Physics and Chemistry of Minerals

, Volume 38, Issue 10, pp 801–807 | Cite as

Density measurements of liquid Fe–Si alloys at high pressure using the sink–float method

  • Ryuji Tateyama
  • Eiji Ohtani
  • Hidenori Terasaki
  • Keisuke Nishida
  • Yuki Shibazaki
  • Akio Suzuki
  • Takumi Kikegawa
Original Paper

Abstract

The compositional dependence on the density of liquid Fe alloys under high pressure is important for estimating the amount of light elements in the Earth’s outer core. Here, we report on the density of liquid Fe–Si at 4 GPa and 1,923 K measured using the sink–float method and our investigation on the effect of the Si content on the density of the liquid. Our experiments show that the density of liquid Fe–Si decreases from 7.43 to 2.71 g/cm3 non-linearly with increasing Si content (0–100 at%). The molar volume of liquid Fe–Si calculated from the measured density gradually decreases in the compositional range 0–50 at% Si, and increases in the range 50–100 at% Si. It should be noted that the estimated molar volume of the alloys shows a negative volume of mixing between Fe and Si. This behaviour is similar to Fe–S liquid (Nishida et al. in Phys Chem Miner 35:417–423, 2008). However, the excess molar volume of mixing for the liquid Fe–Si is smaller than that of liquid Fe–S. The light element contents in the outer core estimated previously may be an underestimation if we take into account the possible negative value of the excess mixing volume of iron–light element alloys in the outer core.

Keywords

Density Fe–Si Non-ideality High pressure 

Introduction

Knowledge of the density of liquid Fe alloys is fundamental to an understanding of the constitution of the Earth’s core. As the Earth’s core has a density deficit compared with the density of pure iron under core conditions, the Earth’s outer core may consist mainly of Fe–Ni alloys with a small amount (8–11 wt%) of light elements, such as S, O, C, Si, and H (e.g. Birch 1952). Because Si has a high cosmic abundance, and is depleted in the mantle relative to other volatile elements, it has been suggested that Si is present in the core (Birch 1952; Ringwood 1959). In addition, the (Fe + Mg + Ni)/Si ratio in the Earth’s mantle is higher than that in chondritic meteorites. The existence of Si in the core can be accounted for by its depletion in the mantle (Allègre et al. 1995; MacDonald and Knopoff 1958; Wänke 1981). Because Si is considered to be a major light element, it is important to clarify the density of liquid Fe–Si alloys at high pressures.

There have been many studies on the physical properties of liquid Fe and liquid Fe alloys at ambient pressure (e.g. Hixson et al. 1990; Nasch et al. 1997). The density and interfacial tension of liquid Fe–Si has been measured at 1 atm and 1,723 K using the sessile drop technique (Dumay and Cramb 1995; Kawai et al. 1974), respectively. However, there have only been a few studies on the measurement of the density of Fe alloys at high pressure. Density measurements on liquid Fe–Si were carried out up to 5 GPa and 1,725 K using an X-ray absorption technique employing synchrotron radiation (Sanloup et al. 2004), and using the sink–float method (Yu and Secco 2008). In the sink–float method, we can obtain a relative density of the sample with respect to the density marker based on its flotation or sinking in the liquid sample, and several experiments are made to bracket the density of the liquid sample. Yu and Secco (2008) used composite spheres composed of a metallic core (Pt or WC) and an Al2O3 mantle as a density marker to prevent any chemical reaction occurring between the Fe alloy sample and the metallic density marker sphere. This technique has the advantage of making composite spheres with different densities by selecting different volumetric ratios between the Al2O3 mantle and the metallic core. Yu and Secco (2008) reported that the density of liquid Fe-17 wt%Si is in the range 6.0–6.8 g/cm3 at 3–12 GPa and 1,723 K.

Sanloup et al. (2004) performed density measurements on liquid Fe-17 wt%Si and liquid Fe-25 wt%Si up to 5 GPa at 1,725 K using an X-ray absorption technique. They estimated the bulk sound velocity of the alloy from their densities thus obtained and compared the effect of the Si content in metallic iron with that of other light elements, such as sulphur. They concluded that the addition of Si into iron increases the bulk sound velocity of liquid iron, which is consistent with Si being a light element in the Earth’s outer core.

