Effect of Carbon on the Volume of Solid Iron at High Pressure: Implications for Carbon Substitution in Iron Structures and Carbon Content in the Earth’s Inner Core
Round 1
Reviewer 1 Report
In order to determine the amount of carbon in Earth’s core, Yang et al. have made an impressive effort to push the precision of constraints on effect of C on the equation of state of Fe-C alloys. The hypothesis is that differences in the structure of Fe (bcc vs. hcp) and mode of incorporation of C (mixing as iron + carbide vs. single phase alloy) result in differences in implied properties of Earth’s core. These authors are specifically motivated by previous eutectic melting experiments that support the presence of hcp Fe-C alloys in the core. Since the amount of C in realistic core-relevant alloys is small, this work is technically challenging. I recommend publication with minor revisions.
Since precision is key to this work, here are a few areas where arguments for precision of the constraints can be strengthened/clarified.
The precision/accuracy of composition of the alloys: since the reported compositions are specified to the 0.01%, the same precision is needed on the correction to the background on the Fe standard. Line 139 gives a background C measurement of ~0.2%, not good enough precision. Uncertainty in this measurement must be reflected in the alloy compositions. Supplementary Figure S1 on the alloy compositions also has some inappropriate significant figures in the line fits, certainly not constrained to that many digits. The uncertainty listed on the compositions in line 142-143 is the standard deviation of the compositions obtained from multiple points on the samples (from Fig S1 caption), right?
Justification of data quality: The XRD data could be presented better. I would prefer to see Figures S3 and S4 as part of the main manuscript, with Figure 1 as inset. Even in these fuller versions of the figures, the 2theta range of the data is not so big, but we do need to see the whole pattern. The insets in Figure 1 don’t really add anything. It could be confusing that the curves in Fig 1 aren’t ordered from least to most carbon, as in S3 and S4. It’s also not really accurate to describe the y axis in Fig 1 as “normalized intensity” because the normalization is done in a weird way: the patterns appear to have first been offset by a constant shift in the y direction, and then normalized, resulting in very different relative intensities. I would rather see the relative intensities of these patterns about the same.
Stress conditions in the DAC: The approach to improve precision on the EOS is definitely appropriate, compressing three compositions together in the same DAC experiment in a quasi-hydrostatic medium. As the authors have documented, the pressure still varies across the sample chamber because the medium is still not really hydrostatic. The fact that the *higher pressure* sample is also *higher volume* helps to support the finding that C increases the volume in the alloy.
However, the variation of pressure implies that the deviatoric stresses also vary across the chamber! Deviatoric stresses may also result in systematic difference in observed volume—typically the experimental geometry in the DAC results in higher volume with higher deviatoric stress. Can the authors offer an analysis of relative deviatoric stress magnitudes for the different samples, either in the samples directly (linewidth analysis?) or via the local lattice strain in the Ne medium?
EOS constraints: Per table 1, the authors used fixed K0’ of 4.79 to match Fei et al. 2016 study of pure Fe. Of the two EOS fits from Fei et al. 2016, this seems like the wrong choice, because V0 in this fit does not agree well with this new study—V0 for Fe was higher than the highest V from the most C-rich alloy. Why use K0’=4.52, which came from the fit with a V0 that matches Fe in this study much better? Differences in V0 for Fe make it harder to directly compare K0 between fits.
Minor text edits and questions:
Recommend reorganizing section 2.2 to describe all synthesis/sample processing before EMPA
Recommend moving some material from beginning of Results section 3 to introduction—the background on the structures of Fe and solubility of C in these structures belongs earlier. Need to also give background to understand whether formation of the bct structure is novel, or expected result for this composition and conditions
Line 31 “a candidate”, not “the candidate”
Line 40 add “the” before hydrostatic
Line 77 “annealed” usually just refers to heating enough to remove stress, not enough to drive chemical changes
Line 92 “synthetic” better than “synthesized”
Line 96 “were” to “was”
Line 104 were samples polished first, or only cut with the knife from bulk?
Lines 116-117 add citations to authors of Dioptas and GSAS software packages
Line 148 better to say c direction diverges to get the bct structure than “with a c/a ratio”
Line 152 “higher angle with increasing pressure and decreasing unit cell size”
Lines 174-175 Sometimes the authors use “quasi-hydrostatic” to mean “almost hydrostatic”, sometimes more to mean “not actually hydrostatic.” Recommend to clarify here to “non-hydrostatic”.
Line 193 300 K AND 1 bar
Line 213: is the effect of increasing carbon content on volume linear?
Lines 222-226 Some authors called out by name, others grouped generally as “Theoretical calculations”, could be confusing. Would be appropriate to add discussion here of which DFT methods are employed and relevance of difference in methods
Line 241 clarify whether the authors here think this 300 GPa is a strongly-constrained, reliably certain pressure for change in C site
Line 285 clarify that “affect” here means “increase”
Line 342 remove extra “the”
Line 385 “dash” should be “dashed”
Section 4.3: comment on whether it is possible to distinguish alloy from iron/carbide mixture on the basis of physical properties alone, not just the melting mechanism
Author Response
Please see the attached word file
Author Response File: 
Author Response.pdf
Reviewer 2 Report
I think this paper is an important contribution to the understanding of the Earth’s core. Aim of this paper is to evaluate the effects of the carbon dissolution in hcp-iron on the constitution and the properties of the Earth’s solid inner core. This paper provides the first data set on the volume of the hcp-Fe containing carbon up to 135 GPa at room temperature to derive their equation of state. These allow us to discuss carbon content and the seismic anisotropy of the inner core.
