Depth-dependent anisotropy in the Earth’s inner core linked to chemical stratification

Domain: earth_science
Published: 2025-12-08
Editorial outcome: major_revision

Abstract
Seismic anisotropy in the Earth’s inner core (IC), including the heterogeneous, depth-dependent anisotropy structure, is a well-documented yet poorly understood feature plausibly related to the alignment of iron alloy crystals. Here, we report the effect of silicon and carbon on the plastic deformation of hexagonal close-packed (hcp) iron using radial X-ray diffraction at pressures up to 128 GPa and temperatures up to 1100 K. Our results reveal a low compressional wave anisotropy (~2%) in the Fe-Si-C alloy, consistent with the seismic anisotropy observed in the outer regions of the IC. These findings, together with the higher anisotropy exhibited by pure hcp-Fe, suggest that the depth-dependent elastic anisotropy of the IC may originate from chemical stratification, i.e., radial gradients in silicon and carbon concentrations, during crystallization.

Introduction
Anisotropy in compressional sound wave velocities is a well-established feature of the Earth’s inner core (e.g., 1). Basic anisotropic models displaying cylindrical symmetry show that compressional sound waves travel around 3–4% faster parallel to the Earth’s rotation axis compared to their velocity in the equatorial direction 1. Moreover, there is evidence for more complex and intricate anisotropic patterns within the inner core 2, including relatively isotropic outer layers displaying compressional wave anisotropy of around 2% or less 3,4 and a central region exhibiting high anisotropy of up to 4–6% 1,3. The origin of the depth-dependent anisotropy within the Earth’s inner core remains, however, unclear.

Possible origins for the observed elastic anisotropy include either shape-preferred orientation (SPO), where the core-forming polycrystalline material exhibits a microstructure elongated in one or two directions, or lattice-preferred orientations (LPO), where the polycrystalline material has a preferred crystallographic alignment (texture) 5. The presence of liquid inclusions within the solid material may result in the development of SPO 6. However, the likelihood of that is low, as the liquid inclusions are likely to be extracted by compaction, effectively halting the development of SPO 7. LPO in the inner core is likely to result from solidification texturing or subsequent deformation 5,8. The deformation should occur predominantly through dislocation creep since diffusion creep is an unfavorable mechanism for deformation development at core conditions 9 and is unable to produce LPO. The driving mechanisms of the deformation may vary between thermal convection, preferential growth in the equatorial regions, or Joule heating, with the significance of the individual processes strongly dependent on the viscosity of core materials 5.

The Earth’s inner core is predominantly composed of iron alloyed with a small percentage of nickel that likely crystallizes in an hcp structure 10. In addition, up to 5–7% of light elements alloyed to Fe–Ni are required to explain the density deficit reported by seismic models (e.g., 11). Geochemical and cosmochemical constraints suggest silicon, carbon, oxygen, sulfur, and hydrogen as the most probable light elements, with several of them likely coexisting in the core 12. Recent computational and experimental studies indicate that silicon and carbon alloyed together with iron can satisfy the seismological constraints both in terms of core density and isotropic sound velocities 13,14. The alignment of hcp crystals in the inner core as a plausible origin for the observed anisotropy in the compressional wave velocities (V P) has been supported by the single-crystal elastic anisotropy (6–8%) theoretically predicted for hcp-Fe at core conditions 15,16 and its relatively low strength revealed by experimental studies (e.g., 17,18). Despite extensive research on the behavior of pure hcp-iron at high pressure regarding its strength (e.g., refs. 17,18), LPO (e.g., refs. 19–21), and sound velocity anisotropy of polycrystalline aggregate (e.g., refs. 19,22,23), the influence of alloying elements on these properties remains poorly constrained. Existing strength studies are limited to the effect of nickel 24 and silicon 25, both of which increase the yield strength of hcp–Fe 24,25, yet the combined effects of multiple light elements have not been explored. Furthermore, temperature-dependent strength measurements at high pressures remain scarce 25–27, and the impact of alloying elements on LPO and elastic anisotropy has yet to be determined.

Here, we investigate the combined effect of silicon and carbon on the deformation behavior of iron at pressures up to 128 GPa and temperatures up to 1100 K, using resistively heated diamond anvil cells (DACs) as a deformation apparatus coupled with in situ X-ray diffraction in radial geometry. We conducted deformation experiments on a polycrystalline iron-silicon-carbon alloy synthesized under high-pressure, high-temperature conditions, with a composition close to that proposed for the inner core by computational and experimental studies 13,14: 2 wt% Si and 0.4 wt% C (hereafter referred to as Fe–2Si–0.4C). We further employed Elasto-Visco-Plastic Self-Consistent (EVPSC) modeling to extrapolate the plastic properties of this alloy to the inner core conditions and compared results with the observed seismic characteristics of the Earth’s inner core.

Results
Strain and strength of Fe–Si–C alloy at extreme conditions
We collected X-ray diffraction patterns of Fe–2Si–0.4C alloy along two isotherms, at room temperature (300 K) up to 128 GPa, at 1100 ± 50 K up to 100 GPa, and along an isobar at 36 ± 3 GPa upon heating to 1100 K. Upon compression above 10 GPa, the starting body-centered cubic (bcc) structured Fe–2Si–0.4C sample begins to transform into the hcp phase, a transformation that is complete at ~27 GPa and 300 K (Supplementary Fig. 1a, b). Upon heating, the hcp phase partially transforms into a face-centered cubic (fcc) structure at 1013 K and 39 GPa. The fcc phase is present as a less abundant component, compared to the hcp phase, and completely disappears at ~55 GPa and 1100 K (Supplementary Fig. 1c, d). We used the unrolled X-ray diffraction patterns to determine the lattice strain parameters Q(hkl), which are a measure of the amplitude of the elastic deformation of a material (see “Methods” for details). For a valid comparison of averaged lattice strain parameters Q(hkl) along 300 K (Supplementary Table 1) and 1100 K (Supplementary Table 2) isotherms, only the lattice strains of (100), (002) and (103) lattice planes were used for averaging, since reflections from other lattice planes are shadowed by the reflections from Be gasket for the experiment at room temperature (Fig. 1a).

When only these three lattice strains are used for averaging, the Q(hkl) values at 1100 K and 300 K overlap within the error bars and remain approximately 0.007 until 60 GPa (Fig. 2a). Q(hkl) at 300 K reaches a value of ~0.008 at 128 GPa, indicating saturation of Q(hkl) at the onset of compression. Conversely, at 1100 K, Q(hkl) starts to decrease above 60 GPa. When considering other available lattice planes at 1100 K (i.e., (100), (002), (101), (102), (110) and (103)), the averaged lattice strain parameter Q(hkl) is lower than presented in Fig. 2a by 8±7%, although the overall trends remain the same. We observe the appearance of new reflections in the X-ray diffraction patterns that correspond to the formation of Fe3C (Fig. 1b). This observation is consistent with the results of Miozzi et al. (2022) 28 who reported the co-existence of Fe3C and hcp–Fe–Si–C alloy at high temperatures. We, thus, attribute the decrease of the Q(hkl) values above 60 GPa at 1100 K to the nucleation of Fe3C in the bulk Fe–2Si–0.4C. Carbon-free compositions, like pure Fe 17, Fe–Ni alloys 24 and Fe–5 wt% Si 25, display smaller Q(hkl) values compared to hcp–Fe–2Si–0.4C (Fig. 2a). Hence, the partial loss of carbon from the starting composition during heating likely causes the decrease in the averaged lattice strain parameter in the iron-silicon-carbon alloy.

The temperature effect on Q(hkl) is not well-constrained experimentally, and, thus, in most studies, ∂Q/∂T is simply assumed to be zero 17,24, providing only the upper bound for Q(hkl). We used our high-temperature data collected over the 36 ± 3 GPa isobar up to 1100 K (Supplementary Fig. 2, Supplementary Table 3) to better constrain ∂Q/∂T and obtained the value of −8.6(±2.2)·10−7 K−1 from a set of lattice planes, namely (100), (002), (101), (102), (110), (103) and (112). Brennan et al. (2021) 25 determined ∂Q/∂T to be −1.6(±0.4)·10−6 K−1 at 43–46 GPa and 300–1800 K from the Q(hkl) values of laser-heated Fe–Si alloys. However, their data are effectively divided into two clusters: one at 300 K and the other at 1400–1800 K (Fig. S1 in ref. 25), with a 1000 K gap. Moreover, laser heating is usually associated with larger radial temperature gradients in the sample, which could explain the discrepancies in the temperature dependence of Q(hkl).

We applied the formalism and assumptions described in ref. 17 to derive the yield strength of the sample, which is a measure of a material’s resistance to flow (see “Methods” for details). The yield strength of hcp–Fe–2Si–0.4C at 300 K increases with pressure, reaching 15 GPa at the pressure of 128 GPa (Fig. 2b). At 1100 K, the yield strength values are lower, reaching 8 GPa at the highest pressure of 100 GPa. Across all studied pressures, the yield strength of hcp–Fe–2Si–0.4C is higher than that of pure hcp–Fe, iron-silicon, and iron-nickel alloys (Fig. 2b). The primary compositional difference between our alloy and the Fe–Si alloys 25 is the presence of carbon in our samples. Therefore, we conclude that the addition of carbon significantly strengthens iron-silicon alloys.

Deformation mechanisms in iron alloys at extreme conditions
We further utilized the X-ray diffraction images to identify LPO in hcp–Fe–2Si–0.4C (see details in “Methods”). The initial sample had extremely weak LPO at ambient conditions (Supplementary Fig. 3). Upon compression at 300 K, we observed the onset of LPO development along the [0001] direction on the inverse pole figure (IPF) in hcp–Fe–2Si–0.4C at 18 GPa, i.e. right after the appearance of the hexagonal phase (Fig. 3a). Subsequent development of lattice-preferred orientation in hcp–Fe–2Si–0.4C leads to a redistribution of the most intense texture direction towards [1100], reaching approximately 8 multiples of random distribution (mrd) at 107 GPa (Fig. 3a) and further remains about the same. This redistribution can be explained by the deformation via prismatic slip, a mechanism common in other hexagonal metals 29. At 1100 K and 36 GPa, we also observe texture along the [0001] direction. However, unlike at room temperature, [0001] remains the primary texture direction up to 100 GPa, with its intensity reaching 5 mrd (Fig. 3b). The development of [0001] textures is commonly associated with plastic deformation by basal slip (0001) 1/3 <1120> 20.

Further, we performed EVPSC modeling 30 that allows calculating the possible preferred orientation of a crystalline material, using its common slip and twinning systems. We compared the results of EVPSC with the experimental observations in order to identify the active deformation mechanisms responsible for the development of LPO in hcp–Fe–2Si–0.4C at 1100 K. We only performed the modeling at 1100 K, as it is more relevant for the application of the results to the high-temperature conditions within the inner core (e.g., 12). For the modeling, we used stiffness tensor components at 1100 K (Supplementary Table 4, for details see “Methods”). The resulting distribution of the orientations of grains after the deformation is transformed into IPFs in the MTEX software 31. For each deformation mechanism, we describe the hardening of the critical resolved shear stresses τ by means of an empirical linear Voce hardening rule:
τ = τ0 + θ1Γ (1)
where Γ is the accumulated plastic shear strain. The initial critical resolved shear stress (CRSS), τ0, and the asymptotic hardening rate, θ1, are the two adjustable parameters. For details, please refer to Merkel et al. (2009) 32, and references therein. We varied the activity of the various deformation mechanisms to identify the parameters (Table 1) that would allow reproducing the experimentally observed IPFs (Fig. 3b, c) and lattice strains from the full set of available lattice planes at 1100 K, i.e. (100), (002), (101), (102), (110) and (103) (Fig. 4).

