Density measurements of liquid Fe–Si alloys at high pressure using the sink–float method
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.
KeywordsDensity Fe–Si Non-ideality High pressure
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.
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
Experimental conditions and results
Excess molar volume
Results and discussion
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 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.
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.
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.
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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