (2003) measured up to 54.5 GPa and 1,907 K and Hirao et al. (2004) measured up to 124 GPa at 300 K. The wide stability field of the bcc phase is also supported by the previous shock experiment; i.e., Fe–19.8 wt% Si which has the same bcc structure as Fe–18 wt% Si has no structural change up to 250 GPa (Balchan and Cowan 1966).
Fig. 3

X-ray diffraction patterns of Run FESI17 before (21.8 GPa, 300 K), during (25.5 GPa, 2,000 K; 24.3 GPa 1,800 K; 30.6 GPa, 1,800 K), and after heating (27.0 GPa, 300 K). These diffraction patterns indicate that the bcc phase is stable in Fe–18 wt% Si alloy. The diffraction lines of Pb from a direct beam stopper behind the carbon mirror in our X-ray optical system are observed in the X-ray profiles. FESI bcc type Fe–18 wt% Si, B1 B1 type-NaCl, B2 B2 type-NaCl, Pb lead. The wavelength of X-ray is 0.42664 Å

The quench textures of the recovered run products also provide a clue for melting of the present alloy. Figure 4a, b, c show back-scattered electron images of the sample recovered from 40 GPa (FESI05), 58 GPa (FESI12), and 119 GPa (FESI15), respectively. It shows clear dendritic textures which are the diagnostic of melting at high pressure (Kuwayama and Hirose 2004).
Fig. 4

a Textures of the polished surface of the recovered sample (FESI05) quenching from 40 GPa and 2,820 K. The dendritic quench texture A indicates that the sample was molten at the experimental condition. The smooth polished sample surface B indicates that the sample was not molten. b Textures of the recovered sample (FESI12) quenching from 58 GPa and 3,070 K, and c those of the recovered sample (FESI15) quenching from 119 GPa and 3,470 K. The dendritic quench textures indicate that the samples were molten at the experimental conditions

The temperature of abrupt change of the heating efficiency may be the minimum bound of the melting temperature, whereas that showing the dendritic texture in the recovered sample is the upper bound of the melting temperature. A phase diagram of Fe–18 wt% Si alloy up to 119 GPa is illustrated in Fig. 5 on the basis of the present results (Table 2). The melting curve of Fe–18 wt% Si representing the abrupt increase of the heating efficiency can be fitted by the Simon’s equation (Simon and Glatzel 1929) as (P(GPa)−P0)/a = (Tm(K)/T0)c where P0 = 0 GPa, T0 = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. Table 2 summarized the maximum temperatures of the experiments, from which the quench textures were observed in the recovered samples. The upper bound of the melting temperature based on the quench texture is also expressed by the Simon’s equation for melting, P(GPa)/a = (Tm(K)/T0)c, with T0 = 1,473 K, a = 2.1 ± 0.7 GPa, and c = 4.9 ± 0.5 and shown in Fig. 5.
Fig. 5

The phase diagram of Fe–18 wt% Si alloy. Solid circles are the lower bound of the melting points determined by the change of laser heating efficiency, which are fitted by the Simon’s equation, P(GPa)/a = (Tm(K)/T0)c, with parameters, T0 = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4 (a solid curve). The upper bound of the melting temperature determined by the quench texture of the sample is also shown as the inverted triangles (white) and fitted by the Simon’s equation with T0 = 1,473 K, a = 2.1 ± 0.7 GPa, and c = 4.9 ± 0.5 (a dashed curve). Cross (white) is the melting temperature measured by Kuwayama and Hirose (2004), cross (black) is that determined by Yang and Secco (1999), solid diamond is the melting temperature determined by Schurmann and Hensgen (1980). Solid triangles are the bcc phase of Fe–18 wt% Si determined by in-situ X-ray diffraction experiments. Asterisk of the solid triangle (96 GPa and 2,000 K) indicates that the X-ray diffraction data were collected at high pressure and room temperature after quenching from 2,000 K