We observed that, in addition to the dominant basal slip, prismatic slip, together with either pyramidal slip (Fig. 5a) or compressive twinning (Fig. 5b), is necessary to explain the observed strains (Fig. 4a) and textures (Supplementary Fig. 4).

The large scattering of experimental data prevents us from distinguishing between pyramidal slip and compressive twinning as complementary mechanisms. Furthermore, employing either of these two combinations results in the same textures, including those extrapolated to core pressures. The derived deformation mechanisms are consistent with those determined by Merkel et al. (2009, 2012) 20,32 but differ from the results of Miyagi et al. (2008) 21, who suggested dominant pyramidal slip in hcp–Fe at high temperatures. This discrepancy might arise from different pressure-temperature paths in our experiment and those of Miyagi et al. (2008) 21, or from compositional differences. Moreover, the experimental textures observed in our study for the hcp–Fe–2Si–0.4C alloy (Fig. 3) are in line with those observed in hcp–Fe at pressures up to at least 278 GPa 33 and temperatures up to 3000 K 34. Our experimental data, supported by the EVPSC modeling, and observations for pure iron at core conditions 35–37, allow us to assume basal slip as the main deformation mechanism in hcp–Fe–2Si–0.4C alloy at core conditions.

Strength and viscosity of the Earth’s inner core
We employ our EVPSC deformation model to extrapolate the data and to derive Q(hkl) values at core pressures (Fig. 4b). Further, we utilized the constrained ∂Q/∂T to calculate Q(hkl) at core temperatures. Finally, by combining the stiffness tensor components from the literature (Supplementary Table 5) and the extrapolated values of Q(hkl), we calculated the yield strength of hcp–Fe–2Si–0.4C at core conditions (Fig. 6, Supplementary Table 6). The uncertainty of the yield strength extrapolations was calculated from the uncertainties in the extrapolation of Q(hkl) to core pressures (Fig. 4b), the temperature coefficient ∂Q/∂T and the shear moduli (Supplementary Table 6).

Hcp–Fe–2Si–0.4C at core conditions exhibits higher strength than pure iron (Fig. 6). The comparison with other alloys is complicated due to the inconsistencies in the available data. The strength of iron-silicon alloys as extrapolated by Brennan et al. (2021) 25, exceeds 80 GPa and is much higher than that of any iron alloys under core conditions (Fig. 6). Within the pressure range investigated in our study, however, hcp–Fe–2Si–0.4C displays higher strength than the iron-silicon alloys studied by Brennan et al. (2021) 25 (Fig. 2b). This discrepancy between the relative magnitudes of experimentally observed and extrapolated strength values likely arises from the method of extrapolation of Q(hkl) values to core conditions. While we use the results of the EVPSC modeling to project Q(hkl) to higher pressures, which saturated due to hardening 32, Brennan et al. (2021) 25 significantly overestimated Q(hkl) at core conditions by linearly extrapolating low-pressure data (Fig. 4b). Similarly, the strength of Fe–Ni alloys 24 also relies on the linear extrapolation of Q(hkl) without considering the diminishing effect of temperature on Q(hkl), which leads to an overestimation of strength.

Under the assumption of deformation-induced anisotropy, the solid-state viscosity of the inner core material is the key parameter influencing the development of anisotropy 5. We employed the values of yield strength of hcp–Fe–2Si–0.4C predicted at the inner core conditions (Fig. 6) to calculate the sample’s viscosity (see details in “Methods”). Our viscosity values (Fig. 7) for hcp–Fe–2Si–0.4C are higher than those for pure iron derived using the same formalism 17, which is consistent with the higher strength of hcp–Fe–2Si–0.4C (Fig. 2b). The viscosity values derived through different approaches 9,15,38,39 show some discrepancies largely due to poorly constrained parameters under inner core conditions, albeit they generally agree on the low viscosities of pure iron, with the exception of ref. 26.

Geophysical observations indicate that the viscosity of the inner core ranges from approximately ~1014 Pa·s (ref. 40) to ~1018 Pa·s (refs. 41,42) (Fig. 7), which are consistent with our viscosity calculations for the hcp–Fe–2Si–0.4C alloy. Consequently, the associated range of shear stresses in the inner core is 103–3·104 Pa, assuming hcp–Fe–2Si–0.4C alloy is the main constituent in the inner core (Fig. 7). The estimation of the magnitudes of the shear stresses produced by various potential sources in the core is generally challenging 5. The current estimates of stress caused by thermal convection range from 103 to 105 Pa (ref. 43), suggesting that thermal convection in the inner core can cause deformation-induced elastic anisotropy in hcp–Fe–2Si–0.4C (Fig. 7).

Anisotropy in the Earth’s inner core
We combined experimental textures at different pressures with calculated elastic stiffness tensor components (Supplementary Table 5) to derive the anisotropy of compressional sound velocities (see “Methods” for details) and extrapolated it further to core conditions. As discussed above, basal slip is the main deformation mechanism in hcp–Fe–2Si–0.4C both at 1100 K and at core conditions. Hence, the results of EVPSC texture modeling at 1100 K enable extrapolations of the V P anisotropy at core pressures.

The V P anisotropy of the hcp–Fe–2Si–0.4C alloy derived from the texture at 300 K reaches 0.3–0.5% (Supplementary Table 7), which is significantly smaller than the 4–5% anisotropy observed for pure hcp-Fe at 300 K and 52–112 GPa 22,23. Our data at 1100 K reveal the anisotropy of approximately 1% without a clear pressure trend (Supplementary Table 8), while the extrapolated anisotropy reaches about 2.0 ± 0.3% at core conditions (Fig. 8); i.e., smaller than the estimated 6.5% anisotropy of pure polycrystalline hcp–Fe at inner core conditions 19. This indicates that Si and C significantly reduce the anisotropy of polycrystalline hcp–Fe.

The anisotropy displayed by hcp–Fe–2Si–0.4C at core conditions aligns well with the anisotropy reported by seismic studies for the outer region of the inner core which is more than 50% lower than that reported for the innermost inner core, ~4–6% 1,3,4. Because of the higher anisotropy at core conditions of pure hcp-Fe 19 compared to hcp–Fe–2Si–0.4C alloy (Fig. 8), we hypothesize that the depth-dependent anisotropy pattern observed in the Earth’s inner core may result from chemical stratification of Si and C following core crystallization. As the crystallization of the Earth’s inner core begins at its center, and proceeds towards the inner core boundary across the temperature gradient 44, solidification of the core material likely starts on the iron-rich side of the eutectic through the crystallization of a hcp-Fe solid solution 12. Whilst temperature decreases, the concentration of Si 45,46 and C 47 in the solid solution increases, suggesting a higher concentration of light elements in the direction of the inner core boundary. Concomitantly, the pressure decrease from the center to the rim of the inner core shifts the eutectic concentrations of Fe–C and Fe–Si to larger light elements concentrations 48, which should further favor the increase of Si and C concentration towards the inner core boundary. Strong chemical stratification in the Earth’s inner core has been also recently proposed to explain the radial sound velocity gradients shown by PREM and AK135 seismic models 49. While calculations of the light element gradient in the inner core requires detailed information on the phase diagram of the Fe–Si–C system at core pressures, and a number of poorly constrained parameters (e.g., 12), we still can propose a qualitative trend for the variation of Si and C concentrations within the inner core (Fig. 9). The strongly anisotropic nature of the central part of the inner core can be thus linked to the depletion of Si and C in that region while the increasing concentration of light alloying elements towards the outer layers of the inner core results in reduced anisotropy.

In conclusion, we performed radial X-ray diffraction measurements on hcp–Fe–2Si–0.4C alloy at pressures up to 128 GPa and temperatures up to 1100 K. The complementary EVPSC modeling provides robust constraints for extrapolating the combined effect of Si and C on deformation mechanisms, yield strength and viscosity of iron alloy at inner-core conditions. This represents a qualitative improvement over earlier models that relied on simple linear extrapolations and/or room-temperature data. We find that the deformation of the hcp–Fe–Si–C alloy at high-temperature, high-pressure conditions is dominated by basal slip and leads to anisotropy of compressional waves of approximately 2% at inner core conditions. This anisotropy is substantially lower than that of pure iron, and lower than seismic estimates for the center of the inner core, although it is consistent with anisotropy inferred for the uppermost inner core. These results therefore suggest that the observed heterogeneous structure of compressional-wave anisotropy within the Earth’s inner core can be linked to variations in chemical composition, particularly stratification of Si and/or C.

Methods
Sample preparation
The Fe–2Si–0.4C sample was synthesized from a mixture of 57Fe powder (CHEMGAS), silicon powder (Aldrich, CAS 7440-21-3) and graphite powder (Aldrich, CAS 7782-42-5). All three powder components were finely ground together in an agate mortar. The synthesis was performed in a piston-cylinder apparatus 50. The starting material was enclosed in a BN crucible. The crucible was placed in crushable alumina cylinders (6 mm outer diameter) and surrounded by a cylindrical graphite furnace, a Duran glass cylinder (Schott, GmbH) and an outer talc sleeve. Pressure calibration was performed using the quartz-coesite transition 51 and the reaction MgCr2O4 + SiO2 = Cr2O3 + MgSiO3 52. The temperature was measured by a W-Re thermocouple (Type D) and regulated to an accuracy of 5 K by a Eurotherm controller (Schneider Electric, Germany). The sample was kept at a temperature of 1673 K and 1 GPa pressure for 24 h and then quenched to below 500 degrees within <5 s by switching off the power supply. In order to avoid carbon contamination of the surface during the microprobe analyses, the sample was cleaned using a plasma cleaner and to further reduce carbon contamination in the sample chamber, a liquid-N cold trap was employed (see details in ref. 53). The composition of the product was characterized by a JEOL 8530F electron microprobe (1–5 μm focused beam, accelerating voltage of 15 keV and beam current of 15 nA, Ir-coated sample). The matrix correction was performed relying on the φ(ρz) procedure 54. For precise carbon calibration, a series of low-carbon steel standards (0.02 to 3.8 wt%, Micro-Analysis Consultants Ltd) and Fe3C (Geller) were used to correct for the carbon background signal. The microprobe analyses showed that the sample was homogeneous in regards to the constituent elements in the sample (Supplementary Fig. 5) with the composition of the alloy being 97.63 ± 0.07 wt% Fe, 1.98 ± 0.04 wt% Si and 0.39 ± 0.03 wt% C. The sample was then removed from the microprobe mount and cut into small pieces (tens of microns in size) using a sharp razor blade and loaded in the DAC. The crystal structure of the as-synthetized sample was determined to be bcc by synchrotron powder X-ray diffraction.

Resistive heating in diamond anvil cells
We employed DACs of the Mao-Bell piston-cylinder type to generate the pressure. The sample for the room temperature experiment was compressed between two diamonds with 50 µm culets. A 20 µm hole was drilled in a Be gasket pre-indented to a thickness of about 15 µm and the sample was loaded into it. For experiments at high temperatures, a modified Mao-Bell type DAC equipped with graphite resistive heaters was employed 55. The cell was equipped with diamond anvils with 150 µm culets. A piece of Kapton held the gaskets of amorphous boron of 25 µm thickness with ~50 µm holes in place. The entire pressure chambers were filled with the iron-silicon-carbon alloy without a pressure-transmitting medium in order to maximize non-hydrostatic stresses. For the high-temperature experiment, small pieces of gold were added to serve as a pressure standard 56. The temperature was controlled by two type-R thermocouples, with one thermocouple in contact with the diamond close to the compression chamber and the second one in contact with the heater. A water-cooled vacuum vessel capable of maintaining 10−4 mbar was used to avoid oxidation of the diamonds, seats, and electrical connections. Additional information about the design and operation of the resistive heated DAC for X-ray diffraction in radial geometry can be found elsewhere 55.