The compositional dependence on the density of liquid Fe alloys at high pressures has been assumed to follow an ideal mixing behaviour (e.g. Poirier 1994). However, recently, a non-ideal mixing behaviour was observed in liquid Fe–S at high pressures (Nishida et al. 2008). Therefore, a study on any non-ideal behaviour is important for estimating the amount of light elements in the Earth’s core. Although we can estimate the density of a liquid with an intermediate composition using a linear combination of the densities of the end member components in the case of an ideal mixing of liquids, it is not possible to estimate the density in the case of a non-ideal mixing of liquids.

In this study, we performed density measurements on liquid Fe–Si at 4 GPa and 1,923 K using the sink–float method combined with X-ray radiography, and investigated the effect of the Si content on the density of the liquid.

Experimental

The density of the liquid Fe–Si alloys was determined from the sink–float behaviour of the density marker that was packed along with the sample in the capsule (Nishida et al. 2008). The sinking and flotation of the density marker in the sample was determined using two procedures: (1) in situ X-ray imaging with synchrotron X-ray radiography, and (2) observation of the recovered sample.

The composite density markers were composed of a Pt disk core with a diameter of 0.83 mm and a sintered polycrystalline Al2O3 tube with outer and inner diameters of 1.3 and 0.85 mm, respectively. We used a fibre laser (DiNY pQ-5, Innovative Berlin Laser Co. Ltd.) to cut the components of the composite marker accurately. The method used to fabricate and tailor the density of the composite marker is described in detail by Nishida et al. (2008), and therefore, only a brief description is given here. Because we prepared the composite marker components very accurately, we did not use any Al2O3-based cement to assemble the composite marker, which led to a decrease in the density error arising from any uncertainty in the density of the cement.

In situ X-ray experiments

Density was measured using the sink–float method using the X-ray radiography. High-pressure in situ X-ray experiments were performed using a KAWAI-type multi-anvil apparatus driven by a 700-ton uniaxial press (MAX-III) located at the BL14C2 beamline at the Photon Factory, KEK, Japan (Suzuki et al. 2011). A white X-ray beam, which passed through the anvil gaps and the sample at high pressure, was converted to a visible light using a YAG: Ce fluorescence screen and detected using a charge-coupled device (CCD) camera (MTV–63, Mintron Enterprise Co.) as an X-ray radiography image. Then, we observed the motion of the density marker (Fig. 1b). Neutral buoyancy of the density marker was confirmed based on its position which did not move within a period of 1 min at the experimental condition. The X-ray diffraction pattern was collected for pressure determination and observation of the sample’s status using a solid-state detector (SSD). We used 22-mm tungsten carbide anvils with a 12-mm truncated edge length as the second stage anvils. Boron nitride was used as the sample container, and graphite was used as the heating element. The temperature was monitored using a W97Re3–W75Re25 thermocouple located just above the capsule (see Fig. 1a). The starting materials were powdered mixtures composed of Fe (99.9%, Wako Pure Chemical Industries, Ltd.), FeSi (99.9%, Kojundo Chemical Laboratory Co. Ltd.), and Si (99.99%, Rare Metallic Co. Ltd.). The sample contained Si in 10% intervals, i.e. Si = 0, 9.3, 20, 28.7, 39.5, 49, 58, 81, and 100 at%. The experimental pressure in the present study was kept constant at 4 GPa, and determined based on the equation of state of hexagonal BN (Urakawa et al. 1996). The temperature was increased using a heating rate of 60 K/min to 1,373 K, which was well below the Fe–FeSi eutectic point of 1,463 K (Schürmann and Hensgen 1980), and then the temperature was increased to 1,923 K using a higher heating rate of 750 K/min to prevent any irregular movement of the density marker during the partial melting of the sample, and this temperature was maintained for a period of 1 min.
Fig. 1

a Cell assembly used in the experiments. b X-ray radiographic images showing single frame steps. The sinking of the density marker in the capsule can be clearly seen. The chemical composition was Fe91Si9. The time required for moving the density marker from the top to the bottom was 20 s

