Role of Defects and Radiation Damage on He Diffusion in Magnetite: Implication for (U-Th)/He Thermochronology

Round 1

Reviewer 1 Report

Recommendation

I strong support publication of this paper. The approach is new and innovative, and helps provide a mechanistic understanding of He diffusion in magnetite. I fully agree with the authors's statement that the development of He magnetite thermochronology will lead to new capabilities for studying the thermal/tectonic histories of magnetite-bearing rocks. The paper is well organized, clearly written, and the methods are well described and supported by appropriate references and figures. 

I have two general comments:

1) The ab-initio molecular dynamic methods used in this study are familiar to me (given what I have learned from others in my department that use these methods), but I found myself a bit overwhelmed by the variety of methods used and the number of assumptions required to define the full model calculation. I suggest that the authors add an overview (no more than 2 paragraphs) at the beginning of section 3 that provides a generalized introduction to the ab-initio method, and also an indication of the potential and limitations of this kind of modeling for studying diffusion of noble gases in crystalline solids. It might also help to indicate the level of completeness provided by the model calculations. It is my sense that calculations on their own are not able to provide a unique and independent solution for He "closure" in magnetite. However, a single plausible solution is indicted when the calculations are guided by the experimental diffusion data. 

2) He diffusion properties in apatite as measured by step-wise heating (Farley and company, CalTech) and by beam methods (Cherniak at RPI) show significant differences. I have long wondered if the step-wish heating experiments are causing modifications to the defect structure of the samples. The ab-initio calculations may provide some way to assess the influence of experimental heating on diffusion properties. 

Specific Comments:

Line 25: demonstrate -> suggest
Lines 71-78: methods (e.g., DFT, MEP, NEB, KMC) should be linked with references when they are first introduced. 
Line 181: Confusing: "can be calculated based on the [52] equation". The reference number does a  poor job of indicating the equation. How about "Einstein's diffusion equation [52]".
Line 193 and else: ?angstrom. SI metric units are preferred. 
Line 206: Odd phrasing: "We presume 1.82 x 10^22 atoms per gram of magnetite". This is a measured property, so why the verb: "presume"

Author Response

Reviewer 1

Dear reviewer,

Thanks for the constructive feedback and suggestions

We corrected all the raised point in the manuscript and corrections were marked in the ms and a complete editing of the manuscripts has been performed.

Sincerely,

Cécile Gautheron on behalf of the co-authors

I strong support publication of this paper. The approach is new and innovative, and helps provide a mechanistic understanding of He diffusion in magnetite. I fully agree with the authors's statement that the development of He magnetite thermochronology will lead to new capabilities for studying the thermal/tectonic histories of magnetite-bearing rocks. The paper is well organized, clearly written, and the methods are well described and supported by appropriate references and figures. 

I have two general comments:

1) The ab-initio molecular dynamic methods used in this study are familiar to me (given what I have learned from others in my department that use these methods), but I found myself a bit overwhelmed by the variety of methods used and the number of assumptions required to define the full model calculation. I suggest that the authors add an overview (no more than 2 paragraphs) at the beginning of section 3 that provides a generalized introduction to the ab-initio method, and also an indication of the potential and limitations of this kind of modeling for studying diffusion of noble gases in crystalline solids. It might also help to indicate the level of completeness provided by the model calculations. It is my sense that calculations on their own are not able to provide a unique and independent solution for He "closure" in magnetite. However, a single plausible solution is indicted when the calculations are guided by the experimental diffusion data. 

A synthetic introduction has been introduced in the head of section 3.

2) He diffusion properties in apatite as measured by step-wise heating (Farley and company, CalTech) and by beam methods (Cherniak at RPI) show significant differences. I have long wondered if the step-wish heating experiments are causing modifications to the defect structure of the samples. The ab-initio calculations may provide some way to assess the influence of experimental heating on diffusion properties. 

