Volume 124, Issue 4 p. 3448-3457
Research Article
Free Access

Melting Curve and Equation of State of β-Fe7N3: Nitrogen in the Core?

Mayu Kusakabe

Corresponding Author

Mayu Kusakabe

Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo, Japan

Correspondence to: M. Kusakabe,

[email protected]

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Kei Hirose

Kei Hirose

Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo, Japan

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Ryosuke Sinmyo

Ryosuke Sinmyo

Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo, Japan

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Yasuhiro Kuwayama

Yasuhiro Kuwayama

Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

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Yasuo Ohishi

Yasuo Ohishi

Japan Synchrotron Radiation Research Institute, Sayo, Japan

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George Helffrich

George Helffrich

Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo, Japan

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First published: 13 March 2019
Citations: 11

Abstract

The chemical composition of carbonaceous chondrites permits up to 0.5 ± 0.4 wt% N in the Earth's core, which potentially affects the melting temperature, density profile, and phase relation of the core iron alloy. Here we have determined the melting curve and the high-temperature equation of state (EoS) of β-Fe7N3, which is stable above 40 GPa as the most Fe-rich iron-nitride. Experiments were performed in a laser-heated diamond-anvil cell up to 136 GPa, together with synchrotron X-ray diffraction measurements. We found that multiple melting criteria gave similar melting temperatures: (1) the appearance of diffuse X-ray scattering, (2) discontinuity in the laser power versus temperature relation, and (3) the reduction in diffraction peak intensity from solid. The validity of these melting criteria was confirmed by textural observation of recovered samples. We also observed rapid recrystallization at temperatures lower than the melting temperatures. The results demonstrate that β-Fe7N3 melts congruently at about 3,100 K at 135 GPa, lower than the melting temperatures of FeSi and FeO and similar to that of FeS. The thermal EoS indicates that the density of Fe7(C,N)3 matches the observed inner core density. Combining the melting curve and the EoS of β-Fe7N3, we also obtain the EoS of liquid Fe7N3. It shows that the density and compressibility of Fe + 10 wt% N is compatible with the outer core density profile. It supports the presence of some nitrogen in the liquid and solid parts of the core, although its concentration is difficult to constrain from the core density.

Key Points

  • We determined the melting curve and thermal equation of state of β-Fe7N3, which is stable above ~40 GPa as the most Fe-rich iron-nitride
  • Melting temperatures obtained by three different melting criteria were consistent with each other
  • The Earth's core could include not only carbon but also nitrogen, and Fe7(C,N)3 is a possible constituent of the inner core

1 Introduction

Nitrogen is depleted in Earth's atmosphere relative to other volatile species such as water, carbon, and most noble gases when compared to their relative abundance in chondrites (Marty, 2012). Nitrogen is known to be a siderophile element, suggesting that missing nitrogen may be stored Earth's metallic core. The metal-silicate partition coefficient of nitrogen DN (metal/silicate) has been determined to be ~104 at ambient pressure, 10–20 above 1 GPa (Roskosz et al., 2013), and about 100 at 24 GPa (Yoshioka et al., 2018). In addition, its solubility into silicate melts is strongly enhanced at low oxygen fugacity (Kadik et al., 2011; Li et al., 2013; Libourel et al., 2003), indicating that nitrogen could be incorporated into core metal in a magma ocean. CI chondrites contain ~3,000 ppm nitrogen by weight (McDonough & Sun, 1995). Previous estimates of the nitrogen content in the Earth's core have been quite variable; Johnson and Goldblatt (2015) calculated 864 ± 310 ppm N in the bulk Earth from nitrogen abundance in carbonaceous chondrites (1,235 ± 440 ppm), using potassium as a proxy to estimate relative depletion in the Earth relative to chondritic concentration. Considering the high metal/silicate partitioning of nitrogen DN = 20 ± 10 (Roskosz et al., 2013), such bulk Earth nitrogen content suggests 2,580 ± 2,000 ppm N in the core (Johnson & Goldblatt, 2015). If we employ the CI chondrites (McDonough & Sun, 1995) instead of the carbonaceous chondrites, similar calculations give 4,830 ± ~4,000 ppm N in the Earth's core.

