Peer review of: Electronic correlations and transport in iron at Earth’s core conditions (2020)

Reviewers' comments: 
 
Reviewer #1 (Remarks to the Author): 
 
The authors attempt to compute the thermal conductivity of the bcc Fe at the PT conditions of the 
inner core. The stability of the bcc Fe in the IC was demonstrated by Belonoshko et al. (Nature, 2003) 
for the EAM model of iron. In 2017, Belonoshko et al. (Nature Geoscience) showed by ab initio MD, that 
the bcc Fe is stabilized by the mechanism of self-diffusion (the authors call this mechanism 'strong 
anharmonic vibrations') 
that allows to release the deviatoric stress. It was demonstrated that to activate that mechanism large 
(by ab initio MD standards) cells (on the order of 1000 atoms and more to reach the convergence) are 
needed. Indeed, Godwal et al. (EPSL, 2015) demonstrated that Vocadlo et al. (Nature, 2003) simulations led 
to configurations of bcc subjected to deviatoric stress, therefore Vocadlo et al. did not demonstrate the 
mechanical (and the more so thermodynamical) stabilization of the bcc phase. 
 
In the submitted manuscript, the authors again try to study small bcc cells where the mechanism of the bcc 
stabilization is 
not and can not be activated (Belonoshko et al., Nature Geosciecne, 2017). Since the thermal disordering is 
critical for 
correct calculations of the thermal conductivity (Fig. 1) and the 2x2x2 and 3x3x3 cells are too small to 
capture that disorder 
correctly, it is highly likely (to put it mildly) that the calculated thermal conductivity is not correct. The 
authors are trying to estimate 
the impact of the supercell size on the obtained data by performing calculations for 2x2x2 and 3x3x3 
supercells. They obtain the difference 
of 6 percent. This is not the evidence for the size converged results, because both cells are way too small for 
the 
stabilization mechanism to be in place and for the relevant configurations to emerge. The disorder in the 
large supercells 
(where the liquid-like diffusion occurs) is much larger than in small ones and that will likely dramatically 
affect the results. 
 
Since, according to authors, they can not calculate thermal conductivity for large cells, revision will not help. 
Therefore, I suggest a 
rejection. 
 
 

Reviewer #2 (Remarks to the Author): 
 
Electronic correlations and transport in iron at Earth’s core conditions 
 
The paper presents the results and analysis of calculations of the electrical and thermal conductivities of bcc 
iron at Earth’s inner core conditions, including the effects of both electron-electron scattering and electron-
lattice scattering. Precise values of the thermal conductivity of iron at these conditions are essential for 
constraining the age and dynamics of the core, with significant implications for magnetic field generation and 
thermal evolution of Earth. However, experimental measurements of these properties at the relevant 
conditions are challenging and, results from much lower temperatures and pressure are often extrapolated 
to predict value at inner core conditions. 
 
Several recent first-principles studies have reported higher values than those predict by the extrapolation 
measurements made at much lower temperature and pressures. However, these neglected the influence of 
electron correlation and their validity has been questioned by later studies. Two scattering mechanisms 
exist: electron-electron scattering and electron-lattice scattering. Previous studies have tended to either 
neglect or approximate one mechanism, whereas the present study provides a full and detailed 
consideration of both. 

The authors find that electron-lattice scattering dominates, with the inclusion of electron-electron scattering 
leading to a reduction in the total calculated thermal conductivity of no more than 20 %. 
 
My feeling is that the results are significant; in particular, the finding that the electron-electron scattering is 
suppressed by thermal disorder. It is quite a technical paper, but comparable to the recent Nature 
Communications paper by Hausoel et al. (2017) on a similar topic and so I believe it fits within the aims and 
scope of the journal. 
 
Some comments and questions: 
 
- I am not an expert in DMFT and so will leave assessment of the method to the other reviewers. They 
authors appear to have carried out convergence tests to investigate possible finite-size effects. 
 
- Is it reasonable to assume same U value for hcp and bcc iron? Were the molecular dynamics calculations 
performed using LDA+U? 
 
- Comparing the result for bcc iron in Fig 2 in the current manuscript with those for fcc Ni in Supplementary 
Fig. 6 of Hausoel et al. (2017), can the author suggest why the effect of thermal disorder is important for 
bcc iron and not for fcc Ni? 
 
