This manuscript presents ⁴⁰Ar/³⁹Ar step heating data for polyhalite samples from the Salt Range Formation in northern Pakistan, with the overarching goal of using the ⁴⁰Ar/³⁹Ar data to interpret when precipitation, recrystallization, and/or thermal resetting took place in the geologic history of the Salt Range Formation. The motivation for attempting to date the polyhalite is clear, as geochronological constraints for the Salt Range Formation are quite sparse otherwise, and evaporite minerals are generally challenging to date. The ⁴⁰Ar/³⁹Ar data are parsed into two types: age spectra, and step-heating experiments used to derive Ar diffusivities. Both types of data are quite complex, with none of the age spectra yielding age plateaus, and the diffusivities determined yielding complex, curved Arrhenius arrays. I think the authors have done a good job of interpreting (and, importantly, not over-interpreting) the age spectra, inferring only maximum and minimum ages of events from their youngest and oldest step ages, respectively. However, I have many issues with the step heating experiments used to derive diffusion parameters. I outline these methodological and interpretive concerns in my line-by-line comments below, but the summary is that I do not think that have provided quantitative or qualitative constraints on the diffusion kinetics of Ar in polyhalite. Given this, and given the limited geochronological utility of the age spectra, I cannot recommend this manuscript for publication in Geochronology.

Line 48: The Reiners et al. textbook is not really an appropriate reference here. I recommend removing the reference and modifying the second part of the sentence to say, “…several studies have applied ⁴⁰Ar/³⁹Ar dating to evaporite minerals.”

Lines 49-52: This sentence is garbled – please revise.

Line 53: Please include a reference for the statement about langbeinite being less susceptible to alteration and Ar diffusion.

Line 60: I recommend removing the parenthetical part of this heading; “Geologic Background” is sufficiently descriptive.

Figures 1 (and 2): There is no legend explaining what the shading means; please include this.

Lines 138-149: There are many details about the step heating experiments missing here, and it is insufficient to cite the Reiners et al. textbook. For example, how have the authors determined that their raster heating approach achieves persistent uniform heating across all grains? And how have they calibrated the temperature measurement? Is the temperature measurement by pyrometer, and if so how have they calibrated the emissivity of polyhalite to relate measured temperature to true temperature? I am skeptical that the approach described would achieve uniform, steady, well-calibrated temperature measurements, which are all essential characteristics to quantify diffusion kinetics from a step heating experiment. Please quantify the uncertainty in temperature for each heating step, which I presume will be quite large. There also needs to be a citation here for the transformation of gas fractions into diffusivities; e.g., many people use the discretized equation of Fecthig and Kalbitzer (1966), with the modified cut off parameters in McDougall and Harrison (1999). How were uncertainties propagated from gas fraction into diffusivities for use in Isoplot? This is a nontrivial calculation because of the cumulative nature of gas fraction, and either requires a Monte Carlo simulation (e.g., see Tremblay et al., 2014), or the analytical solutions derived by Ginster and Reiners (2018). I recommend recalculating the Arrhenius plots using the Excel spreadsheets provided in the supplement of Ginster and Reiners (2018), as this will also allow the authors to put in uncertainties in the temperature. Finally, how did you determine the diffusion domain/grain size? Were grain dimensions measured via microscopy? Are there any concerns about changing the diffusion domain size when the sample was crushed to obtain the polyhalite separates?

Line 151: Please change to “⁴⁰Ar/³⁹Ar dating”; it’s redundant to say “age dating.” Please make similar changes throughout the text (e.g., Table 1).

Line 155: In this sentence and elsewhere, the use of the word apparent is unnecessary. The age spectra are not apparent, they are the observed age spectra and the measured step ages.

Lines 162-164: Please add citations for the plateau criteria.

Lines 177-178: A flat K/Ca spectrum does not imply argon diffusion from a single diffusion domain. If the diffusion domain size. If a mineral of uniform composition is comprised of multiple diffusion domains and/or multiple grain sizes, the K/Ca spectrum will be flat. The authors have not made a convincing argument as to why the grain size represents the diffusion domain for polyhalite. I recommend this sentence and similar statements made elsewhere be removed.

Line 186: Delete the words “quality data is not considered presentable.”

Lines 220-230: Like the methods section, there is a lot of detail that has been left out here in the description of the step heating experiment results, and . Why are only the first three steps and four steps utilized for the linear regression on experiments SRL05 and SRL06, respectively? What was the criteria for choosing which steps to fit? None of the behavior beyond the first few steps is discussed, despite a lengthy discussion on the structural transformation of polyhalite beginning at temperatures below those traversed during the step heating experiments. Why does the Arrhenius plot become curved, and why is there a giant spike in diffusivity around 500 ºC? The temperature labels on the top x-axis of Figure 7 are incorrect, and the bottom x-axis needs units.

