Core-outer Core Boundary Research Articles

Thermodynamics of the system Fe\u2013Si\u2013O under high pressure and temperature and its implications for Earth\u2019s core

The thermodynamics of the system Fe–Si–O under high pressure (P) and temperature (T) was examined, starting with modelling the phase transition between a face-centred cubic (fcc) and hexagonal close-packed (hcp) structure in Fe–Si alloy which was previously examined by experiment under high P–T conditions. The mixing properties of Fe and Si for the iron phases were found to be approximated by ideal mixing under high P and T conditions. The entropy changes upon melting of the end-members of the system are fairly large, and therefore the melting temperature of the Si-bearing fcc or hcp phases needs to be insensitive to the Si content, to account for the reported close compositions of coexisting liquid and solid (< 1 wt%Si at P > 50 GPa). The solidus and liquidus temperatures of Fe–Si iron alloy would therefore, not significantly be changed by the presence of Si at the inner core-outer core boundary, which enables us to evaluate the melting curve of Fe–Si fcc and hcp phases. From thus-constrained melting curve, I assessed a thermal equation of state of Si-bearing iron liquid. I then estimated a seismologically consistent outer core composition as a function of Si and O contents using the EoS for liquids constructed in this study and the literature. The best-fit composition is Fe-5.8(0.6) wt%Si–0.8(0.6) wt%O, which however does not precipitate a solid iron phase that is consistent with the inner core density. Therefore, Earth’s core cannot be fully represented by the system Fe–Si–O and it should include another light element.

Ab Initio Thermoelasticity of Liquid Iron-Nickel-Light Element Alloys

The earth’s core is thought to be composed of Fe-Ni alloy including substantially large amounts of light elements. Although oxygen, silicon, carbon, nitrogen, sulfur, and hydrogen have been proposed as candidates for the light elements, little is known about the amount and the species so far, primarily because of the difficulties in measurements of liquid properties under the outer core pressure and temperature condition. Here, we carry out massive ab initio computations of liquid Fe-Ni-light element alloys with various compositions under the whole outer core P, T condition in order to quantitatively evaluate their thermoelasticity. Calculated results indicate that Si and S have larger effects on the density of liquid iron than O and H, but the seismological reference values of the outer core can be reproduced simultaneously by any light elements except for C. In order to place further constraints on the outer core chemistry, other information, in particular melting phase relations of iron light elements alloys at the inner core-outer core boundary, are necessary. The optimized best-fit compositions demonstrate that the major element composition of the bulk earth is expected to be CI chondritic for the Si-rich core with the pyrolytic mantle or for the Si-poor core and the (Mg,Fe)SiO3-dominant mantle. But the H-rich core likely causes a distinct Fe depletion for the bulk Earth composition.

Phase relations in the system Fe–Ni–Si to 200 GPa and 3900 K and implications for Earth's core

Phase relations in Fe–5 wt%Ni–4 wt%Si alloy was examined in an internally resistive heated diamond anvil cell under high pressure (P) and temperature (T) conditions to about 200 GPa and 3900 K by in-situ synchrotron X-ray diffraction. The hexagonal close-packed (hcp) structure was observed to the highest P–T condition, supporting the idea that the stable iron alloy structure in Earth's inner core is hcp. The P–T locations of the phase transition between the face-centred cubic (fcc) and hcp structures were also constrained to 106 GPa. The transition occurs at 15 GPa and 1000 K similar to for pure Fe. The Clausius–Clapeyron slope is however, 0.0480 GPa/K which is larger than reported slopes for Fe (0.0394 GPa/K), Fe–9.7 wt%Ni (0.0426 GPa/K), and Fe–4 wt%Si (0.0394 GPa/K), stabilising the fcc structure towards high pressure. Thus the simultaneous addition of Ni and Si to Fe increases the dP/dT slope of the fcc–hcp transition. This is associated with a small volume change upon transition in Fe–Ni–Si. The triple point, where the fcc, hcp, and liquid phases coexist in Fe–5 wt%Ni–4 wt%Si is placed at 145 GPa and 3750 K. The resulting melting temperature of the hcp phase at the inner core-outer core boundary lies at 550 K lower than in pure Fe.

