the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Jun 2023
Constraints on average alpha recoil distance during 238U decay in baddeleyite (ZrO2) from atom probe tomography
Abstract. Atom probe tomography of 238U and 206Pb has been applied to baddeleyite crystals from the Hart Dolerite (1791 ± 1 Ma) and the Great Dyke of Mauritania (2732 ± 2 Ma) in an effort to constrain the average nuclear recoil distance of U-series daughter nuclei and thereby correct U-Pb ages determined on small baddeleyite crystals for alpha-recoil loss of Pb. Both crystals were thought to expose natural crystal surfaces providing a boundary where maximum recoil loss could be observed, but both surfaces showed no adjacent variations in Pb concentrations. However, the Great Dyke sample shows U zoning and the associated 206Pb zoning is affected by alpha recoil. A forward modelling approach was used where 206Pb redistribution functions were determined for a range of possible alpha recoil distances and synthetic 206Pb/238U profiles were determined from the convolution of the observed U profile with the redistribution functions. These can be compared to the observed 206Pb/238U profile. A complication is that the 400 nm range of sampling is lower than the range of possible alpha recoil redistribution effects. In order to get a realistic match to the observed 206Pb/238U profile, it was necessary to extrapolate the observed zoning as an oscillatory pattern. This gives a best estimate for the average alpha recoil distance of about 40 nm.
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Interactive discussion
Status: closed
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RC1: 'Comment on gchron-2023-15', Alyssa McKanna, 28 Jul 2023
The comment was uploaded in the form of a supplement: https://gchron.copernicus.org/preprints/gchron-2023-15/gchron-2023-15-RC1-supplement.pdf
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AC1: 'Reply on RC1', Donald Davis, 20 Sep 2023
We thank the reviewers for constructive comments. In particular, we are grateful to the third reviewer for insisting that we include the primary data, which forced the first author to realize that the measured ratio profile of 238U/(206Pb+207Pb) had mistakenly been modelled. This has been corrected and the results on modelling 238U/206Pb show that sample M5 (Mauritania) baddeleyite was sampled at a natural crystal surface that shows strong U zoning. The results of modelling on this sample now constrain the average recoil distance to at least 80 nanometers, which is greater than previous estimates by a factor of 3-4. Despite this change, the structure of the manuscript is essentially the same and most of the reviewer comments, which were largely on presentation rather than results, are still relevant.
Our replies are given in italics after each comment below showing revised line numbers.
AC-1 Comments and replies
This contribution attempts to quantify the average alpha recoil displacement of 206Pb in baddeleyite using atom probe tomography. Ejection of 206Pb from the rims of baddeleyite grains has the potential to produce U-Pb dates that are too young in small baddeleyite crystals with high surface area-to-volume ratios. If the average alpha recoil distance can be measured, Pb ejection corrections can be applied to U-Pb datasets to improve the accuracy of baddeleyite U-Pb geochronology. The study is well designed, and atom probe tomography has the appropriate spatial resolution to address this outstanding question. However, the presentation of the background, results, and discussion should be clarified and expanded (especially Section 4). Specific comments are listed below.
27: By what benchmark are concordant baddeleyite 206Pb/238U dates younger than ~ 1000 Ma “too young”?
AC1-1: The issue is not that young samples are "too young", but 1000 Ma is below the point on the concordia curve where discordant arrays are subparallel to concordia so 207/206 dates are much less precise than 206/238 dates. As the paragraph says, because even high-quality data of this age is generally concordant due to the larger uncertainties in the 207/235 ratio, any disturbance in U-Pb systematics (such as alpha recoil) will manifest as concordant, but inaccurately young, data. This is clarified in the revised version.
32: Radiation damage in zircon and baddeleyite cannot be deconvoluted into structure versus chemistry. The two are inherently linked. Baddeleyite is less susceptible to radiation damage because it typically incorporates less U than zircon, and oxides are more resistant to irradiation than silicates.
AC1-2: We suggest that structure and chemistry do, in fact, produce different effects. The ZrSiO4 molecule is highly reactive with HF, as shown by the fact that metamict zircon readily dissolves in even weak HF. What protects most zircon is the crystal structure. Annealing of highly damaged zircon does not completely restore resistance to HF dissolution because the original inert mono crystal is replaced by randomly oriented microcrystals that are much more reactive (https://doi.org/10.1016/j.gca.2010.06.029). The ZrO2 molecule in baddeleyite seems to be much less chemically reactive so the degree of radiation damage is less important.
42: What is the closure temperature for Pb in baddeleyite? Is there Pb diffusion data available in the literature? Could younger baddeleyite U-Pb ages reflect Pb loss by volume diffusion?
AC1-3: This has not been measured directly, though see discussions in Rioux et al. (2010, https://doi.org/10.1007/s00410-010-0507-1) and Soderlund et al. (2013, http://dx.doi.org/10.1016/j.lithos.2013.04.003) about how Pb diffusion and closure temperatures for baddeleyite must be similar or more retentive than for zircon. Much baddeleyite is dated from mafic dykes that have never see a metamorphic event but that still show discordance.
60: How common is it to date baddeleyite crystals that are so small (10 - 15 μm) as to be affected by alpha recoil? Are larger baddeleyite grains not typically available?
AC1-4: Baddeleyite crystals are typically small (<100 microns) but the main problem is their tabular habit, which means that they can be less than 10 microns thick.
Are there molecular dynamic simulation studies that have estimated alpha recoil distances in baddeleyite?
AC1-5: The alpha recoil distance has been estimate by numerical simulation in zircon (Nasdala et al. 2001 https://doi.org/10.1007/s004100000235). We thank the reviewer for making us aware that we cited the wrong reference. Obtaining reliable tomographic images on zircon is apparently a challenge for the Atomprobe so the recoil distance has never been measured, in contrast, it has never been calculated for baddeleyite. The higher density and molecular weight of baddeleyite would suggest that its average recoil distance should be shorter than in zircon.
Uncertainties 1 or 2 sigma?
AC1-6: All age uncertainties are quoted at 95% confidence limits, which we point out in the revised version.
124: Alpha recoils randomly redistributes U-daughters, not U.
AC1-7: Correct, we rephrase in the revision.
126: Why would the largest U gradient be at the samples surface? Crystals can have all sorts of U-growth zonation. I assume you mean that recoil effects will be most apparent at the crystal surface, since recoil ejects a fraction of Pb atoms from the crystal causing a localized depletion in Pb relative to U.
AC1-8: We are pretty sure that the U gradients are maximum at the surfaces of the crystal if the concentrations can be assumed to effectively go to zero outside the crystal.
134: What are the implications of no localized Pb depletion at the crystal surface if these are indeed crystal faces and not cleavage planes? This possibility should be explored further in the discussion before the authors move forward with their preferred interpretation. The SEM images of the Hart Dolerite crystal in particular really looks like a crystal face. Could you rotate the crystal and sample another face for atom probe?
AC1-9: If it is a real crystal surface with no localized Pb depletion, then alpha recoil distance must be very short (<5 nm, essentially detection limit). But if the larger recoil distance modelled for all the internal features is correct, then the interpretation of a real crystal surface cannot be the case. We have added more comment on this in the paragraph.
173: Do not cite Wikipedia as a primary source.
AC1-10: We now use the citation Bárány and Vu (2008).
194: the “modeled” 206Pb/238U profiles
AC1-11: Correct, ‘modelled’ will be added.
198: Explain how you determined 40 nm to have the closest fit. Visual inspection or by some least squares parameter? What about recoil distances >40 nm?
AC1-12: As explained above we now use the correct measured 206Pb/238U profile, which constrains the average recoil length to be about 80-90 nm. This based on the minimum MSWD values (new Fig. 9) for the most plausible extrapolation of the U profile. Detailed calculations and results are now given in Supplementary Data File-1. Given the uncertainty in the U profile beyond the range of measurement, it is not realistic to put an error on the recoil estimate.
201-204: I am confused by this sentence. Specify what you mean by observed profile. Do you mean projecting the end of the measured U profile downward improves the model fit to the measured 206Pb/238U profile?
AC1-13: Yes, but only for the upper end of the model fit. Improving the lower end requires increasing U concentration beyond the range of measurement at negative distances, suggesting an oscillatory zonation. We have reworded the sentence to make this clearer.
205: While oscillatory growth zoning does commonly occur in some minerals, it is highly speculative to assume that this is the case here for a grain that is totally uncharacterized. Can the authors characterize the growth zoning in this grain or in a suite of other baddeleyite grains from the same sample?
AC1-14: We do not have these data, but it is clear from the limited U profiles in the two samples that oscillatory zoning (rising and lowering of U concentration with distance) is present in the Mauritania specimen but is not evident in the Hart Dolerite one.
