the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Dec 2024
Technical Note: Improved volume and derived value calculations for polished zircon
Abstract. Polishing mounted mineral crystals prior to bulk grain (U-Th)/He thermochronology analysis offers many advantages for characterizing and subsampling each grain via in situ methods to obtain the maximum geologically relevant information. However, polishing introduces complications for calculating grain volume, on which many derived (U-Th)/He data partially depend. Impacted data include isotope concentrations, effective uranium (a proxy for radiation damage), and alpha-ejection correction factors (FT) which are used to correct (U-Th)/He dates. These derived data are integral to interpreting (U-Th)/He dates; without a way to accurately calculate these values for polished grains, the benefits of polishing and in situ measurements can be greatly reduced or negated. This reality has resulted in many studies forgoing polishing and thus missing potentially important data. To address this issue, this paper presents a set of equations encoded in an R script to calculate volume and derived values for polished zircon that can be easily integrated into existing workflows for bulk grain (U-Th)/He analysis.
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RC1: 'Comment on gchron-2024-33', Christoph Glotzbach, 17 Jan 2025
Dear Author,
I have read your technical note on improving grain geometry estimates required for (U-Th)/He measurements in case grains are mounted and polished prior to He measurements. The reasoning why a more accurate method is needed is clear to me, but I would ask you to be more specific in describing the method. From what I understand from your manuscript, your proposed approach will likely under- or overestime the Ft value since you are using volume and surface area calculation of the polished grains for your calculation of Ft. The correct Ft value is dependent on both the original grain geometry and the resulting after polishing and only if half a grain is polished both will be similar. The resulting Ft value calculated with your approach will be smaller than the corresponding Ft value of the whole grain, in case polishing removes less than half of the grain. The opposite is in case more than half the grain is removed during polishing. Either show the difference to the correct value and state the limitation or implement the correct calculation.
Please see my scientific comments and technical corrections for more details:
Technical corrections:
Line 1,16: Specify what you mean with ‘derived value calculation’. Also, later you often say something like ‘other values’. Please make sure that you always specify the measurements you are referring to.
Line 8-17: You state that the proposed protocol is beneficial for in situ measurements (line 14) and later for bulk grain (e.g. line 16). Please state clearly which method (in-situ and/or bulk grain) would benefit.
Line 49-50: You may want to reference to my approach using a set of orthogonal microscopic pictures to derive whole-grain geometries (Glotzbach et al. 2019 – Chemical Geology).
Line 48-58: Please clearly state what your approach is. Measuring only after mounting/polishing or, what I guess, two measurements are required before and after mounting/polishing.
Line 72: The word ‘irrelevant’ is somewhat misleading here, since the depth to which grains are polished is impacted V, SA and other related parameters and is not irrelevant. I guess you mean that it is easy to account/correct for.
Line 74-77: See above, in case you meausure individual grains before and after mounting/polishing this would not be required. Therefore I guess you are measuring only after mounting/polishing and derive the depth of polishing from the glass beads.
Line 85-90: I do not fully understand how you can estimate the correct values of a and b for an ellipsoid (r for cylinder) in case more than half of the grain is polished away. The equations that you state will be minimum values for a and b (e.g. b=W1/2).
Line 86: Specify what the ellipsoid coefficient is.
Line 114-115: Same as for the ellipsoid does apply for a cylinder, it is not possible to correctly determine r when more than half the grain is gone. The equation that you are using r= min(W1,W2) will underestimate r. Why not using equation 1 to estimate the correct radius?
Line 158-186: It is unclear to me if you calculate the Ft for the whole grain or the mounted/polished grain. The Ft value of mounted/polished grains will in most cases be higher/lower than the theoretical value of the whole grain (similar only if exactly half the grain is removed).
Line 187: Please add more details on how you did the comparison, are this read data or synthetic data and give details how the methods of Ketcham and Reiners differ from your approach.
Line 189: Please clarify what you mean with ‘uncorrected method’?
