Preliminary Reference Earth Model Research Articles

Study on the structure, elasticity, and thermal conductivity of orthocarbonate Sr2CO4

Orthocarbonate Sr2CO4 is a recently discovered Sr-carbonate that plays a crucial role in understanding the global long-term carbon cycle. In this work, the structure, equation of state, elasticity, and thermal conductivity of Sr2CO4 were studied by first-principles calculations. The results show that the surfaces of the SrO9 and SrO11 polyhedrons, which make up Sr2CO4, are composed of triangles and quadrangles. By comparison with other alkaline earth metal orthocarbonates, SrCO3 polymorphs, and the Preliminary Reference Earth Model (PREM), Sr2CO4 is found to be a carbonate with high density, low wave velocity, low anisotropy, and low thermal conductivity in the entire Earth’s mantle. This study may help to understand the high-pressure behavior of alkaline earth metal orthocarbonates in the Earth’s interior.

Equation of state and thermodynamic properties of liquid Fe-O in the Earth’s outer core

Equation of state (EoS) plays a crucial role in the prediction of the composition of the outer core. Here, we calculated pressure (P)-volume (V)-temperature (T) data of liquid iron-oxygen alloys (Fe-X wt.% O, X = 0, 2.8, 6.1, and 9.9) under the outer core conditions (∼136–330 GPa, 4000–6000 K) by first-principles molecular dynamics simulations. We established an EoS for liquid Fe-O alloys with parameters including P, T, V, and O concentrations. Consequently, thermodynamic properties of liquid Fe-O alloys such as density (ρ), thermal expansion coefficient, isothermal and adiabatic bulk modulus, and sound velocity (VP) are calculated. To constrain the O content, we predicted the ρ-P and VP-P profiles along the geotherm and compared them with data from the Preliminary Reference Earth Model (PREM). We conclude that the adiabatic T profile as a function of depth affects the prediction of O content dramatically. With several anchored TICB, the composition of Fe-6.1 wt% O matches the PREM data with an acceptable range of error. But strictly speaking, the distribution in the outer core is probably uneven. In such case, we state that the O content in the outer core cannot be higher than approximately 6.1 wt%.

Analysis of the seismicity related to the tidal stress prior to the M w7.8 Kahramanmaras, Türkiye earthquake

Based on the preliminary reference Earth model, we calculated the temporal variation of tidal shear and normal stresses on the focal fault plane of the M w7.8 Kahramanmaras, Türkiye earthquake. For earthquakes (M ≥ 4.0) occurring along and around the East Anatolian fault zone (EAFZ) and the Dead Sea fault zone (DSFZ) between January 2002 and December 2022, we analysed tidal stress-related seismicity from two viewpoints: occurrence time and seismic strain. Seismicity was found to be significantly correlated with semi-diurnal tidal shear stress (TSS) prior to the Kahramanmaras M w7.8 main shock. An area with significant correlation was ∼140 km northeast of the epicentre. For three and more years prior to the Kahramanmaras event, the temporal rate of seismic strain increased during periods of increasing TSS and did not change much during periods of decreasing TSS. From the above results, the increase in TSS may have facilitated the occurrence of earthquakes in the years preceding the Kahramanmaras earthquake. The reason for these tide-triggered earthquakes may be that the seismic region is loaded to a critical state. This observation may shed light on the seismogenic processes that led to the Kahramanmaras earthquake and its precursors.