Solved and unsolved questions in the non-rigid Earth nutation study

AbstractAt the IAU 26th GA held in Prague in 2006, a new precession model (P03) was recommended and adopted to replace the old one, IAU1976 precession model. This new P03 model is to match the IAU2000 nutation model that is for anelastic Earth model and was adopted in 2003 to replace the previous IAU1980 model. However, this IAU2000 nutation model is also not a perfect one for our complex Earth, as stated in the resolution of IAU nutation working group. The Earth models in the current nutation theories are idealized and too simple, far from the real one. They suffer from several geophysical factors: the an-elasticity of the mantle, the atmospheric loading and wind, the oceanic loading and current, the atmospheric and oceanic tides, the (lateral) heterogeneity of the mantle, the differential rotation between the inner core and the mantle, and various couplings between the fluid outer core and its neighboring solids (mantle and inner core). In this paper, first we give a very brief review of the current theoretical studies of non-rigid Earth nutation, and then focus on the couplings near the core-mantle boundary and the inner core-outer core boundary, including the electro-magnetic, viscous, topographic, and gravitational couplings. Finally, we outline some interesting future studies.

High Pressure and High Temperature Equation-of-State of Gamma and Liquid Iron

ABSTRACTShock-wave experiments on pure iron preheated to 1573 K were conducted in the 17–73 GPa range. The shock-wave equation of state of γ-iron at an initial temperature of 1573 K can be fit with us = 4.102 (0.015) km/s + 1.610(0.014) up with ρo = 7.413±0.012 Mg/m3 We obtain for γ-iron's bulk modulus and pressure derivative the values: 124.7±1.1 GPa and 5.44±0.06, respectively.We present new data for sound velocities in the γ- and liquid-phases. In the γ-phase, to a first approximation, the longitudinal sound velocity is linear with respect to density: Vp = −3.13 (0.72) + 1.119(0.084) p(units for Vp and p are km/s and Mg/m3, respectively). Melting was observed in the highest pressure (about 70–73 GPa) experiments at a calculated shock temperature of 2775±160 K. This result is consistent with a previously calculated melting curve (for ε-iron) which is close to those measured by Boehler [1] and Saxena et al. [2]. The liquid iron sound velocity data yields a Grüneisen parameter value of 1.63±0.28 at 9.37±0.02 Mg/m3 at 71.6 GPa. The quantity γρ is 15.2±2.6 Mg/m3, which agrees with the uncertainty bounds of Brown and McQueen [3] (13.3–19.6 Mg/m3). Based on upward pressure and temperature extrapolation of the melting curve of γ-iron, the estimated inner core-outer core boundary temperature is 5500±400 K, the temperature at the core-mantle boundary on the outer core side is 3930±630 K.

Temperatures in Earth's Core Based on Melting and Phase Transformation Experiments on Iron

Experiments on melting and phase transformations on iron in a laser-heated, diamond-anvil cell to a pressure of 150 gigapascals (approximately 1.5 million atmospheres) show that iron melts at the central core pressure of 363.85 gigapascals at 6350 +/- 350 kelvin. The central core temperature corresponding to the upper temperature of iron melting is 6150 kelvin. The pressure dependence of iron melting temperature is such that a simple model can be used to explain the inner solid core and the outer liquid core. The inner core is nearly isothermal (6150 kelvin at the center to 6130 kelvin at the inner core-outer core boundary), is made of hexagonal closest-packed iron, and is about 1 percent solid (MgSiO(3) + MgO). By the inclusion of less than 2 percent of solid impurities with iron, the outer core densities along a thermal gradient (6130 kelvin at the base of the outer core and 4000 kelvin at the top) can be matched with the average seismic densities of the core.

Seismic structure near the inner core‐outer core boundary

A model of P‐wave velocity of the Earth's core 500 km above and below the inner core boundary (ICB) beneath North America is constructed from travel time analysis and broad‐band waveform modeling of core phases at distances from 130° to 160°. Differential travel times between PKPBC (Cdiff) and PKPDF (TBC–TDF) are about 0.5 sec shorter than those computed from PREM at distances from 146° to 152° and increase with distance to nearly the same as those from PREM at 155°. Differential travel times between PKPCD and PKPDF (TCD–TDF) at distances from 130° to 143° are approximately 0.2 sec shorter than those of PREM. Amplitudes of PKPBC (Cdiff) relative to PKPDF (ABC/ADF) at distances 150° to 156° are about 40% larger than those from PREM. These observations require a smaller P‐wave velocity gradient (0.0005 sec−1) in the lowermost 300 km of the outer core than that from PREM (∼0.00065 sec−1), a slower P‐wave velocity (10.96 km/sec) at the top of the inner core, and a larger velocity gradient (0.0005 sec−1) in the uppermost 300 km of the inner core.

