3 - Carbon versus Other Light Elements in Earth’s Core

Summary

This chapter reviews the geochemical and geophysical constraints on the carbon budget in the metallic core of Earth, discusses whether carbon is a dominant light element in the core, and assesses whether the core hosts the largest reservoir of carbon on Earth.

3.1 Introduction

Carbon is a candidate light element in Earth’s core.^1–3 The core consists of a liquid outer shell ranging from 2971 to 5210 km in depth and a solid inner sphere with a radius of 1220 km.⁴ Without direct samples, its iron-dominant composition has been inferred from seismological, geochemical, and cosmochemical observations, together with mineral physics constraints from laboratory measurements and theoretical simulations. Both the outer and inner cores are lighter than iron or iron–nickel alloys at relevant pressure–temperature (P–T) values, indicating the presence of one or more elements with smaller atomic numbers than iron.⁵ Candidates for the light alloying elements of the core include hydrogen (H), carbon (C), oxygen (O), silicon (Si), and sulfur (S).

Earth’s core may be the largest repository for terrestrial carbon. As the fourth most abundant element in the solar photosphere, carbon occurs in carbonaceous chondrites and ordinary chondrites as a major or minor element.⁶ The silicate Earth is depleted in carbon with respect to CI chondrite by more than two orders of magnitude, and by five- to ten-fold after accounting for evaporative loss to outer space during accretion.⁷ Some of the missing carbon in the silicate Earth is likely found in its core, considering the large solubility of carbon in the iron-rich melt^8–10 and the strong affinity of carbon for iron metal during core–mantle differentiation.^11–14 Core sequestration can also explain the ¹³C enrichment in silicate Earth relative to Mars, Vesta, and chondrites.¹⁵ Cosmochemical and geochemical considerations suggest that the core may contain as much as 1 wt.% (5 at.%) carbon.¹⁵ A lower estimate of 0.2 wt.% carbon in the core is derived by assuming that carbon depletion follows the volatility trend.⁷ More details are found in Chapter 2. A core containing 1 wt.% carbon would exceed the combined budget of known carbon in the atmosphere, hydrosphere, biosphere, crust, and mantle by one order of magnitude (Figure 3.1). Even with the lowest estimate of 0.1 wt.% carbon, the core would still account for more than half of Earth’s total carbon budget.

Figure 3.1 Pie diagrams showing the relative sizes of Earth’s carbon reservoirs for two end-member models. The concentrations of carbon are assumed to be 0.2 wt.%, 20 ppm, and 165 ppm in the crust, depleted mantle, and enriched mantle, respectively.¹⁶ With 100 ppm in the atmosphere, biosphere, and hydrosphere,¹⁶ the total carbon in these reservoirs is negligible and hence not shown.

Constraining the carbon budget of the core is crucial for identifying Earth’s building blocks and reconstructing its accretion history. In this chapter, we review constraints on the carbon content of the core from the phase relation, density, and sound velocities of iron–carbon alloys and compare carbon with other light elements in terms of their ability to match the physical properties of the core. We will also provide a brief discussion of how carbon may have redistributed among various Earth reservoirs through geological time.

3.2 Constraints on Carbon versus Other Light Elements in Earth’s Core

3.2.1 Constraints from Phase Relations of Iron–Light Element Systems

Carbon as a core component has attracted special attention through the proposal of a carbide inner core.⁹ Based on long extrapolations of equation of state (EoS) data available at the time, Fe₃C with 6.67 wt.% C was predicted to be the first phase to crystallize from an Fe–S–C liquid to form the inner core, even for carbon contents below 1 wt.%.

Testing the model of a carbide inner core requires knowledge of the phase relations at core pressures. As an initial step, the simplified Fe–C binary system has been investigated through experiments and thermodynamic modeling (Figure 3.2). At 1 bar, the system has a eutectic point between iron and Fe₃C at 4.1 wt.% carbon.¹⁷ At pressures above 10 GPa, the eutectic point lies between iron and Fe₇C₃ with 8.41 wt.% carbon,¹⁸ hence Fe₇C₃ is expected to solidify from any composition on the carbon-rich side of the eutectic point at core pressures.

(a) Schematic phase diagram of the Fe–C binary system near the iron end member. 1 bar: thick black solid line,¹⁷ 14 GPa: gray solid line,¹⁸ 50 GPa and 130 GPa: red solid or dotted lines,²⁰ 20 GPa, 136 GPa, and 330 GPa: thick black solid or dotted lines.²² Solid traces and filled circles are based on experimental measurements. Dotted traces and open circles are based on calculations and/or extrapolations.

(b) Carbon content of the Fe–C eutectic liquid as a function of pressure.

Figure 3.2 Fe–C binary system and eutectic composition.

While some studies support the predicted shift of the eutectic composition toward the iron end member with increasing pressure,^{19, 20} others conclude that the eutectic composition contains 3 ± 1 wt.% carbon between 40 and ~100 GPa in pressure²¹ and ~2 wt.% carbon at the pressure of the inner core boundary (ICB).²² If the outer core contains less carbon than the eutectic composition, then a hexagonal close-packed (hcp) Fe incorporating carbon instead of Fe₇C₃ would be the liquidus phase to form the inner core.

