Density measurement of Fe3C liquid using Xray ... - Wiley Online Library

Click Here

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, B06207, doi:10.1029/2009JB006905, 2010

for

Full Article

Density measurement of Fe3C liquid using X‐ray absorption image up to 10 GPa and effect of light elements on compressibility of liquid iron H. Terasaki,1 K. Nishida,1 Y. Shibazaki,1 T. Sakamaki,1 A. Suzuki,1 E. Ohtani,1 and T. Kikegawa2 Received 25 August 2009; revised 2 January 2010; accepted 17 February 2010; published 23 June 2010.

[1] Density of liquid iron alloy under high pressure is important to constrain the amount of light elements in the Earth’s core. Density measurement of solid and liquid Fe3C was performed using X‐ray absorption image technique up to 9.5 GPa and 1973 K. Density of liquid Fe3C increases from 6.94 g/cm3 to 7.38 g/cm3 with a pressure of 3.6–9.5 GPa at 1973 K. The bulk modulus of liquid Fe3C is obtained to be 50 ± 7 GPa at 1973 K. The effect of carbon on the compressibility of liquid iron is similar to that of sulfur, which significantly decreases the bulk modulus of liquid iron. Since carbon dissolution into liquid iron causes reduction of r and K0T, carbon could be excluded from the candidates of alloying light elements in the Earth’s outer core. Citation: Terasaki, H., K. Nishida, Y. Shibazaki, T. Sakamaki, A. Suzuki, E. Ohtani, and T. Kikegawa (2010), Density measurement of Fe3C liquid using X‐ray absorption image up to 10 GPa and effect of light elements on compressibility of liquid iron, J. Geophys. Res., 115, B06207, doi:10.1029/2009JB006905.

1. Introduction [2] Density of liquid iron alloy under high pressure is a fundamental property to study density deficit and dynamics of the Earth’s and planetary molten cores. The Earth’s outer core is ∼10% less dense than pure iron, known as “core density deficit,” and S, Si, O, H, and C are proposed as possible light elements in the outer core [e.g., Poirier, 1994]. Since the abundance of carbon in the Earth’s mantle is depleted compared with that of carbonaceous chondrites, which are proposed as a source material of the Earth [e.g., McDonough and Sun, 1995], carbon is considered to be stored in the core. In addition, it has recently been proposed that the carbon component may contribute to the outer core via the deep carbon cycle in the present Earth. Carbonate, such as magnesite (Mg(CO)3), is stable without any dissociation up to the core‐mantle boundary condition, although there is a phase transformation at ∼115 GPa [Isshiki et al., 2003]. If carbonate reaches the core‐mantle boundary by subducting slab, diamond will be formed first [Siebert et al., 2005]. Then, carbon tends to dissolve into iron and forms Fe‐C alloy after the interaction between diamond and iron alloy [Rouquette et al., 2008]. Carbon is, therefore, considered to be one of the major constituents of the light elements in the Earth’s outer core. However, the density of Fe‐C liquid has never been measured under high pressure. It is important 1 Department of Earth and Planetary Materials Science, Tohoku University, Sendai, Japan. 2 Photon Factory, High Energy Accelerator Research Institute, Tsukuba, Japan.

Copyright 2010 by the American Geophysical Union. 0148‐0227/10/2009JB006905

to quantify the effect of pressure on the density of liquid Fe‐C alloy to evaluate the validity of carbon as a light element in the core and to estimate the amount of carbon in the outer core. [3] The Earth’s inner core also has a density deficit of 2.5% [e.g., Dubrovinsky et al., 2000]. On the basis of thermodynamic calculations by Wood [1993], Fe3C could be the liquidus phase of the Fe‐C system, and the calculated density of solid Fe3C at the core condition matches the density of the inner core predicted from seismic observation [Dziwonski and Anderson, 1981]. Thus, carbon is proposed as one of the major candidates of the light elements in the inner core [Wood, 1993; Nakajima et al., 2009]. There are several studies of compressibility of solid Fe3C at room temperature and quenched from 1500 K based on high‐pressure experiments [Scott et al., 2001; Li et al., 2002] and on theory [Vocadlo et al., 2002]. The obtained bulk modulus and its pressure derivative are K0T = 174–175 GPa and K0′ = 5.2, respectively. They reported that solid Fe3C could be a possible constituent of the inner core. However, the effect of carbon on the density and bulk modulus of solid iron is still missing under high pressure and high temperature. [4] X‐ray absorption technique enables us to measure density under high pressure based on the Beer‐Lambert law, and this method is effective especially for density measurement of noncrystalline materials [Katayama et al., 1993]. In previous studies, densities of several liquid iron alloys (Fe‐S and Fe‐Si) were measured at high pressure using 1‐D detector (photo diodes) [Sanloup et al., 2000a, 2004] or 2‐D detector (charge‐coupled device (CCD) camera) [Chen et al., 2005]. According to their results, the effect of pressure on the densities of liquid iron alloys are quite different depending on the

