Peer review of: Low thermal conductivity of iron-silicon alloys at Earth’s core conditions with implications for the (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

The authors present the results of experiments to measure the thermal conductivity of solid iron alloys 
at high pressure and temperature. Two techniques are employed. The first technique is used to 
measure thermal conductivity at high pressure and room temperature. The second technique explores 
the simultaneous affects of high pressure and temperature. 

The results are both important and provocative. Recent theoretical calculations have suggested that 
the thermal conductivity of iron alloys is quite high. There is some experimental support for these 
values, but the measurements are not direct estimates of thermal conductivity. Instead, 
measurements of electrical conductivity are related to thermal conductivity using the Wiedemann-
Franz Law. A relationship between thermal and electrical conductivity is quite reasonable, although 
there has been some debate about the numerical constants used to relate these transport quantities. 

The results are provocative because the author advocate for a much lower thermal conductivity than 
that obtained from theory. This reduction in conductivity has enormous consequences for the thermal 
evolution of the core and the origin of the Earth's magnetic field. The authors have done a good job 
conveying the significance of their experiments and providing insightful and quantitative estimates for 
the implications. 

The most important question is whether the experimental measurements and analysis are sufficient to 
reliably support the authors' conclusions. The authors describe their efforts to propagate uncertainty 
through the analysis of their measurements. This is important because the thermal conductivity must 
be extracted from a modelling procedure. Uncertainties in the model parameters will affect the 
outcome. The authors suggest that the uncertainty is about 10-20%. I wonder if these error estimates 
are too low. Figure S4 shows the temperature dependence at various pressures. I would be surprised 
is the erratic pressure dependence is real, which suggests that these variations are reflection of 
experimental uncertainty. Still, the results are sufficient to argue for lower thermal conductivity, even 
with larger experimental uncertainties. 

There is little doubt that this study will motivate future work, either to reproduce these results or to 
extend the experiments to other light elements. It seems likely that silicon will be present at some 
level in the core, so the results should be relevant moving forward. I would encourage the authors to 
make sure that their error estimates will stand the test of time. 

The present study could be published in its current form, although I would encourage the authors to 
be clear early in the paper that the experiments are carried out on solid samples. This detail emerges 
once the experiments are described, but it is sufficiently important to mention in the abstract. Allowing 
for the likely changes due to melting only reinforces the authors' conclusions. 



Reviewer #2 (Remarks to the Author): 

This paper report the results of the direct determination of thermal conductivity of FeSi alloy at high 
pressure, and revealed that it is incorporation of Si in hicp-Fe significantly reduces the thermal 
conductivity of 20 Wm-1K-1. Which implies the heat flux at the CMB reduces to around 3 TW. 

There is a discrepancy of a high thermal conductivity inferred from the electrical conductivity, whereas 
a low thermal conductivity from the transient heating laser method. These discrepancies are very 
significant and provide the different views for the formation of the inner core and the early magnetic 
field. 

The senior author is an expert of the thermal conductivity measurements at room temperature by 
using TDTR technique and the results are considered to be reliable. The thermal conductivity at high 
pressure and high temperature was made by the TH method, which is also considered to be reliable 
since the co-authors have significant experience of the measurements. 

This is a clear and concise paper showing lower thermal conductivity of the Fe-Si alloys. Discussion is 
clear and arguments and conclusion is reasonable. Implications for the formation of the inner core and 
the core dynamo is very important. Therefore this paper can be suitable for this journal. However, 
there are so many incomplete figures and captions. Therefore, the authors should rewrite the figures 
and the captions completely. We cannot accept it in the present version. Major revision is needed for 
publication. 

Specific comments especially on the figures. 

Page 2, First paragraph and Page 6 the first paragraph of discussion: I would like to make some 
discussions on the mechanism of heat transfer at very high pressure and temperature. Generally heat 
is transferred by three mechanisms, such as convection heat transfer, thermal conduction which is 
measured here experimentally, and radiation. I am wondering that the radiation heat transfer may not 
be negligible and this mechanism might be important and can increase the thermal conductivity 
significantly in spite of the low thermal conductivity determined here. We need some discussions on 
the heat transfer mechanism in the core. 

Page 5, 2nd paragraph: The authors used two techniques, TDTR at 300 K and TH at high temperature. 
However, there is no discussion on the consistency of these technique. I would like to see some 
discussions on the consistency of the two data-sets. The data on TDTR at room temperature might 
extrapolate theoretically, and could compare the data by TH. The Si content dependency for TDTR and 
TH are consistent? 

Figure S3: There is no explanation of the blue curve. No explanation for FE (finite-elements) 
calculation. FE calculations should be FE calculation. Please fix this figure. 

Figure S4: The change of the FeSi thermal conductivity shows strange pressure dependency at high 
temperature, i.e. there is a maximum at 106 GPa. Provide a reasonable explanation of the pressure 
dependency at high temperature of 2500-3000 K. Is it due to a two phase mixture of BCC and HCP? If 
the anomalous change is due to uncertainty of the TH method, please provide uncertainty for the plot 
for the measurements. 

Figure S5: Phase diagram shows Fe 2-3.5wt% Si. In the caption, alloy compositions are given as 
atomic in composition. Fe 2-3.5wt%Si should change to atomic ration as shown in the caption. It is 
confusing. 
The symbols of this figure are not clear. There are blue diamonds and upwards triangle, blue open 
circles and downwards triangles, and orange open stars. There are no detailed explanations of the 
symbols. What does the meaning of the top side of the sample and the bottom side of the sample? 
The top side and bottom side of the sample is related to the pulsed side and opposite side given in 
Figure S3? 