The carbide inner core model can also be tested against the density increase across the ICB. Isochemical freezing of pure Fe or an Fe–light element (Fe–L) alloys produces 1.7% or 2.4% increases in density.^{23, 24} These are smaller than the 0.6–0.9 g/cm³ or 4.7–7.1% observed density increases,²⁵ suggesting that the inner core contains less of the light elements than the outer core. In the ICB condition, a candidate Fe–L composition must reproduce the observed density contrast. For a simplified Fe–L binary, a match is possible only if the core composition is on the Fe-rich side of the eutectic point. Moreover, the light element contents of the solid and liquid must be sufficiently high and different to match the density contrast. If the eutectic composition is below 1 wt.%, it is unlikely to find a binary Fe–C composition with 5% density contrast between coexisting solid and liquid. It follows that carbon alone is unable to account for the density contrast at the ICB. The presence of sulfur and/or oxygen could help if they partition more strongly into the liquid phase. If the eutectic carbon content is as high as 3 wt.%, then a match by an Fe–C binary composition is possible (Figure 3.2).

Fe–L binary phase relations at 1 bar differ according to the nature of the light element, as is known from the metallurgy literature.²⁶ The phase relations at pressure and temperature conditions relevant for Earth’s core are drastically different from those at 1 bar (Figure 3.3).

(a) Phase diagrams on the Fe-rich side of Fe–S, Fe–Si, and Fe–O systems at 1 bar (upper) and 330 GPa (lower).²⁷

(b) Eutectic composition as a function of pressure.

Data sources are Refs. 21 and 28–30. bcc = body-centered cubic.

Figure 3.3 Fe–S, Fe–Si, and Fe–O binary phase diagrams and eutectic compositions.

The Fe–S binary exhibits eutectic behavior between Fe and FeS at 1 bar and the sulfur content of the eutectic decreases with pressure (Figure 3.3). At core pressures, we may expect that a eutectic liquid containing <10 wt.% sulfur coexists with a solid with slightly less sulfur.^{23, 29, 31, 32} Therefore, sulfur alone cannot explain the density contrast at the ICB. At least 1–2 wt.% sulfur is likely to be present in the liquid core in addition to carbon and may enhance the stability of carbides or Fe–C alloys on the liquidus.⁹

The Fe–Si binary shows a narrow melting loop and only slight enrichment of silicon in the liquid at pressures up to 120 GPa (Figure 3.3). The eutectic composition contains 25 wt.% silicon at 21 GPa pressure³³ and <10 wt.% silicon at 80 GPa or higher,³⁴ and falls below 1.5 ± 0.1 wt.% at 127 GPa pressure.³⁰ Such a silicon-poor eutectic composition implies that FeSi may be a candidate for the inner core. Because Si stabilizes the body-centered cubic (bcc) structure, the inner core may be hcp Fe alloyed with Si or a mixture of a Si-rich bcc phase and a Si-poor hcp phase.^{35, 36} On the other hand, the silicon-poor eutectic composition and the nearly equal partitioning of silicon between solid and liquid iron at the ICB pressure^{23, 37} imply that silicon alone cannot explain the ICB density contrast.

While oxygen is a leading candidate for the light element in the liquid outer core, little oxygen is expected to be present in the solid inner core. At 1 bar, the Fe–O binary is characterized by a vast liquid miscibility gap.²⁶ At core pressures, the Fe–O system is more likely to be a eutectic with nearly pure Fe coexisting with Fe–O liquid (Figure 3.3). The eutectic oxygen content increases with pressure and exceeds 10 wt.% at >100 GPa.²¹ Given its low solubility in solid Fe, the amount of oxygen in the inner core is probably negligible, but oxygen is the best candidate to explain the density difference between the solid and liquid cores.

3.2.2 Constraints from Densities of Fe–C Alloys and Compounds

The presence of light elements in Earth’s core was initially inferred from comparing the observed density of the core with the measured density of iron under corresponding conditions. The pressure of the core is well constrained by geophysical and seismological data.⁴ The temperature profile of the core is more uncertain and bears at least ±500 K uncertainties.³⁸ Compared with pure iron or iron–nickel alloys at the core P–T conditions,^39–42 the core is lighter than pure iron by 5–8% in the liquid outer shell and by 2–5% in the solid inner sphere.^{5, 43–45}

A viable composition model of the core must account for the density deficits. This is a straightforward and effective test, but requires knowledge of the phase relation and EoS of relevant Fe alloys in solid and liquid states at multi-megabar pressures and temperatures exceeding 4000 K. A wide range of mixtures of iron with C, O, Si, and S have been proposed as possible constituents of the outer core, whereas the solid inner core is most likely an iron alloy or a compound of iron with one of the light elements,^1–3 and therefore the test is somewhat simpler for the inner core.