225: Is the 40 nm value truly “robust” if models yielded high MSWD values? Nor can you really say that 40 nm is significantly higher than 24 ± 7 nm when you can’t place uncertainties on your modeled value.
AC1-15: Again, our conclusions have markedly changed and we now claim an approximate recoil distance of 80-90 nm. Since the present data set strongly suggests that the sample was measured at a natural crystal face, the U can be reliably set to zero on one side of the profile. This, along with the large difference between the measured 206Pb/238U profile over the U peak from the equilibrium value sets a lower limit of about 80 nm with more confidence than we had before. It may be possible to model a larger recoil distance by enhancing the extrapolated U profile but it is not possible to make it less.
Section 3.2: It is not obvious to me from Figure 3 that there are U clusters in M5, and no visuals for Fe and Ti clusters are presented in the manuscript. Can the authors provide a Figures that show this more clearly?? At a minimum, the Fe and Ti data should be included since the data are referenced in the text.
AC1-16: We have now added images showing the clusters in Fig. 10, as well as an MP4 animation that shows rotation of the U distribution in the Mauritania baddeleyite.in the Supplementary Data section. The data output of the Proxigram program is also added to Supplementary Data.
Section 4: There are many methods for correcting (U-Th)/He ages for alpha ejection for different grain geometries, grain sizes, and surface-to-volume ratios. Some (U-Th)/He alpha ejection models even incorporate radionuclide zoning. The literature is fairly extensive on the topic. The discussion here could be expanded significantly by applying some of these methods to the case of Pb ejection in baddeleyite. It is important for the authors to demonstrate – given their preferred 40 nm estimate for alpha recoil – in what scenarios should geochronologist expect Pb ejection from baddeleyite grains to have a meaningful impact on U-Pb dates and how to correct them. Can recoil adequately explain the “too young” baddeleyite ages that the authors cite in the introduction?
AC1-17: We try to do this in the final section. As explained there, the tabular habit of baddeleyite means that most Pb loss occurs from the 001 face, reducing the problem to 1 dimension as now shown in fig 12. Quantitative estimations of resetting are already given in Davis and Davis (2018) so were not repeated.
Figure 2 & 3: It would be helpful to add some labels to the figures indicating where the crystal surface is for readers less familiar with atom probe tomography.
AC1-18: We have added this to the captions.
Figure 4: Label the x-axes. Adding a line at the expected equilibrium 206Pb/238U ratio (0.53) would be helpful.
AC1-19: This has been done.
Figure 5: Label the y-axes. Personally, I find having the y-axis labels in the center of the figure to be distracting.
AC1-20: The Y axes represent relative probability density but this, as pointed out, is a distraction. The important thing to know is that the curves are distribution functions normalized to 1 and that the higher the assumed alpha recoil distance, the broader the curve.
Figure 6: Label the y-axis in A and x-axis in B.
AC1-21: The Y-axis labels are given in the boxes. The Y axes are not directly labelled because, as the reviewer points out, this is distracting in the center of the figure. Figs. 5 and 6 have now been combined.
Figure 10: (now Fig 9) Why not also show the 50 nm case, since it is discussed in the text?
AC1-22: Figs 7 and 8, which show the modelled Pb/U profiles, now include the U profile for comparison. We show models for 40 nm, 80 nm and 120 nm on the figures. Any more would make them illegible. However, the results of modelling and MSWD values for more recoil distances are given in Supplementary Data File-1.
Figure 11 & 12: (now Fig 10 & 11) Why is distance negative in Figure 11 but positive in Figure 12? It may be useful to demonstrate how different R values produce similar model results in Figure 12. I would be helpful to add a line at 0.53 for a better visual of the expected equilibrium value.
AC1-23: The convention in the proximity histogram (Proxigram) program of Hellman et al. (2000) is to make distance from the average cluster boundary positive inward and negative outward. We find this somewhat disconcerting, probably like the reviewer, so we use the convention of positive distances outside the boundary as shown in Fig 10 (formerly Fig 11) and we have made the outside distances positive in Fig 9 (formerly Fig 10).
Supplement: I appreciate the author’s total transparency in sharing all their modeling scenarios, however, including an active workbook with a hundred plots that don’t all have labeled axes or enough context may be overkill. It the workbook is to be included, please label everything.
AC1-24: We have simplified and revised the Supplementary data spreadsheets to make them as transparent as possible, as well as including an explanation of their use in the first sheet.Citation: https://doi.org/10.5194/gchron-2023-15-AC1
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AC1: 'Reply on RC1', Donald Davis, 20 Sep 2023
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RC2: 'Comment on gchron-2023-15', Alberto Pérez-Huerta, 08 Aug 2023
Review Preprint Gchron-2023-15 Title: “Constraints on average alpha recoil distance during 238U decay in baddeleyite (ZrO2) from atom probe tomography”
Authors: Davis et al.
Review:
I would like to preface my comments by indicating that I do not have expertise in geochronology and I can be mainly of assistance commenting on aspects related to atom probe tomography (APT). In general, the preprint contains a lot of interesting and detailed information about the application of APT to understand an aspect of adioactive decay that impacts geochronology applications of baddeleyite, and similar minerals like zircon. Yet, I would argue that the objective is not clear and neither whether the obtained data is sufficiently representative for what the authors intent in this study. Thus, I would recommend publication after major revisions. My comments as follows:
- The objective of the study is not clear. Authors indicate that they use APT to “constrain average alpha recoil distance in baddeleyite for the 238U decay chain”. However, how is this achieved? It would help to have some graphic representation of what happens during alpha recoil in the mineral lattice and then, how APT with its high-spatial resolution can be informative of the process. Also, having some hypotheses that can be tested by APT would be very insightful.- A major weakness of the study is the number of samples. Two tips of two different samples (one of each sample) does not seem to representative or, at least, the authors should explain the contrary. For example, for one tip (M2) of one sample, clusters are recognized. Would these clusters be present in other tips of the same sample (these tips are usually made from sample areas separated at about 2 microns)? Also, could other tips show grain dislocations indicative of the lattice damage by alpha recoil? How homogenous are the crystals? Although not formally established, having three datasets (tips) are considered to be representative of the analyzed area within an isotropic sample that is thought to be fairly homogenous (structurally and chemically).- Details of LEAP measurements are rather limited, which may have implications for reproducibility. A suggested practice of reporting can be found in Blum et al. 2018 (Microstructural Geochronology: Planetary Records Down to Atom Scale. AGU Monograph 232).- Authors indicate that there are several mechanisms to explain discordance in baddeleyite, most of them related to some variation in chemical elements (222Rn, 230Th, 231Pa) that could have been detected by APT. However, authors do not follow up on whether APT chemical data could be informative for checking such mechanisms in analyzed crystals, and potentially other samples of baddeleyite.- It is difficult to visualize the clusters in Fig. 11 (for tip M2). Could authors provide better images? At the given resolution, it is not possible to see whether the other tip has clusters, too. Also, how cluster information was treated? On the other hand, lots of information can be extracted from clusters (for example, see work by Gault et al. 2012 – Materials Today and Blum et al. 2018; https://doi.org/10.1002/9781119227250.ch16) and authors do not maximize this opportunity.- Also, related to cluster analysis, authors indicate that there is no change in Hf between clusters and the matrix, but results are not shown to confirm this. Could authors provide 1D profile from a cluster to matrix to show this?- I guess the alpha recoil produces lattice damage that can be observed with high-resolution TEM images. Adding TEM information would reinforce the APT data. Authors should provide some clarification to the absence of complementary TEM imaging or whether it would be even relevant.- Data files for the supplementary: These excel spreadsheets are internal, working documents for the authors that are of difficult understanding for the general readership. Even if this is a pre-print, authors have to present documents are clear and of use to the readers. I would recommend authors to improve these documents, so there is a clear understanding when there is a reference in the text.Citation: https://doi.org/10.5194/gchron-2023-15-RC2 -
AC2: 'Reply on RC2', Donald Davis, 20 Sep 2023
We thank the reviewers for constructive comments. In particular, we are grateful to the third reviewer for insisting that we include the primary data, which forced the first author to realize that the measured ratio profile of 238U/(206Pb+207Pb) had mistakenly been modelled. This has been corrected and the results on modelling 238U/206Pb show that sample M5 (Mauritania) baddeleyite was sampled at a natural crystal surface that shows strong U zoning. The results of modelling on this sample now constrain the average recoil distance to at least 80 nanometers, which is greater than previous estimates by a factor of 3-4. Despite this change, the structure of the manuscript is essentially the same and most of the reviewer comments, which were largely on presentation rather than results, are still relevant.