Effects of Andrade and Burgers rheologies on glacial isostatic adjustment modeling in Antarctica

Variations in ice mass deform the Earth and modify its gravity field, a process known as Glacial Isostatic Adjustment (GIA). GIA in Antarctica remains poorly constrained due to the cumulative effect of past and present ice-mass changes, the unknown history of the past ice-mass change, and the uncertainties on the mechanical properties of the Earth. This paper investigates the effect of using Andrade and Burgers viscoelastic rheologies, rather than the commonly used Maxwell rheology, to model GIA-induced deformation in Antarctica. The Love number and Green's function formalism are used to compute the radial surface displacements and the gravity changes induced by the past and present ice-mass changes. We consider an Earth model whose elastic properties and radial structure are averaged from the Preliminary Reference Earth Model and two viscosity profiles to account for the recently published results on the present ice-mass changes. Using the three rheological laws affects the temporal response of the Earth differently, leading to smaller discrepancies than those induced by the two viscosity structures. The differences are the largest between Maxwell and Burgers rheologies during the 100–1000 years following the beginning of the surface-mass change. Results show that using the Andrade and Burgers rheologies allows the Earth to respond on decennial to centennial time scales, up to 10 m more than Maxwell. Considering only the recent ice-mass changes, the deformation rates derived from Burgers and Andrade rheologies are several times larger than those estimated by Maxwell rheology.

PREM-like velocity structure in the outermost core from global SKS and ScS waveform modeling

Seismic structure in the Earth's outermost core is important for our understanding of thermochemical stratification in the outer core, and is yet heavily debated. Here we study the compressional velocity structure in the Earth's outermost core based on waveform modeling of a unique untapped SKS and ScS dataset near bifurcation distances, collected from global seismic arrays for earthquakes occurring from 2000 to 2020. Using the SKS-ScS array dataset minimizes the effects of many uncertainties associated with earthquake source parameters and seismic heterogeneities in the mantle, and affords an opportunity to study and assess the seismic structure in the outermost core. We study outer core structure by testing two end-member models: 1) the D″ model that attributes any anomalous seismic observations to the effects of the lowermost mantle structure and is paired with a PREM (the Preliminary Reference Earth's Model) structure in the outermost core and 2) the outer core model that is paired with either a PREM or a tomographic structure in the lowermost mantle and attributes other unexplained seismic signals to an outer core structure. The results of the outer core models present unreasonable large lateral variations of >3.1% in the outermost core, while the inferred D″ models exhibit large-scale seismic anomalies that are consistent with the tomographic models and small-scale anomalies that are confirmed by further analysis of the seismic array data. Our analyses suggest a PREM-like seismic velocity structure and a lack of strong thermochemical anomalies in the topmost ∼200 km of the outer core, placing bounds on possible thermal and compositional conditions in the region of the Earth's outermost core. Our study also identifies the existence of small-scale seismic anomalies and sharp velocity variations in the lowermost mantle beneath the south coast of Alaska, northwestern Atlantic and the middle of Central America.

An estimate of absolute shear-wave speed in the Earth’s inner core

Observations of seismic body waves that traverse the Earth’s inner core (IC) as shear (J) waves are critical for understanding the IC shear properties, advancing our knowledge of the Earth’s internal structure and evolution. Here, we present several seismological observations of J phases detected in the earthquake late-coda correlation wavefield at periods of 15–50 s, notably via the correlation feature I-J, found to be independent of the Earth reference velocity model. Because I-J is unaffected by compressional wave speeds of the Earth’s inner core, outer core, and mantle, it represents an autonomous class of seismological measurements to benchmark the inner core properties. We estimate the absolute shear-wave speed in the IC to be 3.39 ± 0.02 km/s near the top and 3.54 ± 0.02 km/s in the center, lower than recently reported values. This is a 3.4 ± 0.5% reduction from the Preliminary Reference Earth Model (PREM), suggesting a less rigid IC than previously estimated from the normal mode data. Such a low shear-wave speed requires re-evaluating IC composition, including the abundance of light elements, the atomic properties and stable crystallographic phase of iron, and the IC solidification process.

Oxygen-Driven Enhancement of the Electron Correlation in Hexagonal Iron at Earth's Inner Core Conditions.