- The authors do not consider possible saturation of conductivity reported by Gomi et al. (2013) and 
included in the calculations of Xu et al. (2018). Can the authors comment on whether they think that 
saturation occur and if so, its possible influence on their values. 
 
- Though I understand that this is mainly a theoretical study of the importance of the different scattering 
mechanisms in bcc iron, the motivation for the paper is a better understanding of Earth’s core and so I think 
it would be useful for the authors to comment on 
 
- Is a 20 % reduction in thermal conductivity significant? Will it have a major effect on core dynamics? 
- The results presented are for pure bcc iron. What are the authors thoughts on how things will change once 
impurities, such as Ni, O and S, expected in the core are included. 
 
Some further minor comments: 
 
P1 Consider replacing ‘importantly affected’ with ‘greatly affected’. 
P2 Consider replacing ‘close to the melting’ with ‘close to melting’. 
P2 Consider replacing ‘standardly used’ with ‘routinely used’. 
P2 Consider replacing ‘notice that a spread’ with ‘notice that the spread’. 
FIG 1. It would be helpful in the caption to say what density Earth’s core volume corresponds to. 
 
 

Reviewer #3 (Remarks to the Author): 
 
The manuscript by Pourovskii et al. reports on the thermal and electrical conductivities of bcc iron at Earth's 
core pressure. Their calculations take into account electron-electron scattering as well as thermal disorder 
associated to the high temperatures at the center of the planet. 
The long-standing issue that Pourovskii et al. want to address regards the values of these conductivities 
obtained with density functional theory-based calculations, that are too large to explain the convection 
forces needed to currently sustain the geodynamo. 
The conclusions of the manuscript are that the thermal disorder reduces the conductivities in bcc iron and 
that the electron-electron scattering does not play a dominant role. 
Topic-wise the present manuscript is interesting. Below I list some important points which however in my 
opinion ought to be considered in order to make it meet the high goals of Nature Communications. 
-language/style: overall it does not read like a Nature Communications paper. The style is rather closer to a 
more specialized or even technical paper. In order to reach the standards of presentation of a Nature paper, 
the Authors should definitely make an effort and improve many parts of the manuscript. 
 
-poor reference to previous works: the way some references are cited and discussed needs a substantial 
revision. Here I specifically discuss the example of Ref. 19 which I happen to know well, but many other 
References may suffer from the same problem. At the end of page 1 a discussion about the van Hove 
singularity and its slowing down effect on electrons cites only Ref. 22 surprisingly ignoring the fact that this 
is a much more general mechanism discussed in, e.g. Phys. Met. Metallogr. 76, 247–299 (1993) or for the 
specific case of hcp iron with Ni impurities in Ref. 19, indeed. 
Further, in the two paragraphs at the beginning of page 2, credits to previous works is also missing, in 
particular when the authors claim that "disorder and many-electron effects has not been directly assessed in 
previous theoretical studies of transport in considering electron transport in bcc-Fe under conditions relevant 
to the inner core." This may be strictly true for transport calculations but in Ref. 19 a molecular dynamics + 
DMFT calculation has been explicitly carried out (even though indeed only showing its effects on the 
scattering rate) and hence -- at least for the scattering rate -- this study ought to be mentioned here. A 
similar lack of credits to previous MD+DMFT calculations in a similar context can be found in the second 
paragraph of the same page. 
 
-conclusions not supported by explicit calculations: the considerations about the possible similarity of results 
for the hcp phase made at the end of the manuscript are based on mere expectations rather than on results. 
While speculation might be inspiring in certain cases, I am afraid that they cannot be made on this issue, at 
least at this stage. As discussed in Ref. 19, in hcp iron the density of states is much more asymmetric and 
the chemical potential is not right inside a region of high density of states, as in bcc iron. Hence, without an 
explicit calculations, no reliable "extrapolation" of bcc behavior for corresponding hcp case can be made 
safely. The authors may either remove this speculative part completely, or discuss in a critical way all 
possibilities, or of course show further calculations, which however I am perfectly aware that they will be 
time consuming. 
 
-one further comment: I like the "game" of arbitrary increasing/decreasing ImSigma but are the Kramers-
Kronig relations between the real and imaginary part not affected by that? The real part ought to be 
accordingly changed when alpha is varied. 
 
Giorgio Sangiovanni