Figure S6: Provide a reference for the phase diagram of FeSi alloy. It may be ref. 12, but it is 
confusing that black triangles and open circles are the literature data for phase identification by ref. 12, 
but NOT the data points for previous thermal or electrical conductivity measurements. The 
measurement made with TH experiments was for the mixture of hcp and bcc, and not a single phase. 
Please explain the differences of your data points shown in yellow stars and brown stars. Do you show 
the two series of measurements? 
What is “Bottom temperature” in this figure? 
The solid lines for the boundaries of bcc, hcp, fcc may be those of pure Fe instead of Fe0.85Si0.15. 
Therefore it should be deleted. 




Reviewer #3 (Remarks to the Author): 

Review on “Low thermal conductivity of iron-silicon alloys at Earth’s core conditions: implications for 
the geodynamo” by Hsieh et al. 

In this study, the authors measured thermal conductivity of Fe and Fe-Si alloys at high pressures and 
room temperature and at high pressures and high temperatures by means of the transient heating 
method in DAC. They report that the thermal conductivity of Fe-Si alloy is lower than pure Fe at high 
temperatures and ambient temperature. They also report that thermal conductivity of 20-60 W/mK at 
high pressures and temperatures, which is much lower than previously estimated using electrical 
conductivity based on the Wiedemann-Franz’s law. According to these results, they concluded that the 
inner core is older and that the initial core-mantle-boundary is colder than previously estimated. 

I have several scientific comments on this manuscript. 

1. I think that their main conclusion that the Fe-Si alloys have low thermal conductivity than pure Fe is 
invalid at high pressures and temperatures. Figure 2 demonstrates that the thermal conductivities of 
pure Fe and Fe-Si alloys are simply indistinguishable at high temperatures, although it may be the 
case at ambient temperature as shown in Fig. 1. 
2. As shown in Table S1-S3, the measurements for Fe0.96Si0.04 and Fe0.93Si0.07 were conducted at 
a temperature of 2050 K, whereas those for Fe0.85si0.15 were at temperatures of 2300 to 3100 K. 
Therefore, this study does not present consistent experimental results to show the compositional 
dependence of thermal conductivity of Fe-Si alloys. 
3. The thermal conductivity of Fe and Fe-Si alloys increases by adding percent orders of Si to Fe, 
whereas it decreases by adding 15at% of Si. This would indicate that the effect of Si addition is 
monotonic, and therefore, they cannot argue core thermal conductivity simply using that of 
Fe0.85Si0.15 alloy. 
4. Figure S4 shows that the thermal conductivity of Fe0.85Fe0.15 increases with increasing 
temperature at pressures of 47~106 GPa, whereas it is independent from temperature at higher 
pressures. The author need to argue the mechanism to cause these phenomena. 
5. The outer core temperatures are more than 4000 K. The present temperature range is insufficient 
for arguing the core conductivity, because the temperature effect on thermal conductivity does not 
seem simple as argued above. 
6. I doubt that argument of the core thermal history based on thermal conductivity of core materials is 
essential. The core has cooled due to heat release across the CMB. If there were no heat production in 
the mantle, the released heat should be equal to the total surface heat flow. Thus, the core cooling-
rate should be controlled by the surface heat flow of the Earth not by the heat transfer in the core. 
This argument is strengthened by the fact that the thermal conductivity of rocks is much lower than 
that of Fe alloys. Therefore, it is the thermal-boundary-layer structure of the bottom of the Earth that 
controls the amounts of heat released from the core to the mantle. The amounts of heat transfer 
within the core should be adjusted by verbosity of thermal convection in the outer core. I know 
numerous studies argued the cooling history of core based on Fe and Fe-alloy thermal conductivity as 
shown in Table 1 and 2, but I think that they are useless papers. 

I have several comments on the presentation. 

7. Although the abstract states “15 at% Si alloyed in Fe substantially reduces the conductivity by 
about 2 folds at 132 GPa and 3000 K.”, there is no such argument in the main text. 
8. The authors used single-crystal and polycrystalline samples. They used both samples for 
measurements at ambient temperature. However, it is not shown in Fig 1 which sample was used. 
Furthermore, it is unclear whether single-crystal samples were used for high-temperature 
measurement. They also should show which sample was used in each measurement in Table S1-S3. 
9. Page 10. I do not understand why there is a description regarding MORB. 
10. Page 14. It is clear that high-temperature measurements should be much more important than 
ambient-pressure measurements in view of geophysics. Therefore, the descriptions regarding high-
temperature measurement should have larger amounts than those regarding ambient-pressure 
measurements. I wonder what fitting parameters were used for data analyses of high-temperature 
measurements. The authors should provide a similar table to Table S4 for the high-temperature 
measurements. 
11. Page 28. I am afraid that Figure S3 is not used anywhere in the text. 
12. Page 32. The structures of these tables are confusing. One row has six columns and each of three 
columns describes one measurement. Even though space-consuming, each row should describe only 
one measurement. 

As seen from the comments above, I am not supportive to this article. The paper lacks convincing 
experimental data to argue the thermal conductivity of core materials at high pressures and 
temperatures. More essentially, thermal conductivity of I also point out that this paper is organized 
unreasonably. I strongly suggest the authors to reconsider their measurement and arguments, and to 
reorganize the whole parts of the article.