Carbon in the core

Carbon is extremely abundant in the solar system (10 × Si, 20 × S) in Cl carbonaceous chondrites (3.2 wt%) and it dissolves readily in liquid Fe at low pressures (4.3 wt% at 1420 K). Despite these properties it is rarely considered a potential light element in the Fe-rich core, because it is volatile, even at low temperatures as CO. In this paper I show that carbon volatility is a strongly pressure-dependent phenomenon and that it applies during condensation from a solar gas ( ∼ 10 −3 atm), but not at the pressures and temperatures generated during planetary accretion and differentiation (0.01–5 GPa). Thus, impact heating and degassing of the protoearth should have led to an Fe-rich melt with around 2–4 wt% carbon, compared to the 0.01–0.6 wt% in iron meteorites and 0.3–3 ppm C predicted to be present in Fe condensed from the solar gas. Experiments (to 9 GPa) and thermodynamic calculations on the systems Fe C and Fe C S show that carbon solubility in Fe melt increases slightly with pressure but that carbon could not conceivably constitute more than half the light element content of the core. The addition of even very small amounts of carbon ( < 1%) to liquids containing Fe and a light element such as S has, however, a dramatic effect on the properties of the system. At 330 GPa (inner core-outer core boundary) 0.3% of carbon is sufficient to stabilise iron carbide Fe 3C, rather than ε-Fe as the first phase to crystallize in melts with around 10% S. Thus, for most conceivable ratios of S/C, the inner core would be expected to be crystallising Fe 3C, rather than ε-Fe or Fe Ni alloy. Given probable inner core temperatures of around 5000–6000 K, both ε-Fe and the higher pressure α′-Fe are too dense to explain the inner core density of 12.85 Mg m −3. The stability of iron carbide provides a possible solution. I show that, given a plausible equation of state for Fe 3C, this phase acquires the inner core density in the right pressure-temperature range.

The Phase Diagram of Iron and the Temperature of the Inner Core

Birch was the pioneer of understanding the earth's core: that the core was mostly iron; that the solid inner core was nearly pure iron; that the liquid core had most of the impurities; and that the phase diagram (p.d.) of pure iron was complicated with several phases and triple points (t.p.). In 1972 he said, “5000°K, for the central temperature ... may have some standing as an upper limit.” I reconstruct the phase diagram accounting for new experiments and theories arising in the subsequent two decades. I stretch Birch's p.d. to account for the experiments of BOEHLER et al. (1990), BROWN and McQUEEN (B&M) (1982, 1986), and Yoo et al. (1992, 1993). BOEHLER (1993) reports the e-γ-liquid t.p. at 100 GPa. This t.p. plus the solid-solid (ss) transition at 200 GPa reported by B&M require an additional high T phase, α', which has been suggested to be bcc. The new α' phase requires another t.p. near 190 GPa, which implies that the inner core is made largely of bcc iron. I suggest a Tm of about 6500°K for pure iron at the inner core-outer core boundary pressure. The Tm of the inner core itself will be affected by possible inner core impurities and by outer core impurities of larger concentration. To paraphrase Birch, 5700°K for the central temperature may have some standing as an upper limit.