Our replies are given in italics after each comment below showing revised line numbers.
AC-2 Comments and replies
Review:
I would like to preface my comments by indicating that I do not have expertise in geochronology and I can be mainly of assistance commenting on aspects related to atom probe tomography (APT). In general, the preprint contains a lot of interesting and detailed information about the application of APT to understand an aspect of radioactive decay that impacts geochronology applications of baddeleyite, and similar minerals like zircon. Yet, I would argue that the objective is not clear and neither whether the obtained data is sufficiently representative for what the authors intent in this study. Thus, I would recommend publication after major revisions. My comments as follows:
- The objective of the study is not clear. Authors indicate that they use APT to “constrain average alpha recoil distance in baddeleyite for the 238U decay chain”. However, how is this achieved? It would help to have some graphic representation of what happens during alpha recoil in the mineral lattice and then, how APT with its high-spatial resolution can be informative of the process. Also, having some hypotheses that can be tested by APT would be very insightful.
AC2-1: We thank the reviewer for pointing out that we did not adequately explain the role of APT in the Introduction. We have revised the last paragraph of the Introduction to add more information for those unfamiliar with this problem.- A major weakness of the study is the number of samples. Two tips of two different samples (one of each sample) does not seem to representative or, at least, the authors should explain the contrary. For example, for one tip (M2) of one sample, clusters are recognized. Would these clusters be present in other tips of the same sample (these tips are usually made from sample areas separated at about 2 microns)? Also, could other tips show grain dislocations indicative of the lattice damage by alpha recoil? How homogenous are the crystals? Although not formally established, having three datasets (tips) are considered to be representative of the analyzed area within an isotropic sample that is thought to be fairly homogenous (structurally and chemically).
AC2-2: While is always good to have data from multiple samples, this was the first attempt, as far as we are aware, to constrain alpha recoil distance using APT. Only one sample appears to have been sampled at a natural grain surface and shows an inhomogeneous (zoned) distribution of U, which allowed us to attempt to constrain the recoil distance by comparing the distribution of daughter 206Pb atoms to the remaining 238U atoms (we are not concerned about measuring lattice damage). Even here, the scale of the sample is insufficient to encompass the full range of internal zoning affected by alpha recoil, limiting the precision of our alpha recoil estimate. We agree that this is a weakness but it reliably constrains the average alpha recoil distance to an unexpectedly high value. This APT result must be confirmed or explained through more work.- Details of LEAP measurements are rather limited, which may have implications for reproducibility. A suggested practice of reporting can be found in Blum et al. 2018 (Microstructural Geochronology: Planetary Records Down to Atom Scale. AGU Monograph 232).
AC2-3: Given the somewhat qualitative, but nevertheless important, conclusions it did not seem necessary to us to expend a great deal of space on standard analytical details.- Authors indicate that there are several mechanisms to explain discordance in baddeleyite, most of them related to some variation in chemical elements (222Rn, 230Th, 231Pa) that could have been detected by APT. However, authors do not follow up on whether APT chemical data could be informative for checking such mechanisms in analyzed crystals, and potentially other samples of baddeleyite.
AC2-4: This is a reference to suggestion that loss of daughter Pb may be due to loss or initial excess of radionuclides in the U decay chains. It is not practical to analyze such elements using APT because of their very low concentrations. In the case of 231Pa any initial excess (decaying to excess 207Pb) would have decayed away.- It is difficult to visualize the clusters in Fig. 11 (for tip M2). Could authors provide better images? At the given resolution, it is not possible to see whether the other tip has clusters, too. Also, how cluster information was treated? On the other hand, lots of information can be extracted from clusters (for example, see work by Gault et al. 2012 – Materials Today and Blum et al. 2018; https://doi.org/10.1002/9781119227250.ch16) and authors do not maximize this opportunity.
AC2-5: As noted in AC1-16 we have added images showing the clusters in Fig. 10, as well as Supplementary data files.- Also, related to cluster analysis, authors indicate that there is no change in Hf between clusters and the matrix, but results are not shown to confirm this. Could authors provide 1D profile from a cluster to matrix to show this?
AC2-6: Hf is a major element in baddeleyite and would be expected to follow the same pattern as Zr. The clustering affects the trace element U.- I guess the alpha recoil produces lattice damage that can be observed with high-resolution TEM images. Adding TEM information would reinforce the APT data. Authors should provide some clarification to the absence of complementary TEM imaging or whether it would be even relevant.
AC2-7: The study of radiation-induced lattice damage in baddeleyite would be interesting but it is not really relevant to the problem of establishing an average alpha recoil distance and would be another project.- Data files for the supplementary: These excel spreadsheets are internal, working documents for the authors that are of difficult understanding for the general readership. Even if this is a pre-print, authors have to present documents are clear and of use to the readers. I would recommend authors to improve these documents, so there is a clear understanding when there is a reference in the text.
AC2-8: We have simplified these documents and added detailed explanations.Citation: https://doi.org/10.5194/gchron-2023-15-AC2
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AC2: 'Reply on RC2', Donald Davis, 20 Sep 2023
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RC3: 'Comment on gchron-2023-15', Michelle Foley, 30 Aug 2023
The comment was uploaded in the form of a supplement: https://gchron.copernicus.org/preprints/gchron-2023-15/gchron-2023-15-RC3-supplement.pdf
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AC3: 'Reply on RC3', Donald Davis, 20 Sep 2023
We thank the reviewers for constructive comments. In particular, we are grateful to the third reviewer for insisting that we include the primary data, which forced the first author to realize that the measured ratio profile of 238U/(206Pb+207Pb) had mistakenly been modelled. This has been corrected and the results on modelling 238U/206Pb show that sample M5 (Mauritania) baddeleyite was sampled at a natural crystal surface that shows strong U zoning. The results of modelling on this sample now constrain the average recoil distance to at least 80 nanometers, which is greater than previous estimates by a factor of 3-4. Despite this change, the structure of the manuscript is essentially the same and most of the reviewer comments, which were largely on presentation rather than results, are still relevant.
Our replies are given in italics after each comment below showing revised line numbers.AC-3 Comments and replies
General Comments: This work highlights the use of Atom Probe Tomography (APT) to answer specific questions in geochronology and geochemistry, which are unattainable by more conventional techniques (e.g., SIMS, LA-ICP-MS, etc.). In this work, the authors focus on baddeleyite crystals, sourced from two localities dated previously using the high-precision U-Pb technique ID-TIMS. In both cases, the baddeleyite grains were reported to be discordant by up to 3%. The reason for discordance is suggested to be due to Pb loss from alpha recoil processes, thus resulting in Pb loss. The authors therefore use APT to analyze two baddeleyite grains, providing a single APT reconstruction from each respective sample. However, of the two samples, only one APT reconstruction exhibited U and Pb concentration profiles and a gradient in the 206Pb/238U ratio, which the authors suggest being a result of alpha recoil processes. The other sample showed no signs of disturbances, though concentrations of the relevant U and Pb isotope peaks were not detectable above background. Although this work is relevant and needed, as baddeleyite is a widely used geochronometer in lithologies which do not saturate zircon, the data itself is quite sparse to support the quantity of related models and their interpretations presented in this manuscript. Their models for the calculation of alpha recoil are then technically based on one reconstruction – M5 (Ahmeyim Great Dyke). In contrast, M2 (Hart Dolerite) has a uniform U concentration and therefore the data from APT was inconclusive as to why these baddeleyite from the Hart Dolerite are discordant.