Melting phase relations in the Fe–Si system at ambient pressure were investigated and the two eutectic points are located at 1,463 K and 19.1 wt% Si and at 1,488 K and 20.0 wt% Si (Schurmann and Hensgen 1980). Yang and Secco (1999) reported the melting curve of Fe–18 wt% Si alloy up to 5.5 GPa by measuring a change of the electrical resistivity of the Fe–Si alloy sample, indicating that the melting temperature increases with increasing pressure up to 1,703 K at 5.5 GPa. Kuwayama and Hirose (2004) reported that the eutectic temperature and composition in the Fe–FeSi system were 2,093 K and 26 wt% Si at 21 GPa. The melting temperature of pure iron was determined by Williams et al. (1987), Boehler (1993), Ma et al. (2004), and shown in Fig. 6. According to the phase relation in the Fe–Si system determined by Kuwayama and Hirose (2004), the eutectic temperature of the Fe–Si system and the liquidus temperature of Fe–18 wt% Si is lower than that of pure iron at 21 GPa. Recently, Santamaría-Pérez and Boehler (2008) determined experimentally the melting temperature of FeSi up to 70 GPa as shown in Fig. 6. These data are consistent with the present results, which indicates that the melting temperature of Fe–18 wt% Si alloy determined in this work is comparable with that of pure iron as shown in Fig. 6.
Fig. 6

Melting temperatures of Fe–Si alloys and pure iron at high pressure. The black solid and dashed curves are the melting temperatures of Fe–18 wt% Si determined in this work; a blue broken curve, the melting curve of FeSi by Santamaría-Pérez and Boehler (2008); a red dashed curve, the melting temperature of iron by Williams et al. (1987); a red solid curve, melting temperature of iron by Ma et al. (2004); a red dotted curve, melting curve of iron by Boehler (1993), in which the pressure of the γεl triple point of iron by Boehler (1993) was corrected to 70 GPa after Santamaría-Pérez and Boehler (2008)

In order to estimate the temperatures of the CMB and ICB, the present melting curve may be extrapolated to the CMB (135 GPa) and ICB (330 GPa) pressures using the Simon’s equation assuming absence of phase transitions in the subsolidus phase up to the ICB pressure. The extrapolated melting temperature is 3,300–3,500 K at 135 GPa (CMB) and 4,000–4,200 K at 330 GPa (ICB).

The present experiments may give constraints on the thermal structure of the Earth’s core. If the light element in the core is silicon, the lower bound of the CMB temperature is 3,300 K. The melting temperature of Fe–18 wt% Si at the base of the outer core, i.e., ICB, is estimated to be 4,000–4,200 K, which might provide the lower bound of the temperature at around ICB since a possible existence of phase transitions in the iron-silicon alloy (e.g., Lin et al. 2002; Dubrovinsky et al. 2003) to denser phases at higher pressures could increase the melting temperature.

Notes

Acknowledgments

The authors thank Akio Suzuki for his valuable discussion, and Masaaki Miyahara and Yoshinori Ito for their help for sample preparation and scanning electron microscopy. The authors also appreciate Nobumasa Funamori and an anonymous reviewer for their constructive reviews. This study was conducted at the beamline BL13A of Photon Factory, KEK (proposal no. 2005G151 and no. 2006G270). This work was partially supported by the Grant-in-Aid for Scientific Research to E. O. (no. 16075202 and no. 18104009) and T. K. (no. 16340164) from Ministry of Education, Culture, Sports, Science, and Technology of the Japanese Government and conducted as a part of the Global Center-of-Excellence program “Global Research and Education Center for the Dynamics of the Earth and Planets”.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Hidetoshi Asanuma
    • 1
  • Eiji Ohtani
    • 1
  • Takeshi Sakai
    • 1
  • Hidenori Terasaki
    • 1
  • Seiji Kamada
    • 1
  • Tadashi Kondo
    • 1
    • 2
  • Takumi Kikegawa
    • 3
  1. 1.Department of Mineralogy, Petrology and Economic GeologyTohoku UniversitySendaiJapan
  2. 2.Department of Earth and Space Science, Graduate School of ScienceOsaka UniversityOsakaJapan
  3. 3.Photon Factory, High Energy Accelerator Research OrganizationTsukubaJapan

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