B06207

1 of 7

B06207

TERASAKI ET AL.: DENSITY OF Fe3C LIQUID UP TO 10 GPA

B06207

image. Pixel sizes of the CCD camera were 8.7 mm/pixel for BS‐40 and 6.3 mm/pixel for PIXIS2048F with 2 × 2 binning. Typical exposure times for taking images were 45 and 60 s. X‐ray diffractions of the sample and pressure markers (NaCl or Pt) were collected using an imaging plate with exposures of 600–900 s. X‐ray wavelengths, camera length between the sample and the imaging plate, and the tilt angle of the imaging plate was calibrated using CeO2 diffraction. X‐ray radiography images were taken with each 100 K step and X‐ray diffraction of the sample and the pressure marker were collected at 873 and 1073–1123 K. In some experiments, diffraction patterns of the pressure marker were also collected at 2073 K. Figure 1. Schematic of cell assembly. X‐ray direction is a perpendicular to the paper. alloying light elements. In this study, we have measured the density of solid and liquid Fe3C up to 9.5 GPa and 1973 K by using X‐ray absorption image technique and have investigated the compressibilities of solid and liquid Fe3C to estimate the effect of carbon on the compressibility of iron.

2. Experimental Method [5] High‐pressure experiments were conducted using a 700 t Kawai‐type multianvil press (MAX‐III) at BL14C2 beamline, Photon Factory, KEK, Japan [Nishida et al., 2008]. Fe3C powder sample (99.9% in purity, Rare Metallic Co. Ltd.) was ground in agate mortar for 60 min and enclosed in a single crystal sapphire cylinder capsule. In previous X‐ray absorption density measurements for silicate melts [e.g., Ohtani et al., 2005], a single crystal cylindrical diamond capsule was used because it was less deformable and this was important for determination of the sample thickness to obtain the sample density. To avoid a reaction between Fe3C sample and diamond, we used a single crystal cylindrical sapphire capsule that is also less deformable than other conventional ceramic capsules, such as polycrystalline MgO and hBN. Outer and inner diameters of the capsule were 1.5–1.0 mm for the pressure up to 5 GPa and 0.8–0.5 mm for the pressure up to 10 GPa. Top and bottom caps of the capsule were boron nitride. Cylindrical TiB2+BN composite was used as a heater. To minimize X‐ray absorption from the surrounding material, we used boron‐epoxy for X‐ray path of the pressure medium and gasket part. Temperature was monitored using W97%Re3%‐W75%Re25% thermocouple wire. Experimental pressure was determined by collecting diffraction patterns of pressure marker (NaCl or Pt) combined with their equations of state (Brown [1999] for NaCl and Holmes et al. [1989] for Pt). A schematic of the cell assembly is illustrated in Figure 1. Truncated edge length of 22 mm WC cube was 5 mm. The experiments were first taken to the target load pressure and then heated. [6] At beamline BL14C2, we have used monochromatic X‐ray of 40 or 43 keV which was optimized for the best absorption image contrast. Transmitted X‐ray from the sample was converted to a visible light by YAG scintillator and then detected using a Cooled CCD camera (Bitran BS‐40, or PIXIS2048F, Roper Co Ltd.) as an X‐ray radiography

2.1. X‐ray Absorption Profile Fitting [7] Density of the sample was measured using X‐ray absorption image. The relationship between the brightness of incident and transmitted X‐rays in the radiography image can be expressed as follows based on the Beer‐Lambert law [Chen et al., 2005]: B ¼ B0 expð
tÞ ¼ kI0 expð
tÞ;

ð1Þ ð2Þ

where B0 and B denote incident and transmitted brightness, respectively; m is X‐ray mass absorption coefficient and r is density; k is a conversion coefficient from X‐ray intensity (I0) to image brightness assuming a linear conversion [Chen et al., 2005]. The brightness of the sample (Bs) can be denoted as, Bs ¼ kI0 exp½ð
s s ts Þ þ ð
c c tc Þ þ ð
e e te Þ;

ð3Þ

where subscriptions of s, c, and e represent sample, capsule, and environment, respectively. Brightness at the boundary between the sample and the capsule (Bb) is Bb ¼ kI0 exp½ð
c c tb Þ þ ð
e e te Þ;