Synchrotron radial X-ray diffraction
The radial X-ray diffraction measurements were conducted at the Extreme Conditions Beamline of the PETRA III (DESY, Hamburg, Germany). The X-rays were oriented perpendicular to the DAC compression direction and propagated through about 3 millimeters of gasket materials (Be/amorphous boron). The X-ray beam was focused down to 8(H) × 2(V) µm2 by an array of compound refractive lenses. Diffraction patterns were collected using monochromatic X-rays with a wavelength of 0.2904 Å on a Perkin Elmer XRD 1621 flat panel detector. The sample-detector distance was calibrated as 459.1 mm along with the tilt and beam center using a CeO2 standard from NIST (674b) in the DIOPTAS software package 57. We employed 3rd order Birch-Murnaghan equation of state (EOS) of the sample fitted to the data deposited in ref. 58 to determine the pressure in the experiment conducted at room temperature (Supplementary Table 9). The compression curve of hcp–Fe–2Si–0.4C is close to another Fe–Si–C alloy reported before 14,59 (Supplementary Fig. 6). In the high-temperature runs, pressure was determined using the thermal EOS of Au pressure marker 56 (Supplementary Fig. 6, Supplementary Tables 10, 11).

Calculation of the lattice strain parameters and extraction of LPO
Diffraction images were analyzed to retrieve cell parameters and textures by the Rietveld method using the software package MAUD 60. Diffraction images were integrated in a 5-degree step in azimuth angle which resulted in 72 slices and diffraction patterns. Representative unrolled diffraction patterns are presented in Fig. 1. The deviations of the diffraction lines from the straight line are due to the lattice strains (ε D(hkl,ψ)) as described by the Eq. (2) 61:
ε D(hkl,ψ) = (d m(hkl) − d p(hkl)) / d p(hkl) (2)
where d m(hkl) and d p(hkl) are the measured and d-spacing at the pressure, respectively. ψ is the angle between the maximum stress direction and the normal to the diffracting plane 61. The lattice strain can be expressed as:
ε D(hkl,ψ) = 1/3 (1 − 3cos2ψ) Q(hkl) (3)
where coefficient Q(hkl) is the lattice strain parameter for any given hkl diffraction line.

Due to the weak intensity of the diffraction lines of the sample and the overlap of some diffraction lines with the diffraction lines of the gasket material, particularly at room temperature (i.e., Be, Fig. 1a), the precise derivation of the lattice strain parameters could not be performed within MAUD. Thus, we determined the peak positions of the most intense hcp–Fe–2Si–0.4C alloy reflections in the Fityk software package and then calculated the lattice strain parameters using the formalism described above (3).

Fitting of the LPOs was performed using the E-WIMV 62 algorithm implemented with an orientation distribution function (ODF) resolution of 10° and assuming fiber symmetry about the compression direction. The E-WIMV model 62 is based on the WIMV method, extended to be used on irregular grids, which includes a built-in smoothing function. The extracted ODFs were processed using the MTEX software 31 to obtain the IPF.

Yield strength calculations
Using the averaged lattice strain parameter Q(hkl) and Voigt-Reuss-Hill shear modulus G H by 61:
t = 6G H Q(hkl) (4)
Uniaxial stress component t = σ 3 − σ 1 is a measure of the difference between axial σ 3 and radial stress σ 1 components applied to the sample. The maximum uniaxial stress t sustained by a material is determined by its yield strength; that is, t ≤ σ y, where σ y is the material yield strength. The uniaxial stress t is equal to the yield strength if the sample deforms plastically under pressure 61. In our study, we call the uniaxial stress t yield strength for terminological consistency with other studies that used the same experimental approach (e.g., 17,25).

Stiffness tensor components
Stiffness tensor components C ij of the hcp–Fe–2Si–0.4C alloy at 360 GPa and various temperatures were calculated by interpolation of the stiffness tensor components of Fe–Si and Fe–C alloys from the literature 13,63,64 (Supplementary Fig. 7).

The pressure dependence of tensor components was derived by quadratic function C ij = aP2 + bP + c, where P is pressure, and a and b are parameters dependent on Si and C content, while c parameter is temperature-dependent. Parameters a and b were derived by fitting the pressure dependence of various iron-silicon 63 and iron-carbon 64 alloys. Parameter c was adjusted from the values at different temperatures but single pressure 13 (values are in Supplementary Table 12). The derived elastic parameters of hcp–Fe–2Si–0.4C at various pressures and temperatures employed for further calculations are summarized in Supplementary Table 4.

Viscosity calculations
Viscosity (μ eff) can be defined as:
μ eff = τ / ε_ (5)
where ε_ is a strain rate and τ is a shear stress.

The strain rate ε_ is defined by dislocation velocity ν, Burgers vector b and dislocation density ρ D:
ε_ = ρ D b ν (6)

The velocity of dislocation, ν(τ,T), can be determined by Eq. (7) 17:
ν(τ,T) = ν D (a0 b L / w2) exp(−ΔH 0 / kT) sinh(ΔH(τ) / kT) (7)
where ν D – Debye frequency, a0 – Peierls barrier width, b – Burgers vector length, L – dislocation length, w – kink pair width, ΔH 0 – activation enthalpy of dislocation glide at zero stress.

ΔH(τ) changes with applied stress as 17:
ΔH(τ) = ΔH 0 (1 − (τ / τ P) 3/4) 4/3 (8)
where τ is applied shear stress, τ P is Peierls stress which is a stress needed to move a dislocation in a crystal without thermal activation. τ P is proportional to yield strength and we set them equal in our calculations 17.

We calculated ΔH 0 as 65:
ΔH 0 = 0.317 G H b3 (9)
where G H is shear modulus, b – Burgers vector.

Stress dependence of the kink pair width w 66:
w = (h G H b / 8π τ) 1/2 (10)
where h is a kink pair height that is considered equal to b at low stresses 65.

Density of dislocations ρ D can be expressed as 17:
ρ D = α (τ 2 / G H b) (11)
where α is considered a constant of order unity 17.

Debye frequency ν D can be described as:
ν D = (6π2 N a ρ / M) 1/3 V D (12)
where N a is Avogadro constant, ρ is the density of hcp–Fe–2Si–0.4C calculated from the equation of state for hcp–Fe–2Si–0.4C, assuming substitutional and interstitial incorporation mechanisms for Si and C, respectively 59, M is molar mass of Fe–2Si–0.4C iron alloy, V D Debye sound velocity. The values of parameters used in Eqs. (6–12) are summarized in Supplementary Table 13. The density of hcp–Fe–2Si–0.4C at the core conditions was calculated using a 3rd order Birch-Murnaghan EOS 58 and Mie-Grüneisen-Debye model. Parameters for the Mie-Grüneisen-Debye model calculation are taken from pure iron from refs. 67,68 The Debye sound velocity and frequency for viscosity calculations were derived from the Nuclear Inelastic Scattering (NIS) data 58. All raw data are available in the repository associated with the manuscript (https://zenodo.org/records/15119916).