AC3-1: To be clear, all natural baddeleyite crystals should show a degree of discordance that depends on their size, shape and the average alpha recoil distance, because of ejection of U daughter nuclides out of the crystal. We intended to obtain 206Pb/238U profiles at natural surfaces to constrain the recoil distance but the sampled surfaces proved not to be natural grain surfaces. In the case of a uniform U concentration, as with the Hart Dolerite, no useful recoil constraint can be obtained. With the Mauretania Great Dyke sample we observed primary U zoning. Alpha recoil should have the effect of randomly displacing radionuclide daughter elements, resulting in Pb concentration gradients lower than those of U and potentially allowing us to constrain the average alpha recoil distance. Unfortunately, the scale of sampling is lower than the wavelength of zonation, forcing us to extrapolate the zoning pattern and limiting the precision of the alpha recoil distance estimate. Nevertheless, it is a worthwhile exercise because reasonable extrapolations lead to the conclusion that the distance is somewhat larger than previously estimated. It therefore highlights the importance of obtaining a better constrained estimate and shows that APT is fully capable of doing this if one can obtain a concentration profile of shorter wavelength, which is possible by analyzing a natural grain surface as we emphasize in the Conclusions.Specific Comments
My reserve with the manuscript as currently constructed is that it relies entirely on two APT reconstructions from two unique baddeleyite grains. Although they are quite large datasets for APT studies (65 and 62 million atoms), there is always the question of if the volumes analyzed are wholly representative of the system. Is there a reason more weren’t analyzed? As I expect the authors will not analyze more data, I would suggest that the authors take more care into at least displaying more of the two reconstruction volumes (display more images, more angles, the U clustering, an isoconcentration surface if you truly find planar features in the volume…). With only one APT reconstruction per sample, it is difficult to correlate what is observed to a very specific feature in the grain. Complimented by the general lack of corresponding techniques to rule out alternative options – e.g., these two grains could be mounted perpendicular to the FIB sections and imaged for CL at the least to view zonation and evidence for disturbances in the crystal lattice. I find it interesting that the authors chose different locations with respect to crystallography from the two samples. In the Ahmeyim baddeleyite, they took a lift-out from the surface perpendicular to the C-axis, while in the Hart Dolerite baddeleyite they analyzed perpendicular to the A-axis(?). Could this contribute to the observed differences in concentration profiles relating to potential anisotropic differences in elemental diffusivities? Although other studies have detailed the tedious process of extracting U and Pb isotopic concentrations from TOF spectra (e.g., Valley et al. 2014; Blum et al. 2018), I find it imperative that the TOF of these two reconstructions are presented for reader evaluation of the runs as the entire study relies on the ability to resolve and quantify these two peaks in the mass spectra.
AC3-2: We agree that the data set is inadequate to fully constrain average alpha recoil distance. Nevertheless, it provides a good constraint that we think is worth reporting firstly, as an exercise in obtaining useful conclusions from a limited data set and secondly, to show that the experiment should be repeated on more favourable samples (ideally ones with uniform U concentration at natural crystal boundaries). Also, the software developed for this project can be directly applied to profiles from natural surfaces.It’s challenging to follow the discussion of alpha recoil relating to the concentration and ratio profile depicted in Figures 3 and 4, versus U and Pb clustering and the result of alpha recoil from enriched clusters of Uranium? There are no figures depicting this clustering, even though there is an entire discussion section dedicated to this topic: “3.2 Constraints on alpha recoil distance from U clustering”.
AC3-3: We have added images showing the clusters in Fig. 10, as well as Supplementary data files.Most significantly, their interpretation of the 206Pb/238U ratio profile as reflecting alpha recoil is opposite to the measured profile. Processes of alpha recoil at the crystal surface would result in the loss of Pb and result in a younger date (i.e., lower 206Pb/238U ratio) at the surface – while the measured profile indicates the opposite and instead progressively gets older toward the rim. It is possible that these measured profiles instead reflect a diffusive boundary, mirrored by the profile of U concentration. See Figure 10 of Ibanez-Mejia et al. (2014; Chemical Geology) for an example of this process. The authors should thus provide an explanation as to why their Pb compositional gradient could not be diffusion related and more thoroughly defend their interpretation of a gradient due to alpha recoil.
AC3-4: Although the crystal boundary of the Mauritania sample is likely a natural grain surface, U zoning obscures the expected profile. Nevertheless, results of modelling strongly constrain the average alpha recoil distance to at least 80 nm. As we now discuss, one way to explain the fact that this distance is much higher than previously determined would be if, there had been partial diffusion of Pb. Since the metamorphic grade of the same is no higher than greenschist facies, this could not have happened over geologic time. It would be necessary to invoke an artifact of sample preparation, which does not seem likely.Technical Corrections [line 20] It would be better if you could confirm these are indeed oscillatory patterns – e.g., image the grains analyzed or at least grains from these separates.
AC3-5: Perhaps but zoning is often irregular, at least in zircon, so uncertainty about the sample would remain even with images of another grain.[line 24] A comma between lattice and but.
AC3-6: Done[line 31] How does baddeleyite break down into zircon if there’s no supply of Si from the baddeleyite. I understand when zircon (ZrSiO4) breaks down into baddeleyite (ZrO2) and quartz (SiO2).
AC3-7: There is usually a fluid phase involved during metamorphism, which carries dissolved SiO2.[line 83] What are the typical concentrations of U reported in these baddeleyite samples?
AC3-8: The U concentrations were not reported in the ID-TIMS study of the Mauritania sample (M5) because of the difficulty in weighing such small grains.[line 84] Specify that these are ID-TIMS ages. Also, I read in the Ramsay et a. 2019 text that the Hart Dolerite Pb/Pb age is also an upper intercept age.
AC3-9: Done. ID-TIMS is also now defined.[line 94] How does the Cr cap ensure stable evaporation? I understood this would have the opposite effect…
AC3-10: This has been changed to “to provide a conductive surface on the baddeleyite grain surface during FIB treatment, and to identify the original crystal surfaces”[line 100] (mass spectrum in Dalton)
AC3-10: Done[line 104] Where are the TOF spectra for these two APT runs?
AC3-11: We have included spreadsheets in the Supplementary Data repository with TOF results integrated over the area of the sample at 5 nm intervals along its length.[line 112] “Lead was present as 206Pb++ and 207Pb++” – again we just have to take your word without the TOF spectra.
AC3-12: See AC3-11. We are most grateful for this comment as it forced us to realize that we had used the wrong profile in the original version of the manuscript.[line 116] Should the citations be ordered – either ascending or descending?
AC3-12: Now ordered youngest to oldest.
[line 120] I understand that APT is never the same as other methods, but it's interesting that the U is so low for the Hart Dolerite when the ID-TIMS gives U concentrations from 551 to 1682 ppm.
AC3-13: We cannot comment on this except to say that variations in U can occur although 23 ppm U is quite a low concentration for baddeleyite in general.[line 127] “the largest U gradient should be encountered at the surface” – based on what? You could have oscillatory zones which have greater U concentration from earlier growth zones?
AC3-14: We now write ‘the natural surface of a grain’ to make this clearer. The U concentration should drop from whatever it is in the grain to near-zero along this boundary, assuming that the adjacent material contained near-average U concentration for the rock.[line 153] “the planar symmetry of a zoned U distribution” - your reconstructions don't appear as having a plane of concentration change whereby indicating that this reflects a clear oscillatory zone/boundary? It's also challenging to see if this indeed is a boundary with only one view of the tip... the one chosen for Figure 3 is not particularly convincing.
AC3-15: The assumption of planar symmetry is an approximation but it is consistent with the tomography of the sample and what would be expected whether the cap represented a natural surface or a cleavage plane.[line 173] I’m sure you can find a source other than Wikipedia.
AC3-16: We now use the citation Bárány and Vu (2008).[line 235] The entire 3.2 constraints on alpha recoil distance from U clustering derives from U clustering which is never depicted in the figures?
AC3-17: We now show this in Fig 10.[line 239] Do you have an explanation for why Ti of all elements is enriched in these clusters? No other elements?
AC3-18: We do not understand the cause of clustering except that we cannot see how it could be not be a primary feature of crystallization.[line 254] I think that Valley et al. 2014 and 2015 gave some explanations for clustering.
AC3-19: We now add a reference to the Valley et al. (2014) paper and note that the clustering they observed does not affect U but only Pb and other trace elements. These were probably mobilized during high-grade metamorphism, which is not the case here.[line 262] You should also cite Peterman et al. 2019 for trace element enriched linear features.
AC3-20: This has been cited but the features described are again due to high-grade metamorphism so they are not relevant to low-grade samples such as ours..[line 270] the clusters of U are primary, formed during initial crystallization: can you provide examples of this in the literature? Or explain this further?
AC3-21: We are not aware of other examples like this in zircon. We cited Putnis et al., 1992; and Wu et al., 2019 in relation to the possibility of incomplete nanoscale zoning, but further discussion is beyond the scope of the manuscript.[line 317] You confirm that you did not measure Pb depletion profiles yet go ahead and assume you can calculate alpha recoil from this profile? This Pb compositional gradient could be something other than alpha recoil: diffusion.
AC3-22 : Given the low temperature history of the sample and the high blocking temperature for diffusion of Pb in baddeleyite, the Pb compositional gradient cannot be due to diffusion, although we now discuss this.Figure 3: I suppose the concentration profiles are taken with respect to the observed volume? You should also plot the background levels with respect to each element analyzed here. What are the errors associated with each concentration point?
AC3-23 : These data are now given in the spreadsheet of TOF results in Supplementary Data and errors are shown for the Pb/U ratio profiles.Figure 4: Where are the labels for each axis? Also the errors associated with these measurements??