ð4Þ

Then, using equations (3) and (4), Bs ¼

Bb exp½ð
c c tb Þ þ ð
e e te Þ  exp½ð
s s ts Þ þ ð
c c tc Þ þ ð
e e te Þ

¼ Bb exp½ð
s s ts Þ 
c c ðtc  tb Þ

ð5Þ ð6Þ

Therefore, rs can be calculated if we obtain brightness at the sample and the boundary, ms, mcrc and thicknesses of the sample and capsule. [8] From the X‐ray radiography image, we obtained a 2‐D distribution of X‐ray intensity. Then, we averaged horizontally 5–20 pixels of the entire vertical intensity line profile and treated it as an X‐ray absorption profile. Since the insertion device for the synchrotron X‐ray of the beamline BL14C2 is a vertical wiggler, the vertical X‐ray intensity of this beamline is constant (fluctuation of X‐ray counts is less than 5%) in approximately 4.5 mm height. On the other hand, in the horizontal direction, the constant X‐ray intensity region is 0.8–1.0 mm in width [Nishida et al., 2008]. Thus, we used a vertical line to obtain the sample X‐ray absorption profile. The sample density (rs) can be obtained by fitting the

2 of 7

B06207

TERASAKI ET AL.: DENSITY OF Fe3C LIQUID UP TO 10 GPA

B06207

Figure 2. Capsule and sample geometries and shapes for fitting. Gray and white colors show the sapphire capsule and the Fe3C sample, respectively. (a) Circular shape. (b) Ellipsoidal shape. absorption profile with use of equation (6). In terms of thickness ts and tc − tb, if the sample is not deformed and shows circular shape as shown in Figure 2a, ts and tc − tb can be written as follows; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ts ¼ 2 r2  ðz  z0 Þ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : tc  tb ¼ 2 R2  ðz  z0 Þ2  2 r2  ðz  z0 Þ2  2 R2  r2 ð7Þ

[9] However, if the sample is deformed, the following equation is used for the fitting, assuming that the sample part is deformed to ellipsoidal shape as shown in Figure 2b. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n offi 2 0Þ ts ¼ 2a 1  ðzz b2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n offi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0Þ  2 R2  b2 1  ðzz tc  tb ¼ 2 R2  ðz  z0 Þ2  2a 2 b ð8Þ

[10] If a = b = r in equation (8), equation (8) is equivalent to equation (7). Since the ellipsoidal equation is also applicable for the circular shape, we basically used equation (8) for the sample shape fitting combined with the modified Beer‐ Lambert equation of equation (6) for fitting of the X‐ray absorption profile.

3. Results and Discussion [11] X‐ray absorption technique for the density measurement with a 2‐D detector has a big advantage to collect the absorption profile much faster than conventional 1‐D detector technique, because 2‐D image at single image exposure provides 2‐D absorption data. X‐ray absorption profile was obtained from a vertical line intensity scan of X‐ray radiography. This method is basically the same as Chen et al. [2005]. A typical example of an obtained X‐ray radiography image at 9.5 GPa and 1973 K is shown in Figure 3. X‐ray absorption profile of solid Fe3C was fitted by circle shape

(equation (8) with a = b). However, in most cases, after the sample was molten, the absorption profile could not be fitted by circular shape, but it could be fitted successfully by ellipse shape (equation (8) with a ≠ b), suggesting that the sample was deformed. After the fitting for the absorption profile, we could obtain mr value of the sample. Therefore, the sample density (r) can be calculated from the mr value by using equation (6). The X‐ray mass absorption coefficient (m) of the sample was estimated from the Fe3C solid density obtained by X‐ray diffraction spectra at high temperature (1073 or 1123 K) before melting and from the mr value obtained from the X‐ray absorption profile. We assumed that the m values of solid and liquid Fe3C are the same and independent of pressure and temperature as suggested by Sanloup et al. [2000a]. The densities of liquid and solid Fe3C were measured in the ranges of 3.6–9.5 GPa and 1073–1973 K. The errors of the measured density are ∼0.3 g/cm3, which covers all the experimental errors originating mainly from the fitting error for the absorption profile (∼0.06 g/cm3) and the selections of used data for the fitting (∼0.2 g/cm3). 3.1. Effects of Temperature and Pressure on Density of Fe3C [12] Figure 4 shows a typical example of the effects of temperature on the densities of Fe3C at 5.4 GPa. This temperature trend was observed in all the experimental pressure conditions. The density of the solid Fe3C decreases (7.65– 7.45 g/cm3) with increasing temperature (1073–1373 K) and then drops ∼0.5 g/cm3 between 1373 and 1473 K. Shape change of the Fe3C sample was observed from the rectangular to rounded shape (Figure 4, inset) at the point of density drop. Thus, this abrupt jump of the density corresponds to the volume change in the melting of the sample. This melting temperature is consistent with the eutectic temperature of Fe3C reported by Chabot et al. [2008] and slightly (∼100 K) below that reported by Nakajima et al. [2009]. After melting, the density does not show a clear tendency to temperature. According to the phase diagram of Fe‐C by Nakajima et al. [2009], this could be because Fe3C melts incongruently, suggesting that liquid coexists with solid graphite below