Anisotropy calculations
We combined experimental and modeled textures (IPFs) at corresponding pressures with calculated elastic stiffness tensor components (Supplementary Tables 4, 12, respectively) and derived the anisotropy of compressional sound velocities in MTEX software 31. We determine sound velocity anisotropy as:
Anisotropy = 2 * (V Max − V Min) / (V Max + V Min) * 100% (13)
where V Max and V Min are maximal and minimal velocities along the compression direction, respectively. The anisotropy calculation does not allow for the calculation of the uncertainty directly. However, we varied the stiffness tensor components within their uncertainty (Supplementary Tables 4, 12) to propagate the possible range of the anisotropy values of experimentally observed data (Supplementary Tables 7, 8) and of extrapolation to core conditions (±0.3%).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript report diamond anvil cell experiments performed with resistive heating and radial diffraction. Data were collected along two isotherms and an isobar. The results are then modelled and extrapolated to define the main deformation mechanism in the core, used to calculate the strength, viscosity and anisotropy.\nI found the manuscript interesting and praise the authors for their efforts, however I also found it hard to follow and partially incomplete. I needed multiple iterations between the manuscript, the methods and the supplementary to figure out multiple portions of the paper. And some portions are still kind of ambiguous. For example, from the displayed data it seems like the experimental data might or might not support the results of the model about the prismatic and pyramidal deformation and same for the compressive twinning, because there isn’t enough resolution to discriminate. Nevertheless, the authors in the results declare an agreement with the deformation styles proposed by previous authors.\nImportant papers on the Fe-Si-C system relevant for the current study are not discussed (more details in the comments below). A discussion on the errors and models’ uncertainties is missing, uncertainties are not reported for any of the extrapolations, and I am also wondering if the main conclusion about anisotropy in the core and the concentration curve in Figure 6 is based on thermodynamic calculations or is a representation from the authors.\nBy reading the current version I feel like the letter format might not be ideal for this paper, but I am happy to read an improved version once the authors have addressed my comments and questions. Until then I can’t really recommend it for publication.\nMajor comments:\nStarting material: Figure S5: The caption of the figure needs to be improved as not all the reader might have seen before chemical maps made in an EPMA. I am guessing that the interpretation of the color bar is: red pixels have a high quantity of the element, blue have a low quantity of the element? It would be useful for the authors to provide more details. And is there a reason for which the backscattered electrons image is not the same field of view of the compositional map?\n- From the backscattered electron image there seems to be some preferential orientation of the grains. It is hard to tell with certainty as the polishing of the sample is not ideal (a lot of line marks). Can the authors comment on this and if possible improve on the polishing and provide a new image for the manuscript?\n- Measuring carbon in the probe is challenging. Have the authors used a cold finger, N2 and plasma cleaning of the sample surface? And can they provide a plot of the carbon content measured on the same spot at different times to show that there is no carbon contamination from the hydrocarbons likely present in the vacuum chamber of the instrument?\n- How were the dimension of the measured sample and how was the sample prepared for diamond anvil cell?\n- Line 288: I am a bit confused, which gasket material is giving a contribution strong enough to cover some of the peaks? From what I have read previously I thought Be and BN contribution to a diffraction pattern was minimal. Have the authors collected a diffraction pattern where the contribution of the gasket is well visible that they can show?\n- The comparison with the EPSVC model is hard to follow for a reader who does not do this type of work every day. Fig.1 is clear but the informations are divided between the main text, the methods and the supplementary, which makes everything really hard to follow. Here below a series of points that I would like to see clarified:\n- I see how the basal slip hypothesis is supported by the model at 1100K. Does the model also reproduce the prismatic slip as the dominant deformation at 300 K?\n- Lines 93-95: If the experiments at 1100K show that the main deformation mechanism is basal slip, why do the authors say that their results are consistent previous authors and the model where also a prismatic and pyramidal components are observed? I understand the EPSVC models shows those two components should have a role too but there aren’t any experiments shown having a prismatic and pyramidal contribution at high temperature. The in the methods it is shown that the models fit the data also with compressing twin contribution and the authors mention their data are not suitable to resolve those differences, so way in the main text saying that you are consistent with previous authors? It seems to me that yes, the basal plane slip is consistent, but then there are two possible models and it’s not possible to discriminate so you might or might not agree with previous authors.\n- Line 332-333: Not being a specialist of deformation experiments I am failing to see how Figure 7 represent the best match between the experiments and the model. What Figure 7 is telling me (and please correct me if I am wrong) is that basal slip represents the most likely deformation mechanism? Because then when I go looking into the results the authors write that at 300K the dominant deformation mechanism observed is a prismatic slip.\n- The reference for few of the key numbers used for the model and reported in Table S12 (ref 5) does not seem to be available for download. By doing a google search I have found a university of Munster page with what I guess is the description of the thesis (page only in german) but no link for download and the DOI written on the page does not produce any result when looked up online. It would be important to have this reference available to understand if a comparison of the equations of state data has been done, especially in respect to the work of Pamato et al. (2020) where the authors show that the mechanisms of solution of the carbon and silicon in the Fe produce non-negligible differences in the density of the alloy.\n- Lines 134-135: If I understand correctly, we are looking at an extrapolation from 100GPa to 360 GPa. The red points representing the data at 1100K in Figure 2 do not seem to correspond to those in figure S3. In the latter the higher-pressure point for 1100K is at 75GPa while in figure 2 there are points at 100 GPa. And also, the other data seem off, has the images been rescaled in a particular manner or only certain data have been used?\n- It would be useful if the authors can provide uncertainties on their numbers. Starting from the fit to obtain ∂Q/∂T and define how it propagates in pressure and temperature. Data collected at 1100K and 36 GPa are used to extrapolate values at 360 GPa and temperatures likely higher than 4000K, there need to be uncertainties.\n- It would also be interesting to see how uncertainties of the parameters used for the calculation of the models affect the outcome of the investigation. Because the numbers used for the EoS are different from those reported in previous literature as for example Pamato et al. 2020 or Miozzi et al. 2020. Have the authors tried to do the same modelling using these other values as a test?\n- On this, it would be useful if the authors can provide an estimate of the uncertainties also for the viscosity calculations. Many of the models/calculations come from multiple iterations of the collected experimental data plus numbers coming from other experimental and modelling work. I would like to see how the experimental error on the used parameters and the uncertainties on the previously determined parameters affect the results.\n- Line 193: The reference here (N41, komabayashi et al) discuss only the behavior of the Fe-Si system. Have the authors confronted their results with the pressure and temperature evolution of the phase diagram proposed by Hasegawa et al. 2021?\n- Lines 190-194: Which data were used to calculate the evolution of the light elements concentration in the core displayed in Figure 6?\nIs the increment in light elements in the solid solution related to the shift of the ternary eutectic or to the shape of the solid solution line between the solidus and the liquidus?\n- Two recent papers discuss the effects of carbon and silicon incorporation in hcp Fe and the melting properties of the system respectively (Pamato et al. 2020: Equation of State of hcp Fe‐C‐Si Alloys and the Effect of C Incorporation Mechanism on the Density of hcp Fe Alloys at 300 K and Hasegawa et al. 2020 Liquidus Phase Relations and Solid-Liquid Partitioning in the Fe-Si-C System Under Core Pressures). A comparison of the equations and density used, along with the partitioning data used for the concentration calculations would have been appropriate, can the authors provide one? And I imagine a comparison with Pamato et al. might have been in the work cited in reference5, but because that work seems to be not accessible it’s hard to explain why the parameters of the 300K EoS from that study are different from those reported in the current manuscript.", "reviewer_2": "This manuscript shows X-ray diffraction measurements on an Fe-Si-C alloy at high pressure and high temperature. The sample’s deformation behavior is extrapolated to Earth’s core conditions. The main conclusion is that the properties of the specific composition analyzed match the seismic anisotropy in the Earth’s core.\nThe effort the authors devoted to all the steps of the experiment and the analysis is very clear. The careful sample preparation in piston-cylinder apparatus followed by microprobe compositional analysis is very much appreciated, as well as the difficult resistive heating experiments with a panoramic diamond anvil cell. The radial X-ray diffraction data analysis is also challenging and the authors clearly show that they master all these complicated steps. However, the results are shown quickly, leaving the reader with a long list of unaddressed questions. A solid interpretation and understanding of the results is missing, while much effort is devoted to discussing extrapolated parameters in relation to Earth’s core. Unfortunately, the extrapolations are presented without confidence intervals, leaving the reader uncertain about their true significance.\nThe structure of the manuscript is also quite unfriendly: Conclusions are missing, in the Methods are presented results (for example lines 332 – 338) and the reader continuously has to jump between methods, supplementary material, figures captions and literature to have basic fundamental information of what is being presented.\nI thus believe that the authors need to revisit their work strengthening the robustness of their findings as well as improving the form of the manuscript before it can be published.\nMajor comments:\n- Line 99: The authors state that the lattice strain parameter at 300 K and at 1100 K overlap within the uncertainty up to 60 GPa. In Line 110 the authors determine the variation of the lattice strain parameter as a function of temperature at 36 GPa. These two findings are in contradiction. From Fig. 2 the dQ/dT value seem to vary a lot with pressure (as the authors state, the 1100 K values decrease with pressure while the 300 K values increase). What is the significance of a dQ/dT calculated only at one pressure? How does this compare with the other pressures (even if with only two measured temperatures)?\nMoreover, the dQ/dT is compared with the literature, but the PT conditions of validity of the literature value are not mentioned.\n- Line 101: The decrease is very small and within the uncertainty. Is the same decrease visible for the considered lattice planes? Or is it just an effect of the average?\nThe authors claim this decrease is due to the formation of cementite. Can they quantify from the diffraction patterns the amount of cementite present in their sample and check if this is consistent with their hypothesis? If cementite is forming it means that the alloy is heterogeneously depleted in carbon and more silicon rich. How would this affect the results shown?\n- Fig.2 : Fe-5Si data from ref [18] are shown, while in Supplementary Fig. 3 are shown Fe-5Si and Fe-9Si data from ref [10]. If they are the same data, please refer to them consistently. Why are Fe-9Si data missing in Fig.2? Please specify in the caption the temperature of all data sets.\n- Supplementary Fig.1: it would be useful to show here which lattice planes were used for the determination of Q.\nMinor comments:\n- Line 65: probably here it’s worth mentioning that the sample is polycrystalline and synthetized at high pressure and temperature. Why did the authors choose this specific composition?\n- Line 78: The scale indicating the multiples of mrd in Fig. 1 goes maximum to 4. I understand that the scale is not the same for the 300 K and the 1100 K cases.\n- Line 137: Too many information missing. I suggest you to change the sentence with something like: “Finally, by combining the stiffness tensor components from the literature and the extrapolated value of Q, we calculated the yield strength of Fe-2Si-0.4C at core conditions.”\nThe uncertainty of this value, as shown in Supplementary Fig. 4 looks very small. Have the authors propagated the uncertainties over the extrapolation? In any case, it is worth mentioning how this uncertainty was determined, before claming that it is smaller than the previous one.\n- Line 222: some “shades” are visible in the backscattered electron image, while the compositions look completely homogeneous. Are the two images taken on the exact same spot?