Quenching experiments

High-pressure experiments were carried out using a 3,000-ton Kawai-type multi-anvil device installed at Tohoku University in Japan (Ohtani et al. 1998). The second stage anvils were 26-mm tungsten carbide anvil cubes. The cell assembly was basically the same as that used in the in situ X-ray experiment as shown in Fig. 1a. The X-ray path made of boron + epoxy was replaced by a centre part of ZrO2 pressure medium in the present cell assembly. The temperature was increased at the same rate as used in the in situ experiments, and this was maintained for a period of 5 min. The sample was quenched by terminating the power to the heater, and we recovered the sample by releasing pressure. The recovered samples were mounted in epoxy resin and polished for textural observations using a scanning electron microscope. The composition of the recovered samples is listed in Table 1, and was measured using an electron probe microanalyser (EPMA) (JSM-5410, JEOL Ltd).
Table 1

Experimental conditions and results

Sia (at%)

Densityb (g/cm3)

Fitted value

Molar volume

Excess molar volume

Pressure

Lower limit

Upper limit

(g/cm3)

(cm3/mol)

(cm3/mol)

(GPa)

0

7.32 (2)

7.73 (2)d

7.43

7.52

0

4.30 (2)

9.3 (2)

7.07 (2)

7.45 (2)

7.07

7.53

–0.26

3.34 (5)

20 (1)

7.02 (3)

7.02 (3)

6.87

7.32

–0.77

3.67 (7)

28.7 (6)

6.87 (2)

6.87 (2)

6.80

7.04

–1.30

4.4 (3)

39.5 (1)

6.67 (2)

6.67 (2)

6.72

6.68

–1.97

3.23 (5)

49.0 (6)

6.60 (2)

6.55

6.45

–2.47

4.28 (2)

58 (3)

5.65 (2)

6.23

6.38

–2.80

4.30 (2)

81 (3)

3.91c,d

4.94 (3)

4.48

7.45

–2.39

3.58 (3)

100

3.91c,d

2.71

10.38

0

4.0 (5)

All the experiments were performed at 1,923 K

aThe error in the Si content is indicated in parentheses

bThe error in the density is indicated in parentheses

cThe density marker was composed of pure Al2O3

dQuenching experiment

Results and discussion

A summary of the experimental conditions used and the results obtained is listed in Table 1. We obtained X-ray radiography images of the movement of the density marker in the capsule, and the X-ray radiographic images shown in Fig. 1b represent an example of the sinking of the density marker from the centre of the capsule to the bottom of the capsule. The sink–float behaviour of the composite density marker was clearly observed from textural observations of the recovered samples and from the X-ray radiographs (Fig. 2). All the quenched samples had homogeneous dendritic textures, as shown in Fig. 3, indicating that the samples were fully molten under the experimental conditions used. We performed chemical analysis on the recovered samples using an electron microprobe, and confirmed that there was no Pt contamination of the sample. This means that there was no chemical reaction between the Fe–Si samples and the Pt disk, which was the inner material of the composite marker.
Fig. 2

a, b Cross-sections of the recovered samples, and c an X-ray radiographic image. The chemical compositions were a Fe51Si49b Fe51Si49 and c Fe80Si20, respectively. a, b, c Show floating, sinking, and neutral, respectively

Fig. 3

The quenched texture of Fe–Si samples that show typical textures of a quenched Fe–Si liquid. The chemical compositions were a Fe91Si9 and b Fe61Si39 (back-scattered electron image). The bright area represents the Fe-rich part and the darker area represents the Si-rich part

As shown in Fig. 4, the density of liquid Fe–Si decreases non-linearly with increasing Si content at 4 GPa and 1,923 K. We have also plotted the previously reported density data of previous studies on liquid Fe–Si at high pressure (Yu and Secco 2008; Sanloup et al. 2004) and at ambient pressure (Nasch and Steinmann 1995; Dumay and Cramb 1995; Kawai et al. 1974) in Fig. 4. All the density data were corrected to that at 1,923 K using following temperature derivative, dρ/dT ~ −0.002 for Si = 3.9 at%, −0.001 for Si = 9.5 at%, 18.2 and 33 at% and 0.0002 for Si = 49.6 at% (Kawai et al. 1974). dρ/dT was interpolated for the Si contents between the compositions described above. The density of liquid Fe–Si does not decrease significantly in the compositional range 0–50 at% Si, whereas it decreases markedly in the range 50–100 at% Si. The value of the density determined in this work was higher than that determined in previous studies (Sanloup et al. 2004; Yu and Secco 2008). In previous sink–float measurements, the volume of the composite sphere marker was estimated by measuring the size of the sphere from the recovered sample. In addition, the amount of Al2O3-based cement used in the composite spheres may not have been negligible. These potential sources of error could increase the uncertainty in the density. Therefore, the discrepancy between our results at high pressure and those of Yu and Secco (2008) might be because of an uncertainty in the density of the composite sphere. The difference in the pressure and temperature standards used in these works and the uncertainty in the mass absorption coefficient for the X-ray absorption method used by Sanloup et al. (2004) may also be potential causes of this discrepancy.
Fig. 4