This is an out of reach task for the DFT, because what is needed is the temperature dependence of the lattice stability while DFT calculates motionless atoms and moves them to search for the stable configuration. In such an approach the temperature is always 0. The goal could perhaps be followed by molecular dynamic simulations which can be run at a given temperature, provided that the duration of the simulation is long enough to explore the configurations. Although ab-initio methods are well adapted to compute the energy of different configurations, even for different pressures, to our knowledge they are not suited for following directly the transitions from one to the other when changing the temperature

Specific Comments:

Line 25: demonstrate -> suggest DONE

Lines 71-78: methods (e.g., DFT, MEP, NEB, KMC) should be linked with references when they are first introduced. 

We added citations with references for DFT (Hohenberg and Kohn, 1964 and Kohn and Sham, 1965), Djimbi et al. 2015 for the in-house KMC code and Mills, 1995 and Jonsson et al., 1998 for the NEB modeling. See lines 74-78.

Line 181: Confusing: "can be calculated based on the [52] equation". The reference number does a  poor job of indicating the equation. How about "Einstein's diffusion equation [52]".

Good suggestion, done.

Line 193 and else: ?angstrom. SI metric units are preferred. 

We do not share this proposition. It is always more suggestive to use a unit of magnitude similar to the phenomena we are studying. For the same reason we use eV instead of J when dealing with atomic processes. Only when we go to macroscopic scale, as for D, we use cm²/s.

Line 206: Odd phrasing: "We presume 1.82 x 10^22 atoms per gram of magnetite". This is a measured property, so why the verb: "presume"

yes, we rephrase the sentence and use rather calculated. See line 293

Author Response File: Author Response.pdf

Reviewer 2 Report

Minerals review - Bassal et al.

The manuscript by Bassal et al. presents density functional theory (DFT) and kinetic Monte Carlo (KMC) calculations of He diffusion through a magnetite crystal considering a defect-free lattice, natural point defects, and defects due to radiation damage. These calculations demonstrate that He diffusion in magnetite is isotropic and defect-free grains exhibit a low closure temperature (35 C for a 10C/Myr cooling rate, 250 micron diffusion domain length scale) – which is far lower than has been previously reported (note however - everyone is citing the same, lone Blackburn et al., 2007 diffusion experiment!). The authors compare their DFT calculations with magnetite diffusion kinetic data from this Blackburn et al. diffusion experiment, as well as calculated closure temperatures and alpha dose from the Bala kimberlite and Rocher Blanc magnetite data. With these comparisons, they suggest that natural vacancies and radiation damage, even at low alpha dose, control He diffusion in magnetite.

This is an important contribution and I think it should be published after the authors have addressed the comments below that amount to moderate revisions.

(1) Some elements of the Blackburn et al. data do not appear to be fully explained by defects and recoil damage. In figure 4, the authors present the full 4-He diffusion experiment data from the supplement of Blackburn et al. (2007), and they compare this diffusion data with their calculations (Fig. 4) to make important inferences about the role of defects in He diffusion in magnetite. However, what is causing the different slope (i.e., different activation energy) of the low to mid- temperature part of the Bala magnetite data? In lines, 339-340 – the authors argue that the low temperature part reflects the activation energy of crystal defects (Fig. 4A). But this agreement between the calculated green dashed line and Bala data is defined by literally one data point. What about the subsequent retrograde steps, and more importantly, the prograde steps between the dashed green and dashed blue (recoil damage) lines? This zig-zag Arrhenius pattern is suggestive of multi-domain diffusion behavior (as first described in Farley and Flowers, 2012, for hematite). Is it possible the Bala magnetite data has internal domains? The authors should discuss this important portion of the Bala Arrhenius diagram in their discussion and provide an explanation for it.

(2) In other phases such as apatite, damage is generated but it can also anneal. Although this paper does not present data that bears on the temperatures of damage annealing (that would be an entirely different study), it would be helpful if authors could comment on/acknowledge the possibility that accumulated damage may anneal over the post-mineralization thermal history that a sample experiences.