\nCan you add a compositional scale to the elemental X-ray distribution maps? What do the colors represent?"}, "author_response": "Response to Reviewer 1:\nThe manuscript report diamond anvil cell experiments performed with resistive heating and\nradial diffraction. Data were collected along two isotherms and an isobar. The results are then\nmodelled and extrapolated to define the main deformation mechanism in the core, used to\ncalculate the strength, viscosity and anisotropy. I found the manuscript interesting and praise\nthe authors for their efforts, however I also found it hard to follow and partially incomplete.\nWe thank Reviewer #1 for acknowledging the importance of our results and for the\npositive evaluation of our experimental work.\nI needed multiple iterations between the manuscript, the methods and the supplementary to\nfigure out multiple portions of the paper. And some portions are still kind of ambiguous. For\nexample, from the displayed data it seems like the experimental data might or might not support\nthe results of the model about the prismatic and pyramidal deformation and same for the\ncompressive twinning, because there isn’t enough resolution to discriminate. Nevertheless, the\nauthors in the results declare an agreement with the deformation styles proposed by previous\nauthors. Important papers on the Fe-Si-C system relevant for the current study are not discussed\n(more details in the comments below). A discussion on the errors and models’ uncertainties is\nmissing, uncertainties are not reported for any of the extrapolations, and I am also wondering\nif the main conclusion about anisotropy in the core and the concentration curve in Figure 6 is\nbased on thermodynamic calculations or is a representation from the authors. By reading the\ncurrent version I feel like the letter format might not be ideal for this paper, but I am happy to\nread an improved version once the authors have addressed my comments and questions. Until\nthen I can’t really recommend it for publication.\nAnswer:\nFollowing the reviewer’s suggestions we have reorganized the structure of the manuscript to\nincrease its clarity. Added/modified parts are highlighted in yellow, and rearranged parts are\nhighlighted in turquoise. The responses to specific points of criticism are provided below.\nMajor comments:\nQuestion: Starting material: Figure S5: The caption of the figure needs to be improved as not\nall the reader might have seen before chemical maps made in an EPMA. I am guessing that the\ninterpretation of the color bar is: red pixels have a high quantity of the element, blue have a\nlow quantity of the element? It would be useful for the authors to provide more details.\nAnswer: Indeed, the interpretation of the color maps is as suggested by the reviewer. We have\nadded this clarification to Supplementary Fig. 6 (former Supplementary Fig. 5). Please note,\nthat the color maps there are qualitative and, thus, the quantitative legend cannot be provided.\nQuestion: And is there a reason for which the backscattered electrons image is not the same\nfield of view of the compositional map? - From the backscattered electron image there seems\nto be some preferential orientation of the grains. It is hard to tell with certainty as the polishing\nof the sample is not ideal (a lot of line marks). Can the authors comment on this and if possible\nimprove on the polishing and provide a new image for the manuscript?\nAnswer: The compositional maps were taken from the same spot as the backscattered electron\nimage. We have taken compositional maps only in the squared form (the centers of images are\nthe same). We have modified the figure caption accordingly. The differences in the SEM image\nbetween lighter and darker areas are caused by electron channelling due to different crystal\norientations. We have checked also the LPO in non-compressed Fe-2Si-0.4C alloy and it is\nextremely weak (below 1.1 mrd, see Supplementary Fig. 3). The line marks are indeed\nscratches from imperfect polishing. Unfortunately, the sample is no longer accessible since it\nwas fully used in the experiments. Therefore, we cannot provide a new image or improve the\npolishing.\nQuestion: Measuring carbon in the probe is challenging. Have the authors used a cold finger,\nN2 and plasma cleaning of the sample surface? And can they provide a plot of the carbon\ncontent measured on the same spot at different times to show that there is no carbon\ncontamination from the hydrocarbons likely present in the vacuum chamber of the instrument?\nAnswer: Yes, we used plasma cleaning (to avoid C contamination at the surface), and N and\n2\ncold finger. Details are given in Berndt & Klemme (2022) in the methods section. We have\nmodified the text accordingly. The sample is no longer accessible, therefore we cannot provide\ncarbon content on the same spot at different times. We used a series of low-carbon steels and\nFe C for blank carbon correction. We have added this information to the methods section (lines\n3\n301-304, 307-309).\nQuestion: How were the dimension of the measured sample and how was the sample prepared\nfor diamond anvil cell?\nAnswer: The initial sample size was on the order of several millimetres. In order to load it to\nthe DAC, we took the sample from the microprobe mount and then cut small pieces (tens of\nmicrons) with the razor blade to fully fill in the pressure chambers with them. We have added\nthis information to the text (lines 312-313).\nLine 288:\nQuestion: I am a bit confused, which gasket material is giving a contribution strong enough to\ncover some of the peaks? From what I have read previously I thought Be and BN contribution\nto a diffraction pattern was minimal. Have the authors collected a diffraction pattern where the\ncontribution of the gasket is well visible that they can show?\nAnswer: The material that creates additional diffraction lines is the beryllium gasket. It has Be\nand BeO in the composition. The experiment geometry requires the orientation of the DAC\ncompression direction to be perpendicular to the X-ray beam, and, thus, the X-ray has to\npropagate through about 3 mm of the gasket material before reaching the samples. Therefore,\nalthough being made of light material, the gasket contributes a lot to the pattern compared to\nthe sample due to several orders of magnitude higher volume exposed to the X-ray beam. We\nhave added a diffraction pattern with the contribution of Be and BeO as Supplementary Fig.\n1b and to the text (lines 332-334).\nQuestion: The comparison with the EPSVC model is hard to follow for a reader who does not\ndo this type of work every day. Fig.1 is clear but the informations are divided between the main\ntext, the methods and the supplementary, which makes everything really hard to follow. Here\nbelow a series of points that I would like to see clarified:\nI see how the basal slip hypothesis is supported by the model at 1100K. Does the model also\nreproduce the prismatic slip as the dominant deformation at 300 K?\nAnswer: We have performed EVPSC modeling for our results at 1100 K, but not at 300 K.\nThe EVPSC modeling requires significant computational resources, while results at 300 K\nwould be still irrelevant for the inner core. We have added this information to the text (lines\n147-151). Therefore, we made assumptions based on the literature results on the prismatic slip\nin hcp structures (Pochettino et al. (1992)). In addition, we have made one simulation of\ndeformation with activation of only prismatic slip in hcp and present the resulting inverse pole\nfigure in Response Fig. 1 here below. The direction of the LPO development in Response Fig.\n1 is the same as at 300 K upon compression to above 60 GPa (Fig. 2a) (former Fig. 1a).\nResponse Fig. 1. Simulation of deformation by a single prismatic slip in an hcp structure (not\nthe modeling to fit the actual data).\nLines 93-95:\nQuestion: If the experiments at 1100K show that the main deformation mechanism is basal\nslip, why do the authors say that their results are consistent previous authors and the model\nwhere also a prismatic and pyramidal components are observed? I understand the EPSVC\nmodels shows those two components should have a role too but there aren’t any experiments\nshown having a prismatic and pyramidal contribution at high temperature. The in the methods\nit is shown that the models fit the data also with compressing twin contribution and the authors\nmention their data are not suitable to resolve those differences, so way in the main text saying\nthat you are consistent with previous authors? It seems to me that yes, the basal plane slip is\nconsistent, but then there are two possible models and it’s not possible to discriminate so you\nmight or might not agree with previous authors.\nAnswer: The deformation usually occurs by a combination of several different mechanisms.\nWe refer to the studies of Merkel et al. (2012) and Miyagi et al. (2008) performed on hexagonal\niron at high temperatures (600-1950 K). The results of Miyagi et al. (2008) indeed differ from\nours, and we have changed the text accordingly. Our results are consistent with Merkel et al.\n(2012) in considering basal slip as the dominant deformation mechanism. However, in addition\nto the basal slip, Merkel et al. (2012) also suggest twinning, prismatic and pyramidal slips as\ncomplementary active deformation mechanisms at high temperatures. We have checked our\nstatement in the text and modified it to be more precise (lines 153-163). In Supplementary\nFig. 5a we show that a single basal slip cannot explain the development of 〈𝑄(ℎ𝑘𝑙)〉, and the\naddition of prismatic and pyramidal slips or twinning is necessary.\nLines 332-333:\nQuestion: Not being a specialist of deformation experiments I am failing to see how Figure 7\nrepresent the best match between the experiments and the model. What Figure 7 is telling me\n(and please correct me if I am wrong) is that basal slip represents the most likely deformation\nmechanism? Because then when I go looking into the results the authors write that at 300K the\ndominant deformation mechanism observed is a prismatic slip.\nAnswer: Fig. 3 (former Fig.7) does not show the likelihood of the deformation mechanism but\nthe mechanisms active at various pressures based on our EVPSC model, that matches best to\nexperimentally observed textures (Fig. 2) and lattice strains (Supplementary Fig. 5). Fig. 3\nindeed shows that the basal slip is the most active deformation mechanism at 1100 K. Please\nnote, that Fig. 3 depicts the results for 1100 K not for 300 K.\nQuestion: The reference for few of the key numbers used for the model and reported in Table\nS12 (ref 5) does not seem to be available for download. By doing a google search I have found\na university of Munster page with what I guess is the description of the thesis (page only in\ngerman) but no link for download and the DOI written on the page does not produce any result\nwhen looked up online. It would be important to have this reference available to understand if\na comparison of the equations of state data has been done, especially in respect to the work of\nPamato et al. (2020) where the authors show that the mechanisms of solution of the carbon and\nsilicon in the Fe produce non-negligible differences in the density of the alloy.\nAnswer: We have modified the link for the online available data\n(https://zenodo.org/records/15119916). We have added to this the pressure-volume data, the\ndensity of phonon states and derived Debye velocities. The detailed comparison of the EOS\nparameters with the results of Pamato et al. (2020) would be indeed interesting, but falls out of\nthe scope of the present study and will be published elsewhere. We add the data of Pamato et\nal. (2020) to Supplementary Fig. 7, and their results are quite close to ours, particularly at\nhigher pressures. The existing discrepancy between our results and those of Pamato et al.\n(2020) likely comes from compositional differences. Note, that we assume the same\nincorporation mechanism for Si and C as Pamato et al (2020) and we highlighted that now in\nthe text (lines 433-434). We are currently preparing for submission of another paper dedicated\nspecifically to the EOS of Fe-Si-C alloys where we do a detailed comparison. Please also note,\nthat the derived equation of state is only used in the current manuscript for calculating the\npressure for the 300 K experiment (thus not affecting the data at 1100 K used for the\nextrapolation to core conditions) and for the viscosity calculations we address this point in the\nresponse below.\nLines 134-135:\nQuestion: If I understand correctly, we are looking at an extrapolation from 100 GPa to 360\nGPa. The red points representing the data at 1100K in Figure 2 do not seem to correspond to\nthose in figure S3. In the latter the higher-pressure point for 1100K is at 75GPa while in figure\n2 there are points at 100 GPa. And also, the other data seem off, has the images been rescaled\nin a particular manner or only certain data have been used?\nAnswer: Indeed, the red points representing data at 1100 K do not match in Fig. 1a (former\nFig.2) and Supplementary Fig. 5 (former Fig. S3). In Fig. 1a we plot data at 1100 K as\naveraged over (100), (002), and (103) lattice planes for a direct comparison with the data at\na more complete set of the lattice planes ((100), (002), (101), (102), (110), (103)) that were\naccessible in the high-temperature data set. We used the same set of lattice planes from the\nEVPSC modeling for comparison with the experimental data. In Supplementary Fig. 5, we\nuse the pressure points without significant precipitation of cementite Fe C, i.e. until 60 GPa.\n81, 117-118). The other common data plots in Fig. 1a and Supplementary Fig. 5 are Fe-2Si-\n0.4C at 300 K, Fe-5Si and Fe-9Si, they are plotted from the same data but may look differently\ndue to the different scales in the two figures.\nQuestion: It would be useful if the authors can provide uncertainties on their numbers. Starting\nfrom the fit to obtain ∂Q/∂T and define how it propagates in pressure and temperature. Data\ncollected at 1100K and 36 GPa are used to extrapolate values at 360 GPa and temperatures\nlikely higher than 4000K, there need to be uncertainties.