3 of 7

B06207

TERASAKI ET AL.: DENSITY OF Fe3C LIQUID UP TO 10 GPA

B06207

Figure 3. X‐ray radiography image and its absorption profile at 9.5 GPa and 1973 K. (a) X‐ray radiography image of liquid Fe3C. (b) X‐ray absorption profile of the area shown by rectangle in Figure 3a. Closed and open circles indicate raw data and used data for fitting, respectively. Dotted curve shows a fitting curve using equation (6). 5 GPa and with solid Fe7C3 above 5 GPa, approximately 200– 250 K above the eutectic temperature. Therefore, the range between 1473 and 1773 K at 5.4 GPa is likely to be in partial molten region. When we considered the density of liquid Fe3C, we did not take into account this region of partial melting to avoid the effect of solid graphite or Fe7C3 on the liquid density. However, the effect of temperature on the density of the liquid Fe3C above 1773 K, corresponding to a complete melt region, shows almost constant (6.96– 6.94 g/cm3 at 1773–1973 K) and no clear tendency compared with that of the solid Fe3C. There are several previous studies of temperature effect on the density of liquid Fe‐C at ambient pressure [Ogino et al., 1984; Lucas, 1964]. The density change with temperature for Fe‐4.1%C liquid is expressed as: r (kg/m3) = 7775 – 0.5075 T (K), corresponding to a density change of 0.102 g/cm3 in a temperature difference of 200 K. This density difference is within the density error of this study. Therefore, the effect of temperature on the density of the liquid phase is likely to be weaker than that of the solid phase. To confirm this trend, more precise density measurement (for example, using higher‐resolution CCD with 1–2 mm pixel size) is required. [13] The effect of pressure on the density of solid and liquid Fe3C are plotted in Figure 5. The density of solid Fe3C shown in Figure 5 was determined from the volume data using X‐ray diffraction spectra at 1073–1123 K. Both solid and liquid densities increase with increasing pressure (3.6–9.5 GPa). The solid Fe3C densities are fitted with a third‐order Birch‐ Murnaghan equation of state (EOS). The density of solid Fe3C at ambient pressure and at 1073 K was calculated using the Fe3C density (7.679 g/cm3) and volume (154.8 A3) at 300 K and thermal expansivity (a = (−4 × 10−5) + (1.6 × 10−7) T) [Wood et al., 2004]. The liquid densities are fitted together

with the density of liquid Fe3C at ambient pressure [Takeuchi, 1966] using a third‐order Birch‐Murnaghan EOS as shown in Figure 5. Assuming K′ (= dK/dP) = 4 for both solid and liquid Fe3C, isothermal bulk modulus (K0T) is estimated to be 111 ± 5 GPa for solid Fe3C at 1073 K and 54 ± 3 GPa for liquid at 1973 K. If K′ of the liquid phase is changed from 4 to 7, obtained K0T is ranged from 54 ± 3 to 46 ± 2 GPa. We could

Figure 4. Effect of temperature on the density of Fe3C at 5.4 GPa. Inset figures indicate X‐ray radiography images at (left) 1373 K and (right) 1473 K.

4 of 7

B06207

TERASAKI ET AL.: DENSITY OF Fe3C LIQUID UP TO 10 GPA

Figure 5. Effect of pressure on the density of Fe3C. Open and closed symbols show solid at 1073–1173 K and liquid Fe3C at 1973 K, respectively. Circle symbols indicate the data of this study. Square symbols indicate ambient pressure data. Solid Fe3C density at 1 atm was calculated using a volume data at 300 K and thermal expansion of Wood et al. [1994]. Liquid Fe3C density at 1 atm corresponds to data of Takeuchi [1966]. Shaded curves show the fitting using Birch‐ Murnaghan EOS for both solid and liquid in case of K′ = 4. not constrain the K′ because the number of the density data of this study is not enough for the fitting to obtain the K′ with a small error. Therefore, 50 ± 7 GPa is a more relevant value as K0T with maximum error at 1973 K for liquid Fe3C. [14] Solid Fe3C (cementite) has orthorhombic structure and does not have any phase transformations at least up to 73 GPa and up to 1500 K [Scott et al., 2001]. Fe7C3 is stable from 5 GPa and at least to 29 GPa [Nakajima et al., 2009]. If there are no phase transformations in the solid phase just below the melting point (i.e., liquidus phase), the structure of liquid is generally stable and does not have any phase transformations. Therefore, the structure of liquid Fe3C is expected to be stable up to 29 GPa and may possibly be stable up to 73 GPa, suggesting that the bulk moduli of solid and liquid Fe3C obtained in this study could be relevant at least up to this pressure. However, Gao et al. [2008] reported that there is a magnetic phase transition from magnetic to nonmagnetic phase in Fe3C between 4.3 and 6.5 GPa. The effect of this magnetic transition on the compressibility is discussed in the next section. 3.2. Effect of Magnetic Transition on the Compressibility of Solid Fe3C [15] If there is a magnetic phase transition in Fe3C between 4.3 and 6.5 GPa as Gao et al. [2008] reported, there might be a volume change or compressibility change. As shown in Figure 5, there is no obvious density change (i.e., volume change) between 4.3 and 6.5 GPa. However, the compressibility of solid Fe3C seems to have an inflection point at