Stimulated by the suggestion that the density of Fe₃C should be close to the observed value of the inner core,⁹ measurements and calculations of the densities and elastic properties of iron carbides have been carried out (Tables 3.1 and 3.2). First-principles simulations coupled with structure search algorithms have been used to predict the iron–carbon alloys that are likely to be stable at Earth’s inner core conditions. The energetically competitive stoichiometry ranges from Fe:C of 3:1 to 1:1 and includes Fe₃C, Fe₇C₃, Fe₅C₂, Fe₂C, and FeC stoichiometry.^{46, 47}

Table 3.1 Elasticity parameters for solid Fe–C alloys

Composition (wt.% L)	ρ0 (g cm–3)	K0 (GPa)	K0ʹ	P (GPa)	T (K)	Method	Ref.
Density
Fe3C
	7.70(1)	175(4)	5.2(3)	0–73	300	PXD	121
	7.70(1)	174(6)	4.8(8)	0–30	300	PXD	61
	8.03(1)	290(13)	3.76(18)	0–187	300	PXD	50
	7.67	167	6.7	0–35	300	PXD	49
fm Fe3Ca	7.68(1)	192(3)	4.5(1)	0–31	300–1473	PXD	63
pm Fe3C		161(2)	5.9(2)	0–50	300	SXD	62
pm Fe7C3	7.68(1)	201(12)	8.0(1.4)	4–158	300	SXD	64
nm Fe7C3	7.75(2)	307(6)	3.2(1)	7–167	300	SXD	64
fm Fe7C3	7.62(1)	186(5)	6.9(2.2)	0–7	300	PXD	70
Nonlinear Fe7C3	7.59(2)	166(13)	4.9(1.1)	7–20	300	PXD
pm Fe7C3	7.68(2)	196(9)	4.9(2)	20–66	300	PXD
fm Fe7C3	7.61(1)	201(2)	4 (fixed)	0–18		PXD
pm Fe7C3b	7.70(2)	253(7)	3.6(2)	18–72	300–1973	PXD	41
	V0 (m/s)	V = a0 + a1•ρ
VP		a0	a1
Fe bcc	5800						89
Fe3C	5330–5140						122
	5890	–3990	1290	0–50	300	NRIXS	55
	6103(413)	–8671	1900	0–68	300	HERIX	123
		–1138	9823	60–153	300	NRIXS	54
Fe7C3		2160	660	70–154	300	NRIXS	69
VS
Fe bcc	3000						89
Fe3C	3010–3030						122
	3050(70)	1450	240	0–50	300	NRIXS	55
				0–50	300– 1450	NRIXS	94
		–961	4429	60–153	300	NRIXS	54
Fe7C3		843	242	70–154	300	NRIXS	69

^a Θ₀ = 490(120) K, γ₀ = 2.09(4), q = –0.1(3).

^b Θ₀ = 920(14) K, γ₀ = 2.57(5), q = 2.2(5).

HERIX = high-energy-resolution inelastic X-ray scattering; NRIXS = nuclear resonant inelastic X-ray scattering; PXD = powder X-ray diffraction; SXD = single-crystal X-ray diffraction.

Table 3.2 Elasticity parameters for liquid Fe–L alloys

Composition (%L)		ρ0 (g cm–3)	K0 (GPa)	K0ʹ	P (GPa)	T (K)	Method	Ref.
wt.%	at.%
Fe
		7.02	109.7(7)	4.66(4)		1811	Shockwave	44
		5.19(3)	24.6(6)	6.65(4)	50–350	7000	FPMD	82
Fe–S
10	6	5.2	48.0(2.0)	4	0–6	1770	X-ray absorption	124
10		5.5	63	4.8	0–20	1773–2123	Sink–float	125
20	12.5	4.41	35(1)	4.9	0–8	1673	Ultrasonic	96
27	17.4	4.07	25(1)	5.3	0–8	1673	Ultrasonic
30	19.7				0–5.4	1573–1673	Ultrasonic	126
11.7	7	6.28	83.7	4.98	150–300	4000	FPMD	97
		5.43	49.6	5.08		6000
16	9.8	5.72	64.4	4.94		4000
		5.06	42.9	5.02		6000
Fe–C
0–4	0–0.9	a			0	1523–1823	Sessile drop	73
3.5	0.8	6.91	83.9	5.9(2)	0–4	1700	Ultrasonic	127
		6.91	100(1)	6.2(6)		1700
		7.02(1.5)	55.3(2.5)	5.2(1.5)	2–7	1500
2.0–4.0	0.4–0.9		65.0	6.0	42	3000	X-ray diffraction	66
	10.9(4)
	12.1(4)
5.7	1.3		Similar to Tera10		0–5.4		X-ray absorption	128
			Larger		5.4–7.8
3.9	16	6.51	110(9)	5.1(3)	7–70	2500	X-ray absorption	65
6.7	1.5	6.5	54(3)	4	0–10	1973	X-ray absorption	129
Fe–Si
17	9.3	5.88	68(1)	4	0–12	1773	Sink–float	130
17		6.33	75	4	0–5	1650	X-ray absorption	131
Fe–O
22	7.5	5.45	128	3.85		5000	Thermo	132
Fe–H
0.8	0.01	6.2	82.4	4.79	125–200	4000	FPMD	101
		5.63	62.9	4.76		6000
1.2	0.02	5.88	73.1	5.02		4000
		5.23	53.2	4.82		6000

^a ρ = 7.10 – 0.0732x – (8.28 – 0.874x)•10^–4•(T – 1823), x = wt.% C, T in K.

FPMD = first-principles molecular dynamics.