AC3-24 : We have added labels where necessary in accordance with the comments of reviewer 1.Figure 7: Again what is the title for the y-axis? The points are incredibly difficult to see. I would suggest extending the graph to the full width of the page and spacing out the points so that you can see which correlate? Maybe use different symbols and not all circles?
AC3-25 : It is unfortunately necessary to squeeze a great deal of visual information into the comparative profile figures so the symbols have to be small but the colours seem to effectively distinguish the different profiles on Figs 7 and 9 provided they can be reproduced at page width.Citation: https://doi.org/10.5194/gchron-2023-15-AC3
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AC3: 'Reply on RC3', Donald Davis, 20 Sep 2023
Interactive discussion
Status: closed
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RC1: 'Comment on gchron-2023-15', Alyssa McKanna, 28 Jul 2023
The comment was uploaded in the form of a supplement: https://gchron.copernicus.org/preprints/gchron-2023-15/gchron-2023-15-RC1-supplement.pdf
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AC1: 'Reply on RC1', Donald Davis, 20 Sep 2023
We thank the reviewers for constructive comments. In particular, we are grateful to the third reviewer for insisting that we include the primary data, which forced the first author to realize that the measured ratio profile of 238U/(206Pb+207Pb) had mistakenly been modelled. This has been corrected and the results on modelling 238U/206Pb show that sample M5 (Mauritania) baddeleyite was sampled at a natural crystal surface that shows strong U zoning. The results of modelling on this sample now constrain the average recoil distance to at least 80 nanometers, which is greater than previous estimates by a factor of 3-4. Despite this change, the structure of the manuscript is essentially the same and most of the reviewer comments, which were largely on presentation rather than results, are still relevant.
Our replies are given in italics after each comment below showing revised line numbers.
AC-1 Comments and replies
This contribution attempts to quantify the average alpha recoil displacement of 206Pb in baddeleyite using atom probe tomography. Ejection of 206Pb from the rims of baddeleyite grains has the potential to produce U-Pb dates that are too young in small baddeleyite crystals with high surface area-to-volume ratios. If the average alpha recoil distance can be measured, Pb ejection corrections can be applied to U-Pb datasets to improve the accuracy of baddeleyite U-Pb geochronology. The study is well designed, and atom probe tomography has the appropriate spatial resolution to address this outstanding question. However, the presentation of the background, results, and discussion should be clarified and expanded (especially Section 4). Specific comments are listed below.
27: By what benchmark are concordant baddeleyite 206Pb/238U dates younger than ~ 1000 Ma “too young”?
AC1-1: The issue is not that young samples are "too young", but 1000 Ma is below the point on the concordia curve where discordant arrays are subparallel to concordia so 207/206 dates are much less precise than 206/238 dates. As the paragraph says, because even high-quality data of this age is generally concordant due to the larger uncertainties in the 207/235 ratio, any disturbance in U-Pb systematics (such as alpha recoil) will manifest as concordant, but inaccurately young, data. This is clarified in the revised version.
32: Radiation damage in zircon and baddeleyite cannot be deconvoluted into structure versus chemistry. The two are inherently linked. Baddeleyite is less susceptible to radiation damage because it typically incorporates less U than zircon, and oxides are more resistant to irradiation than silicates.
AC1-2: We suggest that structure and chemistry do, in fact, produce different effects. The ZrSiO4 molecule is highly reactive with HF, as shown by the fact that metamict zircon readily dissolves in even weak HF. What protects most zircon is the crystal structure. Annealing of highly damaged zircon does not completely restore resistance to HF dissolution because the original inert mono crystal is replaced by randomly oriented microcrystals that are much more reactive (https://doi.org/10.1016/j.gca.2010.06.029). The ZrO2 molecule in baddeleyite seems to be much less chemically reactive so the degree of radiation damage is less important.
42: What is the closure temperature for Pb in baddeleyite? Is there Pb diffusion data available in the literature? Could younger baddeleyite U-Pb ages reflect Pb loss by volume diffusion?
AC1-3: This has not been measured directly, though see discussions in Rioux et al. (2010, https://doi.org/10.1007/s00410-010-0507-1) and Soderlund et al. (2013, http://dx.doi.org/10.1016/j.lithos.2013.04.003) about how Pb diffusion and closure temperatures for baddeleyite must be similar or more retentive than for zircon. Much baddeleyite is dated from mafic dykes that have never see a metamorphic event but that still show discordance.
60: How common is it to date baddeleyite crystals that are so small (10 - 15 μm) as to be affected by alpha recoil? Are larger baddeleyite grains not typically available?
AC1-4: Baddeleyite crystals are typically small (<100 microns) but the main problem is their tabular habit, which means that they can be less than 10 microns thick.
Are there molecular dynamic simulation studies that have estimated alpha recoil distances in baddeleyite?
AC1-5: The alpha recoil distance has been estimate by numerical simulation in zircon (Nasdala et al. 2001 https://doi.org/10.1007/s004100000235). We thank the reviewer for making us aware that we cited the wrong reference. Obtaining reliable tomographic images on zircon is apparently a challenge for the Atomprobe so the recoil distance has never been measured, in contrast, it has never been calculated for baddeleyite. The higher density and molecular weight of baddeleyite would suggest that its average recoil distance should be shorter than in zircon.
Uncertainties 1 or 2 sigma?
AC1-6: All age uncertainties are quoted at 95% confidence limits, which we point out in the revised version.
124: Alpha recoils randomly redistributes U-daughters, not U.
AC1-7: Correct, we rephrase in the revision.
126: Why would the largest U gradient be at the samples surface? Crystals can have all sorts of U-growth zonation. I assume you mean that recoil effects will be most apparent at the crystal surface, since recoil ejects a fraction of Pb atoms from the crystal causing a localized depletion in Pb relative to U.
AC1-8: We are pretty sure that the U gradients are maximum at the surfaces of the crystal if the concentrations can be assumed to effectively go to zero outside the crystal.
134: What are the implications of no localized Pb depletion at the crystal surface if these are indeed crystal faces and not cleavage planes? This possibility should be explored further in the discussion before the authors move forward with their preferred interpretation. The SEM images of the Hart Dolerite crystal in particular really looks like a crystal face. Could you rotate the crystal and sample another face for atom probe?
AC1-9: If it is a real crystal surface with no localized Pb depletion, then alpha recoil distance must be very short (<5 nm, essentially detection limit). But if the larger recoil distance modelled for all the internal features is correct, then the interpretation of a real crystal surface cannot be the case. We have added more comment on this in the paragraph.
173: Do not cite Wikipedia as a primary source.
AC1-10: We now use the citation Bárány and Vu (2008).
194: the “modeled” 206Pb/238U profiles
AC1-11: Correct, ‘modelled’ will be added.
198: Explain how you determined 40 nm to have the closest fit. Visual inspection or by some least squares parameter? What about recoil distances >40 nm?
AC1-12: As explained above we now use the correct measured 206Pb/238U profile, which constrains the average recoil length to be about 80-90 nm. This based on the minimum MSWD values (new Fig. 9) for the most plausible extrapolation of the U profile. Detailed calculations and results are now given in Supplementary Data File-1. Given the uncertainty in the U profile beyond the range of measurement, it is not realistic to put an error on the recoil estimate.
201-204: I am confused by this sentence. Specify what you mean by observed profile. Do you mean projecting the end of the measured U profile downward improves the model fit to the measured 206Pb/238U profile?
AC1-13: Yes, but only for the upper end of the model fit. Improving the lower end requires increasing U concentration beyond the range of measurement at negative distances, suggesting an oscillatory zonation. We have reworded the sentence to make this clearer.
205: While oscillatory growth zoning does commonly occur in some minerals, it is highly speculative to assume that this is the case here for a grain that is totally uncharacterized. Can the authors characterize the growth zoning in this grain or in a suite of other baddeleyite grains from the same sample?
AC1-14: We do not have these data, but it is clear from the limited U profiles in the two samples that oscillatory zoning (rising and lowering of U concentration with distance) is present in the Mauritania specimen but is not evident in the Hart Dolerite one.
225: Is the 40 nm value truly “robust” if models yielded high MSWD values? Nor can you really say that 40 nm is significantly higher than 24 ± 7 nm when you can’t place uncertainties on your modeled value.
AC1-15: Again, our conclusions have markedly changed and we now claim an approximate recoil distance of 80-90 nm. Since the present data set strongly suggests that the sample was measured at a natural crystal face, the U can be reliably set to zero on one side of the profile. This, along with the large difference between the measured 206Pb/238U profile over the U peak from the equilibrium value sets a lower limit of about 80 nm with more confidence than we had before. It may be possible to model a larger recoil distance by enhancing the extrapolated U profile but it is not possible to make it less.