Earth's inner core (IC) consists of mainly iron with some light elements. Understanding its structure and related physical properties has been elusive as a result of its required extremely high pressure and temperature conditions. The phase of iron, elastic anisotropy, and density-velocity deficit at the IC have long been questions of great interest. Here, we find that the electron correlation effect is enhanced by oxygen and modifies several important features, including the stability of iron oxides. Oxygen atoms energetically stabilize hexagonal-structured iron at IC conditions and induce elastic anisotropy. Electrical resistivity is much enhanced in comparison to pure hexagonal close-packed (hcp) iron as a result of the enhanced electron correlation effect, supporting the conventional thermal convection model. Moreover, our calculated seismic velocity shows a quantitative match with geologically observed preliminary reference Earth model (PREM) data. We suggest that oxygen is the essential light element to understand and model Earth's IC.

Self-diffusion coefficient and sound velocity of Fe-Ni-O fluid: Implications for the stratification of Earth's outer core

It is experimentally reported that the stratified layer atop Earth's outer core is hundreds of kilometers thick with a maximum sound velocity reduction of 0.3% relative to the preliminary reference Earth model. However, why the sound velocity atop the outer core is reduced remains theoretically unclear. In this paper, the Ni and vital light O in the outer core were both considered to have implications for the stratification of Earth's core, including the stratification thickness and the sound velocity profile. Ab initio molecular dynamics simulations were performed on the Fe-Ni-O fluid under the conditions of Earth's outer core, and the self-diffusion coefficients and ion-ion dynamic structure factors were calculated. The self-diffusion coefficient of O was calculated to be (19.56 ± 0.83) × 10−9 m2s−1 at the core-mantle boundary. Combining the diffusion equation with the time evolution of the O self-diffusion coefficient, the calculated stratification thickness at present is 194.7 km. The calculated ion-ion dynamic structural factors indicate that the sound velocity in the outmost outer core near the stratified layer is 7.86 km/s, which is lower than the preliminary reference Earth model values (∼8.05 km/s). These results show that Fe-Ni-O liquid atop the outer core featuring an appropriate thickness and a reduced sound velocity, thereby shedding light on the dynamic behavior of Earth's core.

Magnetism and equation of states of fcc FeHx at high pressure

Abstract Hydrogen is a strong candidate for light alloying elements in terrestrial cores. Previous first-principles studies on non-stoichiometric hexagonal close-packed (hcp) and double hexagonal close-packed (dhcp) FeHx predicted a discontinuous volume expansion across the magnetic phase transition from non-magnetic (NM) or antiferromagnetic (AFM) to ferromagnetic (FM) state with increasing the hydrogen content, x at 0 K. However, previous high-pressure and -temperature neutron diffraction experiments on face-centered cubic (fcc) FeHx did not reveal such nonlinearity. The discrepancy between theory and experiment may be due to differences in the crystal structure, magnetism, or temperature. In this study, we computed the equation of states for fcc FeHx using the Korringa-Kohn-Rostoker method combined with the coherent potential approximation (KKR-CPA). In addition to the four types of ground-state magnetism (FM, AFM-I, AFM-II, and NM), we calculated the local magnetic disorder (LMD) state, which approximates the paramagnetic (PM) state with local spin moment above the Curie temperature. Our results show that even though FM, AFM-I, AFM-II, and NM calculations predict a discontinuity in the volume at 0 K, the volume becomes continuous above the Curie temperature, consistent with the previous neutron experiment. From the enthalpy comparison at 0 K, FM fcc FeH (x = 1) becomes the NM state above ~48 GPa. The magnetic transition pressure decreases with decreasing hydrogen content. Therefore, below the magnetic transition pressure, local spin moments affect the density and elastic wave velocity of fcc FeHx, which may be important for small terrestrial bodies such as Mercury and Ganymede. By contrast, at the Earth’s core pressure above 135 GPa, fcc FeHx becomes NM. Thus, we calculated the density and bulk sound velocity as a function of pressure at 0 K for NM fcc FeHx. The density at 360 GPa decreases with increasing hydrogen content, with FeH0.5 best matching the preliminary reference Earth model (PREM) of the inner core. Since the density decreases with increasing temperature, this value constrains the upper limit of hydrogen content, assuming that the inner core is fcc FeHx. On the other hand, the bulk sound velocity at 360 GPa increases with increasing hydrogen content, with FeH0.3 best matching the PREM, which may give a lower bound. Assuming that Poisson’s ratio of the FeHx alloy is equal to that of the inner core, we examined the effects of temperature on density and bulk sound velocity. The results suggest that the fcc FeHx alloy alone cannot explain the inner core density and bulk sound velocity simultaneously unless the temperature is extremely low (T < 4000 K).