B06207

approximately 5 GPa in Figure 5. When the density data are fitted separately at a boundary of 5 GPa using Birch‐ Murnaghan EOS, the obtained K0T below 5 GPa is 99 ± 4 GPa and that obtained above 5 GPa is 204 ± 65 GPa. K0T above 5 GPa has a large uncertainty because there are not enough data points for the fitting and the r0 value is treated as a free parameter since we cannot constrain the r0 of the nonmagnetic phase at ambient pressure. [16] There is a discrepancy in the compressibility of solid Fe3C among the results of previous studies [Scott et al., 2001; Li et al., 2002; Vocadlo et al., 2002; Dodd et al., 2003; Gao et al., 2008]. We tried to compare these bulk moduli with the present results. K0T by fitting the data below 5 GPa is 99 ± 4 GPa. This value is slightly smaller than the value obtained by using all the present data (111 ± 5 GPa) and consistent with the results of Dodd et al. [2003] (105–125 GPa) measured at 1 bar and 295 K. K0T above 5 GPa is 204 ± 65 GPa, which is significantly higher than the value below 5 GPa. This value is slightly higher than the previous results of Scott et al. [2001] (175 ± 5 GPa) and Li et al. [2002] (174 ± 6 GPa) obtained at 300 K and is in the range of K0T reported by Gao et al. [2008] (175–435 GPa). [17] The increase of bulk modulus due to the magnetic transition from magnetic phase to nonmagnetic phase of solid Fe3C is predicted by an ab initio calculation [Vocadlo et al., 2002] and by high‐pressure X‐ray emission spectroscopy [Lin et al., 2004]. The increase of incompressibility observed in this study is consistent with this tendency. This tendency also may explain the discrepancy between the bulk modulus obtained at 1 bar or at below 5 GPa (K0T ∼ 99–125 GPa) and that obtained at higher pressures (K0T ∼ 175–435 GPa). However, it is difficult to say that the compressibility change clearly occurs because of the magnetic transition at approximately 5 GPa according to the present results since the present bulk modulus obtained above 5 GPa has a large uncertainty. More data points are needed to conclude this discussion. On the other hand, there is no obvious density change or compressibility change in the liquid Fe3C, suggesting that the effect of magnetic transition on the compressibility of liquid Fe3C can be ignored. 3.3. Effect of Light Elements on Compressibility of Liquid Iron [18] The effect of light elements on density and compressibility of liquid iron is shown in Figures 6a and 6b, respectively. In order to compare the effect of various light elements on the compressibility of liquid iron, we corrected the K0T values of Fe‐S and Fe‐Si liquids of Sanloup et al. [2000a, 2004] and that of pure Fe liquid of Hixon et al. [1990] to 1973 K. We assumed that (dK/dT)P of Fe‐S and Fe‐Si liquids is similar to that of liquid iron (−0.0104 GPa/K) [Hixson et al., 1990]. Carbon reduces significantly the K0T of liquid iron and shows the similar effect with sulfur [Sanloup et al., 2000a]. On the other hand, silicon has only a minor contribution on K 0T as reported by Sanloup et al. [2004]. Therefore, the effect of dissolving light elements on the compressibility is quite different depending on the alloying element as shown in Figure 6b, although all these light elements reduce the density of liquid iron (Figure 6a). One possible explanation for these different behaviors on the compressibility is location of the light elements in liquid iron. Both carbon and sulfur are interstitial atoms in liquid iron at

5 of 7

B06207

TERASAKI ET AL.: DENSITY OF Fe3C LIQUID UP TO 10 GPA

B06207

hand, silicon replaces the iron site in the local structure because of its relatively large atomic size and thus has only a small influence on the liquid structure [Sanloup et al., 2002], suggesting that the compressibility of liquid Fe‐Si is similar to that of liquid iron. Consequently, the location of the light elements in the liquid iron structure is likely to be a key factor for the discussion of the density and the compressibility of liquid iron alloy. 3.4. Geophysical Implication [19] Compressional seismic wave velocity (VP) data are important to understand the outer core because they provide direct information from the Earth’s liquid outer core. Since VP can be expressed as functions of r and K0T as shown below, observed VP data can be directly linked to the density and compressibility of the outer core. Birch [1952] suggested that VP of the Earth’s outer core is larger than that of pure iron, since alloying light element in the core reduces the density but increases the VP. VP can be written as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KS þ 4
=3 ð1 þ T ÞK0T þ 4
=3 VP ¼ ¼ ;  