3.2.2.1 Fe₃C

The natural form of Fe₃C (cementite) occurs in iron meteorites and is known as cohenite. The composition of synthetic Fe₃C ranges from C deficiency with 4.2 wt.% or 17 at.% C (roughly Fe₅C) to C excess with 8.8 wt.% or 31 at.% C (exceeding Fe₇C₃).⁴⁸ At 1 bar and 300 K, Fe₃C has an orthorhombic structure (Figure 3.4). Although metastable at ambient conditions, the crystal structure remains unchanged to 187 GPa at 300 K^{49, 50} and to 25–70 GPa and 2200–3400 K.⁵¹ Upon heating at pressures above 145 GPa, Fe₃C decomposes into a mixture of solid orthorhombic Fe₇C₃ and hcp Fe, then melts incongruently above 3400 K.⁵² Cemenite is ferromagnetic at ambient conditions and its Curie temperature is sensitive to small deviations from stoichiometry.⁵³ It undergoes ferromagnetic to paramagnetic transition and spin-pairing transition at high pressures.^54–56

Figure 3.4 Atomic-scale structures of crystalline and molten iron carbide alloys. (a) Orthorhombic Fe₃C (space group Pnma), (b) hexagonal Fe₇C₃ (space group P6₃mc) and (c) orthorhombic Fe₇C₃ (space group Pbca). In both Fe₃C and Fe₇C₃ polymorphs, the fundamental building blocks are triangular prisms (CFe₆). Three such prisms are connected via shared vertices in a triangular arrangement (triads). The triads are stacked up along the c-axes for hexagonal polymorphs and along b-axes for orthorhombic polymorphs of Fe₇C₃. The carbon atoms are shown as gray spheres and the iron atoms are colored based on the distinct Wyckoff sites.^{57, 58} (d) A snapshot of a molten iron carbide alloy from molecular dynamics simulations. The computational supercell is shown and has orthogonal axes with x = y = z. The diffusion trajectory of a carbon atom is shown for reference.

The density of Fe₃C at ambient conditions is 2.5% smaller than that of fictive hcp iron, corresponding to ~1.4% density reduction for 1 wt.% carbon (i.e. a compositional expansion coefficient α_c of 1.4).⁵⁹ Pressure-induced magnetic transitions lead to abrupt but small reductions in density and/or compressibility.^{54, 55, 57, 60} The calculated density of Fe₃C at the ICB pressure and 300 K is comparable to that of the inner core, but too low when thermal expansion is considered (Figure 3.5). A more appropriate test requires knowledge of the thermoelastic parameters of the non-magnetic phase.

Figure 3.5 Density of Fe–C alloys and compounds as a function of pressure of iron carbides. CMB = core–mantle boundary. Preliminary reerence Earth model (PREM): black crosses;⁴ hcp Fe at 300 K: black solid curve;⁴⁰ hcp Fe at 5000–7000 K calculated using the Mie–Grüneisen–Debye EoS.⁴² Fe₃C at 300 K;^{49, 50, 61, 62} Fe₃C at 5000–7000 K.⁶³ Fe₇C₃ at 300 K;⁶⁴ Fe₇C₃ at 5000–7000 K.⁴¹ Uncertainties are shown as error bars.⁶⁴ Liquid with Fe₈₄C₁₆ compoisition.⁶⁵ Liquid with Fe₈₈C₁₂ composition.⁶⁶

3.2.2.2 Fe₇C₃

The metallurgical form of Fe₇C₃, known as Eckström–Adcock carbide, adopts a hexagonal structure at 1 bar and 300 K (Figure 3.3). An orthorhombic structure is also observed and may be stabilized with silicon impurities.⁶⁷ Non-stoichiometry is also observed in Fe₇C₃ and ranges from 8.0 to 10.8 wt.% (29–36 at.%) C, where the C-excess end member exceeds Fe₂C stoichiometry.⁴⁸ The crystal structure of Fe₇C₃ remains stable up to 185 GPa and 5200 K,^{52, 68} but it undergoes pressure-induced magnetic transitions.^{18, 69–71} At ambient conditions, the compositional expansion coefficients of h-Fe₇C₃ (~1.0) is smaller than that of Fe₃C (~1.4). The calculated density of the non-magnetic Fe₇C₃ is broadly consistent with that of the inner core at the relevant pressures and temperatures, thus supporting the carbide inner core model (Figure 3.5).

3.2.2.3 Fe–C Alloy Near the Iron End Member

In the simplified Fe–C model, the inner core may consist of an Fe–C alloy rather than a carbide.²² The Fe–C alloy would contain no more than 1 wt.% carbon according to geochemical considerations and the measured solubility of carbon at pressures greater than 40 GPa.^{20, 21} However, 1.0–2.5 wt.% carbon may not be sufficient to reproduce the density deficit of the inner core⁷² and hence would require the presence of other light elements.

3.2.2.4 Liquid Fe–C Alloy

A carbide inner core implies that the liquid outer core contains more carbon than the eutectic composition at relevant pressures (Figure 3.2). Even if the solid inner core is not made of carbides, a substantial amount of carbon may still be present in the liquid outer core, which occupies more than 90% of the core by mass or volume.