Sound velocity of hexagonal close-packed iron to the Earth’s inner core pressure

Here we determine the compressional and shear wave velocities (vp and vs) of hexagonal close-packed iron, a candidate for the main constituent of the Earth’s inner core, to pressures above 300 gigapascals using a newly designed diamond anvil cell and inelastic X-ray scattering combined with X-ray diffraction. The present results reveal that the vp and vs of the Preliminary reference Earth model (PREM) inner core are 4(±2)% and 36(±17)% slower than those of the pure iron, respectively at the centre of the core. The density and sound velocity of the PREM inner core can be explained by addition of 3(±1) wt% silicon and 3(±2) wt% sulphur to iron‒5 wt% nickel alloy. Our suggested inner core composition is consistent with the existing outer core model with oxygen, as the growth of the inner core may have created a secular enrichment of the element in the outer core.

Sound Velocity of (Mg0.91Fe0.09)2SiO4 Wadsleyite and Its Implications to Water Distribution in Mantle Transition Zone

AbstractThe current elasticities of major mantle transition zone minerals and their hydrous counterparts, such as wadsleyite, ringwoodite, and majorite garnet, have the velocity gradients several times lower than those of the Earth models. Here we use ultrasonic interferometry technique to measure the sound velocities of wadsleyite (Mg0.91Fe0.09)2SiO4 at pressures up to 14 GPa and room temperature. Compared with previous studies, we have obtained possibly the highest ∂VP/P and ∂KS/P value at transition zone pressure, which are still noticeably lower than the Earth models, such as the preliminary reference Earth model, ak135, iasp91, etc. The results indicate that the VP contrast of “dry” olivine‐wadsleyite transition at 410 km is higher than previous thought, while that of wadsleyite‐ringwoodite transition at 520 km is noticeably low. Using the current and previous data on “dry” and hydrous wadsleyite a water “gradient” model at upper mantle transition zone were proposed and discussed.

CCMOC: A new view of the Earth's outer core through the global coda correlation wavefield

Increasing seismic evidence has accumulated, suggesting that the Earth's outer core consists of distinct zones of low P-wave velocities in the top and bottom regions relative to the Preliminary Reference Earth Model (PREM). Seismically detected low velocities in the outer core could be linked with the stratification, essential for understanding the geodynamo and thermochemical evolution of the liquid core. However, a consistent globally-averaged radial structure of the outer core has not been obtained due to the incomplete coverage of sampling body waves. To remedy this problem, we explore the seismic structure of Earth's outer core by employing a new theoretical and observational concept termed coda correlation wavefield. We construct the global correlogram in the 15–50 s period range by stacking cross-correlations of the long-duration coda waves from the selected ten large earthquakes. We then assemble a dataset of prominent correlation features from the global correlogram that are sensitive to the outer core. The waveforms of these features are fit by computing synthetic correlograms through various outer core models. The obtained optimal model displays P-wave velocities in both the outer core's top and bottom, consistent with Coda Correlation Reference Earth Model (CCREM) and reduced relative to PREM. The P-wave velocity is ∼1% lower in the core's top than that in PREM, and the slow anomaly gradually approaches zero at about 800 km below the core-mantle boundary. The low seismic velocities in the top of the outer core could likely imply the formation of a thermal and/or compositional stratification.