\n𝜕𝑄\nAnswer: We determined the value of as -8.6(±2.2)∙10⁻⁷ K⁻¹ from the fit in Supplementary\n𝜕𝑇\nFig. 2 (also lines 99-100 in the main text). It would be indeed interesting to see the uncertainty\n𝜕𝑄\npropagation of with pressure and temperature. However, its experimental determination is\n𝜕𝑇\n𝜕𝑄\nalready quite challenging. Please note that in most of the previous studies was simply\n𝜕𝑇\nassumed to be zero. The value, determined in our study, although at a single pressure point and\na limited temperature range, thus, provides some experimental estimation.\nQuestion: It would also be interesting to see how uncertainties of the parameters used for the\ncalculation of the models affect the outcome of the investigation. Because the numbers used\nfor the EoS are different from those reported in previous literature as for example Pamato et al.\n2020 or Miozzi et al. 2020. Have the authors tried to do the same modelling using these other\nvalues as a test?\nAnswer: Our EVPSC modelling does not directly provide the uncertainties. However, in order\nto estimate the uncertainties of the model, we have varied all the stiffness tensor components\nwithin their uncertainties (Supplementary Table 13), thus resulting in a range of possible\n〈𝑄(ℎ𝑘𝑙)〉 values up to core conditions that are now displayed in Supplementary Fig. 5).\nEstimation of uncertainty for anisotropy was also added (line 236, lines 444-448) Parameters\nof the EOS are not involved in the calculation of the EVPSC model. However, we have verified\nthe effect of the choice of the EOS, i.e. the one presented in the manuscript and of Pamato et\nal. (2020). in the viscosity calculations (see below).\nQuestion: On this, it would be useful if the authors can provide an estimate of the uncertainties\nalso for the viscosity calculations. Many of the models/calculations come from multiple\niterations of the collected experimental data plus numbers coming from other experimental and\nmodelling work. I would like to see how the experimental error on the used parameters and the\nuncertainties on the previously determined parameters affect the results.\nAnswer: We have employed the uncertainties of parameters in Supplementary Table 14 and\ncalculated the uncertainty of viscosity that is now added to Fig. 5, line 221. In particular,\nviscosity derived with the application of the parameters from the EOS of Pamato et al. (2020)\nfalls within our uncertainty range.\nLine 193:\nQuestion: The reference here (N41, komabayashi et al) discuss only the behavior of the Fe-Si\nsystem. Have the authors confronted their results with the pressure and temperature evolution\nof the phase diagram proposed by Hasegawa et al. 2021?\nAnswer: Following the reviewer’s suggestion we have modified the references accordingly.\nWe need to clarify that our statement here also comes from the general suggestion of the form\nof the solidus curve. The results of Hasegawa et al. (2021) also support our results. Pressure\ndecrease shifts the eutectic concentrations of Fe-C and Fe-Si to larger light elements\nconcentrations. Therefore, it is intact with the idea that Si and C concentration increases to the\ninner core boundary. We have clarified these points in lines 253-258.\nLines 190-194:\nQuestion: Which data were used to calculate the evolution of the light elements concentration\nin the core displayed in Figure 6? Is the increment in light elements in the solid solution related\nto the shift of the ternary eutectic or to the shape of the solid solution line between the solidus\nand the liquidus?\nAnswer: The evolution of the light elements concentration in now Fig. 7 (former Fig. 6) was\nnot calculated, it is a schematic representation based on the results of Fischer et al. (2013) and\nOzawa et al. (2016) for Si and Mashino et al. (2019) for C and a general understanding of the\nform of the solidus curve. Calculation of exact amounts of the light elements in the inner core\nrequires detailed information on a phase diagram of the Fe-Si-C system at core pressures, the\ntemperature profile of the outer and inner core, and many other parameters that are still not\ntightly constrained, and, thus, would introduce large uncertainties, likely comparable to the\nvalues themselves. We have added this consideration to the text (lines 258-262). Yet, we still\ncan propose a trend for variation of their concentrations within the inner core. The increment\nis related to the shape of the solid solution line between the solidus and the liquidus.\nQuestion:- Two recent papers discuss the effects of carbon and silicon incorporation in hcp Fe\nand the melting properties of the system respectively (Pamato et al. 2020: Equation of State of\nhcp Fe‐C‐Si Alloys and the Effect of C Incorporation Mechanism on the Density of hcp Fe\nAlloys at 300 K and Hasegawa et al. 2020 Liquidus Phase Relations and Solid-Liquid\nPartitioning in the Fe-Si-C System Under Core Pressures). A comparison of the equations and\ndensity used, along with the partitioning data used for the concentration calculations would\nhave been appropriate, can the authors provide one? And I imagine a comparison with Pamato et\nal. might have been in the work cited in reference5, but because that work seems to be not\naccessible it’s hard to explain why the parameters of the 300K EoS from that study are different\nfrom those reported in the current manuscript.\nAnswer: The detailed comparison of the EOS parameters with the results of Pamato et al.\n(2020) would be indeed interesting, but it is beyond the scope of the present study. EOS\nparameters, as well as density, are not involved in the EVPSC modeling, and hence, anisotropy\ncalculation. Viscosity calculation indeed includes density, though that is merely one parameter\namong several others. However, as previously mentioned, we tried to put the density of the\nalloy from Pamato et al. (2020) to the viscosity calculation and the obtained value of viscosity\nwithin the uncertainty range.\nWe have not performed concentration calculations based on partitioning as we mentioned\npreviously, and added the reason to the text (lines 258-262). Such concentration calculation\nwould require many parameters that are not currently available. Therefore, instead of\ncalculation, we employed a qualitative trend based on general considerations of the solidus\ncurve.\nResponse to Reviewer 2:\nThis manuscript shows X-ray diffraction measurements on an Fe-Si-C alloy at high pressure\nand high temperature. The sample’s deformation behavior is extrapolated to Earth’s core\nconditions. The main conclusion is that the properties of the specific composition analyzed\nmatch the seismic anisotropy in the Earth’s core. The effort the authors devoted to all the steps\nof the experiment and the analysis is very clear. The careful sample preparation in piston-\ncylinder apparatus followed by microprobe compositional analysis is very much appreciated,\nas well as the difficult resistive heating experiments with a panoramic diamond anvil cell. The\nradial X-ray diffraction data analysis is also challenging and the authors clearly show that they\nmaster all these complicated steps.\nWe thank Reviewer #2 for the positive evaluation of our experimental work.\nHowever, the results are shown quickly, leaving the reader with a long list of unaddressed\nquestions. A solid interpretation and understanding of the results is missing, while much effort\nis devoted to discussing extrapolated parameters in relation to Earth’s core. Unfortunately, the\nextrapolations are presented without confidence intervals, leaving the reader uncertain about\ntheir true significance. The structure of the manuscript is also quite unfriendly: Conclusions\nare missing, in the Methods are presented results (for example lines 332 – 338) and the reader\ncontinuously has to jump between methods, supplementary material, figures captions and\nliterature to have basic fundamental information of what is being presented. I thus believe that\nthe authors need to revisit their work strengthening the robustness of their findings as well as\nimproving the form of the manuscript before it can be published.\nAnswer:\nFollowing the reviewer’s suggestions we have reorganized the structure of the manuscript to\nincrease its clarity and added a conclusion (lines 266-272) Added/modified parts are\nhighlighted in yellow, and rearranged parts are highlighted in turquoise. The responses to\nspecific points of criticism are provided below.\nMajor comments: -\nLine 99:\nQuestion: The authors state that the lattice strain parameter at 300 K and at 1100 K overlap\nwithin the uncertainty up to 60 GPa. In Line 110 the authors determine the variation of the\nlattice strain parameter as a function of temperature at 36 GPa. These two findings are in\ncontradiction. From Fig. 2 the dQ/dT value seem to vary a lot with pressure (as the authors\nstate, the 1100 K values decrease with pressure while the 300 K values increase). What is the\nsignificance of a dQ/dT calculated only at one pressure? How does this compare with the other\npressures (even if with only two measured temperatures)? Moreover, the dQ/dT is compared\nwith the literature, but the PT conditions of validity of the literature value are not mentioned.\nAnswer: There was indeed an unclear statement regarding the temperature effect on the lattice\nstrain parameter. We observe an overlap of 〈𝑄(ℎ𝑘𝑙)〉 values at 300 K and 1100 K within the\nerror bars if we use lattice strains of (100), (002), and (103) lattice planes for its determination.\nWe plot the 〈𝑄(ℎ𝑘𝑙)〉 averaged only over these planes because we can use exclusively their\nreflections for the entire pressure range at 300 K. Therefore, at 1100 K in Fig. 1 (former Fig.\n2) we also show 〈𝑄(ℎ𝑘𝑙)〉 calculated only from (100), (002), and (103) lattice strains for a\ncorrect comparison. We have modified the text accordingly to clarify this point (lines 77-81,\n𝜕𝑄\n117-118). For the calculation of we were able to use a more complete set of planes, namely\n𝜕𝑇\n(100), (002), (101), (102), (110), (103) and (112).\nThe decrease of 〈𝑄(ℎ𝑘𝑙)〉 at 1100 K above 60 GPa occurs because of the precipitation of Fe C,\n3\nwhich means the release of carbon from the alloy and we find this data not representative for\n𝜕𝑄\nthe calculation of .\n𝜕𝑇\n𝜕𝑄\nThe correct comparison of at different pressures is difficult with the available data since at\n𝜕𝑇\n𝜕𝑄\nWe agree that the determination of at different pressures would be interesting, however,\n𝜕𝑇\neven its determination along one isobar is already quite challenging. Please note that in most\n𝜕𝑄\nof the previous studies was simply assumed to be zero. We have used 7 temperature points,\n𝜕𝑇\n𝜕𝑄\nthat were distributed relatively uniformly in the range of 373-1073 K to calculate at 36±3\n𝜕𝑇\nGPa (Supplementary Fig. 2). To the best of our knowledge, there is only one determination\n𝜕𝑄\nof by Brennan et al. (2021) at 43-46 GPa and 300-1800 K. However, their results are\n𝜕𝑇\neffectively divided into two clusters, with one point at 300 K and others at 1400-1800 K\n(Brennan et al. (2021), Figure S1) with a 1000 K gap. Moreover, Brennan et al. (2021) obtained\ntheir results by laser heating which is usually associated with large temperature gradients, while\nwe used uniform resistive heating. Following the reviewer’s suggestion, we have added the\npressure-temperature conditions of Brennan et al. (2021) to the main text (lines 101-102).\nLine 101:\nQuestion: The decrease is very small and within the uncertainty. Is the same decrease visible\nfor the considered lattice planes? Or is it just an effect of the average? The authors claim this\ndecrease is due to the formation of cementite. Can they quantify from the diffraction patterns\nthe amount of cementite present in their sample and check if this is consistent with their\nhypothesis? If cementite is forming it means that the alloy is heterogeneously depleted in\ncarbon and more silicon rich. How would this affect the results shown?\nAnswer: We see either a decrease or the same level of individual 𝑄(ℎ𝑘𝑙) at 1100 K and above\nindeed small, yet without precipitation of Fe C, it is not expected to occur at all. Quantification\n3\nof the amount of cementite (Fe C) unfortunately is not possible since cementite crystallizes in\n3\na small number of single-crystal grains (see Supplementary Fig. 1a) that precluded a proper\nRietveld refinement. We observe a qualitative increase in the amount of Fe C diffraction lines\n3\nwith time and, therefore, with pressure increase. To minimize the influence of the\ncompositional changes of the sample on our results, we do not use data above 60 GPa for\ncomparison with the EVPSC modeling, so it does not affect the results.\nQuestion: Fig.2 : Fe-5Si data from ref [18] are shown, while in Supplementary Fig. 3 are shown\nFe-5Si and Fe-9Si data from ref [10]. If they are the same data, please refer to them consistently.\nAnswer: The reference numbers in the main text and supplementary of the Nature\nCommunication journal are independent. Following the reviewer’s suggestion to improve\nclarity, we modified the reference in Supplementary Fig. 5 (former Supplementary Fig. 3)\nto Brennan et al. (2021).\nQuestion: Why are Fe-9Si data missing in Fig.2? Please specify in the caption the temperature\nof all data sets.\nAnswer: We have not displayed Fe-9Si initially so as not to overload the plot, since Fe-9Si\ndata points are similar to Fe-5Si. Now we have modified Fig. 1 (former Fig. 2) and added Fe-\n9Si. We have added the temperature conditions to the caption (lines 119, 122).\nQuestion: Supplementary Fig.1: it would be useful to show here which lattice planes were used\nfor the determination of Q.\nAnswer: We have marked the Laue indices of the planes that were used for the calculation of\n𝑄(ℎ𝑘𝑙) in Supplementary Fig. 1.\nMinor comments: -\nLine 65:\nQuestion: probably here it’s worth mentioning that the sample is polycrystalline and\nsynthetized at high pressure and temperature. Why did the authors choose this specific\ncomposition? –\nAnswer: We have modified the text accordingly (lines 65-66), mentioning that the sample is\npolycrystalline and it was obtained at high-temperature high-pressure conditions. We have\nchosen this composition because of its proximity to the suggested compositions for the Earth’s\ninner core (e.g., Li et al. (2018), Miozzi et al. (2020)) (lines 66-67).