At ambient pressure, adding 1.3–2.8% carbon only reduces the density of liquid Fe by ~1% (α_c = 0.4–0.8).⁷³ Experimental measurements of an Fe liquid with 2.8 wt.% carbon suggest an α_c of 2–4 at the core–mantle boundary (CMB) pressure of 136 GPa and 3000 K,⁶⁶ which is in broad agreement with the calculated value of 1.3,⁷⁴ considering uncertainty and extrapolation. The larger α_c values at core pressures are consistent with Fe–C liquid being less compressible than Fe liquid.⁶⁵ Even with α_c = 2–4, 1.8–2.7 wt.% carbon is needed to explain the 5–8% density deficit in the outer core. This is higher than the upper limit from cosmochemical and geochemical considerations; hence, carbon cannot be the sole light element in the outer core.

3.2.2.5 Other Light Elements

All candidate light elements have been shown to reduce the density of solid Fe (Figure 3.6). The fitted compositional expansion coefficients of light elements in solid Fe alloys are comparable to the calculated results for liquid Fe alloys.⁷⁴ On the per wt.% basis, carbon may be slightly more efficient than O, Si, and O at reducing the density of iron, and therefore a slightly smaller amount is needed to account for the 5–8% density deficit in the outer core (Table 3.3). Combinations of light element such as that of sulfur and silicon⁷⁵ are found to satisfy the density constraints.

Figure 3.6 Compositional expansion coefficients of light elements in solid iron alloys. The values are derived from fits to solid Fe–L alloys and compounds.³

Table 3.3 Compositional expansion coefficients

	Solida	Liquid at CMBb	Liquid at ICBb	LE, wt.%c	LE, wt.%d
H	8.7	–	–	0.6	0.9
C	1.4	1.3	1.3	4	6
O	1.2	1.1	1.0	4	7
Si	0.8	0.7	0.6	6	10
S	0.8	0.8	0.7	6	10

Compositional expansion coefficient is defined as the relative amount of density reduction per wt.% light element.⁵⁹

^a Li and Fei.³

^b Badro et al.⁷⁴

^c Amount of light element needed to account for 5% density deficit in the outer core.

^d Amount of light element needed to account for 8% density deficit in the outer core.

LE = light element.

3.2.3 Constraints from Sound Velocities of Fe–C Alloys and Compounds

Comparison between the preliminary reerence earth model (PREM) and iron reveals a prominent mismatch in the shear wave velocity, V_S, between the inner core and Fe or Fe–Ni alloys at corresponding pressures and 300 K (Figure 3.7). The discrepancy cannot be explained by the effect of temperature alone^76–78 and has been attributed to partial melting,⁷⁹ strong pre-melting effects,^{80, 81} and/or the presence of light elements.⁵⁵ In contrast, the compressional wave velocity, V_P, in the inner core is broadly consistent with that of hcp Fe (Figure 3.7). In the outer core, the bulk sound velocity may be comparable to or as much as 4% higher than liquid iron at corresponding conditions.^{43, 82} The presence of light elements, therefore, should not significantly affect the V_P of iron for this match to hold.

Figure 3.7 Sound velocity of Fe–C alloys and compounds. V_P and V_S of Fe carbides and liquid Fe–C as a function of density. Data are from Refs. 54, 65, 69, 89, and 90. The velocities of Fe–Ni alloys (not shown)⁹¹ are similar to that of Fe. The top axis denotes the pressure range of the outer core (OC) and inner core (IC) according to the density–pressure relationship in PREM.

The sound velocities in the core increase linearly with density, following Birch’s law (Figure 3.7). The velocity–density relations of solid and liquid Fe are consistent with Birth’s law, but for solid Fe the V_P slope at 300 K or along a Hugoniot is steeper than that of the core. For V_S, deviation from Birch’s law behavior was predicted by theory⁸³ and observed at high temperatures,⁷⁷ although this is not resolved in all studies.⁸⁴ A candidate Fe–L alloy must reproduce the velocity gradients in the core.

The speed of sound traversing the inner core is anisotropic by 3–4% in V_P and ~1% in V_S.^{85, 86} The anisotropy in sound speed may reflect convective alignment of anisotropic hcp Fe crystals⁸⁷ or an Fe–L alloy.⁸⁸ A candidate inner core phase needs to exhibit large enough elastic anisotropy to match the observations.

3.2.3.1 Fe₃C

As a candidate for the inner core phase, Fe₃C stands out in terms of its potential to account for the observed anisotropy. If the measured and calculated strong anisotropy in the sound velocity of Fe₃C at ambient conditions^{92, 93} is applicable at core conditions, then only a small degree of alignment would be needed for Fe₃C to match the observations.

Existing data suggest that Fe₃C may provide a good match for the V_S in the inner core. At ambient conditions, the V_S of Fe₃C is similar to that of bcc Fe (Table 3.1). At 300 K, a magnetic transition near 5 GPa leads to a reduction in the V_S and its Birch’s law slope so that the extrapolated V_S of Fe₃C at the inner core pressure is much smaller than that of hcp Fe and closer to the core values.⁵⁵ The high-spin to low-spin transition near 50 GPa leads to a further decrease in the Birch’s law slope.⁵⁴ Moreover, at high temperatures, the V_S of Fe₃C deviates from Birch’s law behavior toward the inner core values; hence, it can potentially explain the anomalously low V_S in the inner core without invoking partial melt or strong pre-melting effects.⁹⁴

A potential match in V_P is also consistent with existing data. The range of measured V_P of Fe₃C at 1 bar and 300 K encompasses that of bcc Fe (Table 3.1). The magnetic transition to the paramagnetic phase of Fe₃C results in elastic softening and a shallower Birch’s law slope of V_P, whereas the paramagnetic to non-magnetic transition does not seem to produce a visible effect.⁵⁴ At 300 K and inner core pressures, the extrapolated V_P of Fe₃C is higher than that of the inner core (Figure 3.7). A close match is possible if V_P at high temperature is lowered by a suitable amount as a result of deviation from Birch’s law.