The electronic and mechanical properties of Fe16N2 up to 150 GPa: First-principles calculation

The electronic and mechanical properties of a tetragonal Fe–N binary compound have been investigated under extreme pressure using density functional theory with the generalized gradient approximation. The results of formation enthalpy, phonon dispersion, and elastic stability criterion show that an Fe–N binary compound is stable up to 150 GPa. On the one hand, the electronic properties of Fe16N2 have been demonstrated by the band structures and density of states. On the other hand, the elastic constants, shear, and compressional modulus derived from elastic constants impact on compressional velocity (Vp) greatly. The shear modulus of a binary compound with N is about 14.7% lower than the data of pure Fe. The density and Vp of an Fe–N binary compound, which are closer with the value of a preliminary reference earth model (PREM), are lower than the pure Fe's, especially in the part of higher pressure. In addition, the density of an Fe–N binary compound is about 5.3% lower than the Fe's. The effect of the temperature is not considered in this work, but the varying tendency indicates that the light element N incorporating in pure Fe is helpful for building an earth's core model.

Contribution of GRACE Satellite Mission to the Determination of Orthometric/Normal Heights Corrected for Their Dynamics—A Case Study of Poland

Physical heights were traditionally determined without considering the dynamic processes of the Earth induced from temporal mass variations. The Gravity Recovery and Climate Experiment (GRACE) mission provided valuable data that allow the estimation of geoid/quasigeoid height changes and vertical deformations of the Earth’s surface induced from temporal mass loading, and thereby temporal variations of physical heights. The objective of this investigation is to discuss the determination of orthometric/normal heights considering mass transports within the Earth’s system. An approach to determine such heights was proposed. First, temporal variations of orthometric/normal heights (ΔH/ΔH*) were determined using the release 6 GRACE-based Global Geopotential Models together with load Love numbers obtained from the preliminary reference Earth model. Then, those variations were modelled and predicted using the seasonal decomposition (SD) method. The proposed approach was tested on the territory of Poland. The main results obtained reveal that ΔH/ΔH* over the area investigated are at the level of a couple of centimetres and that they can be modelled and predicted with a millimetre accuracy using the SD method. Orthometric/normal heights corrected for their dynamics can be determined by combining modelled ΔH/ΔH* with orthometric/normal heights referred to a specific reference epoch.

Analysis of seismic strain release related to the tidal stress preceding the 2008 Wenchuan earthquake

Abstract. Tidal stresses could load or unload focal media and trigger small to moderate earthquakes in and around the focal region before a large or great earthquake. Based on the preliminary reference Earth model, we calculated the time series of tidal Coulomb failure stress (TCFS) acting on the focal fault plane of the Wenchuan earthquake. For earthquakes (2.5≤ML≤4.0) that occurred in and around the focal region from January 1990 to April 2008, we calculated the time rate of TCFS, ΔTCFS, at the occurrence time of each earthquake. These earthquakes were divided into two categories on the basis of the signs of ΔTCFS: one is positive earthquakes (PEQs) occurring at times of ΔTCFS > 0 and the other negative earthquakes (NEQs) occurring at times of ΔTCFS < 0. First, we obtained cumulative seismic strain release (CSSR) curves of NEQs and PEQs and found that the two curves nearly overlapped prior to September 2004 and then began to separate increasingly with time. We used a parameter Rp, the proportion of seismic strain release of PEQs, to investigate the effect of TCFS on earthquake occurrence and found that Rp was significantly higher than 0.5 about 6 months before the Wenchuan event at a 99 % confidence level, indicating a significant correlation between earthquake occurrence and increasing TCFS. Furthermore, we calculated the slope k (time rate) of the CSSR curve vs. time for PEQs and NEQs separately. It was observed in the pre-event period that the seismic strain release accelerated when TCFS increased but decelerated when TCFS decreased. The difference in the time rate of seismic strain release between PEQs and NEQs was quantified using Rk, the ratio of k for PEQs to that for NEQs. We discovered stable Rk values (around 1.0) until they began to rise rapidly with time in early 2005, reaching their highest value of 2.7 just before the Wenchuan event. Rk could reveal the promoting and inhibiting effects of tidal stress on seismic strain release. When kp increases alone or kn decreases alone, Rk will increase. Thus, an increase in Rk corresponds to a promoting effect during times of increasing TCFS and an inhibiting one during that of decreasing TCFS. Both effects were observed in the focal region prior to the Wenchuan mainshock. The b value in the Gutenberg–Richter relationship decreases as the tectonic stress in the crust increases. We also calculated the temporal evolution of the b value in the study region. It was observed that after 2.5 years of increasing tectonic stress, the focal region became unstable, and the tidal stress began to take effect. The effects of the tidal stress were gradually enhanced as the tectonic stress increased further. The increase in the tidal Coulomb failure stress may have aided the occurrence of earthquakes, whereas the decrease had the opposite effect. This observation may shed light on the seismogenic processes that led to the Wenchuan earthquake and its precursors.