Two Fe-rich iron-nitrides are known at 1 bar; γ’-Fe4N and ε phases (Fe3NX, 0.5 < x < 1.3 at 1,000 K). Face-centered cubic γ-Fe can include up to 1 wt% nitrogen (Wriedt et al., 1987). The stability and compressibility of the ε phase were examined at 300 K by Adler and Williams (2005) up to 50 GPa. More recently the formation of β-Fe7N3 phase from the ε phase has been discovered (Minobe et al., 2015); Fe4N decomposes into Fe + β-Fe7N3 above 41 GPa at ~1,000 K, indicating that the β phase is the most Fe-rich iron-nitride under core conditions. Minobe et al. (2015) and others found that β-Fe7N3 is similar in crystal structure, volume, and compressibility to Fe7C3, whose density and sound velocities may be consistent with those of the Earth's inner core (Chen et al., 2014; Prescher et al., 2015). Considering their similarities in stoichiometry and crystal structure, it is possible that β-Fe7N3 and Fe7C3 form a solid solution Fe7(C,N)3 in the inner core (Minobe et al., 2015). In this study, we determined the high-temperature EoS of β-Fe7N3 based on unit-cell volume measurements up to 136 GPa in pressure and to 2,560 K in temperature in a laser-heated diamond-anvil cell (DAC).

In addition, while the melting curve of β-Fe7N3 is of importance as one possible end-member of inner core material, it offers an opportunity to validate melting criteria because β-Fe7N3 melts congruently. In earlier DAC studies, several different melting criteria have been employed to determine melting temperatures in a DAC, which can be a source of inconsistency; for example, the reported melting temperature of pure iron varies by as much as 1,000 K at the core-mantle boundary (CMB) pressure (e.g., Anzellini et al., 2013; Boehler, 1993; Zhang et al., 2016). Here we examined the melting temperature of β-Fe7N3 up to 126 GPa using both in situ and ex-situ melting criteria. The results based on the different criteria are compared, and their validity is discussed.

Moreover, we obtain the EoS of liquid Fe7N3 from the EoS of solid Fe7N3 and its melting curve. We argue for the presence of nitrogen in the core, based on the comparisons between the compressibility of liquid Fe-N and the seismologically deduced outer core density profile and between the density of Fe7(C,N)3 and the inner core density.

2 Experimental Methods

We performed high-pressure and-temperature (P-T) experiments in a laser-heated DAC. The culet size of the diamond anvil ranged from 120 to 300 μm, depending on the target pressure. The starting material was ε-Fe7N3 powder from Kojundo Chemical Lab. Co. Ltd. ε-Fe7N3 was pelletized to about 10 μm thick and loaded together with a thermal insulator of NaCl and KCl (for volume measurements) or Al2O3 (for melting temperature determinations) into a hole drilled in to a Re gasket preindented to ~30 μm thick (volume measurements and melting experiments were made in separate runs).

After loading, the whole DAC was dried in a vacuum oven at 423 K for at least 10 hr. The cell was then introduced into an argon atmosphere, and the sample was compressed to the pressure of interest. Heating was made from both sides with a pair of fiber lasers with spot sizes of about 30 to 40 μm. Temperature was determined by fitting the Planck radiation function to thermal radiation spectra (Ohishi et al., 2008). Temperature at each side of the sample is the average over 5- to 6-μm area at a laser-heated hot spot, which corresponds to the full width at half maximum of the monochromatic incident X-ray beam (see below). The melting temperature reported in this study is the average of both sides of the sample, except for runs #1, #9, and #10 because the temperature was obtained only for a single side of the sample. Temperature difference between the two sides was always ~100 K. We consider the temperature uncertainty to be the larger of either ±5% (Mori et al., 2017) or one standard deviation from the average (Table 2). We aligned the X-ray beam spot with the laser-heating and temperature measurement spots by using fluorescent light induced by X-rays and transmitted light going through a sample chamber.