Figure 6. (a) Effect of light element concentration on density of liquid iron alloy at 4 GPa and different temperatures. Closed circle, open circles, open squares, and closed square represent the liquid densities of Fe3C at 1973 K (this study), Fe‐S at 1770 K [Sanloup et al., 2000a], Fe‐Si [Sanloup et al., 2004] at 1625 and 1725 K, and Fe at 1923 K [Nasch and Steinemann, 1995; Hixon et al., 1990], respectively. (b) Effect of light element concentration on bulk modulus of liquid iron alloys at 1973 K. Closed circle shows the data of Fe3C liquid of this study. The bulk moduli of (open circles) Fe‐S and (open squares) Fe‐Si correspond to data of Sanloup et al. [2000a] and Sanloup et al. [2004], respectively. The bulk modulus of liquid Fe (closed square) is from Hixon et al. [1990]. These bulk moduli are corrected to the value at 1973 K. ambient pressure [Waseda, 1980] and at high pressure [Urakawa et al., 1998; Sanloup et al., 2002]. These interstitial atoms modify the local structure of liquid iron, which is reported to have a mixture of body‐centered cubic (bcc)‐like and face‐centered cubic (fcc)‐like structures at 5 GPa and up to 2300 K [Sanloup et al., 2000b], and increase the Fe‐Fe nearest‐neighbor distance by their interstitial occupancy. Therefore, the increase of the nearest‐neighbor distance is likely to reduce the liquid iron incompressibility. On the other

where m, a, and g represent shear modulus, thermal expansivity, and Gruneisen parameter, respectively. In the liquid phase, we can ignore the m‐related term of the above equation because m is 0. Alloying carbon and sulfur into liquid iron reduces both K0T and r (Figures 6a and 6b), with the result that VP decreases with the increase in these element concentrations. On the other hand, silicon decreases only r but not K0T (Figure 6), which increases VP compared with the VP of pure iron as suggested by Sanloup et al. [2004]. Dissolution of silicon in the outer core can only explain the observed VP, which is higher than VP of liquid iron. VP of liquid Fe‐C cannot explain the observed VP of the outer core; therefore, carbon is not a suitable candidate for the light element in the outer core. However, further density measurement of liquid Fe‐C at higher pressure is required to know the bulk modulus more precisely and to evaluate the light element in the outer core. [20] In the case of the inner core, recent inelastic X‐ray scattering measurement of solid Fe3C shows that VP of preliminary reference Earth model (PREM) at the inner core condition can be explained by 1 wt% of carbon in the inner core [Fiquet et al., 2009]. Carbon is still a possible light element in the inner core. If bulk modulus changes because of the magnetic transition of Fe3C proposed from theoretical study [Vocadlo et al., 2002] and experimental studies [Lin et al., 2004; Gao et al., 2008], further measurement of bulk modulus of Fe3C in the stability field of the nonmagnetic phase is required to constrain the light element in the inner core.

4. Conclusions [21] Density measurement of solid and liquid Fe3C was performed using X‐ray absorption image technique up to 9.5 GPa and 1973 K. Density of liquid Fe3C increases (6.94– 7.38 g/cm3) with pressure (3.6–9.5 GPa). The compressibility of liquid Fe3C is obtained to be 50 ± 7 GPa at 1973 K. The effect of carbon on the compressibility of liquid iron is similar to that of sulfur. This effect may be explained by modification

6 of 7

B06207

TERASAKI ET AL.: DENSITY OF Fe3C LIQUID UP TO 10 GPA

of liquid iron local structure derived from carbon interstitial occupancy. Since carbon dissolution causes reduction of r and K0T of pure iron, carbon cannot be a major light element in the Earth’s outer core. However, carbon is still a possible light element in the inner core based on recent inelastic scattering measurement. [22] Acknowledgments. The authors acknowledge R. Tateyama and R. Shiraishi for their technical assistance and acknowledge the anonymous reviewers for their constructive comments. This work is partly supported by grants from the Japan Society for the Promotion of Science (grants 18104009 and 16075202 to E.O. and 17654102 to A.S.) and by the “Global Education and Research Center for the Earth and Planetary Dynamics.” The experiments have been performed under contract of the Photon Factory (proposal 2007S2‐002).