3.2.3.2 Fe₇C₃

The most compelling support for an Fe₇C₃ inner core comes from its ability to match the anomalously low V_S and high Poisson ratio, in addition to reproducing the density deficit.^{58, 69} While the ferro- to para-magnetic transition at 7.0–7.5 GPa does not seem to have obvious effect on sound velocities, significant shear softening accompanies the magnetic collapse at 40–50 GPa, resulting in pronounced reductions in V_P, V_S, and their Birch’s law slopes (Figure 3.7). At pressures relevant to Earth’s inner core, the extrapolated value of V_S of Fe₇C₃ at 300 K is only slightly higher than the observed value. There is likely a good match for V_S after considering further reduction at high temperature. It remains to be tested whether Fe₇C₃ can simultaneously match V_S, V_P, and anisotropy.

3.2.3.3 Fe–C Alloy Near the Iron End Member

First-principles calculations show that adding 1.0–2.5 wt.% carbon into the hcp Fe crystal structure increases its V_P and decreases its V_S, and this would help explain the observed anisotropy in compressional wave velocities, although there is a mismatch in shear wave anisotropy.⁷²

3.2.3.4 Liquid Fe–C Alloy

Adding carbon increases the V_P of liquid iron (Table 3.1). For 1 at.% carbon, the average effect is 0.2% at 1 bar. It may increase to an estimated value of 0.8–1.2% at the core conditions, presumably because liquid Fe–C is less compressible than liquid Fe,⁶⁵ or remains at 0.2% at high pressures and high temperatures.⁷⁴ In any case, the V_P of an Fe–C alloy with <1 wt.% carbon would be consistent with the observed value in the outer core.

3.2.3.5 Other Light Elements

The sound velocities of other Fe–L alloys remain poorly constrained (Figure 3.8 and Table 3.4). The effect of sulfur on the sound velocities is not yet sufficiently understood to allow firm tests of Fe–S models for the core.^{28, 74, 95–98} Further studies are needed to resolve the disagreements concerning oxygen as a major light element in the core.^{74, 99} Computations suggest that an Fe–H alloy with 1 wt.% H can reproduce the density and V_P of the liquid outer core and therefore could be the primary alloy element, but Fe–H alloys cannot reproduce the V_S of the inner core.^{100, 101}

Figure 3.8 Sound velocities of Fe–H, Fe–O, Fe–S, and Fe–Si alloys and compounds. Compressional wave velocity V_P (a) and shear-wave velocity V_S (b) versus density relations. PREM;⁴ hcp Fe at 300 K: solid line;⁸⁹ hcp Fe at temperatures between 700 and 1700 K: solid circles;⁷⁷ Fe from shockwave experiments: dashed line;⁷⁶ Fe₉₂Ni₈ at 300 K: crosses;⁹¹ Fe₃S at 300 K;¹⁰² Fe₈₅Si₁₅ at 300 K;⁹¹ FeO at 300 K;¹⁰³ FeH_x at 300 K;¹⁰⁴ FeH at 300 K;¹⁰⁵ Fe₇₄S₃O₂₃ from shockwave experiments;¹⁰⁶ Fe₉₃Ni₄Si₃ at 300 K.¹⁰⁷

Table 3.4 Melting curve parameters of Fe–L alloys

	a	c	P0 (GPa)	T0 (K)	Teut CMB (K)	Xeut CMB (at.%)	dT/dx (K/at.%)
Fe–C	8.5	3.8	0	1420	2990(200)	11(5)	110(80)
Fe–O	17	3.8	0	1800	3200(200)	30(3)	33(11)
Fe–18 wt.% Si	23.6	1.89	0	1600	–	4	–
Fe–S	10.5	3	21	1260	2870(200)	15(5)	89(56)

The parameters are fitted to the Simon–Glatzel equation (T_m/T_m0)^c = (P_m – P_m0)/a. Data are from Morard et al.⁷⁵

3.2.4 Constraints from Melting Temperatures of Fe–C Alloys

An independent constraint on the carbon content of the outer core can be obtained from the melting temperatures of iron alloys (Figure 3.8). The outer core is entirely molten, whereas the base of the mantle is mostly solid;¹⁰⁸ hence, the melting temperature of a candidate Fe–C alloy must be lower than the solidus of overlying mantle at the CMB pressure. In addition, as the geotherm is expected to follow an adiabat, which has a smaller dT/dP slope than the melting curve, the temperature at CMB is expected to be 400–900 K lower than its crystallization temperature at the ICB.^{38, 45}

The solidus temperature at the CMB is estimated at 4100–4200 K for peridotitic composition.¹⁰⁹ For comparison, core temperature profiles for pure Fe or Fe–Ni alloys would lead to a temperature at the CMB of 5400–5900 K,³⁸ which clearly exceeds the upper bounds on the mantle side (Figure 3.9); thus, these compositions are incompatible with a molten iron alloy and solid silicate coexisting at the CMB.