We first synthesized β-Fe7N3 from the ε-phase upon heating to >1,000 K above 40 GPa, except in run #1 carried out at 21 GPa (Table 2) and subsequently measured its volume in situ at high P-T (Ohishi et al., 2008). X-ray diffraction (XRD) patterns were collected on a digital X-ray flat panel detector at BL10XU, SPring-8. The incident X-ray wavelength was 0.4133 to 0.4151 Å. The XRD patterns of β-Fe7N3 demonstrate that all peaks are assigned with the hexagonal structure with the space group P63mc (Minobe et al., 2015; this study), the same as that for Fe7C3 (Herbstein & Snyman, 1964). The lower symmetry structures were recently proposed for Fe7C3 based on single-crystal XRD data (orthorhombic Pbca by Prescher et al., 2015, or Pmcn by Litasov et al., 2015) but splitting of multiple reflections that distinguishes the hexagonal structure from the distorted orthorhombic structures cannot be observed in powder XRD patterns obtained in both Minobe et al. (2015) and this study. Pressure was determined from the volume of pressure medium: NaCl (Fei et al., 2007) or KCl (Dewaele et al., 2012) using the thermal EoS proposed by. According to Campbell et al. (2009), effective temperature of the pressure medium is considered as
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0001(1)

Since the mean temperature of the pressure standard was the midpoint between sample surface and anvil surface, we employed the temperature of NaCl (or KCl) from equation 1; Campbell et al., 2009) when calculating pressure at high temperature from its P-V-T EoS. The error in pressure is obtained from the uncertainty in the temperature of NaCl or KCl. Since the thermal expansivity of KCl is small (Dewaele et al., 2012), its temperature uncertainty affects pressure determinations little.

We also determined the melting temperature of β-Fe7N3 (Table 2), in which temperature was measured with increasing laser output power by every 0.2–2.0 W. After the phase transition to the β-phase, XRD images were obtained every 1 s during heating. Sample pressure was calculated from the EoS of β-Fe7N3 obtained in this study at the temperature one step before the melting signal was observed. Its uncertainty was derived from errors in temperature and the volume of β-Fe7N3 observed (Table 2). After releasing pressure, a sample cross section was prepared with a Focused Ion Beam (FIB, Versa 3D, FEI), and the textural and compositional characterizations were made in the dual-beam FIB system with a field-emission-type scanning electron microscope and an energy-dispersive X-ray analyzer.

3 Results

3.1 Thermal EoS of β-Fe7N3

Figure 1 summarizes the P-V-T data of β-Fe7N3 obtained between 43 and 136 GPa in four separate sets of experiments by using NaCl pressure standard. The error bars of plotted P-V data were estimated by calculating the standard deviation of the error-weighted mean of the experimental data collected in a single heating cycle at each temperature range. The lattice parameters of β-Fe7N3 at 43 GPa are a = 6.610(1), c = 4.278(1), and a/c = 1.545(1) at 300 K, and a = 6.654(2), c = 4.295(6), and a/c = 1.549(5) at 1,900 ± 100 K. At 139 GPa, a = 6.287(1), c = 4.065(2), and a/c = 1.546(2) at 300 K, and a = 6.291(0), c = 4.054(0), and a/c = 1.552(0) at 1,900 ± 100 K. The lattice parameters observed are similar to those of Fe7C3 (Nakajima et al., 2011). The uncertainty in lattice parameter corresponds to one standard deviation from the mean when they were calculated using seven XRD peaks from β-Fe7N3. The third-order Birch-Murnaghan EoS was fitted to the room-temperature data from this study and Minobe et al. (2015):
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0002(2)
Details are in the caption following the image
Compression curves of β-Fe7N3 at 300 K (solid line), 2,000 K (dashed line), and 3,000 K (dotted line). Circles (black, 300 K; purple, 1,500–1,800 K; blue, 1,800–2,100 K; green, 2,100–2,400 K; red, >2,400 K) represent data from this study, and triangles are from Minobe et al. (2015). The uncertainties are estimated by calculating the standard deviation of the error-weighted mean of the experimental data collected in a single heating cycle at each temperature range. The vertical error bars are smaller than symbols.

where K0 and V0 are bulk modulus and unit-cell volume at 1 bar and 300 K, respectively. Both K0 and V0 were obtained by least squares method, where each data is weighted based on experimental uncertainties in P and V. The fitting provides K0 = 256(6) GPa and V0 = 184.5(5) Å3 when the pressure derivative of the bulk modulus K′ is fixed at 4. With K′ = 3.2, same as that obtained for nonmagnetic Fe7C3 by Chen et al. (2012), we find K0 = 316(5) GPa and V0 = 181.4(5) Å3, where the numbers in parentheses indicate uncertainty in the last digit (Table 1).