\nLine 78:\nQuestion: The scale indicating the multiples of mrd in Fig. 1 goes maximum to 4. I understand\nthat the scale is not the same for the 300 K and the 1100 K cases. –\nAnswer: We have modified Fig. 2 (former Fig. 1) and now there are two different scales for\nLine 137:\nQuestion: Too many information missing. I suggest you to change the sentence with something\nlike: “Finally, by combining the stiffness tensor components from the literature and the\nextrapolated value of Q, we calculated the yield strength of Fe-2Si-0.4C at core conditions.”\nAnswer: We have modified the text accordingly (lines 177-179).\nQuestion: The uncertainty of this value, as shown in Supplementary Fig. 4 looks very small.\nHave the authors propagated the uncertainties over the extrapolation? In any case, it is worth\nmentioning how this uncertainty was determined, before claming that it is smaller than the\nprevious one.\nAnswer: The uncertainty of the yield strength extrapolations comes from the uncertainty of\n〈𝑄(ℎ𝑘𝑙)〉 at high-pressure high-temperature conditions and the uncertainties of the shear\nmodulus value that originate from the uncertainties of the stiffness tensor components.\nAlthough the EVPSC modelling does not directly provide the uncertainties for the 〈𝑄(ℎ𝑘𝑙)〉\nvalues, in order to estimate the uncertainties of the model, we have varied all the stiffness tensor\ncomponents within their uncertainties (Supplementary Table 13). That provides us the ability\nto calculate the range of possible 〈𝑄(ℎ𝑘𝑙)〉 values up to the core conditions. We have added the\npropagations of uncertainties to the determination of 〈𝑄(ℎ𝑘𝑙)〉 at high pressure in\n𝜕𝑄\nSupplementary Fig. 5. Also we have added the uncertainty of the determination of\n𝜕𝑇\n(Supplementary Fig. 2) Applying the uncertainties of 〈𝑄(ℎ𝑘𝑙)〉 modeling at high pressure, we\nchanged the uncertainties propagation of the yield strength (Fig. 5). We have modified the text\naccordingly (lines 179-182).\n- Line 222:\nQuestion: some “shades” are visible in the backscattered electron image, while the\ncompositions look completely homogeneous. Are the two images taken on the exact same spot?\nCan you add a compositional scale to the elemental X-ray distribution maps? What do the\ncolors represent?\nAnswer: The compositional maps were taken from the same spot as the backscattered electron\nimage. We have taken compositional maps only in the squared form (the centers of images are\nthe same). The differences in the SEM image in lighter and darker areas are caused by electron\nchannelling due to different crystal orientations. Interpretation of the color bar is: red pixels\nhave a high quantity of the element while blue pixels have a low quantity of the element. We\nhave added these clarifications to the caption of Supplementary Fig. 6. Please note, that the\ncolor maps there are qualitative and, thus, the quantitative legend cannot be provided."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have now looked at the revised version of the manuscript “Depth-dependent anisotropy in the Earth’s inner core linked to chemical stratification” by Kolesnikov and co-authors. Before getting into the details, I want to apologize with the authors for the delay of my review and thank them for the thorough response to my previous comments.\nThe authors made a great effort in making the manuscript more accessible and clearer for the reader and I think it has improved in respect to the first version, but it still requires some work.\nI have few more questions and some comments that I think will improve the paper. After this I think the work will be a nice contribution to the field.\nThe authors start discussing the results without mentioning what is the stable crystallographic structure and potentially the chemistry of the sample. Only after a while hcp Fe-2Si-0.4C starts being mentioned. It would be great if a mention to the structure and chemistry could be added so that a reader can understand better.\nOn the iron side, starting at 36 GPa with the high temperature data the authors might cross the fcc stability field before the hexagonal structure becomes the stable one? It would be great if the author can comment on this. The only mention of the chemistry comes in line 89 where the manuscript states “We observe the appearance of new reflections in the X-ray diffraction patterns that correspond to the formation of Fe3C” and then in line 90 there is a reference about hcp being stable with Fe3C but there are no reference to what are the structures are before that or even in the image of the diffraction patterns in the supplementary.\nIt should also be mentioned what is the initial structure of the alloy (maybe in the methods where the sample is described?) and not only in the caption of supplementary Figure 3.\nAdditionally, the Fe-Si-C alloy is defined in different ways across the paper, e.g., it starts as hcp Fe-2Si-0.4C , then in line 360 it is defined as hcp Fe alloy then in line 190 and further down it is referred to as Fe-2Si-0.4C. I’d suggest using one of the three across all the parts of the paper to improve clarity for the reader.\nOn this note, I think Figure Supplementary 1 needs some clarity. This is the first image in which raw data are shown, it would be great if there can be some more details to make it more understandable. What is the color scale? And what are the other phases for the 1100 K data? Why in the figure at 1100 K only the peaks of Fe3C are shown?\nI would also add to the caption of figure b that it is to show the contribution of the gasket to the diffraction pattern, as readers might wonder why there is no sample listed.\n“Carbon-free compositions, like pure Fe17, Fe-Ni alloys24 and Fe-5 wt % Si25, display smaller 〈(cid:1)(ℎ(cid:2)(cid:3))〉 values compared to Fe-2Si-0.4C (Fig. 1a). Hence, the partial loss of carbon from the starting composition during heating likely causes the decrease in the averaged lattice strain parameter in the iron-silicon-carbon alloy.”\nThe data the authors are comparing with, are data collected with another scope in mind and consequently trying to be as hydrostatic as possible and with another beamline geometry (axial and not radial). Because their conclusion for this portion is based on the comparison, can the authors comment on how reliable it is to compare datasets collected in such different ways?\nIn line 252 the authors mention the concentration of C in the solid solution changing with temperature\nThe data proposed were collected in axial standard geometry, does it matter?\nLine 46: “explain the density deficit compared to reported by seismic models” Seems like maybe only compared to or reported by should be kept?\nLine 76 and 78: Q(hkl) are written with different formalisms.\nLine 81: Typo: “lattice stains”\nLine 87: “Compared to presented” there is a subject missing?\nLine 90: “co-existence of Fe3C and hcp-Fe-Si-C alloy” I think Miozzi et al. observed hexagonal structured iron from the diffraction pattern and they used the volume increase to infer the presence of Si and C in the structure of the iron. Is the same structuring and volume observed for the “material” in this work to confirm that indeed is a similar phase?\nLine 97: “providing only the upper boundary for 〈(cid:1)(ℎ(cid:2)(cid:3))〉.” What do the authors mean?\nSupplementary figure 1: The spacing between top and bottom needs to be bigger. Both the figures look like it is only one and not two.\nLine 176: “to derive 〈(cid:1)(ℎ(cid:2)(cid:3))〉 values that are further utilized the constrained (cid:4)(cid:1) (cid:4)(cid:5) to calculate 〈(cid:1)(ℎ(cid:2)(cid:3))〉 at core temperatures.”\nNot clear what the authors meant here, maybe it was “to constrain (cid:4)(cid:1) (cid:4)(cid:5)”?\nLines 193-196: “Within the pressure range investigated in our study, however, hcp-Fe-2Si-0.4C displays higher strength than the iron-silicon alloys studied by Brennan et al. (2021)25 (Fig. 1b). This discrepancy likely arises from the extrapolation of 〈(cid:1)(ℎ(cid:2)(cid:3))〉 values to core conditions.”. I am confused by this sentence, how can a discrepancy in the studied pressure range depend on an extrapolation at core condition? Maybe the authors meant something else?\nLine 232: “experimental Vp anisotropy”. If the Vp is estimated (line 231) from the texture modelling I think it shouldn’t be called “experimental”. It might lead people to think it was an experimentally observed quantity, while it is an estimate, from a model in turn based on the experiments.", "reviewer_2": "The authors indeed put some effort in trying to ameliorate the structure of their manuscript, which now reads better than the previous version. However, the manuscript still does not stand alone as too many essential information (especially Figures) have to be looked for in the supplementary materials to be able to understand what the authors are talking about.\nMoreover, the authors tried to answer the question about previous line 101 (current 84) referencing to the data in table 2 of supplementary materials. I plotted these data and I performed a linear fit of the average over all the lattice planes indicated in line 86. The result I obtain is y = 9e-06 x + 0.0053, which is increasing over pressure and not decreasing as stated in lines 85-87. The statement in line 91 and the related conclusions are thus not supported by the data presented in the paper. The statement in line 91 is also in contradiction with what is shown in Supplementary Figure 5.\nI thus feel that still some work has to be done to make this manuscript ready for publication and that Nature Communications is probably not the suitable choice of journal."}, "author_response": "REVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nI have now looked at the revised version of the manuscript “Depth-dependent anisotropy in the Earth’s inner core linked to chemical stratification” by Kolesnikov and co-authors. Before getting into the details, I want to apologize with the authors for the delay of my review and thank them for the thorough response to my previous comments.\nThe authors made a great effort in making the manuscript more accessible and clearer for the reader and I think it has improved in respect to the first version, but it still requires some work. I have few more questions and some comments that I think will improve the paper. After this I think the work will be a nice contribution to the field.\nWe thank Reviewer #1 for the positive evaluation of our revised work. We have further refined the structure of the manuscript: added or modified parts are highlighted in yellow, and moved parts are highlighted in turquoise.\nThe authors start discussing the results without mentioning what is the stable crystallographic structure and potentially the chemistry of the sample. Only after a while hcp Fe-2Si-0.4C starts being mentioned. It would be great if a mention to the structure and chemistry could be added so that a reader can understand better.\nWe have unified the sample naming throughout the text to hcp-Fe-2Si-0.4C, where applicable.\nOn the iron side, starting at 36 GPa with the high temperature data the authors might cross the fcc stability field before the hexagonal structure becomes the stable one? It would be great if the author can comment on this. The only mention of the chemistry comes in line 89 where the manuscript states “We observe the appearance of new reflections in the X-ray diffraction patterns that correspond to the formation of Fe3C” and then in line 90 there is a reference about hcp being stable with Fe3C but there are no reference to what are the structures are before that or even in the image of the diffraction patterns in the supplementary.\nWe have clarified the transformation path for the samples in the lines 75-77, and added example XRD patterns in Supplementary Fig. 1. The starting material was bcc-structured Fe-2Si-0.4C, which began to transform into the hcp phase above 10 GPa and 300 K. The process of transformation completes at ~27 GPa.\nDuring the resistive heating experiments, we indeed observed face-centered cubic (fcc) structure; however, it was as a less abundant component, compared to hcp phase, and completely disappears at ~55 GPa and 1100 K. We added the reference to lines 77-80.\nIt should also be mentioned what is the initial structure of the alloy (maybe in the methods where the sample is described?) and not only in the caption of supplementary Figure 3.\nAdditionally, the Fe-Si-C alloy is defined in different ways across the paper, e.g., it starts as hcp Fe-2Si-0.4C , then in line 360 it is defined as hcp Fe alloy then in line 190 and further down it is referred to as Fe-2Si-0.4C. I’d suggest using one of the three across all the parts of the paper to improve clarity for the reader.\nThe initial structure of the sample (bcc) is now explicitly mentioned in line 75 and in the Methods section (lines 354-355), in addition to the Supplementary Fig. 3 caption. We have also unified the sample naming as hcp-Fe-2Si-0.4C throughout the text, where applicable.\nOn this note, I think Figure Supplementary 1 needs some clarity. This is the first image in which raw data are shown, it would be great if there can be some more details to make it more understandable. What is the color scale? And what are the other phases for the 1100 K data? Why in the figure at 1100 K only the peaks of Fe3C are shown?\nI would also add to the caption of figure b that it is to show the contribution of the gasket to the diffraction pattern, as readers might wonder why there is no sample listed.\nWe have moved former Supplementary Fig. 1 to the main text as Fig. 1 and added additional legends to improve clarity. In the diffraction pattern collected at 300 K, the identified phases are Be, BeO, and the hcp-Fe-2Si-0.4C sample (marked by Laue indices at the top). At 1100 K, the observed phases are Au (pressure standard), Au (outside of the pressure chamber), Fe C impurity, 3 and the hcp-Fe-2Si-0.4C sample (also marked by Laue indices at the top). Previously, these phases were indicated by symbols, described in the figure caption; we have now added their names alongside the symbols for clarity. The color scale represents the square root of intensity, as stated in the legend.