Melting of the Fe [sbnd]FeO and the Fe [sbnd]FeS systems at high pressure: Constraints on core temperatures

Melting temperatures of FeO, FeS and FeS 2 have been accurately determined in a hydrostatic, inert pressure environment up to about 0.5 Mbar using a new yttrium-lithium-fluoride (YLF) heating laser. The melting curve for FeO is in perfect agreement with data obtained from multi-anvil experiments at 160 kbar [1], but is in stark disagreement with previous laser heating experiments [2]. Preliminary measurements show strong melting depression on mixtures of Fe and FeS, whereas mixtures of Fe and FeO were observed to melt close to the melting curve of iron. The Kraut-Kennedy melting relationship [3], in which the melting temperature is a linear function of volume, is successfully tested in this study for Li, Na, K, Fe, FeS, FeS 2 and FeO, to compressions up to > 30%. At 1.36 Mbar (core-mantle boundary, CMB) FeO, Fe, and FeS are estimated to melt at 3670, 3260 and 3060 (± 100) K respectively. Assuming outer core compositions with about 60% Fe and about 40% FeO or FeS, and a solid solution system, the melting temperature at the CMB, on the core side, would be 3300 K (± 200 K), compared to a temperature at the bottom of the mantle of 2650 ± 100 K. If these systems exhibit eutectic behaviour, the melting gradient through the outer core would have to be substantially higher than the adiabatic gradient in order to maintain a thermal boundary at the CMB. The present melting data, and experimental constraints on the adiabatic gradient in the outer core suggest a temperature at the inner core-outer core boundary of nearly 4200 K.

Motions of the inner core and mantle coupled via mutual gravitation: regular precessional modes

Abstract According to a model of the Earth's interior where the inner core symmetry axis is allowed to deviate from the mantle symmetry axis, motions of the inner core and of the mantle are coupled predominantly via a mutual gravitational torque. Solutions corresponding to regular precession have been studied in detail in this paper in order to produce predictions that may, in principle, be observationally tested. In particular, the Chandler wobble frequency is expected to be split by the presence of the inner core, giving rise to two frequencies on either side. The inner core is found to exhibit a differential rotation at the inner core surface of the order of 1 m s −1 , which corresponds to a period of ∼ 90 days. According to conventional wisdom, which assumes that the inner core co-rotates passively with the rest of the Earth, this value represents an unacceptably fast shear at the inner core-outer core boundary. These two predictions are provisional, however, in the sense that several refinements alluded to in this paper are yet to be undertaken.

The Melting Curve of Iron to 250 Gigapascals: A Constraint on the Temperature at Earth's Center

The melting curve of iron, the primary constituent of Earth's core, has been measured to pressures of 250 gigapascals with a combination of static and dynamic techniques. The melting temperature of iron at the pressure of the core-mantle boundary (136 gigapascals) is 4800 +/- 200 K. whereas at the inner core-outer core boundary (330 gigapascals), it is 7600 +/- 500 K. Corrected for melting point depression resulting from the presence of impurities, a melting temperature for iron-rich alloy of 6600 K at the inner core-outer core boundary and a maximum temperature of 6900 K at Earth's center are inferred. This latter value is the first experimental upper bound on the temperature at Earth's center, and these results imply that the temperature of the lower mantle is significantly less than that of the outer core.

The melting of iron up to 200 kbar

The effect of pressure on the melting temperature of iron has been measured by passing current through a very fine wire of pure iron held under pressure in a diamond anvil pressure cell. The temperature was measured by optical pyrometry, and the pressure was calculated from the lattice parameters of iron at room temperature after being heat-treated. On the basis of recent work by Strong et al. on measuring the δ-γ-liquid triple point and the initial slope between γ and liquid iron, we have calculated the melting temperature for γ iron to about 200 kbar. A third-order polynomial equation fitted to our data yields the following equation: Tm = 1718 + 3.85(P − 52) − 1.95×10−2(P − 52)2 + 6.24×10−5(P − 52)3, where Tm is the melting temperature in degrees Celsius and P is the pressure in kilobars. When the linear relationship of Tm-ΔV/V0 proposed by Kraut and Kennedy (1966) was used, the extrapolation of the present data to the inner core-outer core boundary, 3.3 Mbar, yields temperatures between 3460° and 3870°C if the inner core consists of pure iron with the γ phase.

Melting of Iron

Summary A theoretical melting curve for iron is determined in the pressure range of the Earth's core by a relation derived from the Ross-Lindemann melting criterium. On this basis the melting point of pure iron is estimated to be about 4800°C at the mantle-core boundary, and 6600°C at the inner core-outer core boundary with a melting point gradient of about 0.8 deg/km.