(3) In lines 347-348, the authors briefly mention chemical substitutions and how they might impact the defect fraction. I think this is a very important point and should be highlighted in the conclusions. Although most magnetite has low U (and Th), as the author emphasize throughout the discussion, chemical substitutions are likely common (e.g., Ti) and may play a bigger role than we realize.

(4) There are number of terms in the manuscript that are not defined and this will make it hard for thermochronologists – a key audience for this paper – to understand. Please include sentences that describe and/or explain terms like: DFT Hamiltonian, Kohn-Sham, Hubbard parameter, Dudarev approach, Brillouin zone, Monkhort-Pack scheme, GGA and PBE.

(5) Thermochronologists who read this paper may be confused by the way in which the term “amorphous” is being used. In essence, here, any region of the crystal that does not have a regular crystal lattice is considered “amorphous,” even at the scale of a single recoil event. I think some people may visualize something like an amorphous zircon grain (such as N17 in Guenthner et al., 2013), and thus assume that you are talking about a larger fraction of the grain being amorphous. So clarifying/defining what is meant by amorphous in this contribution will help alleviate any confusion.

ADDITIONAL COMMENTS

331-332: The authors need to be clear that the Gerin et al. model is for apatite (not magnetite). Although it is great that it works, this distinction should be clear, because it is an assumption that the apatite model applies to magnetite.

Overall, the manuscript is very well written, but some sentences could be revised for clarity. Here are few examples and suggestions:

48: unique should be only

53-53: I’d rephrase to “… by a scarcity of minerals that be analyzed with (U-Th)/He thermochronology”

54: I’d change to “This new tool has been used to constrain the timing and duration of fossil hydrothermal...”

63: one should be “we”

94: which should be that

198: recoils should be recoil (singular)

269-271: this is important content and also confusing. Helpful to rephrase.

320-321: helpful to cite Gautheron et al. 2020 here, which had a similar takeaway message.

383: Unless I missed something, this is the first time that the Rocher Blanc magnetite is being mentioned – some context here is useful.

Figure 5: delete the “?” in the Rocher Blanc magnetite label. Also B in Blanc should be capitalized.

Author Response

Reviewer 2

Dear reviewer,

Thanks for the constructive feedback and suggestions

We corrected all the raised point in the manuscript and corrections were marked in the ms and a complete editing of the manuscripts has been performed.

Sincerely,

Cécile Gautheron on behalf of the co-authors

The manuscript by Bassal et al. presents density functional theory (DFT) and kinetic Monte Carlo (KMC) calculations of He diffusion through a magnetite crystal considering a defect-free lattice, natural point defects, and defects due to radiation damage. These calculations demonstrate that He diffusion in magnetite is isotropic and defect-free grains exhibit a low closure temperature (35 C for a 10C/Myr cooling rate, 250 micron diffusion domain length scale) – which is far lower than has been previously reported (note however - everyone is citing the same, lone Blackburn et al., 2007 diffusion experiment!). The authors compare their DFT calculations with magnetite diffusion kinetic data from this Blackburn et al. diffusion experiment, as well as calculated closure temperatures and alpha dose from the Bala kimberlite and Rocher Blanc magnetite data. With these comparisons, they suggest that natural vacancies and radiation damage, even at low alpha dose, control He diffusion in magnetite.

This is an important contribution and I think it should be published after the authors have addressed the comments below that amount to moderate revisions.

(1) Some elements of the Blackburn et al. data do not appear to be fully explained by defects and recoil damage. In figure 4, the authors present the full 4-He diffusion experiment data from the supplement of Blackburn et al. (2007), and they compare this diffusion data with their calculations (Fig. 4) to make important inferences about the role of defects in He diffusion in magnetite. However, what is causing the different slope (i.e., different activation energy) of the low to mid- temperature part of the Bala magnetite data? In lines, 339-340 – the authors argue that the low temperature part reflects the activation energy of crystal defects (Fig. 4A). But this agreement between the calculated green dashed line and Bala data is defined by literally one data point. What about the subsequent retrograde steps, and more importantly, the prograde steps between the dashed green and dashed blue (recoil damage) lines? This zig-zag Arrhenius pattern is suggestive of multi-domain diffusion behavior (as first described in Farley and Flowers, 2012, for hematite). Is it possible the Bala magnetite data has internal domains? The authors should discuss this important portion of the Bala Arrhenius diagram in their discussion and provide an explanation for it.