\n“Carbon-free compositions, like pure Fe17, Fe-Ni alloys24 and Fe-5 wt % Si25, display smaller 〈(ℎ𝑘𝑙)〉 values compared to Fe-2Si-0.4C (Fig. 1a). Hence, the partial loss of carbon from the starting composition during heating likely causes the decrease in the averaged lattice strain parameter in the iron-silicon-carbon alloy.”\nThe data the authors are comparing with, are data collected with another scope in mind and consequently trying to be as hydrostatic as possible and with another beamline geometry (axial and not radial). Because their conclusion for this portion is based on the comparison, can the authors comment on how reliable it is to compare datasets collected in such different ways?\nWe consider the comparison reliable, because in all cited studies, namely pure Fe (Gleason & Mao (2013)), Fe-Ni alloys (Reagan et al. (2018)) and Fe-5 wt % Si (Brennan et al. (2021)), 〈𝑄(ℎ𝑘𝑙)〉 values were measured under intentionally non-hydrostatic conditions using radial X-ray diffraction geometry. Our experiments were conducted under the same type of conditions, ensuring that the comparison is meaningful.\nIn line 252 the authors mention the concentration of C in the solid solution changing with temperature\nThe data proposed were collected in axial standard geometry, does it matter?\nThe discussion in line 302 (former line 252) concerns the Fe-C phase relations at inner core conditions. The results of Mashino et al. (2019) obtained using axial geometry under quasi-hydrostatic conditions are directly applicable because the Earth’s inner core is also under quasi-hydrostatic conditions, with the hydrostatic pressure exceeding 3.29·1011 Pa and estimated shear stresses <106 Pa, i.e., at least five orders of magnitude lower. Therefore, the change of C concentration with temperature inferred from Mashino et al. (2019) remains relevant for inner core conditions.\nLine 46: “explain the density deficit compared to reported by seismic models” Seems like maybe only compared to or reported by should be kept?\nWe have modified the sentence accordingly (line 46).\nLine 76 and 78: Q(hkl) are written with different formalisms.\nHere, in lines 81 and 83 (former 76, 78) we use different formalisms in order to make a distinction between the lattice strain parameter 𝑄(ℎ𝑘𝑙) of individual lattice planes and the averaged lattice strain parameter 〈𝑄(ℎ𝑘𝑙)〉 that is averaged from 𝑄(ℎ𝑘𝑙) of several lattice planes.\nLine 81: Typo: “lattice stains”\nWe appreciate the thorough reading of Reviewer#1 and have corrected the typo.\nLine 87: “Compared to presented” there is a subject missing?\nWe have modified the statement in line 103 (former line 87) to make it clearer.\nLine 90: “co-existence of Fe3C and hcp-Fe-Si-C alloy” I think Miozzi et al. observed hexagonal structured iron from the diffraction pattern and they used the volume increase to infer the presence of Si and C in the structure of the iron. Is the same structuring and volume observed for the “material” in this work to confirm that indeed is a similar phase?\nWe observe the same structure (i.e., hcp) and similar unit cell volumes as Pamato et al. (2020) and Miozzi et al. (2020), as we show in Supplementary Fig. 6.\nLine 97: “providing only the upper boundary for 〈(ℎ𝑘𝑙)〉.” What do the authors mean?\nHere in line 114 (former line 97), we mean that since 𝜕𝑄/𝜕𝑇 is a negative value, therefore, previous assessments that considered 𝜕𝑄/𝜕𝑇 as simply zero, provided only a maximum value, i.e., an upper bound for 〈𝑄(ℎ𝑘𝑙)〉.\nSupplementary figure 1: The spacing between top and bottom needs to be bigger. Both the figures look like it is only one and not two.\nWe have modified Fig. 1 (former Supplementary Fig. 1) accordingly.\nLine 176: “to derive 〈(ℎ𝑘𝑙)〉 values that are further utilized the constrained 𝜕𝑄 𝜕𝑇 to calculate 〈𝑄(ℎ𝑘𝑙)〉 at core temperatures.” Not clear what the authors meant here, maybe it was “to constrain 𝜕𝑄 𝜕𝑇”?\nWe first use our EVPSC deformation model to obtain 〈𝑄(ℎ𝑘𝑙)〉 at core pressures, which are higher than the experimentally observed range. We then apply the previously determined 𝜕𝑄/𝜕𝑇 to these values to account for the effect of temperature, thereby estimating the averaged lattice strain parameter of hcp-Fe-2Si-0.4C at core pressures and temperatures. We have modified the sentence for clarity (lines 225-227).\nLines 193-196: “Within the pressure range investigated in our study, however, hcp-Fe-2Si-0.4C displays higher strength than the iron-silicon alloys studied by Brennan et al. (2021)25 (Fig. 1b). This discrepancy likely arises from the extrapolation of 〈(ℎ𝑘𝑙)〉 values to core conditions.”. I am confused by this sentence, how can a discrepancy in the studied pressure range depend on an extrapolation at core condition? Maybe the authors meant something else?\nWithin the experimentally observed pressure range (Fig. 2b) hcp-Fe-2Si-0.4C demonstrates higher strength than the Fe-Si alloys studied by Brennan et al. (2021). However, when extrapolated to core conditions (Fig. 6), the extrapolated strength of the Fe-Si alloys is much higher than that of hcp-Fe-2Si-0.4C. We attribute this apparent discrepancy to the linear extrapolation applied by Brennan et al. (2021). We have modified the sentence for clarity (lines 245-246).\nLine 232: “experimental Vp anisotropy”. If the Vp is estimated (line 231) from the texture modelling I think it shouldn’t be called “experimental”. It might lead people to think it was an experimentally observed quantity, while it is an estimate, from a model in turn based on the experiments.\nWe agree with the reviewer that this may be confusing and therefore we have modified the sentence to clarify that the velocities are derived from the experimental textures (line 283, former line 232). Anisotropy at core conditions obtained using the EVPSC texture modeling are referred to as extrapolated like in line 281 (former line 231) and line 287.\nReviewer #2\n(Remarks to the Author):\nThe authors indeed put some effort in trying to ameliorate the structure of their manuscript, which now reads better than the previous version. However, the manuscript still does not stand alone as too many essential information (especially Figures) have to be looked for in the supplementary materials to be able to understand what the authors are talking about.\nWe thank Reviewer#2 for the positive evaluation of our efforts. We have moved several figures, a table and Discussion from the Supplementary to the main text to improve the presentation of our study. We have further refined the structure of the manuscript: added or modified parts are highlighted in yellow, and moved parts are highlighted in turquoise.\nMoreover, the authors tried to answer the question about previous line 101 (current 84) referencing to the data in table 2 of supplementary materials. I plotted these data and I performed a linear fit of the average over all the lattice planes indicated in line 86. The result I obtain is y = 9e-06 x + 0.0053, which is increasing over pressure and not decreasing as stated in lines 85-87. The statement in line 91 and the related conclusions are thus not supported by the data presented in the paper. The statement in line 91 is also in contradiction with what is shown in Supplementary Figure 5.\nI thus feel that still some work has to be done to make this manuscript ready for publication and that Nature Communications is probably not the suitable choice of journal.\nWe appreciate Reviewer#2’s effort to verify the reproducibility of our results. We performed the same procedure, plotting the averaged lattice strain parameter 〈𝑄(ℎ𝑘𝑙)〉, calculated from planes (100), (002), (101), (102), (110) and (103) in Response Figure 1 using the data reported in Supplementary Table 2. For convenience, we reproduce below Supplementary Table 2.\nWe observe that 〈𝑄(ℎ𝑘𝑙)〉 increases up to ~60 GPa and then decreases, as noted in lines 101-104 (former lines 84-87), 107-108 (former line 91). A linear fit of 〈𝑄(ℎ𝑘𝑙)〉 versus pressure over the entire dataset yields a negative slope of -6(±2)·10-6 GPa-1. When considering only the decreasing region above 60 GPa, a linear fit gives a slope of -1.4(±0.3)·10-5 GPa-1 (Response Figure 1). These results are fully consistent with our statements in lines 101-104 and 107-108 of the main text (former lines 84-87 and 91).\nWe were unable to reproduce the positive slope (y = 9e-06 x + 0.0053) reported by Reviewer#2. To improve clarity, we have modified lines 107-108 (former line 91) to explicitly highlight that the decrease of 〈𝑄(ℎ𝑘𝑙)〉 at 1100 K occurs above 60 GPa, eliminating the apparent contradiction with Fig. 4 (former Supplementary Fig. 5)."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I have now looked at the revised version of the paper. I think the manuscript reads well in its current form and I thank the authors for their work. They clarified the points that I had questions on, and made the manuscript approachable despite the short format. I have no further comments.", "reviewer_2": "I apologize with the authors for my mistake trying to verify their results. Their statement about the pressure evolution of the averaged lattice strain parameter <Q(hkl)> was indeed correct.\nThe manuscript indeed reads much better now than in the previous versions, and the findings are more clearly presented and discussed.\nStill, I don’t understand the relevance of showing lattice strain parameter averaged on a different set of reflections (Fig. 2 and Fig. 4.), especially given that the trend of the average over pressure changes according to the number of reflections considered: for example, in Fig 2 (average over 3 reflections) the general trend is that d<Q>/dP is negative, while in Figure 4 (average over 6 reflections) it is positive.\nMoreover, I think it would be appreciable to have a more developed and dedicated conclusion paragraph.\nIn conclusion, in this manuscript it is shown how the anisotropy is dependent on the chemistry. Measurements up to about 100 GPa and 1100 K are used to model the deformation mechanisms, yield strength and viscosity of hcp Fe-2Si-0.4C at core conditions. My only reservation is whether such a technical work meets the criteria for a high-impact journal."}, "author_response": "Response to reviewers\nREVIEWER COMMENTS\nReviewer #1\n(Remarks to the Author): I have now looked at the revised version of the paper. I think the manuscript\nreads well in its current form and I thank the authors for their work. They clarified the points that I had\nquestions on, and made the manuscript approachable despite the short format. I have no further\ncomments.\nWe thank Reviewer #1 for the positive evaluation of our revised work.\nReviewer #2 (Remarks to the Author):\nI apologize with the authors for my mistake trying to verify their results. Their statement about the\npressure evolution of the averaged lattice strain parameter <Q(hkl)> was indeed correct.\nThe manuscript indeed reads much better now than in the previous versions, and the findings are more clearly presented\nand discussed.\nWe thank Reviewer #2 for the positive evaluation of our revised work.\nStill, I don’t understand the relevance of showing lattice strain parameter averaged on a different set of\nreflections (Fig. 2 and Fig. 4.), especially given that the trend of the average over pressure changes\naccording to the number of reflections considered: for example, in Fig 2 (average over 3 reflections)\nthe general trend is that d<Q>/dP is negative, while in Figure 4 (average over 6 reflections) it is positive.\nFig. 2 shows the comparison of the entire dataset of the derived 〈𝑄(ℎ𝑘𝑙)〉 values at 300 K and at 1100\nK. Since only 3 lattice planes are available at 300 K, we also used only these 3 lattice planes at 1100 K\nfor a correct comparison. Fig. 4, in turn, displays only the data that were used for the comparison with\nthe EVPSC modeling, explicitly excluding the data above 60 GPa that show a negative trend as\nunreliable. For a more accurate comparison with the EVPSC modeling, we use the full set of available\nlattice planes. We, thus, believe that both figures are necessary for the correct representation of our data\nand for the correct use of our data in future studies.\nMoreover, I think it would be appreciable to have a more developed and dedicated conclusion\nparagraph. In conclusion, in this manuscript it is shown how the anisotropy is dependent on the\nchemistry. Measurements up to about 100 GPa and 1100 K are used to model the deformation\nmechanisms, yield strength and viscosity of hcp Fe-2Si-0.4C at core conditions. My only reservation is\nwhether such a technical work meets the criteria for a high-impact journal.\nWe have modified the conclusions accordingly (lines 248-260). We kindly disagree with the\nreviewer that our work is too technical for a high-impact journal. We modeled the deformation\nof hcp-Fe-Si-C alloy up to the core pressures, and the results of our modeling qualitatively\ncorrespond to the observations at extreme conditions in refs 1,2. We note that our work\nconstraints for the first time the combined effect of two key candidate light elements, C and Si,\non the anisotropy of hcp-Fe at high-temperature conditions. Hence, the results allow for a more\nreliable extrapolation of the anisotropy estimates at inner core conditions compared to previous\nmodels based on linear extrapolations and/or room temperature data. Moreover, our results\ntogether with literature data for hcp-Fe provide for the first time qualitative constraints on the\neffect of chemical stratification on the anisotropy pattern of the inner core. We thus consider\nthat these results are of great interest for the broad scientific community.\nResponse references\n1. Ikuta, D. et al. Sound velocity of hexagonal close-packed iron to the Earth’s inner core\npressure. Nat Commun 13, 7211 (2022).\n2. Sakamaki, T. et al. Constraints on Earth’s inner core composition inferred from\nmeasurements of the sound velocity of hcp-iron in extreme conditions. Sci. Adv. 2,\ne1500802 (2016)."}]

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