Earth Structure from Free Oscillations and Travel Times

An extensive set of reliable gross Earth data has been inverted to obtain a new estimate of the radial variations of seismic velocities and density in the Earth. The basic data set includes the observed mass and moment of inertia, the average periods of free oscillation (taken mainly from the Dziewonski-Gilbert study), and five new sets of differential travel-time data. The differential travel-time data consists of the times of PcP-P and ScS-S, which contain information about mantle structure, and the times of P′_(AB) - P′_(DF) and P′_(BC)-P′_(DF) which are sensitive to core structure. A simple but realistic starting model was constructed using a number of physical assumptions, such as requiring the Adams-Williamson relation to hold in the lower mantle and core. The data were inverted using an iterative linear estimation algorithm. By using baseline-insensitive differential travel times and averaged eigenperiods, a considerable improvement in both the quality of the fit and the resolving power of the data set has been realized. The spheroidal and toroidal data are fit on the average to 0·04 and 0·08 per cent, respectively. The final model, designated model B1, also agrees with Rayleigh and Love wave phase and group velocity data. The ray-theoretical travel times of P waves computed from model B1 are about 0·8s later than the 1968 Seismological Tables with residuals decreasing with distance, in agreement with Cleary & Hales and other recent studies. The computed PcP, PKP, and PKiKP times are generally within 0·5 s of the times obtained in recent studies. The travel times of S computed from B1 are 5–10 s later than the Jeffreys-Sullen Tables in the distance range 30° to 95°, with residuals increasing with distance. These S times are in general agreement with the more recent data of Kogan, Ibrahim & Nuttli, Lehmann, Cleary, and Bolt et al. Model B1 is characterized by an upper mantle with a high, 4·8 km s^(−1), S_n velocity and a normal, 3·33 g cm^(−3), density. A low-velocity zone for S is required by the data, but a possible low-velocity zone for compressional waves cannot be resolved by the basic data set. The upper mantle transition zone contains two first-order discontinuities at depths of 420 km and 671 km. Between these discontinuities the shear velocity decreases with depth. The radius of the core, fixed by PcP-P times and previous mode inversions, is 3485 km, and the radius of the inner core-outer core boundary is 1215 km. There are no other first-order discontinuities in the core model. The shear velocity in the inner core is about 3·5 km s^(−1).

The Melting Relations of Iron, and Temperatures in the Earth's Core

Thermodynamic data on the phases of iron are assembled in the form of speculative projections on the temperature-volume plane. Following a proposal by Kraut and Kennedy, the melting curves, for each phase, are assumed to be straight lines in this representation. As the position of the triple point, gamma-epsilon-liquid, is unknown, two hypothetical locations are considered: (1) at about 4 Mb, (2) at about 1 Mb. In the former case, the gamma phase is in equilibrium with the liquid at core pressures, in the latter, the epsilon phase. Nothing is known directly about the slopes of these melting curves, but the gamma melting temperatures are estimated to lie some 700° above the projection given by Higgins and Kennedy, with epsilon melting temperatures still higher. The relation of the isentropes of the liquid to these melting curves is also unknown, but ‘conventional’ isentropes, originating on the melting curve, may be found which lie in the liquid field at the pressures of the outer core. Application to the Earth is complicated by the requirement for a light alloying element in the outer core; if the alloying element is silicon, a proportion of about 15 per cent by weight accounts satisfactorily for the density-velocity relation. The phase relations may be considerably modified by the presence of so much silicon: it is conjectured that the gamma phase is suppressed or confined to low pressures, that the epsilon phase will be the stable solid phase at core pressures, and that the isentrope originating at the melting temperature of the inner core-outer core boundary lies entirely in the liquid phase.

The adiabatic gradient and the melting point gradient in the core of the Earth

The melting gradient and the adiabatic gradient throughout the core of the earth are compared. The temperature of melting of iron at pressures equivalent to the inner core-outer core boundary is estimated to be circa 4250°C with a melting point gradient of approximately 500° through the outer core. The adiabatic gradient through the outer core is estimated to be circa 1250°; therefore, for the outer core to be liquid, its temperature must be considerably above the temperature in adiabatic equilibrium with the inner-outer core boundary. The temperature distribution throughout the outer core is deduced to follow a melting point curve. This temperature distribution should provide a substantial inhibition to radial components of convection in the outer core.