Sound Velocity Measurements of B2‐Fe‐Ni‐Si Alloy Under High Pressure by Inelastic X‐Ray Scattering: Implications for the Composition of Earth's Core

AbstractElastic properties of B2‐Fe0.67Ni0.06Si0.27 (15 wt.% Si) alloy have been investigated by combined high‐resolution inelastic X‐ray scattering and powder X‐ray diffraction in diamond anvil cells up to 100 GPa at room temperature. Densities (ρ), compressional (VP) and shear (VS) wave velocities were extrapolated to inner core conditions to enable comparison with the preliminary reference Earth model. The modeled aggregate compressional and shear wave velocities and densities of the two‐phase mixture of B2‐Fe0.67Ni0.06Si0.27 and hcp‐Fe‐Ni are consistent with inner core PREM values of VP, VS, and ρ based on a linear mixing model with 30(5) vol % B2‐Fe0.67Ni0.06Si0.27 and 70(5) vol % hcp Fe‐Ni, which corresponds to ∼3–5 wt.% Si and ∼5–12 wt.% Ni.

The Accuracy Assessment of the PREM and AK135-F Radial Density Models

The Earth’s synthetic density and gravitational models can be used to validate numerical methods for global (or large-scale) gravimetric forward and inverse modelling formulated either in the spatial or spectral domains. The Preliminary Reference Earth Model (PREM) density parameters can be adopted as a 1-D reference density model and further refined using more detailed 2-D or 3-D crust and mantle density models. Alternatively, the AK135-F density parameters can be used for this purpose. In this study, we investigate options for a refinement of the Earth’s synthetic density model by assessing the accuracy of available 1-D density models, specifically the PREM and AK135-F radial density parameters. First, we use density parameters from both models to estimate the Earth’s total mass and compare these estimates with published results. We then estimate the Earth’s gravity field parameters, particularly the geoidal geopotential number W0 and the mean gravitational attraction and compare them with published values. According to our results, the Earth’s total mass from the two models (the PREM and the AK135-F) differ less than 0.02% and 0.01%, respectively, when compared with the value adopted by the International Astronomical Union (IAU). The geoidal geopotential values of the two models differ from the value adopted by the IAU by less than 0.1% and 0.04%, respectively. The values of the mean gravitational attraction of the two models differ less than 0.02% and 0.08%, respectively, when compared with the value obtained from the geocentric gravitational constant and the Earth’s mean radius. These numerical findings ascertain that the PREM and AK135-F density parameters are suitable for defining a 1-D reference density model.