The density of liquid Fe–Si for various Si contents. The black downwards and upwards pointing triangles denote the density of the sinking and floating density markers, respectively. The density of the Fe–Si samples was within the range of these triangles. The solid circles represent a neutral value where the density of the density marker was the same as that of the sample. The grey squares and triangles denote data from previous studies on liquid Fe–Si liquid at high pressures (Funamori and Tsuji 2002; Sanloup et al. 2004; Yu and Secco 2008). The open squares, circles, and diamonds denote the density of liquid Fe–Si at ambient pressures from Dumay and Cramb (1995), Kawai et al. (1974), and Sasaki et al. (1994) respectively

The effect of pressure on the density of liquid Fe–Si can be estimated from the data shown in Fig. 4. The increase in density from ambient pressure to 4 GPa was 5% for pure liquid Fe, whereas it increased by 29% in the liquid alloy with a composition of Fe40Si60. This result indicates that the effect of pressure on the density of liquid Fe–Si is likely to reach a maximum value for a composition of 50–60 at% Si. In other words, the bulk modulus decreases with increasing Si content in the range 0–50 at% Si. This tendency is consistent with the results of Sanloup et al. (2004).

The molar volume of liquid Fe–Si can be calculated from the density determined in this work. Figure 5 shows the change in molar volume of liquid Fe–Si as a function of Si content at 4 GPa and 1,923 K. In the range 0–50 at% Si, the molar volume decreased slightly with increasing Si content. On the other hand, the molar volume increased markedly in the range 50–100% Si.
Fig. 5

The molar volume of liquid Fe–Si with various Si contents at 1,923 K and 4 GPa. The black downwards and upwards pointing triangles denote the molar volume of the upper and lower limits, respectively. The open squares, circles, and triangles denote the molar volume of liquid Fe–Si samples at 1,723 K and ambient pressure by Dumay and Cramb (1995), Kawai et al. (1974), and Sasaki et al. (1994), respectively

The observed change in molar volume with Si content (Fig. 5) may be explained by the site occupancy of Si in liquid Fe–Si. Based on a structural study of liquid Fe–Si, the nearest neighbour distance of liquid Fe–Si is reported to decrease with increasing Si content, and Si atom substitutes Fe sites in the compositional range 0–30 at% Si (Waseda 1980; Morard et al. 2008). Therefore, the molar volume is also likely to decrease with increasing Si content in the range 0–30 at% Si. On the other hand, the molar volume of liquid Fe–Si with more Si content is considered to increases. This tendency might be explained by the structural difference of the liquid from Fe–FeSi (e.g. Sanloup et al. 2002) to FeSi–Si systems (e.g. Funamori and Tsuji 2002).

The dotted line shown in Fig. 5 shows that the molar volume expected for an ideal mixing of Fe and Si liquids. It is noted that the molar volume determined here deviates from that expected of an ideal mixing between Fe and Si. The molar volume at ambient pressure (Dumay and Cramb 1994) is also plotted in Fig. 5. The molar volume at 4 GPa is less than that at ambient pressure. The observed change in the molar volume of the liquid with Si content at 4 GPa, i.e. a negative deviation from the volume expected from ideal mixing, is consistent with that at ambient pressure.