Good point! Your remark is meaningful. We added a sentence specifying that the Arrhenius diagram features a multi-domain pattern, so thank you again for your point. We had in mind a possible interpretation of the small domains, although the mineral seems made of a single large grain, as the subsurface collection of the single defects and this guided what we wrote in the old version. However, we must admit that this idea is still very speculative and needs to be ascertained by some modeling that we do not have done yet. Therefore, in the new version, although we still show the results for the point-defects we do not claim anything from its comparison to the data. See line 300-305

(2) In other phases such as apatite, damage is generated but it can also anneal. Although this paper does not present data that bears on the temperatures of damage annealing (that would be an entirely different study), it would be helpful if authors could comment on/acknowledge the possibility that accumulated damage may anneal over the post-mineralization thermal history that a sample experiences.

We inserted at the end of section 2.2 a discussion on this point.

(3) In lines 347-348, the authors briefly mention chemical substitutions and how they might impact the defect fraction. I think this is a very important point and should be highlighted in the conclusions. Although most magnetite has low U (and Th), as the author emphasize throughout the discussion, chemical substitutions are likely common (e.g., Ti) and may play a bigger role than we realize.

The impact of substitutions on diffusion is mainly mediated by the different size of substitutes which may narrow the diffusion channel. If the substitution level is not more than a few percents and if diffusion is almost isotropic the effect is negligible because the diffusing atom easily finds bypassing paths. On the contrary in case of 1D diffusion, with all diffusion channels aligned along one direction, like in goethite, those steric effects or channel quenching are significant because they cannot be bypassed.

(4) There are number of terms in the manuscript that are not defined and this will make it hard for thermochronologists – a key audience for this paper – to understand. Please include sentences that describe and/or explain terms like: DFT Hamiltonian, Kohn-Sham, Hubbard parameter, Dudarev approach, Brillouin zone, Monkhort-Pack scheme, GGA and PBE.

We understand this criticism, however explaining all these terms would require us to emphasize strongly the section devoted to the theory and it would unbalance the article, inflating this part against the outcomes for thermochronologists. In fact we consider that there are two classes of readers: i) readers having some expertise in theoretical calculations, for them all details should be specified in order that calculations could be replayed or even criticized, this is why all details and acronyms are specified and they do not need to be explained. ii) Readers not experts in quantum calculations but interested in their use and the consequences. For them even if the acronyms and the details are explained and exhibited they will not get a better insight in the physical phenomena. However, at the request of reviewer 1 we added in the opening of section 3 some features of the theoretical modeling, emphasizing the assets and limitations.

(5) Thermochronologists who read this paper may be confused by the way in which the term “amorphous” is being used. In essence, here, any region of the crystal that does not have a regular crystal lattice is considered “amorphous,” even at the scale of a single recoil event.

No in case of point defects the lattice is still alive and cannot be considered as amorphous, as clearly stated at lines 210-212 of the old version (208-210 in the new version). We define as amorphous a domain extending over several cell sizes in which the lattice collapsed. This is what we stated in lines 205-206 of both versions. We tried to clarify this point by relating explicitly amorphisation to recoil damage.

 I think some people may visualize something like an amorphous zircon grain (such as N17 in Guenthner et al., 2013), and thus assume that you are talking about a larger fraction of the grain being amorphous. So clarifying/defining what is meant by amorphous in this contribution will help alleviate any confusion.

We made clearer the difference between the defects created along the α-particle where point-defects remain as created, and the recoils where the clustering of defects leads to a local collapse of the lattice, creating an amorphous domain.