Table 1. EoS Parameters for Solid (β-Phase) and Liquid Fe7N3
V0 K0 θD
(cc/mol) (GPa) K0 q (K) γ0 Reference
Solid
β-Fe7N3 54.6(2) 316(5) 3.2 (fixed) 4.5(9) 430 (fixed) 2.1(3) This study
nm-Fe7C3a 55.1(1) 307(6) 3.2 (1) Chen et al. (2012)
Liquid
Fe7N3 55.2(4) 316(5) 3.1(0) 1.0(2) 740 (260) 1.7(2) This study
  • a nm = nonmagnetic.
In order to extend the EoS to high temperature, the present high P-T data were fit to a Mie-Grüneisen-Debye EoS (e.g., Jackson & Rigden, 1996), in which total pressure is the sum of an isothermal pressure at a reference temperature P(V,Tref) and thermal pressure ΔPth(V,T) as
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0003(3)
For the isothermal pressure term, the third-order Birch-Murnaghan EoS for 300 K obtained above was used. The thermal pressure term can be expressed by the Mie-Grüneisen relation:
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0004(4)
where γ and Eth are the Grüneisen parameter and thermal energy, respectively. The thermal energy is described by the Debye model:
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0005(5)
where R is gas constant, n is the number of atoms per formula unit, and θ is the Debye temperature. The volume dependences of the Debye temperature and the Grüneisen parameter are assumed as
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0006(6)
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0007(7)
where θ0 and q are the Debye temperature at a reference condition and a dimensionless parameter, respectively. In this study, θ0 is fixed at 430 K, the same as that obtained for pure iron by Shen et al. (2004), because it is difficult to determine when the experimental temperature is much higher than the estimated Debye temperature. Both q and γ0 were obtained by a least squares method, where each data is weighted based on experimental uncertainties in P and V. It is noted, however, that we found similar values for other parameters when we assume the Debye temperature to be 800 K (approximately the double of 430 K). Our fitting provides q = 4.9(0) and γ0 = 2.3(0) for K0 = 256(6) GPa and K′ = 4, and q = 4.5(9) and γ0 = 2.1(3) for K0 = 316(5) GPa and K′ = 3.2 (Table 1), where the numbers in parentheses indicate uncertainties in the last digits.

We have performed additional measurements of the volume of β-Fe7N3 at high P-T, in which KCl was employed as a pressure standard. The measurements were made with increasing temperature to 2,000 K in two separate runs at ~70 and ~110 GPa (see the supporting information). The P-V-T data obtained with the KCl pressure marker are in good agreement with the high-T isothermal compression curves obtained by the NaCl pressure standard (Figure S1 in the supporting information), when considering the difference between pressures at 300 K given by these two pressure markers.

3.2 Melting Curve of β-Fe7N3

Ten separate sets of melting experiments were conducted in the pressure range from 21 to 126 GPa (Table 2). The uncertainty of P in each run, the melting temperature of β-Fe7N3 was examined on the basis of four different in situ melting criteria: (1) the appearance of diffuse X-ray signal characteristic of liquid (Anzellini et al., 2013), (2) the change in the slope of the laser output power versus sample temperature relation (Lord et al., 2010), (3) reduction in the intensity of solid diffraction peak (Ma et al., 2004), and (4) the onset of rapid recrystallization (Andrault et al., 2011).