Internal structures and magnetic moments of rocky planets

Context. For a planet to be considered habitable on its surface, it is an important advantage for it to have a magnetic field that protects its atmosphere from stellar winds as well as cosmic rays. The magnetic protection of potentially habitable planets plays a key role in determining the chances of detecting atmospheric biosignatures. In making an estimate of a planet’s magnetic field, its internal structure must first be known. Aims. This study proposes to use the Preliminary Reference Earth Model (PREM) internal structure as the base of a numerical model, as it is considered the best available option for estimating the internal structure of rocky exoplanets. With this model, we estimate the magnetic properties of dry and water-rich Earth-like and Super-Earth-like planets and we apply it to the first 176 planets of this kind confirmed by the Transiting Exoplanet Survey Satellite exoplanet mission (TESS). Methods. Using PREM as a reference, we estimated the internal structure of dry and water-rich rocky planets. This model provides an estimation of the average density and core size of the planet, which are the key ingredients for estimating its magnetic moment, depending on whether it is tidally locked or not. Our model estimates the thermodynamic variables as a function of pressure and including saltwater as a component of water-rich exoplanets. In addition, we did not use the perfect layer differentiation approximation. We validated our model based on the selection of planets and satellites in the Solar System with similar characteristics. Results. Using our model, we estimated the internal structure and magnetic moment of selected dry and water-rich rocky planets and satellites in the Solar system. The differences with the observed values in the internal structure characteristics, mass, average density, moment of inertia factor, and local Rossby number are remarkably low or even negligible. The estimated magnetic moments are also very similar to the observed ones. We applied the model to the first dry and water-rich rocky planets confirmed by TESS, 176 in total, and we find, from an astrobiological perspective, that TOI-700 d and TOI-2257 b are the most interesting examples, as they are located in the habitable zone. However, we note that their magnetic moments are only about 0.01 of the Earth’s magnetic moment.

The influence of nitrogen proportion on the mechanical property of Fe–Ni alloy at extreme pressure

Proportions of doping elements is one of the important factors influencing the physical properties of the alloy. In this work, ab initio electronic calculations, applying density-functional theory, was used to investigate the mechanical properties of Fe–Ni–N alloys under the extreme pressure. Firstly, the stability of Fe11Ni3N2, Fe10Ni3N3, Fe9Ni3N4 and Fe8Ni3N5 alloys were estimated using binding energy and elastic constants. Fe11Ni3N2 and Fe9Ni3N4 were both stable basing on the Born criterion. Secondly, the density of Fe11Ni3N2 and Fe9Ni3N4 were smaller than that of Fe and closed to the one of preliminary reference earth model(PREM). The elastic properties of Fe11Ni3N2 and Fe9Ni3N4 which are stable were analyzed under pressure 130–360 GPa. The higher the proportion of N in ferroalloys, the larger elastic modulus and the faster the shear velocity (Vs).

Iron‐Carbon Alloy Under Shock Compression: Implications for the Carbon Concentration in Earth’s Inner Core

AbstractCarbon has been proposed to be a potential light element in the Earth’s solid inner core. However, its presence and concentration in the core remain limited constrained. In this study, we measured the equation of state of an iron‐carbon alloy with ∼1.5 wt.% (∼6.64 at.%) carbon up to ∼185 GPa and ∼3,750 K via shock compression. The Hugoniot equation of state of the Fe‐1.5wt.%C alloy was determined to be Us (km/s) = 3.94 (0.15) + 1.62 (0.08) Up with an initial density of 7.77 (0.03) g/cm3, where Us and Up are the shock wave velocity and particle velocity, respectively. Hugoniot data combined with the Mie‐Grüneisen equation of state allow us to build the thermal equations of state of the Fe‐C alloy at high pressure‐temperature (P‐T) conditions. Investigations on the pressure‐density relation of Fe‐C alloys by the shock experiments and synchrotron X‐ray diffraction measurements by Pamato et al. (2020), https://doi.org/10.1029/2020jb020159 have indicated that carbon should occupy interstitial sites of iron lattice at high P‐T conditions. The thermal equation of state of the Fe‐1.5wt.%C alloy provided here shows that Fe‐1.5wt.%C is ∼1.65% denser than the inner core under conditions relevant to the inner‐core boundary. This study indicates that iron alloyed with an upper bound of ∼2.2 (0.3) wt.% (∼10.7 [1.6] at.%) carbon may match with the Preliminary Reference Earth Model (PREM) in the Earth’s inner core. Thus, interstitial carbon in iron helps to explain the observed density deficit of the inner core, although other light elements are also expected.