ADDITIONAL COMMENTS

331-332: The authors need to be clear that the Gerin et al. model is for apatite (not magnetite). Although it is great that it works, this distinction should be clear, because it is an assumption that the apatite model applies to magnetite.

No it is not a model for apatite, it is a more general physical model, that we applied to apatite, but also zircon (Gautheron et al., 2020) and now we apply it to magnetite The premises of the model are general:

1) Existence of interstitial sites regularly spaced (lattice) with an energy barrier connecting each one to its neighbors.

2) A small number of the above sites are defects having an energy bottom deeper than interstitial sites.

That’s all. There is no assumption on the structure of the lattice.

Overall, the manuscript is very well written, but some sentences could be revised for clarity. Here are few examples and suggestions:

48: unique should be only CORRECTED

53-53: I’d rephrase to “… by a scarcity of minerals that be analyzed with (U-Th)/He thermochronology” CORRECTED

54: I’d change to “This new tool has been used to constrain the timing and duration of fossil hydrothermal...” CORRECTED

63: one should be “we” CORRECTED

94: which should be that CORRECTED

198: recoils should be recoil (singular) CORRECTED

269-271: this is important content and also confusing. Helpful to rephrase. We changed the paragraph

320-321: helpful to cite Gautheron et al. 2020 here, which had a similar takeaway message. Effectively, we added a sentence.

383: Unless I missed something, this is the first time that the Rocher Blanc magnetite is being mentioned – some context here is useful. Good point, we added details in the modified text

Figure 5: delete the “?” in the Rocher Blanc magnetite label. Also B in Blanc should be capitalized. CORRECTED

Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Authors,

Thank you and congratulations on the great work reported on the manuscript “Role of defects and radiation damage on He diffusion in magnetite: implication for (U-Th)/He thermochronology”

The results reported are important and will help advance the development of the (U-Th)-He geochronology and thermochonology beyond magnetite. They will especially be important for interpretation of He data from magnetite as stated in the manuscript. I am happy with the manuscript as is even though I recommend the following edits that can be made during the proofing stage.

Line 85: FCC is not given in full anywhere else.

Line 133: Unclear to reader why testing was done with values between 2 and 7 eV.

Line 204: remove comma after survive.

Line 408: Studies instead of studied.

Author Response

Reviewer 3

Dear reviewer,

Thanks for the constructive feedback and suggestions

We corrected all the raised point in the manuscript and corrections were marked in the ms and a complete editing of the manuscripts has been performed.

Sincerely,

Cécile Gautheron on behalf of the co-authors

Dear Authors,

Thank you and congratulations on the great work reported on the manuscript “Role of defects and radiation damage on He diffusion in magnetite: implication for (U-Th)/He thermochronology”

The results reported are important and will help advance the development of the (U-Th)-He geochronology and thermochonology beyond magnetite. They will especially be important for interpretation of He data from magnetite as stated in the manuscript. I am happy with the manuscript as is even though I recommend the following edits that can be made during the proofing stage.

Line 85: FCC is not given in full anywhere else. We added that FCC is Face-Centered Cubic (line 86)

Line 133: Unclear to reader why testing was done with values between 2 and 7 eV.

Sorry about that. We add in the new version, more information about the used value.

The optimal value for Uefff in magnetite is between 3.7 eV and 5.3 eV depending on DFT method, and calculation parameters between the lattice cell size and volume. Our tests showed that 3.75 eV is the optimal value of Ueff for our DFT approach assuring the best agreement between computational results and experimental measurements. We have chosen to test U values between 2 and 7 eV aiming to scan all tested values found in the literature. Any way, it has been confirmed also by our tests and calculations. In addition, it was no need to use value of 1, or 8 or 9, because the further away from the optimal value (Ueff=3.75 eV) the worse are the computational results (increasing of difference the-exp).

In order to not, add too much information about the calculation in a geologic contribution, we only add a small sentence and two references in line 137.

Line 204: remove comma after survive. DONE

Line 408: Studies instead of studied. DONE

Author Response File: Author Response.pdf