Table 2. Summary of Melting Experiments
Melting T (K)
PRc
Run # P (GPa) DSa TLb Half Quarter FRd
1 21(1) 1610(80) 1470(70) n.d. n.d. 1520(80)
2_1e 42(2) 1400(70)
2_2 46(2) 2060(100) 1850(90) 2060(100) 2130(110) 1490(80)
3 45(3) 1910(100) 1840(90) 1910(100) 1960(100) 1640(80)
4 52(2) 1990(100) 2240(110) 1990(100) 2050(110) 1770(90)
5 57(1) 2150(110) 2150(110) 2150(110) 2240(110) 1730(90)
6 58(1) 2160(110) 2160(110) 2110(110) 2160(110) 1590(80)
7 71(3) 2450(160) n.d. 2450(160) 2680(190) 2050(110)
8 86(2) 2730(140) 2730(140) 2410(120) 2730(140) 1990(120)
9 118(2) n.d. 2980(150) 2780(140) 2980(150) 1970(100)
10 126(2) 3060(150) 3060(150) 2940(150) 3060(150) 1760(90)
  • Note. Melting criteria: DS = appearance of diffuse scattering; TL = change in temperature versus laser output power curve; PR = reduction in X-ray diffraction peak intensity to half and quarter; FR = onset of fast recrystallization. n.d. = not determined.
  • a Quenched when fast recrystallization started.

Figure 2 shows the diffuse signal in XRD patterns observed in run #5 at 57 GPa. The signal appeared at 2,150 ± 110 K and became stronger to 2,240 ± 110 K. Signal enhancement is expected because of the enlargement of the liquid portion in to both the radial and axial directions. In this run, the laser power-temperature relationship also changed at 2,150 ± 110 K (Figure 3). While temperature increased as a linear function of laser output power to 2,150 ± 110 K, the rate of temperature increase per a given increment of laser power diminished substantially at higher temperatures, possibly because the laser power was consumed for the latent heat of melting (Lord et al., 2010). Also in run #5, while the XRD peak intensities from β-Fe7N3 did not change up to 2,080 ± 100 K, the most intense 121 peak decreased to half at 2,150 ± 110 K, and further to a quarter at 2,240 ± 110 K (Figure 2). All three of the melting criteria are consistent with melting at 2,150 ± 110 K in this experiment.

Details are in the caption following the image
X-ray diffraction patterns of a sample during heating β-Fe7N3, corundum (pressure medium), and unknown peaks (*) are labeled. (a) In run #5 at 57 GPa, they were obtained at 2,080 ± 100 K (black), 2,150 K ± 110 K (red), and 2,240 ± 110 K (blue). Diffuse signal (blue) appeared from 2,150 ± 110 K. (b) In run #10 at 126 GPa, diffuse signal appeared above 3,060 ± 150 K (red). β-Fe7N3 is stable to melting temperatures.
Details are in the caption following the image
Laser output power versus sample temperature plot in run #5 at 57 GPa. We started measuring temperature at 1,430 ± 70 K, and the power-temperature relation changed at 2,150 ± 110 K where diffuse scattering appeared in a XRD pattern as illustrated in Figure 2.

On the other hand, when the temperature reached 1,730 ± 90 K, the number of XRD spots in the two-dimensional image increased rapidly and began to appear and disappear at each XRD exposure. This is often called fast recrystallization and has been argued to be indicative of coexistence of crystal and melt (e.g., Andrault et al., 2011). However, 1,730 ± 90 K is much lower than the melting temperature inferred from the other three melting criteria.

We prepared thin sections using an FIB for samples recovered from runs #2–1, #3, and #9 (Table 2) and then examined textures and chemical compositions in their cross sections to further test the validity of the four melting criteria. Run #3 was performed at 45 GPa, and the sample was quenched from 2,480 ± 120 K that is substantially higher than the melting temperature obtained by any criteria (≤1,910 ± 100 K). The scanning electron microscope image and X-ray elemental maps of its cross section demonstrate that a part of the sample intruded into the Al2O3 pressure medium, indicating that the sample was likely molten (Figure 4). The image for run #9 quenched from 118 GPa and 3,050 ± 150 K also shows that liquid seeped into the Al2O3 pressure layer. In this experiment, the sample temperature was increased to 3,050 ± 150 K only a little higher than 2,980 ± 150 K, at which a gradient in laser power versus temperature curve changed and the solid XRD peak intensity reduced to a quarter. In these samples, the composition at the center of a laser-heated spot (the hottest part) was found to be Fe7N3, suggesting that β-Fe7N3 melts congruently. On the other hand, a similar melting texture was not found in the sample cross section for run #2-1 that was quenched from 1,400 ± 70 K at 42 GPa, right after the fast recrystallization was observed.