Applying an asymmetric regular solution for liquid Fe–Si, the molar volume (V) of the liquid can be expressed as follows
$$ V = V^{0}_{\text{Fe}} X_{\text{Fe}} + V^{0}_{\text{Si}} X_{\text{Si}} + (\alpha X_{\text{Si}} + \beta X_{\text{Fe}} )X_{\text{Si}} X_{\text{Fe}} , $$
where \( V^{0}_{\text{Fe}} \) and \( V^{0}_{\text{Si}} \) are the molar volumes of Fe and Si, respectively, XFe and XSi are the concentrations of iron and Si in atomic ratios, and α and β are constant parameters. The term (αXSi + βXFe)XSiXFe indicates the deviation of the molar volume of mixing from the ideal mixing case. Using the molar volume determined in this study, we obtained values of α = −18.5 cm3/mol and β = −1.6 cm3/mol. The excess molar volume (Vex), which corresponds to the difference in the molar volume (V) from that of ideal mixing (Vid), is defined as
$$ V_{\text{ex}} = V - V_{\text{id}} . $$
The obtained molar volumes and the excess molar volumes are summarised in Table 1. The excess molar volume of liquid Fe–Si determined at 4 GPa is plotted in Fig. 6. The non-ideal mixing behaviour with a negative excess molar volume observed in this study is similar to that of liquid Fe–S determined at 4 GPa and 1,923 K (Nishida et al. 2008). However, the value of our excess molar volume is smaller than that of liquid Fe–S, indicating that the degree of the non-ideality of liquid Fe–Si is less than that of liquid Fe–S (Fig. 6). Although Nishida et al. (2008) assumed a symmetric regular solution for their fitting of the molar volume of liquid Fe–S based on their measurements in the composition range S = 0–50 at%, there is the possibility that liquid Fe–S may behave as an asymmetric regular solution if we consider the entire compositional range, i.e. S = 0–100 at%.
Fig. 6

Change in the excess molar volume from an ideal mixing of Fe and Si at 1,923 K and 4 GPa. The solid curve shows Vex = −(18.5XSi + 1.6XFe)XSiXFe

The different values of the negative excess molar volume between liquid Fe–Si and Fe–S might be explained by a difference in the local structures of their liquids. According to a structural study on liquid Fe–Si and Fe–S at 0–5 GPa and 1,400–2,300 K (Sanloup et al. 2002), liquid Fe–Si has an Fe-like local order, whereas liquid Fe–S has poor local ordering, suggesting that S strongly modifies the liquid Fe local structure compared with Si. The different effect of S and Si on the liquid local structure may be related to the different non-ideality of liquid Fe–Si and Fe–S.

The excess molar volume at high pressure is very important for estimating the light element content of the Earth’s outer core based on the density deficit of the core. The negative value of the excess mixing molar volume of Si determined in this study, together with that of S reported previously (Nishida et al. 2008), suggests that the amount of the light elements in the core may be larger than that estimated previously assuming an ideal mixing behaviour of the liquid iron–light element alloy (e.g. Poirier 1994). We need further detailed studies on the effects of pressure and temperature on the non-ideality of liquid iron–light element alloys to make a quantitative estimate of the amount of light elements in the outer core.

Conclusions

The density of liquid Fe–Si was measured at 4 GPa and 1,923 K using a sink–float method and an in situ sink–float method with a composite density marker. The density of liquid Fe–Si decreased non-linearly with increasing Si content at 4 GPa and 1,923 K. The effect of the Si content on the density was larger for Si-rich compositions. In the compositional range 0–50 at% Si, the molar volume decreased with increasing Si content, whereas it gradually increased with increasing Si content in the compositional range 50–100 at% Si. The excess molar volume from the ideal mixing of Fe and Si at 4 GPa has a negative value. The observed trend in excess molar volume with Si content is consistent with that observed at ambient pressure. The lighter elements in the Earth’s outer core estimated previously may be underestimated if we take into account the possible negative value of the excess volume of mixing of the alloys in the outer core.

Notes

Acknowledgments

The synchrotron X-ray diffraction studies at the BL-14C2 were performed with the approval of the Photon Factory Advisory Committee (Proposal No. 2007S2-002). This work was partly supported by grants from the Japan Society for the Promotion of Science (Grant Nos 18104009 and 22000002 to Eiji Ohtani and Nos 21684032 and 20103003 to Akio Suzuki).

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Ryuji Tateyama
    • 1
  • Eiji Ohtani
    • 1
  • Hidenori Terasaki
    • 1
    • 2
  • Keisuke Nishida
    • 1
  • Yuki Shibazaki
    • 1
  • Akio Suzuki
    • 1
  • Takumi Kikegawa
    • 3
  1. 1.Department of Earth and Planetary Materials ScienceTohoku UniversitySendaiJapan
  2. 2.Department of Earth and Space ScienceOsaka UniversityToyonakaJapan
  3. 3.Photon FactoryHigh Energy Accelerator Research Institute (KEK)TsukubaJapan

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