References Birch, F. (1952), Elasticity and constitution of the Earth’s interior, J. Geophys. Res., 57, 227–286, doi:10.1029/JZ057i002p00227. Brown, J. M. (1999), The NaCl pressure standard, J. Appl. Phys., 86, 5801– 5808, doi:10.1063/1.371596. Chabot, N. L., A. J. Campbell, W. F. McDonough, D. S. Draper, C. B. Agee, M. Humayun, H. C. Watson, E. Cottrell, and S. A. Saslow (2008), The Fe‐C system at 5 GPa and implications for Earth’s core, Geochim. Cosmochim. Acta, 72, 4146–4158, doi:10.1016/j.gca.2008.06.006. Chen, J., D. J. Weidner, L. Wang, M. T. Vaughan, and C. E. Young (2005), Density measurements of molten materials at high pressure using synchrotron X‐ray radiography: Melting volume of FeS, Adv. High Pressure Technol. Geophys. Appl., 185–194. Dodd, S. P., G. A. Saunders, M. Cankurtaran, B. James, and M. Acet (2003), Ultrasonic study of the temperature and hydrostatic‐pressure dependences of the elastic properties of polycrystalline cementite (Fe3C), Phys. Status Solidi, 198(2), 272–281, doi:10.1002/pssa.200306613. Dubrovinsky, L. S., S. K. Saxena, F. Tutti, S. Rekhi, and T. LeBehan (2000), In situ X‐ray study of thermal expansion and phase transition of iron at multimegabar pressure, Phys. Rev. Lett., 84, 1720–1723, doi:10.1103/PhysRevLett.84.1720. Dziewonski, A. M., and D. L. Anderson (1981), Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, 297–356, doi:10.1016/ 0031-9201(81)90046-7. Fiquet, G., J. Badro, E. Gregoryanz, Y. Fei, and F. Occelli (2009), Sound velocity in iron carbide (Fe3C) at high pressure: Implications for the carbon content of the Earth’s inner core, Phys. Earth Planet. Inter., 172, 125–129, doi:10.1016/j.pepi.2008.05.016. Gao, L., et al. (2008), Pressure‐induced magnetic transition and sound velocities of Fe3C: Implications for carbon in the Earth’s inner core, Geophys. Res. Lett., 35, L17306, doi:10.1029/2008GL034817. Hixson, R. S., M. A. Winkler, and M. L. Hodgon (1990), Sound speed and thermophysical properties of liquid iron and nickel, Phys. Rev. B, 42, 6485–6491, doi:10.1103/PhysRevB.42.6485. Holmes, N. C., J. A. Moriarty, G. R. Gathers, and W. J. Nellis (1989), The equation of state of platinum to 660 GPa (6.6 Mbar), J. Appl. Phys., 66, 2962–2967, doi:10.1063/1.344177. Isshiki, M., T. Irifune, K. Hirose, S. Ono, T. Ohishi, T. Watanuki, E. Nishibori, M. Tanaka, and M. Sakata (2003), Stability of magnesite and its high‐pressure form in the lowermost mantle, Nature, 427, 60–63, doi:10.1038/nature02181. Katayama, Y., K. Tsuji, J.‐Q. Chen, N. Koyama, T. Kikegawa, K. Yaoita, and O. Shimomura (1993), Density of liquid tellurium under high pressure, J. Non Cryst. Solids, 156–158, 687–690, doi:10.1016/0022-3093 (93)90046-Z. Li, J., H. K. Mao, Y. Fei, E. Gregoryanz, M. Eremets, and C. S. Zha (2002), Compression of Fe 3C to 30 GPa at room temperature, Phys. Chem. Miner., 29, 166–169, doi:10.1007/s00269-001-0224-4. Lin, J.‐F., V. V. Struzhkin, H.‐K. Mao, R. J. Hemley, P. Chow, M. Y. Hu, and J. Li (2004), Magnetic transition in compressed Fe3C from X‐ray emission spectroscopy, Phys. Rev. B, 70, 212405, doi:10.1103/ PhysRevB.70.212405. Lucas, L.‐D. (1964), Viscosite du Fer Pur et du Systeme Fe‐C Jusqu’a 4,8% C en poids, C. R. Acad. Sci. Paris, 259, 3760–3767.