Details are in the caption following the image
Sample cross section recovered from run #3 performed at 45 GPa. A part of the Fe7N3 sample intruded into Al2O3 pressure medium, which is the clear evidence for melting. (a) Scanning electron microscope image, and X-ray elemental maps for (b) nitrogen, (c) iron, (d) oxygen, and (e) aluminum.

The melting temperatures obtained on the basis of three melting criteria (1)–(3) are plotted and compared in Figure 5a. These results provide a single melting curve that is consistent with textural observations of recovered samples. The melting curve was parameterized as T = T0 {(P − P0)/a + 1}1/c with P0 = 40 GPa (fixed), T0 = 1,814 ± 31 K, a = 29, and c = 2.6 (Simon & Glatzel, 1929). We compare in Figure 5b the melting curve of β-Fe7N3 with those of pure Fe and iron compounds such as FeS, FeSi, and FeO.

Details are in the caption following the image
(a) Melting temperature of β-Fe7N3 determined by diffuse signal (DS, red), discontinuity in laser power versus temperature relation (TL, blue), and reduction of XRD peak intensity to half (PR1/2, orange) and a quarter (PR1/4, gray). Same notations as in Table 2. Fast recrystallization (FR, green) occurred at much lower temperatures. The melting curve is based on a Simon equation. (b) Comparison of melting curves of iron compounds. Fe, Anzellini et al. (2013; purple) and Aquilanti et al. (2015; red); FeSi, Lord et al. (2010; green); FeO, Fischer and Campbell (2010; blue); FeS, Boehler (1992; yellow); Fe7N3, this study (black).

3.3 EoS for Liquid Fe7N3

We developed an EoS for liquid Fe7N3 using the experimentally determined melting points (Figure S2), thermodynamic data for Fe-N liquids, and the solid EoS for β-Fe7N3. Along the melting curve, the free energy ΔGr of the reaction
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0008(8)
is zero. The free energy Gliq(T) of liquid Fe-N mixtures at 1 bar is given by Frisk (1991). To incorporate the effects of pressure requires the volume of the mixture of liquid Fe-N for Fe7N3 composition be known. For solid Fe7N3, in contrast, the volume is known from the EoS experiments, but there is no 1 bar thermodynamic data. Hence,
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0009(9a)
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0010(9b)
with unknown Vliq and urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0011. In order to solve this, we can use the Clapeyron slope of the melting curve, dP/dT = ΔSV and an estimated ΔS for melting of Fe7N3 to obtain the volume change on melting ΔV, and hence Vliq. Ohashi and Ohashi (1981) estimated the systematics of the melting of metals and determined that the entropy change on melting, ΔSm = R × log (2) per mol-atom; R is the ideal gas constant. The slope of the melting curve is approximately 14.4 ± 1.15 K/GPa (Figure S2), yielding a ΔVm = 0.83 ± 0.06 cc/mol. Hence, urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0012 0.83 cc/mol, an approximation that holds along the melting curve. Similarly, urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0013 along the melting curve may be obtained from the known urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0014 by adding in the melting entropy ΔSm:
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0015(10)
where ∆Hm is a fitting constant (essentially the melting enthalpy) to make ∆Gr = 0 along the melting curve.

The volume equation of state for the Fe-N liquid is parameterized using the same thermal EoS as for the solid. Hence, unknown parameters for it are V0, K0, K′, q, θ0, and γ0. We fit the melting curve data to determine ∆Hm and the EoS parameters, with the initial estimate for V0 provided by the solid volume and the volume change on melting (Figure S1). The fitting results, including melting slope uncertainty, give ∆Hm = −101(30) kJ, V0 = 55.2(4) cc/mol, K0 = 316(5) GPa, K′ = 3.14(2), q = 1.0(2) θ0 = 740(260) K, and γ0 = 1.7(2).

