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

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1 Phys Chem Minerals (2011) 38: DOI /s ORIGINAL PAPER 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 Received: 29 December 2010 / Accepted: 8 August 2011 / Published online: 30 August 2011 Ó Springer-Verlag 2011 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/cm 3 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 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: , 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 R. Tateyama (&) E. Ohtani H. Terasaki K. Nishida Y. Shibazaki A. Suzuki Department of Earth and Planetary Materials Science, Tohoku University, Sendai , Japan tateyama925@gmail.com H. Terasaki Department of Earth and Space Science, Osaka University, Toyonaka , Japan T. Kikegawa Photon Factory, High Energy Accelerator Research Institute (KEK), Tsukuba, Japan 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

2 802 Phys Chem Minerals (2011) 38: sample. Yu and Secco (2008) used composite spheres composed of a metallic core (Pt or WC) and an Al 2 O 3 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 Al 2 O 3 mantle and the metallic core. Yu and Secco (2008) reported that the density of liquid Fe-17 wt%si is in the range g/cm 3 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. 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 Al 2 O 3 -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 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 Al 2 O 3 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 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 Fe 91 Si 9. The time required for moving the density marker from the top to the bottom was 20 s

3 Phys Chem Minerals (2011) 38: Table 1 Experimental conditions and results Si a (at%) Density b (g/cm 3 ) Fitted value Molar volume Excess molar volume Pressure Lower limit Upper limit (g/cm 3 ) (cm 3 /mol) (cm 3 /mol) (GPa) (2) 7.73 (2) d (2) 9.3 (2) 7.07 (2) 7.45 (2) (5) 20 (1) 7.02 (3) 7.02 (3) (7) 28.7 (6) 6.87 (2) 6.87 (2) (3) 39.5 (1) 6.67 (2) 6.67 (2) (5) 49.0 (6) 6.60 (2) (2) 58 (3) 5.65 (2) (2) 81 (3) 3.91 c,d 4.94 (3) (3) c,d (5) All the experiments were performed at 1,923 K a The error in the Si content is indicated in parentheses b The error in the density is indicated in parentheses c The density marker was composed of pure Al 2 O 3 d Quenching experiment 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 W 97 Re 3 W 75 Re 25 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. 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 ZrO 2 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). 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. As shown in Fig. 4, the density of liquid Fe Si decreases non-linearly with increasing Si content at 4 GPa

4 804 Phys Chem Minerals (2011) 38: Fig. 2 a, b Cross-sections of the recovered samples, and c an X-ray radiographic image. The chemical compositions were a Fe 51 Si 49 b Fe 51 Si 49 and c Fe 80 Si 20, 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 Fe 91 Si 9 and b Fe 61 Si 39 (back-scattered electron image). The bright area represents the Fe-rich part and the darker area represents the Si-rich part 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, dq/dt * for Si = 3.9 at%, for Si = 9.5 at%, 18.2 and 33 at% and for Si = 49.6 at% (Kawai et al. 1974). dq/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 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 Al 2 O 3 -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. 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 Fe 40 Si 60. 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 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 % Si. 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

5 Phys Chem Minerals (2011) 38: 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 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 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 ¼ VFe 0 X Fe þ VSi 0 X Si þðax Si þ bx Fe ÞX Si X Fe ; where VFe 0 and V0 Si are the molar volumes of Fe and Si, respectively, X Fe and X Si are the concentrations of iron and Si in atomic ratios, and a and b are constant parameters. The term (ax Si? bx Fe )X Si X Fe 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 a =-18.5 cm 3 /mol and b =-1.6 cm 3 /mol. The excess molar volume (V ex ), which corresponds to the difference in the molar volume (V) from that of ideal mixing (V id ), is defined as V ex ¼ V V 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 = at%. 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

6 806 Phys Chem Minerals (2011) 38: increased with increasing Si content in the compositional range 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. 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 and to Eiji Ohtani and Nos and to Akio Suzuki). 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 V ex = -(18.5X Si? 1.6X Fe )X Si X Fe 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 References Allègre CJ, Poirier JP, Humler E, Hofmann AW (1995) The chemical composition of the Earth. Earth Planet Sci Lett 134: Birch F (1952) Elasticity and constitution of the Earth s interior. J Geophys Res 57: Dumay C, Cramb AW (1995) Density and interfacial tension of liquid Fe Si alloys. Metall Mat Trans B 26: Funamori N, Tsuji K (2002) Pressure-induced structural change of liquid silicon. Phys Rev Lett 88: doi: /physrev Lett Hixson RS, Winkler MA, Hodgdon ML (1990) Sound speed and thermophysical properties of liquid iron and nickel. Phys Rev B42: Kawai Y, Mori K, Kishimoto M, Ishikura K, Shimoda T (1974) Surface tension of liquid Fe C Si alloys. Tetsu-to-Hagané 60:29 37 MacDonald GJ, Knopoff L (1958) On the chemical composition of the outer core. Geophys J R Astron Soc 1: Morard G, Sanloup C, Guillot B, Fiquet G, Mezouar M, Perrillat JP, Garbarino G, Mibe K, Komabayashi T, Funakoshi K (2008) In situ structural investigation of Fe S Si immiscible liquid system and evolution of Fe S bond properties with pressure. J Geophys Res 113:B doi: /2008jb Nasch PM, Steinmann SG (1995) Density and thermal expansion of molten manganese, iron, nickel, copper, aluminum and tin by means of the gamma-ray attenuation technique. Phys Chem Liq 29:43 58 Nasch PM, Manghnani MH, Secco RA (1997) Anomalous behavior of sound velocity and attenuation in liquid Fe Ni Si. Science 277: Nishida K, Terasaki H, Ohtani E, Suzuki A (2008) The effect of sulfur content on density of the liquid Fe S at high pressure. Phys Chem Miner 35: Ohtani E, Moriwaki K, Kato T, Onuma K (1998) Melting and crystal liquid partitioning in the system Mg 2 SiO 4 Fe 2 SiO 4 to 25 GPa. Phys Earth Planet Inter 107:75 82 Poirier JP (1994) Light elements in the Earth s outer core: a critical review. Phys Earth Planet Inter 85: Ringwood AE (1959) On the chemical evolution and densities of the planets. Geochim Cosmochim Acta 15: Sanloup C, Guyot F, Gillet P, Fei Y (2002) Physical properties of liquid Fe alloys at high pressure and their bearings on the nature of metallic planetary cores. J Geophys Res 107:2272. doi: /2001JB000808

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