Figure 3.9 Melting temperatures of Fe-rich alloys. (a) Melting curves of pure iron,³⁸ and Fe–10 wt.% Si¹¹⁰ and eutectic melting curves of Fe–Fe₃S (dashed line,³¹ solid line²⁹), Fe–FeO,²¹ and Fe–Fe₃C (dashed line,¹¹¹ solid line²¹). The different melting curves are represented over the pressure range at which experiments were performed without any extrapolation. Pressures for the CMB and ICB are indicated by thick vertical dashed lines. (b, top) Liquidus temperatures in Fe–X systems compared with melting temperatures of mantle materials at the CMB (136 GPa), represented as linear interpolations between the melting point of pure Fe³⁸ and the eutectic compositions.²¹ Solidi at CMB pressure for the peridotitic¹⁰⁹ and mid-ocean ridge basalt mantle¹¹² are represented by horizontal bands. (b, bottom) Extrapolated liquidus under ICB pressure for sulfur,²⁹ oxygen,²¹ silicon,¹¹⁰ and carbon.^{21, 52}

Carbon reduces the melting point of iron. Using linear interpolation between pure Fe and the eutectic liquid, the melting point reduction is estimated at >100 K per at.% carbon at 136 GPa.²¹ At the ICB pressure, the melting point reduction effect of carbon may be similar to that at the CMB⁵² or as much as 350 K/at.%.²¹

Experimentally determined eutectic melting temperatures agree within 150 K for the Fe–S, Fe–Si, and Fe–O systems.^{3, 21, 30} Adding 1 at.% C, O, Si, and S to liquid iron reduces its melting point by 100 K for C and S, 50 K for O, and <30 K for Si at the pressure of the CMB (Figure 3.8). To pass the physical state test, a core with a single light element must contain at least 5 at.% S or C, or at least 15 at.% O.²⁹ The melting points of Fe–Si alloys are too high and therefore silicon cannot be the only light element in the outer core. The presence of other light elements such as carbon, oxygen, and/or sulfur are required to lower its crystallization temperature.

Compositions containing two or more lighter elements exhibit more complex behavior. While the alloying effect of oxygen on the eutectic point of the Fe–S system was found to be minor,¹¹³ shock experiments at 100–200 GPa estimated that the presence of 8 wt.% (2.4 at.%) oxygen and 2 wt.% (1.2 at.%) sulfur would reduce the melting point of iron by 600 K.^{106, 114} This is more than twice the combined reductions of oxygen (120 K) and sulfur (120 K), suggesting non-ideal mixing in the ternary system.

3.3 Implications of Carbon as a Major Light Element in the Core

If the inner core consists of Fe₇C₃ with 8.41 wt.% carbon, the average concentration of carbon in the core would be at least ~0.3 wt.%, implying that the core has nearly one order of magnitude more carbon than the total amount in the surface reservoirs and silicate Earth, and hence it is by far the largest carbon reservoir in Earth (Figure 3.1). The bulk Earth would contain 0.1 wt.% carbon, higher than the estimated 0.03 wt.% for a half-mass condensation temperature of 40 K.^{7, 115} This result would question the validity of the volatility trend for highly volatile elements such as carbon.

Recent experiments show that Fe₇C₃ exhibits the highest electrical resistivity among all Fe–L alloys.¹¹⁶ As a major element in the core, carbon may influence the thermal transport properties of the core, with implications for the evolution of the geodynamo.

3.4 Carbon in the Core Over Time

Carbon may move across the CMB over geological time if chemical disequilibrium was introduced during Earth’s accretion or subsequent evolution. Earth’s core may have been initially out of equilibrium with the mantle,¹¹⁷ or the silicate Earth may have acquired most of its highly volatile elements through a late veneer.¹¹⁸ Furthermore, chemical equilibrium at the CMB may have been perturbed as a result of secular cooling or inner core growth, which may have enriched or depleted carbon in the outer core depending on the carbon partitioning between the solid and liquid (Figure 3.2). Experiments suggest that mobility of carbon along grain boundaries may allow its transport over geologically significant length scales of 10 km over the age of Earth.¹¹⁹ Facilitated by mantle convection, rapid grain-boundary diffusion may have brought core-derived carbon to Earth’s surface and thus connected the billion-year deep carbon cycle to the near-surface million-year shallow carbon cycle.

Ongoing carbon sequestration by the core may have resulted from subduction of the hydrothermally altered oceanic lithosphere carrying carbonates and organic matter into the deep Earth. While CaCO₃ in slabs may have been preserved under reducing lower-mantle conditions, the MgCO₃ component could have been destabilized by metallic iron-form diamonds or iron carbides.¹²⁰ Slab-derived Fe–C mixtures are expected to partially melt in the D´´ layer.¹¹¹ The melt may have accumulated near the CMB over time and episodically drained into the core (Figure 3.10).