Citation: https://doi.org/10.5194/gchron-2024-33-RC1 -
AC1: 'Reply on RC1', Barra Peak, 21 Jan 2025
The comment was uploaded in the form of a supplement: https://gchron.copernicus.org/preprints/gchron-2024-33/gchron-2024-33-AC1-supplement.pdf
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AC1: 'Reply on RC1', Barra Peak, 21 Jan 2025
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RC2: 'Comment on gchron-2024-33', John He, 04 Mar 2025
The author provides a set of equations to calculate volume and surface area, which seems generally uncontroversial, as far as I can tell. The R code may be useful for some. Generally, the manuscript could be improved if it more clearly stated what measurements are actually required as input for each of the geometric cases, and if the equations were appropriately justified when they are introduced. As it is, there's insufficient discussion to justify some of the assumptions going into the equations, and many of the variables+equations are poorly explained or not explained at all.
Other comments:
First, I would suggest that the author reconsider the use of “volume and derived value” in the title, which could be more informative if it specified, for example, “improved calculation of volume, FT correction, and other derived values for polished zircon”… At the end of the day, the FT correction is what most readers are interested in.
Second, the manuscript would be much improved with greater discussion of the specifics of how the proposed calculations differ from previous protocols (e.g. in Lines 210-215). The equations are presented, but not much is done to demonstrate their superiority, besides Figure 2. Which cases lead to the large (95%) variation? It seems to be just a single grain or two? In what cases/geometries/grain sizes generally have minimal difference between the different protocols? Is it small grains that are particularly effected? or when very little of the grain is polished, or a lot of it is polished away?
A histogram could be provided showing the % difference between the different protocols for each grain in the dataset.. Is there a systematic skew towards overestimating or underestimating FT?
Notably, Fig. 2 only shows that these protocol are different. But it's not immediately clear why, practically speaking, the additional complication of assigning grains to particular sub-classes of geometries and degrees of polishing based on limited 2D measurements from a polished mount wouldn't simply be introducing more assumptions and/or errors. I could certainly imagine how these detailed calculations here could be better - but I don't think that's necessarily the case, and the author needs to demonstrate that.
For example, the author states that “The Reiners et al. method of accounting for FT corrections due to polishing, while frequently resulting in < 5 % difference, can also vary more significantly, likely due to simplifying assumptions made by this method regarding grain geometry, orientation, and depth of polishing.” The author should expand on this sentence and explicitly discuss those simplifying assumptions. How and when exactly do they vary so significantly? And most importantly, for many readers, the question is whether it is practical to move beyond those simplifying assumptions. It would be helpful if the author distinguished the specifics of the cases (e.g. the one with the 92% difference) that led to the large difference. Why and how are the approximations that are used here (particularly for the c-axis parallel cases) better/different than the simplifying assumptions used by others?
Third, when polished perpendicular to the c-axis, the calculations would essentially be the same case as the fragmentation correction for grains with one end broken, which we discussed in a similar paper (He and Reiners, 2022). For these cases, I imagine the modified FT would be exactly the same as the protocol propose here?
Finally, something additional that would be relevant to add in the discussion: the idea that the SA/V of polished grains can be used to modify FT corrections assumes that the polynomial function relating SA/V to FT is nearly identical for most geometries. But it is not entirely identical, and polished grains would deviate pretty far from ideal geometries used to determine the SA/V-FT functions.
Other comments:
-It’s not clear from Fig. 1 what the different labels (e.g. w1 wp) are referring to in many of the diagrams.
-What you call SA is not actually surface area - but rather something like the alpha-ejection-affected-surface area. I suggest using a subscript to clarify this (SAα), or something similar, as it is can be confusing to readers. Note that in He and Reiners 2022, we called βα =the ratio of alpha-ejection-affected surface area to volume.
-There should be more details about the test dataset: what was the measurement protocol? the range of grain sizes? how were the grains assigned into different geometries if they were already polished?
Citation: https://doi.org/10.5194/gchron-2024-33-RC2
Interactive computing environment
polished_ZHe_derived_values_v1.0.R Barra A. Peak https://github.com/Barra-Peak/polished-ZHe-derived-values
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