This manuscript is very well structured and citations are appropriate. However, there are two parts that need to be reorganized.
In Discussion, the authors mentioned carbon substitution mechanism is unknown and two mechanisms, interstitial solid solution and substitutional solid solution, are possible mechanisms for carbon dissolution in hcp-Fe at high pressures. The author, however, clearly states in Abstract that carbon is contained in hcp-Fe by interstitial substitution (lines 14, 22-23). This is confusing and also misleads the readers. Abstract should be rewritten.
It is difficult to understand how the authors calculate carbon content in the inner core in second paragraph in Section 4.3 (lines 357-377). I can’t understand the equations shown in lines 362-364. For example, what does (1-0.31%)fFe(P,T) mean? This is a very important part in Discussion. The authors should explain the derivation of the carbon content of the inner core using proper formulas.
Specific comments on manuscript are below.
Line 204 and Table 1:
The unit cell volumes at the ambient conditions for fixed K0’ are not consistent among text and Table 1.
Table S1 and S2:
How does the authors estimate the errors of pressure in Table S1 and S2? At high pressure, Ne pressure medium is solidified as shown in paper to introduce the non-hydrostatic component of stress (deviatric stress). Are those effects on error of pressure included?
Figure S6:
Reference in the legend may be wrong. Fe and Brosh > Fei and Brosh.
Author Response
Please see the attached word file
Author Response File: Author Response.pdf
Reviewer 3 Report
Review of « Effect of Carbon on the Volume of Solid Iron at High Pressure: Implications for Carbon Substitution in Iron Structures and Carbon Content in the Earth’s Inner Core »
by Yang et al
submitted to /Minerals/
General comments:
The manuscript by Yang and co-workers aim to constrain the carbon content in the Earth’s inner core by investigating the compression behavior (in-situ X-ray diffraction measurements up to 135 GPa) of Fe-C alloys (with 0.31 and 1.37 wt% carbon), along with pure iron. The main conclusion of the present work is that the required C contents to explain the density deficit of Earth’s inner core are 1.3 and 0.43 wt.% at inner core boundary temperatures of 5000 K and 7000 K, respectively. However, this conclusion is drawn assuming that carbon is the only element present with Fe in the inner core. This assumption is unrealistic given the geochemical constraints. For instance, silicon is an important light element of the Earth’s core with about 2.3 wt.% and 2.8 wt.%in the inner core and outer core, respectively (Badro et al., 2007). So, that the conclusion of carbon alone stand with such amounts of silicon in the inner core? The authors need to discuss this matter.
In addition, several studies based on geochemical and cosmochemical constraints (Dasgupta and Walker, 2008; Dasgupta and Hirschmann, 2010; Dasgupta, 2013; Wood et al., 2013) concluded that given the low expected abundance of bulk Earth carbon that participated in metal-silicate fractionation, carbon is always going to be a minor light element in the core. This same conclusion was reached by a joint geochemical and geophysical argument as well (Badro et al., 2014). All numbers point to carbon abundance in the core being <1 wt.%, and mostly <0.3 wt.%. A lower estimate of 0.2 wt.% carbon in the core is derived by assuming that carbon depletion follows the volatility trend (McDonough, 2003). The authors need thus to discuss the most plausible range of C content in the Earth’s core (inner and outer core) and show that the numbers given in the present manuscript are consistent with the geochemical and cosmochemical constraints.
In summary, I found the experimental work presented in this paper to be compelling, however, the present results need to be discussed in the light of the available geochemical and cosmochemical constraints on the contents of carbon in the Earth’s core. Subject to the revisions suggested above, I recommend the publication of this paper in /Minerals/.
Minor comments:
1-Abstract: line 17: the authors need to precise that the in-situ X-ray diffraction up to 135 GPa is for pure iron, 87 GPa and 109 GPa for Fe-0.31C and Fe-1.37C, respectively.
2-Line 70: there is a typo … and pure Fe powder (instead of power).
3-Line 86: can the authors provide the analyses of their samples by EMPA (a table in the supplementary materials can be useful)?
4-Lines 133-135: I do not think that BSE images of polished samples can prove the homogeneity of the recovered samples. Additional chemical analyses of the recovered samples can be more convincing.
5-Lines 192-195: can the authors provide the units of the parameters (P, T, etc …) of the 3BM equation of state?
6-Lines 278-280: same comment for the modified Birch-Murnaghan EOS.
7-Lines 338-340: Carbon is _NOT_ the dominant light element in the Earth’s core. See the most recent models by Rubie et al. (2015), Badro et al. (2014) … The authors need to discuss their results within the plausible range of carbon content in the core.
8-Lines 347-349: Please provide the units of the parameters used in the thermal pressures equation.
9-Lines 355-356: The authors conclude that less than 1.37 wt.% carbon in the inner core is required to explain the density deficit. What about if another light element is present in the inner core such as silicon (see my general comments)?
10-Lines 375-377: Carbon is NOT the only light element in the Earth’s inner core.
11- Lines 395-396: Can the authors be more quantitative rather than just saying the amount of C would be reduced if other light elements also exist in the inner core?
Kind regards,
Author Response
Please see the attached word file
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
No additional comments.
The authors answer to all my comments of the first version of the present manuscript, and I found that the authors improved their second version of the manuscript.