Figure 3.10 Carbon transport from subducted slabs to Earth’s core. Schematic illustration of slab-derived Fe–C melt bringing carbon from Earth’s surface to the core, modified after Liu et al.¹¹¹ The upper oval-shaped balloon shows elemental carbon or iron carbides (gray) associated with metallic iron (white) in the mantle at depths greater than 250 km. Three rectangular boxes represent Fe–C melts at the base of the mantle (heights are exaggerated): (a) Fe–C melt (yellow) that wets the solid silicate matrix (gray); (b) non-wetting Fe–C melt (yellow) coexisting with a small degree of silicate melt (green) in a solid silicate matrix (gray); and (c) solid phases (yellow–gray) that have become iron rich through reaction with the Fe–C melt. The lower oval-shaped balloon indicates dynamic stirring, which may prevent or slow down the draining of dense Fe–C melts to the core.

3.5 Conclusion

We have evaluated constraints on the carbon budget of Earth’s core by comparing the density, velocity, and elastic anisotropy of Fe–C alloys and compounds at core conditions with seismic observations. Existing data support the model of the inner core consisting of iron carbide Fe₇C₃, which could solidify from an Fe–C–S liquid core containing up to 1 wt.% carbon. Fe₇C₃ is unique in its ability to match the anomalous V_S and high Poisson ratio of the inner core. Its density and V_P are also broadly consistent with the PREM, but need to be further tested against the anisotropy observations. On the contrary, Fe₃C seems unstable and too light to match the inner core density. Given the upper limit of 1 wt.% carbon in the core, an Fe–C alloy is unable to generate the observed density deficit in the inner core.

The presence of 1 wt.% carbon in the outer core provides a good match to the V_P and is consistent with the coexistence of a molten iron alloy with solid silicate at the CMB. However, 1 wt.% carbon is insufficient to account for the density deficit in the outer core and cannot reproduce the density contrast at the ICB, and therefore other light elements such as H, O, S, or Si must be present in the outer core.

Earth’s core remains potentially by far the largest carbon reservoir of the planet. It may participate in the long-term global carbon cycle through carbon transport across the CMB via grain-boundary diffusion, mantle convection, and sequestering slab-derived Fe–C melts.

The outer core likely contains multiple light elements. At least 1–2 wt.% sulfur is likely to be present in the outer core and would help account for its density deficit and the core’s largely molten state. Oxygen may be required in the liquid outer core to explain the density contrast at the ICB, although the amount of oxygen remains uncertain. Silicon does not help explain the density contrast across the ICB or the coexistence of the liquid core with the overlying solid mantle. Existing data are insufficient to resolve the competing models of core composition because of limited data coverage in the relevant pressure–temperature–composition space and uncertainties in experimental measurements and theoretical simulations. Future studies should focus on expanding the experimental data range and investigating complex systems that contain more than one light element.

3.6 Limits to Knowledge and Unknowns

Earth’s core is potentially by far the largest carbon reservoir of the planet. To assess the role of the core in Earth’s deep carbon cycle, we need to test the hypothesis of iron carbide as the dominant component of the solid inner core and quantify the carbon content of the liquid outer core. In the past decade, research in deep carbon has significantly improved our knowledge of the physical properties and melting behavior of carbon-bearing iron alloys at the extreme pressure and temperature conditions in the deep Earth. Limits to our knowledge mainly stem from incomplete data coverage for the relevant pressures, temperatures, and compositions. For simplified compositions, the properties of liquid iron or iron alloys are still limited to relatively low pressures and temperatures far below the relevant ranges of the core. Investigations of complex iron alloys containing nickel and two or more light elements have only covered small subsets of the entire plausible pressure–temperature–composition space. Effects of temperature on the magnetic transitions and elasticities of solid iron alloys remain poorly constrained. Direct measurements of the densities and velocities of solids at inner core pressures are not yet available.

Acknowledgments

The authors thanks Rajdeep Dasgupta, James Badro, an anonymous reviewer, and Dave Walker for providing critical comments and constructive suggestions. JL acknowledges NSF EAR-1763189, NSF AST-1344133, and Sloan Foundation Deep Carbon Observatory Grant G-2017-9954. BC acknowledges NSF EAR‐1555388 and NSF EAR‐1565708. MM acknowledges XSEDE resources, NSF EAR-1634422, and NSF EAR-1753125.

Questions for the Classroom

1 How do researchers infer the presence of volatile elements such as carbon in Earth’s liquid outer core?

2 As a candidate for the principal light element in Earth’s core, what are the strongest arguments for and against carbon?

3 What is the plausible range of carbon content in Earth’s core, and how do we know this?

4 Why was an iron carbide proposed as a candidate for the dominant component of Earth’s solid inner core? How can we test this hypothesis?

5 Why is the knowledge of the eutectic composition of binary systems Fe–X, where X is an element lighter than iron such as hydrogen, carbon, oxygen, silicon, or sulfur, important for constraining Earth’s core composition?

6 How do pressure and temperature affect magnetism in iron-rich alloys?

7 What are “spin-pairing” or “high-spin to low-spin” transitions in iron-rich alloys?

8 How is the elasticity of an iron alloy affected by pressure-induced magnetic transition?

9 How do light elements such as carbon affect the thermodynamic stability of iron–nickel alloys?