B06207

McDonough, W. F., and S. Sun (1995), The composition of the Earth, Chem. Geol., 120, 223–253, doi:10.1016/0009-2541(94)00140-4. Nakajima, Y., E. Takahashi, T. Suzuki, and K. Funakoshi (2009), “Carbon in the core” revisited, Phys. Earth Planet. Inter., 174, 202–211, doi:10.1016/j.pepi.2008.05.014. Nasch, P. M., and S. G. Steinemann (1995), Density and thermal expansion of molten manganese, iron, nickel, copper, aluminum and tin by means of the gamma‐ray attenuation technique, Phys. Chem. Liquids., 29, 43–58, doi:10.1080/00319109508030263. Nishida, K., A. Suzuki, H. Terasaki, E. Ohtani, T. Sakamaki, Y. Shibazaki, H. Hayashi, M. Funayama, and T. Kikegawa (2008), Density measurements of liquid FeS at high pressure using X‐ray absorption image, Activity Rep. 2007, 25, p. 198, Photon Factory, Tsukuba, Japan. Ogino, K., A. Nishiwaki, and Y. Hosotani (1984), Density of molten Fe‐C alloys, J. Iron Steel Inst. Jpn., 10, 1004–1010. Ohtani, E., A. Suzuki, R. Ando, S. Urakawa, K. Funakoshi, and Y. Katayama (2005), Viscosity and density measurement of melts and glasses at high pressure and temperature by using the multi‐anvil apparatus and synchrotron X‐ray radiation, Adv. High‐Press Technol. Geophys. Appl., 195–209. Poirier, J.‐P. (1994), Light elements in the Earth’s outer core: A critical review, Phys. Earth Planet. Inter., 85, 319–337, doi:10.1016/00319201(94)90120-1. Rouquette, J., D. Dolejs, I. Y. Kantor, C. A. McCammon, D. J. Frost, V. B. Prakapenka, and L. S. Dubrovinsky (2008), Iron‐carbon interactions at high temperatures and pressures, Appl. Phys. Lett., 92, 121912, doi:10.1063/1.2892400. Sanloup, C., F. Guyot, P. Gillet, G. Fiquet, M. Mezouar, and I. Martinez (2000a), Density measurements of liquid Fe‐S alloys at high‐pressure, Geophys. Res. Lett., 27, 811–814, doi:10.1029/1999GL008431. Sanloup, C., F. Guyot, P. Gillet, G. Fiquet, R. J. Hemley, M. Mesouar, and I. Martinez (2000b), Structural changes in liquid Fe at high pressures and high temperatures from synchrotron X‐ray diffraction, Europhys. Lett., 52, 151–157, doi:10.1209/epl/i2000-00417-3. Sanloup, C., F. Guyot, P. Gillet, and Y. Fei (2002), Physical properties of liquid Fe alloys at high pressure and their bearings on the nature of metallic planetary cores, J. Geophys. Res., 107(B11), 2272, doi:10.1029/ 2001JB000808. Sanloup, C., G. Fiquet, E. Gregoryanz, G. Morard, and M. Mezouar (2004), Effect of Si on liquid Fe compressibility: Implications for sound velocity in core materials, Geophys. Res. Lett., 31, L07604, doi:10.1029/ 2004GL019526. Scott, H. P., Q. Williams, and E. Knittle (2001), Stability and equation of state of Fe3C to 73 GPa: Implications for carbon in the Earth’s core, Geophys. Res. Lett., 28(9), 1875–1878, doi:10.1029/2000GL012606. Siebert, J., F. Guyot, and V. Malavergne (2005), Diamond formation in metal‐carbonate interactions, Earth Planet. Sci. Lett., 229, 205–216, doi:10.1016/j.epsl.2004.10.036. Takeuchi, S. (1966), Structure and physical properties of liquid metals, Bull. Jpn. Inst. Meterol., 5, 479–499. Urakawa, S., N. Igawa, K. Kusaba, H. Ohno, and O. Shimomura (1998), Structure of molten iron sulfide under pressure, Rev. High Pressure Technol., 7, 286–288. Vocadlo, L., J. Brodholt, D. P. Dobson, K. S. Knight, W. G. Marshall, G. D. Price, and I. G. Wood (2002), The effect of ferromagnesian on the equation of state of Fe3C studied by first‐principle calculations, Earth Planet. Sci. Lett., 203, 567–575, doi:10.1016/S0012-821X(02)00839-7. Waseda, Y. (1980), The Structure of Non‐crystalline Materials: Liquids and Amorphous Solids, McGraw‐Hill, New York. Wood, B. J. (1993), Carbon in the core, Earth Planet. Sci. Lett., 117, 593– 607, doi:10.1016/0012-821X(93)90105-I. Wood, I. G., L. Vocadlo, K. S. Knight, D. P. Dobson, W. G. Marshall, G. D. Price, and J. Brodholt (2004), Thermal expansion and crystal structure of cementite, Fe 3 C, between 4 and 600 K determined by time‐of‐flight neutron powder diffraction, J. Appl. Cryst., 37, 82–90, doi:10.1107/S0021889803024695. T. Kikegawa, Photon Factory, High Energy Accelerator Research Institute, Tsukuba, Japan. K. Nishida, E. Ohtani, T. Sakamaki, Y. Shibazaki, A. Suzuki, and H. Terasaki, Department of Earth and Planetary Materials Science, Tohoku University, Sendai 980‐8578, Japan. ([email protected])

7 of 7