4 Discussion

4.1 Validity of Melting Criteria

Since Fe7N3 melts congruently and thus the liquid portion suddenly increases at the melting point, clear diffuse scattering was observed at the onset of melting (Figure 2) in all runs except run #9. We also confirmed discontinuity in the laser output power versus temperature curve (Figure 3). While a temperature plateau was observed in previous studies (Lord et al., 2010; Shen & Lazor, 1995), the temperature continued rising slowly after the onset of melting in this study. Disappearance of XRD peaks is a natural consequence of melting (Ma et al., 2004). Since there is a temperature variation in a laser-heated sample and an X-ray beam has a tail, XRD peaks were not lost completely but diminished to a large extent in this study when melting initiated at the hottest part of a sample (Figure 2). We therefore report temperatures at which the β-Fe7N3 121 peak intensity became half and quarter in Table 2. Fast recrystallization occurred at temperatures much lower than melting (Figure 5a). The temperatures for the onset of such fast recrystallization tend to increase with increasing pressure but did not show a clear correlation with melting.

Diffuse X-ray scattering is characteristic of liquid and certain evidence for melting (Anzellini et al., 2013). On the other hand, the validity of other melting criteria has been a matter of debate. For example, XRD peaks can disappear upon extensive grain growth of a solid phase (Nishiyama et al., 2003). In this study, the sample was heated in run #9 to 3,050 ± 150 K only a little higher than 2,980 ± 150 K, at which the laser power-temperature relation changed and β-Fe7N3 121 peak diminished to a quarter. After recovering this sample, a clear melting texture was found in its cross section, supporting that both the melting criteria based on change in laser output power versus temperature relation and reduction in XRD peak intensity are also attributed to melting. The melting points obtained using these criteria are in better agreement with those at which the XRD peak intensity reduced to a quarter rather than a half in this study (Figure 5a).

4.2 Nitrogen in the Outer Core?

We examine the possible presence of nitrogen in the outer core liquid, using the EoS of liquid Fe7N3 obtained in this study (Table 1). The isentropic temperature profile of the outer core is estimated as
urn:x-wiley:21699313:media:jgrb53372:jgrb53372-math-0016(11)
where ρ is density from the Preliminary Reference Earth model (PREM; Dziewonski & Anderson, 1981) and γ is Grüneisen parameter proposed to be 1.5 for liquid iron in the whole outer core by Vocadlo et al. (2003). We employ TX = 4,000 K and ρX for the CMB. The density of liquid Fe7N3 is calculated to be 9.96 g/cm3 at CMB (136 GPa, 4,000 K) and 12.51 g/cm3 at the inner core boundary (ICB; 329 GPa, 5440 K) from its EoS given in Table 1.

We found that the presence of 10 wt% N in liquid Fe explains the density deficit of the outer core at the CMB, assuming linear density change between liquid Fe and Fe7N3 as a function of nitrogen concentration. Figure 6 illustrates the density profile of liquid Fe + 10 wt% N, which is 2.5% higher than the PREM density at the ICB. Indeed, the 10 wt% N in the outer core is not feasible when considering CI chondrites include only ~3,000 ppm N (McDonough & Sun, 1995) and the core might contain up to 0.5 ± 0.4 wt% N. Nevertheless, the similar compressibility of liquid Fe-N to that of the outer core supports the presence of nitrogen in the core, although its concentration is difficult to constrain from the core density.

Details are in the caption following the image
Comparison of liquid density profiles of pure Fe (Umemoto et al., 2014), Fe7N3 (this study), and Fe + 10 wt% N with the Preliminary Reference Earth model (PREM). These are calculated along isentropic temperature profile (4,000 K at core-mantle boundary and 5,440 K at inner core boundary [ICB]).

4.3 Fe7(C,N)3 in the Inner Core?

Recently, it has been argued that Fe7C3 would crystallize at the ICB even if carbon is minor in the outer core (Chen et al., 2014; Nakajima et al., 2015), because (1) the melting temperature of Fe7C3 is high (much higher than that of pure Fe; Fei & Brosh, 2014) and (2) crystallization of carbide is enhanced when sulfur is included in liquid iron (Wood, 1993). Such Fe7C3 may explain the low shear velocity (or high Poisson's ratio) of the inner core (Chen et al., 2014; Prescher et al., 2015). The density of Fe7C3 is calculated from the room-temperature EoS for the nonmagnetic state (>53 GPa) according to Chen et al. (2012), and its thermal parameters are assumed to be the same as those for β-Fe7N3 described above. Under the ICB condition, nonmagnetic Fe7C3 exhibits a similar or slightly lower density than that observed for the inner core (Figure 7).