Section 3.2: It is not obvious to me from Figure 3 that there are U clusters in M5, and no visuals for Fe and Ti clusters are presented in the manuscript. Can the authors provide a Figures that show this more clearly?? At a minimum, the Fe and Ti data should be included since the data are referenced in the text.
AC1-16: We have now added images showing the clusters in Fig. 10, as well as an MP4 animation that shows rotation of the U distribution in the Mauritania baddeleyite.in the Supplementary Data section. The data output of the Proxigram program is also added to Supplementary Data.
Section 4: There are many methods for correcting (U-Th)/He ages for alpha ejection for different grain geometries, grain sizes, and surface-to-volume ratios. Some (U-Th)/He alpha ejection models even incorporate radionuclide zoning. The literature is fairly extensive on the topic. The discussion here could be expanded significantly by applying some of these methods to the case of Pb ejection in baddeleyite. It is important for the authors to demonstrate – given their preferred 40 nm estimate for alpha recoil – in what scenarios should geochronologist expect Pb ejection from baddeleyite grains to have a meaningful impact on U-Pb dates and how to correct them. Can recoil adequately explain the “too young” baddeleyite ages that the authors cite in the introduction?
AC1-17: We try to do this in the final section. As explained there, the tabular habit of baddeleyite means that most Pb loss occurs from the 001 face, reducing the problem to 1 dimension as now shown in fig 12. Quantitative estimations of resetting are already given in Davis and Davis (2018) so were not repeated.
Figure 2 & 3: It would be helpful to add some labels to the figures indicating where the crystal surface is for readers less familiar with atom probe tomography.
AC1-18: We have added this to the captions.
Figure 4: Label the x-axes. Adding a line at the expected equilibrium 206Pb/238U ratio (0.53) would be helpful.
AC1-19: This has been done.
Figure 5: Label the y-axes. Personally, I find having the y-axis labels in the center of the figure to be distracting.
AC1-20: The Y axes represent relative probability density but this, as pointed out, is a distraction. The important thing to know is that the curves are distribution functions normalized to 1 and that the higher the assumed alpha recoil distance, the broader the curve.
Figure 6: Label the y-axis in A and x-axis in B.
AC1-21: The Y-axis labels are given in the boxes. The Y axes are not directly labelled because, as the reviewer points out, this is distracting in the center of the figure. Figs. 5 and 6 have now been combined.
Figure 10: (now Fig 9) Why not also show the 50 nm case, since it is discussed in the text?
AC1-22: Figs 7 and 8, which show the modelled Pb/U profiles, now include the U profile for comparison. We show models for 40 nm, 80 nm and 120 nm on the figures. Any more would make them illegible. However, the results of modelling and MSWD values for more recoil distances are given in Supplementary Data File-1.
Figure 11 & 12: (now Fig 10 & 11) Why is distance negative in Figure 11 but positive in Figure 12? It may be useful to demonstrate how different R values produce similar model results in Figure 12. I would be helpful to add a line at 0.53 for a better visual of the expected equilibrium value.
AC1-23: The convention in the proximity histogram (Proxigram) program of Hellman et al. (2000) is to make distance from the average cluster boundary positive inward and negative outward. We find this somewhat disconcerting, probably like the reviewer, so we use the convention of positive distances outside the boundary as shown in Fig 10 (formerly Fig 11) and we have made the outside distances positive in Fig 9 (formerly Fig 10).
Supplement: I appreciate the author’s total transparency in sharing all their modeling scenarios, however, including an active workbook with a hundred plots that don’t all have labeled axes or enough context may be overkill. It the workbook is to be included, please label everything.
AC1-24: We have simplified and revised the Supplementary data spreadsheets to make them as transparent as possible, as well as including an explanation of their use in the first sheet.Citation: https://doi.org/10.5194/gchron-2023-15-AC1
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AC1: 'Reply on RC1', Donald Davis, 20 Sep 2023
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RC2: 'Comment on gchron-2023-15', Alberto Pérez-Huerta, 08 Aug 2023
Review Preprint Gchron-2023-15 Title: “Constraints on average alpha recoil distance during 238U decay in baddeleyite (ZrO2) from atom probe tomography”
Authors: Davis et al.
Review:
I would like to preface my comments by indicating that I do not have expertise in geochronology and I can be mainly of assistance commenting on aspects related to atom probe tomography (APT). In general, the preprint contains a lot of interesting and detailed information about the application of APT to understand an aspect of adioactive decay that impacts geochronology applications of baddeleyite, and similar minerals like zircon. Yet, I would argue that the objective is not clear and neither whether the obtained data is sufficiently representative for what the authors intent in this study. Thus, I would recommend publication after major revisions. My comments as follows:
- The objective of the study is not clear. Authors indicate that they use APT to “constrain average alpha recoil distance in baddeleyite for the 238U decay chain”. However, how is this achieved? It would help to have some graphic representation of what happens during alpha recoil in the mineral lattice and then, how APT with its high-spatial resolution can be informative of the process. Also, having some hypotheses that can be tested by APT would be very insightful.- A major weakness of the study is the number of samples. Two tips of two different samples (one of each sample) does not seem to representative or, at least, the authors should explain the contrary. For example, for one tip (M2) of one sample, clusters are recognized. Would these clusters be present in other tips of the same sample (these tips are usually made from sample areas separated at about 2 microns)? Also, could other tips show grain dislocations indicative of the lattice damage by alpha recoil? How homogenous are the crystals? Although not formally established, having three datasets (tips) are considered to be representative of the analyzed area within an isotropic sample that is thought to be fairly homogenous (structurally and chemically).- Details of LEAP measurements are rather limited, which may have implications for reproducibility. A suggested practice of reporting can be found in Blum et al. 2018 (Microstructural Geochronology: Planetary Records Down to Atom Scale. AGU Monograph 232).- Authors indicate that there are several mechanisms to explain discordance in baddeleyite, most of them related to some variation in chemical elements (222Rn, 230Th, 231Pa) that could have been detected by APT. However, authors do not follow up on whether APT chemical data could be informative for checking such mechanisms in analyzed crystals, and potentially other samples of baddeleyite.- It is difficult to visualize the clusters in Fig. 11 (for tip M2). Could authors provide better images? At the given resolution, it is not possible to see whether the other tip has clusters, too. Also, how cluster information was treated? On the other hand, lots of information can be extracted from clusters (for example, see work by Gault et al. 2012 – Materials Today and Blum et al. 2018; https://doi.org/10.1002/9781119227250.ch16) and authors do not maximize this opportunity.- Also, related to cluster analysis, authors indicate that there is no change in Hf between clusters and the matrix, but results are not shown to confirm this. Could authors provide 1D profile from a cluster to matrix to show this?- I guess the alpha recoil produces lattice damage that can be observed with high-resolution TEM images. Adding TEM information would reinforce the APT data. Authors should provide some clarification to the absence of complementary TEM imaging or whether it would be even relevant.- Data files for the supplementary: These excel spreadsheets are internal, working documents for the authors that are of difficult understanding for the general readership. Even if this is a pre-print, authors have to present documents are clear and of use to the readers. I would recommend authors to improve these documents, so there is a clear understanding when there is a reference in the text.Citation: https://doi.org/10.5194/gchron-2023-15-RC2 -
AC2: 'Reply on RC2', Donald Davis, 20 Sep 2023
We thank the reviewers for constructive comments. In particular, we are grateful to the third reviewer for insisting that we include the primary data, which forced the first author to realize that the measured ratio profile of 238U/(206Pb+207Pb) had mistakenly been modelled. This has been corrected and the results on modelling 238U/206Pb show that sample M5 (Mauritania) baddeleyite was sampled at a natural crystal surface that shows strong U zoning. The results of modelling on this sample now constrain the average recoil distance to at least 80 nanometers, which is greater than previous estimates by a factor of 3-4. Despite this change, the structure of the manuscript is essentially the same and most of the reviewer comments, which were largely on presentation rather than results, are still relevant.
Our replies are given in italics after each comment below showing revised line numbers.
AC-2 Comments and replies
Review:
I would like to preface my comments by indicating that I do not have expertise in geochronology and I can be mainly of assistance commenting on aspects related to atom probe tomography (APT). In general, the preprint contains a lot of interesting and detailed information about the application of APT to understand an aspect of radioactive decay that impacts geochronology applications of baddeleyite, and similar minerals like zircon. Yet, I would argue that the objective is not clear and neither whether the obtained data is sufficiently representative for what the authors intent in this study. Thus, I would recommend publication after major revisions. My comments as follows:
- The objective of the study is not clear. Authors indicate that they use APT to “constrain average alpha recoil distance in baddeleyite for the 238U decay chain”. However, how is this achieved? It would help to have some graphic representation of what happens during alpha recoil in the mineral lattice and then, how APT with its high-spatial resolution can be informative of the process. Also, having some hypotheses that can be tested by APT would be very insightful.