Details are in the caption following the image
Isothermal density profiles of solid pure Fe (Dewaele et al., 2006), β-Fe7N3 (this study) and nonmagnetic Fe7C3 by Chen et al. (2012) with thermal expansivity same as that for β-Fe7N3 at 5440 K. Solid lines employ q = 4.5 obtained for β-Fe7N3 in this study, while dotted lines use q = 2.2 determined previously for paramagnetic Fe7C3 by Nakajima et al. (2011).

On the other hand, the density of β-Fe7N3 is found to be 12.97 g/cm3 at the ICB (329 GPa, 5440 K) from its thermal EoS obtained in this study, which is a little higher than the PREM density (Figure 7). Note that here we use the EoS of β-Fe7N3 with K′ = 3.2, identical to that determined for nonmagnetic Fe7C3 (Chen et al., 2012). We compare in Figure 7 the isothermal density profiles of both β-Fe7N3 and nonmagnetic Fe7C3 at 5440 K with the PREM. It suggests that the inner core may include not only carbon but also nitrogen and Fe7(C,N)3 is a possible constituent of the inner core. The crystal structure, volume, and compressibility of β-Fe7N3 are similar to those of Fe7C3 (Chen et al., 2012; Minobe et al., 2015; this study). These support that Fe7N3 forms continuous solid solution with Fe7C3 under inner core conditions. Indeed, Fe7(C,N)3 has been found as inclusions in diamond (Kaminsky & Wirth, 2017).

In these calculations, we consider a large pressure effect on the thermal expansivity of β-Fe7N3 (q = 4.5) found in the present experiments. The high q value has been also reported for stishovite (q = 6.1; Nishihara et al., 2005) that exhibits high bulk modulus like β-Fe7N3. Indeed, the density of β-Fe7N3 at the inner core conditions changes little with different q values. When we assume q = 2.2 that was determined for Fe7C3 by Nakajima et al. (2011) and accordingly recalculate θ0 and γ0 considering our measured thermal expansivity at the CMB pressure, we obtain only 0.07 g/cm3 (0.54%) smaller density for β-Fe7N3 at the ICB (Figure 7).

5 Summary and Conclusions

We report the thermal EoS and the melting curve of recently discovered β-Fe7N3 in this study, which is the most Fe-rich iron nitride above ~40 GPa. Experiments were carried out in a laser-heated DAC up to 136 GPa. We found that three different in situ melting criteria, (1) the appearance of diffuse X-ray signals, (2) the change in laser output power versus sample temperature relation, and (3) reduction in the intensity of solid XRD peak, gave melting temperatures very similar to each other. The melting temperatures are also consistent with ex-situ textural observations of recovered samples. Rapid recrystallization, on the other hand, occurred at much lower temperatures. A sample that showed rapid recrystallization during heating did not show a melting texture in its cross section.

It has been argued that Fe7C3 could explain the low shear velocity (or high Poisson's ratio) of the inner core, but it is slightly lighter than the inner core density when we apply the same thermal expansivity as that determined for isostructural β-Fe7N3. Nevertheless, the density of β-Fe7N3 is marginally higher than the observed inner core density. It is probable that Fe7N3 and Fe7C3 form a solid solution due to their similarity in crystal structure, volume, and compressibility. Therefore, Fe7(C,N)3 may potentially account for the inner core density as well as its low shear velocity (Chen et al., 2014; Prescher et al., 2015).

We also obtained the EoS of liquid Fe7N3 from that of solid Fe7N3 and its melting curve. The observed outer core density profile is consistent with that of liquid Fe + 10 wt% N, assuming a linear change in the density of liquid Fe-N with increasing nitrogen concentration. Indeed, 10 wt% N in the Earth's core is not feasible. Nevertheless, similar compressibility of liquid Fe-N with that of outer core liquid supports the presence of nitrogen in the core, although its concentration is not constrained from the core density.

Acknowledgments

We thank K. Yonemitsu for her technical supports. Comments from two anonymous referees were very helpful to improve the manuscript. In situ XRD measurements were conducted at BL10XU, SPring-8 (proposal 2016A0080 and 2016B0080). Data supporting Figure 5a are given in Table 2, and the EoS parameters used to calculate densities in Figures 6 and 7 are shown in Table 1.