AC2-1: We thank the reviewer for pointing out that we did not adequately explain the role of APT in the Introduction. We have revised the last paragraph of the Introduction to add more information for those unfamiliar with this problem.- A major weakness of the study is the number of samples. Two tips of two different samples (one of each sample) does not seem to representative or, at least, the authors should explain the contrary. For example, for one tip (M2) of one sample, clusters are recognized. Would these clusters be present in other tips of the same sample (these tips are usually made from sample areas separated at about 2 microns)? Also, could other tips show grain dislocations indicative of the lattice damage by alpha recoil? How homogenous are the crystals? Although not formally established, having three datasets (tips) are considered to be representative of the analyzed area within an isotropic sample that is thought to be fairly homogenous (structurally and chemically).
AC2-2: While is always good to have data from multiple samples, this was the first attempt, as far as we are aware, to constrain alpha recoil distance using APT. Only one sample appears to have been sampled at a natural grain surface and shows an inhomogeneous (zoned) distribution of U, which allowed us to attempt to constrain the recoil distance by comparing the distribution of daughter 206Pb atoms to the remaining 238U atoms (we are not concerned about measuring lattice damage). Even here, the scale of the sample is insufficient to encompass the full range of internal zoning affected by alpha recoil, limiting the precision of our alpha recoil estimate. We agree that this is a weakness but it reliably constrains the average alpha recoil distance to an unexpectedly high value. This APT result must be confirmed or explained through more work.- Details of LEAP measurements are rather limited, which may have implications for reproducibility. A suggested practice of reporting can be found in Blum et al. 2018 (Microstructural Geochronology: Planetary Records Down to Atom Scale. AGU Monograph 232).
AC2-3: Given the somewhat qualitative, but nevertheless important, conclusions it did not seem necessary to us to expend a great deal of space on standard analytical details.- Authors indicate that there are several mechanisms to explain discordance in baddeleyite, most of them related to some variation in chemical elements (222Rn, 230Th, 231Pa) that could have been detected by APT. However, authors do not follow up on whether APT chemical data could be informative for checking such mechanisms in analyzed crystals, and potentially other samples of baddeleyite.
AC2-4: This is a reference to suggestion that loss of daughter Pb may be due to loss or initial excess of radionuclides in the U decay chains. It is not practical to analyze such elements using APT because of their very low concentrations. In the case of 231Pa any initial excess (decaying to excess 207Pb) would have decayed away.- It is difficult to visualize the clusters in Fig. 11 (for tip M2). Could authors provide better images? At the given resolution, it is not possible to see whether the other tip has clusters, too. Also, how cluster information was treated? On the other hand, lots of information can be extracted from clusters (for example, see work by Gault et al. 2012 – Materials Today and Blum et al. 2018; https://doi.org/10.1002/9781119227250.ch16) and authors do not maximize this opportunity.
AC2-5: As noted in AC1-16 we have added images showing the clusters in Fig. 10, as well as Supplementary data files.- Also, related to cluster analysis, authors indicate that there is no change in Hf between clusters and the matrix, but results are not shown to confirm this. Could authors provide 1D profile from a cluster to matrix to show this?
AC2-6: Hf is a major element in baddeleyite and would be expected to follow the same pattern as Zr. The clustering affects the trace element U.- I guess the alpha recoil produces lattice damage that can be observed with high-resolution TEM images. Adding TEM information would reinforce the APT data. Authors should provide some clarification to the absence of complementary TEM imaging or whether it would be even relevant.
AC2-7: The study of radiation-induced lattice damage in baddeleyite would be interesting but it is not really relevant to the problem of establishing an average alpha recoil distance and would be another project.- Data files for the supplementary: These excel spreadsheets are internal, working documents for the authors that are of difficult understanding for the general readership. Even if this is a pre-print, authors have to present documents are clear and of use to the readers. I would recommend authors to improve these documents, so there is a clear understanding when there is a reference in the text.
AC2-8: We have simplified these documents and added detailed explanations.Citation: https://doi.org/10.5194/gchron-2023-15-AC2
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AC2: 'Reply on RC2', Donald Davis, 20 Sep 2023
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RC3: 'Comment on gchron-2023-15', Michelle Foley, 30 Aug 2023
The comment was uploaded in the form of a supplement: https://gchron.copernicus.org/preprints/gchron-2023-15/gchron-2023-15-RC3-supplement.pdf
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AC3: 'Reply on RC3', Donald Davis, 20 Sep 2023
We thank the reviewers for constructive comments. In particular, we are grateful to the third reviewer for insisting that we include the primary data, which forced the first author to realize that the measured ratio profile of 238U/(206Pb+207Pb) had mistakenly been modelled. This has been corrected and the results on modelling 238U/206Pb show that sample M5 (Mauritania) baddeleyite was sampled at a natural crystal surface that shows strong U zoning. The results of modelling on this sample now constrain the average recoil distance to at least 80 nanometers, which is greater than previous estimates by a factor of 3-4. Despite this change, the structure of the manuscript is essentially the same and most of the reviewer comments, which were largely on presentation rather than results, are still relevant.
Our replies are given in italics after each comment below showing revised line numbers.AC-3 Comments and replies
General Comments: This work highlights the use of Atom Probe Tomography (APT) to answer specific questions in geochronology and geochemistry, which are unattainable by more conventional techniques (e.g., SIMS, LA-ICP-MS, etc.). In this work, the authors focus on baddeleyite crystals, sourced from two localities dated previously using the high-precision U-Pb technique ID-TIMS. In both cases, the baddeleyite grains were reported to be discordant by up to 3%. The reason for discordance is suggested to be due to Pb loss from alpha recoil processes, thus resulting in Pb loss. The authors therefore use APT to analyze two baddeleyite grains, providing a single APT reconstruction from each respective sample. However, of the two samples, only one APT reconstruction exhibited U and Pb concentration profiles and a gradient in the 206Pb/238U ratio, which the authors suggest being a result of alpha recoil processes. The other sample showed no signs of disturbances, though concentrations of the relevant U and Pb isotope peaks were not detectable above background. Although this work is relevant and needed, as baddeleyite is a widely used geochronometer in lithologies which do not saturate zircon, the data itself is quite sparse to support the quantity of related models and their interpretations presented in this manuscript. Their models for the calculation of alpha recoil are then technically based on one reconstruction – M5 (Ahmeyim Great Dyke). In contrast, M2 (Hart Dolerite) has a uniform U concentration and therefore the data from APT was inconclusive as to why these baddeleyite from the Hart Dolerite are discordant.
AC3-1: To be clear, all natural baddeleyite crystals should show a degree of discordance that depends on their size, shape and the average alpha recoil distance, because of ejection of U daughter nuclides out of the crystal. We intended to obtain 206Pb/238U profiles at natural surfaces to constrain the recoil distance but the sampled surfaces proved not to be natural grain surfaces. In the case of a uniform U concentration, as with the Hart Dolerite, no useful recoil constraint can be obtained. With the Mauretania Great Dyke sample we observed primary U zoning. Alpha recoil should have the effect of randomly displacing radionuclide daughter elements, resulting in Pb concentration gradients lower than those of U and potentially allowing us to constrain the average alpha recoil distance. Unfortunately, the scale of sampling is lower than the wavelength of zonation, forcing us to extrapolate the zoning pattern and limiting the precision of the alpha recoil distance estimate. Nevertheless, it is a worthwhile exercise because reasonable extrapolations lead to the conclusion that the distance is somewhat larger than previously estimated. It therefore highlights the importance of obtaining a better constrained estimate and shows that APT is fully capable of doing this if one can obtain a concentration profile of shorter wavelength, which is possible by analyzing a natural grain surface as we emphasize in the Conclusions.Specific Comments
My reserve with the manuscript as currently constructed is that it relies entirely on two APT reconstructions from two unique baddeleyite grains. Although they are quite large datasets for APT studies (65 and 62 million atoms), there is always the question of if the volumes analyzed are wholly representative of the system. Is there a reason more weren’t analyzed? As I expect the authors will not analyze more data, I would suggest that the authors take more care into at least displaying more of the two reconstruction volumes (display more images, more angles, the U clustering, an isoconcentration surface if you truly find planar features in the volume…). With only one APT reconstruction per sample, it is difficult to correlate what is observed to a very specific feature in the grain. Complimented by the general lack of corresponding techniques to rule out alternative options – e.g., these two grains could be mounted perpendicular to the FIB sections and imaged for CL at the least to view zonation and evidence for disturbances in the crystal lattice. I find it interesting that the authors chose different locations with respect to crystallography from the two samples. In the Ahmeyim baddeleyite, they took a lift-out from the surface perpendicular to the C-axis, while in the Hart Dolerite baddeleyite they analyzed perpendicular to the A-axis(?). Could this contribute to the observed differences in concentration profiles relating to potential anisotropic differences in elemental diffusivities? Although other studies have detailed the tedious process of extracting U and Pb isotopic concentrations from TOF spectra (e.g., Valley et al. 2014; Blum et al. 2018), I find it imperative that the TOF of these two reconstructions are presented for reader evaluation of the runs as the entire study relies on the ability to resolve and quantify these two peaks in the mass spectra.
AC3-2: We agree that the data set is inadequate to fully constrain average alpha recoil distance. Nevertheless, it provides a good constraint that we think is worth reporting firstly, as an exercise in obtaining useful conclusions from a limited data set and secondly, to show that the experiment should be repeated on more favourable samples (ideally ones with uniform U concentration at natural crystal boundaries). Also, the software developed for this project can be directly applied to profiles from natural surfaces.It’s challenging to follow the discussion of alpha recoil relating to the concentration and ratio profile depicted in Figures 3 and 4, versus U and Pb clustering and the result of alpha recoil from enriched clusters of Uranium? There are no figures depicting this clustering, even though there is an entire discussion section dedicated to this topic: “3.2 Constraints on alpha recoil distance from U clustering”.
AC3-3: We have added images showing the clusters in Fig. 10, as well as Supplementary data files.Most significantly, their interpretation of the 206Pb/238U ratio profile as reflecting alpha recoil is opposite to the measured profile. Processes of alpha recoil at the crystal surface would result in the loss of Pb and result in a younger date (i.e., lower 206Pb/238U ratio) at the surface – while the measured profile indicates the opposite and instead progressively gets older toward the rim. It is possible that these measured profiles instead reflect a diffusive boundary, mirrored by the profile of U concentration. See Figure 10 of Ibanez-Mejia et al. (2014; Chemical Geology) for an example of this process. The authors should thus provide an explanation as to why their Pb compositional gradient could not be diffusion related and more thoroughly defend their interpretation of a gradient due to alpha recoil.
AC3-4: Although the crystal boundary of the Mauritania sample is likely a natural grain surface, U zoning obscures the expected profile. Nevertheless, results of modelling strongly constrain the average alpha recoil distance to at least 80 nm. As we now discuss, one way to explain the fact that this distance is much higher than previously determined would be if, there had been partial diffusion of Pb. Since the metamorphic grade of the same is no higher than greenschist facies, this could not have happened over geologic time. It would be necessary to invoke an artifact of sample preparation, which does not seem likely.Technical Corrections [line 20] It would be better if you could confirm these are indeed oscillatory patterns – e.g., image the grains analyzed or at least grains from these separates.
AC3-5: Perhaps but zoning is often irregular, at least in zircon, so uncertainty about the sample would remain even with images of another grain.[line 24] A comma between lattice and but.
AC3-6: Done[line 31] How does baddeleyite break down into zircon if there’s no supply of Si from the baddeleyite. I understand when zircon (ZrSiO4) breaks down into baddeleyite (ZrO2) and quartz (SiO2).
AC3-7: There is usually a fluid phase involved during metamorphism, which carries dissolved SiO2.[line 83] What are the typical concentrations of U reported in these baddeleyite samples?
AC3-8: The U concentrations were not reported in the ID-TIMS study of the Mauritania sample (M5) because of the difficulty in weighing such small grains.[line 84] Specify that these are ID-TIMS ages. Also, I read in the Ramsay et a. 2019 text that the Hart Dolerite Pb/Pb age is also an upper intercept age.
AC3-9: Done. ID-TIMS is also now defined.[line 94] How does the Cr cap ensure stable evaporation? I understood this would have the opposite effect…
AC3-10: This has been changed to “to provide a conductive surface on the baddeleyite grain surface during FIB treatment, and to identify the original crystal surfaces”[line 100] (mass spectrum in Dalton)
AC3-10: Done[line 104] Where are the TOF spectra for these two APT runs?
AC3-11: We have included spreadsheets in the Supplementary Data repository with TOF results integrated over the area of the sample at 5 nm intervals along its length.[line 112] “Lead was present as 206Pb++ and 207Pb++” – again we just have to take your word without the TOF spectra.
AC3-12: See AC3-11. We are most grateful for this comment as it forced us to realize that we had used the wrong profile in the original version of the manuscript.[line 116] Should the citations be ordered – either ascending or descending?
AC3-12: Now ordered youngest to oldest.
[line 120] I understand that APT is never the same as other methods, but it's interesting that the U is so low for the Hart Dolerite when the ID-TIMS gives U concentrations from 551 to 1682 ppm.
AC3-13: We cannot comment on this except to say that variations in U can occur although 23 ppm U is quite a low concentration for baddeleyite in general.[line 127] “the largest U gradient should be encountered at the surface” – based on what? You could have oscillatory zones which have greater U concentration from earlier growth zones?
AC3-14: We now write ‘the natural surface of a grain’ to make this clearer. The U concentration should drop from whatever it is in the grain to near-zero along this boundary, assuming that the adjacent material contained near-average U concentration for the rock.[line 153] “the planar symmetry of a zoned U distribution” - your reconstructions don't appear as having a plane of concentration change whereby indicating that this reflects a clear oscillatory zone/boundary? It's also challenging to see if this indeed is a boundary with only one view of the tip... the one chosen for Figure 3 is not particularly convincing.
AC3-15: The assumption of planar symmetry is an approximation but it is consistent with the tomography of the sample and what would be expected whether the cap represented a natural surface or a cleavage plane.[line 173] I’m sure you can find a source other than Wikipedia.
AC3-16: We now use the citation Bárány and Vu (2008).[line 235] The entire 3.2 constraints on alpha recoil distance from U clustering derives from U clustering which is never depicted in the figures?
AC3-17: We now show this in Fig 10.[line 239] Do you have an explanation for why Ti of all elements is enriched in these clusters? No other elements?
AC3-18: We do not understand the cause of clustering except that we cannot see how it could be not be a primary feature of crystallization.[line 254] I think that Valley et al. 2014 and 2015 gave some explanations for clustering.
AC3-19: We now add a reference to the Valley et al. (2014) paper and note that the clustering they observed does not affect U but only Pb and other trace elements. These were probably mobilized during high-grade metamorphism, which is not the case here.[line 262] You should also cite Peterman et al. 2019 for trace element enriched linear features.
AC3-20: This has been cited but the features described are again due to high-grade metamorphism so they are not relevant to low-grade samples such as ours..[line 270] the clusters of U are primary, formed during initial crystallization: can you provide examples of this in the literature? Or explain this further?
AC3-21: We are not aware of other examples like this in zircon. We cited Putnis et al., 1992; and Wu et al., 2019 in relation to the possibility of incomplete nanoscale zoning, but further discussion is beyond the scope of the manuscript.[line 317] You confirm that you did not measure Pb depletion profiles yet go ahead and assume you can calculate alpha recoil from this profile? This Pb compositional gradient could be something other than alpha recoil: diffusion.
AC3-22 : Given the low temperature history of the sample and the high blocking temperature for diffusion of Pb in baddeleyite, the Pb compositional gradient cannot be due to diffusion, although we now discuss this.Figure 3: I suppose the concentration profiles are taken with respect to the observed volume? You should also plot the background levels with respect to each element analyzed here. What are the errors associated with each concentration point?
AC3-23 : These data are now given in the spreadsheet of TOF results in Supplementary Data and errors are shown for the Pb/U ratio profiles.Figure 4: Where are the labels for each axis? Also the errors associated with these measurements??
AC3-24 : We have added labels where necessary in accordance with the comments of reviewer 1.Figure 7: Again what is the title for the y-axis? The points are incredibly difficult to see. I would suggest extending the graph to the full width of the page and spacing out the points so that you can see which correlate? Maybe use different symbols and not all circles?
AC3-25 : It is unfortunately necessary to squeeze a great deal of visual information into the comparative profile figures so the symbols have to be small but the colours seem to effectively distinguish the different profiles on Figs 7 and 9 provided they can be reproduced at page width.Citation: https://doi.org/10.5194/gchron-2023-15-AC3
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AC3: 'Reply on RC3', Donald Davis, 20 Sep 2023
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Donald Wayne Davis
Steven Denyszyn
Denis Fougerouse
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