Table 2: This table is unnecessary, I recommend simply discussing existing diffusion parameters for other minerals in the text.

Lines 264-301: This is an excellent discussion of the structural transformations that polyhalite undergoes at various temperatures. Unfortunately, as the authors point out, all of their heating steps in their step heating experiments occur at temperatures above the temperatures at which these structural transformations occur. So I think describing the step heating experiments as a semi-quantitative measure of the Ar diffusion kinetics in polyhalite is unwarranted. Instead, their step heating experiments most likely document the release of Ar from two langbeinite-type phases, per their eq. 3. This likely explains the complex Arrhenius behavior the authors observed. I recommend adding discussion to this effect.

Lines 333-341: This is a nice discussion of the potential effects of deformation on recrystallization and Ar diffusion. However, if intracrystalline domains are known to be present in these samples, that seems to contradict repeated statements in the text that Ar diffusion from their samples occurs from a single domain represented by the grain size. If anything, this is a compelling observation to expect the presence of complex, multi-diffusion domain behavior.

Lines 356-366: Given the dubious geologic significance of the oldest and youngest step ages, I recommend against quoting the step age uncertainties here. Instead, I suggest that you quote approximate ages, e.g., “~514 Ma” rather than “514 ± 3 Ma” in the first sentence.

Supplementary files: Again, I urge the authors to use the supplemental spreadsheets of Ginster and Reiners (2018) so that they can propagate uncertainty in temperature and gas release fraction into the calculated diffusivities and therefore their linear regressions.

New references cited:

Fechtig, H. and Kalbitzer, S.: The Diffusion of Argon in Potassium-Bearing Solids, in: Potassium Argon Dating, Springer Berlin Heidelberg, Berlin, Heidelberg, 68–107, https://doi.org/10.1007/978-3-642-87895-4_4, 1966.

Ginster, U. and Reiners, P. W.: Error Propagation in the Derivation of Noble Gas Diffusion Parameters for Minerals From Step Heating Experiments, 19, 3706–3720, https://doi.org/10.1029/2018GC007531, 2018.

Tremblay, M. M., Shuster, D. L., and Balco, G.: Diffusion kinetics of ³He and ²¹Ne in quartz and implications for cosmogenic noble gas paleothermometry, 142, 186–204, https://doi.org/10.1016/j.gca.2014.08.010, 2014.

Marissa Tremblay

Purdue University

June 27, 2021

General comments:

This manuscript reports Ar/Ar step-heating results from polyhalite in the Salt Range Formation in northern Pakistan. The authors aim to provide geochronologic age constraints for this formation (on the timing of precipitation, deformation, and/or thermal resetting), and to determine diffusion parameters for polyhalite. Polyhalite is a potassium-bearing salt [K₂Ca₂Mg(SO₄)₄•2H₂O], formed in evaporite environments, so is an interesting target for Ar/Ar geochronology, especially as this phase has only rarely been analysed via this technique. Unfortunately, it appears that the samples chosen for this study have experienced a complicated geological history of deformation and reheating, with none of the samples yielding Ar/Ar age plateaus. The Arrhenius diffusion results are also non-linear, and likely confounded by dehydration and structural reconfiguration reactions, complicating attempts to calculate diffusion parameters for polyhalite.

The results of this study could possibly be suitable for publication in Geochronology, as even less than ideal analyses may potentially be useful when reporting results for a little-studied mineral or region. However, this usefulness would require the results and discussions to be conservative, noting the pitfalls in the data in a consistent way, and framed to highlight aspects that could lead to improvements. This manuscript has several crucial points that require resolution before it would be suitable for publication.

Specific comments:

The most important points that need improvement are as follows:

• Line 19: states ‘the established early Cambrian age of the formation’. However, Figure 2 indicates that the that the Salt Range Formation is Ediacaran-Early Cambrian. If no other geological constraints are available, the upper limit for the age of the formation is 635 Ma (the base of the Ediacaran) - not 541 Ma (the base of the Cambrian).
• The methods section currently lack sufficient details about the diffusion experiments. The methods section (around line 138) does not detail the technique used to measure the step temperature, which is crucial for diffusion experiments. The methods section must therefore be expanded to explain the methodology for the diffusion experiments and how the diffusion parameters were calculated.
• Line 150-218: the entire section for the step-heating results needs improvement. The current separation of the age spectra and results section into Figures 4 (the ‘good’ data) and Figure 5 (‘erroneous data’) is confusing, as some of the samples currently in Figure 5 (06-2.1, 06-3.2) have similar spectra to those in Figure 4. I would recommend splitting the results into 1) aliquots with high K/Ca (i.e., separates of polyhalite), and 2) aliquots with low K/Ca, imprecise step ages, and uninterpretable results. Crucially, for samples with low K/Ca, this observation indicates that the phase sampled and analysed was likely not polyhalite but is instead another mineral with lower potassium.
• Line 150-218: in a revised results section, please reduce the amount of duplicated information between paragraphs and between the main text and tables. Also ensure the results are not over interpreted - caution should be applied in attributing geological significance to the youngest and oldest steps from a disturbed heating spectrum, particularly if there is no reproducibility between aliquots. A conservative interpretation of the data presented in this manuscript indicates: 1) That the Salt Range Formation is likely older than ~500 Ma (i.e., the oldest step with good precision (Fig 6). 2) That the polyhalite Ar/Ar results yielded a broad range in ages from ~500 to 200 Ma, likely due to variable and incomplete resetting of the polyhalite via tectonic and thermal events in the region. 3) That the most recent geological event in the region that affected the polyhalite occurred less than ~200 Ma (based on the youngest step with good precision (Fig. 6)). However, if the youngest step was only partially reset by that geological event (or events), the event could be much younger than 200 Ma - especially given that tectonic activity in the Himalayas is occurring in the modern day.
• Line 153: states that ‘Polyhalite single crystals, polycrystals and grain aggregates taken from larger samples underwent step-heating 40Ar/39Ar age dating.’ However, from the information provided it is not clear which samples were single crystals, polycrystals, or aggregates. This information must be provided somewhere (e.g., in Table 1) for each of the aliquots analysed. Also, please briefly explain the difference between a polycrystal and a grain aggregate.
• The results of the diffusion experiments (lines 220-226) are far too brief. This section only spans six lines, and this text is not useful, only containing a series of numbers already presented on Figure 7. The authors need to explain the choice of samples used for the diffusion experiments, outline how the diffusion parameters were calculated, and describe the features seen on the diffusion diagrams (e.g., slope, slope changes, spike at 500°C).
• As this study represents analyses of a relatively unstudied mineral (polyhalite), it could be beneficial to have a clear list of what worked, what didn’t work, and what could be improved for future analyses. There are aspects of this study that were successful include 1) that some samples yielded high and consistent K/Ca values, indicating the aliquots analysed had a consistent mineralogy; and 2) that the samples had high percentage of radiogenic argon (i.e., that polyhalite is reasonably good at keeping the Earth’s atmosphere out of its mineral structure). Both are basic – but non-trivial – observations.
• It may also be useful to have some recommendations for future work, including further groundwork studies on polyhalite. Presumably such groundwork studies could be more easily done in areas with a simpler geological history.
• In the documents supplied for review, I was unable to find a table containing the analytical results, which is crucial for reporting Ar/Ar data. Please ensure such a table is incorporated (likely as a supplementary dataset), and that it includes all information required (see Renne et al. 2009 Data reporting norms for 40Ar/39Ar geochronology. Quaternary Geochronology v4 p346-352).
• Several areas of text are poorly written or confusing. Please go over the full manuscript and ensure clarity for both general writing and scientific concepts. Some particularly notable examples include lines 14-18, 24, 62-63, 130, 303-304, 315-318, 326-327 (which has quite a jump in context between line 326 (talking about processes in the Permian) and 327 (talking about modern day processes), 359-366, 371.

Technical corrections:

Line 30: write the chemical formula for halite – all the other minerals in this portion of the text have formulae.

Line 35: start a new paragraph.

Line 59: ‘…the deformation history’.

Figure 1: label the x and y axes as ‘Longitude (°E)’ and ‘Latitude (°N)’.

Figure 1: in the caption, mention that the study site is the Kewera mine. On the figure, can the authors write ‘Kewera’ in a different font (e.g., red)? This will be useful to draw the reader to the site.

Lines 88-102: this text is essentially a duplication of information in Figure 2. The main text would be streamlined and improved by removing this text or moving it to the figure caption.

Lines 106-111: the minerals described are not identifiable in the hand-sample images of Figure 3A and 3B. Could the authors also supply other images that identify these minerals if available e.g., close-up photos/thin section photos/SEM.

Figure 3 caption: extra text is required to explain what can be seen in these images. Also, please specify the scale.

Lines 115-138 (and elsewhere in the manuscript): please ensure correct use of superscripts and subscripts.

Line 115: what was the grainsize of the crushed aliquots?

Line 118: replace ‘alteration’ with ‘dissolve’.

Line 124: J factors are reported with too many digits and should be limited to significant figures only.

Line 124: which J factors correspond to what samples?

Line 126: what was the frequency of air pipettes? How many air pipette analyses were included in the discrimination calculation?

Line 129: write the abbreviation ‘IR’ out in full.

Line 155-157: delete the following text as it is poorly written and unnecessary in the main text.  ‘Apparent age spectra plots display the apparent ages for each step of the experiment and are calculated representing a percentage of cumulative 39Ar released with the last step resulting in 100% 39Ar released from the sample. Stacked below each age plot are the K/Ca ratios.’

Line 162-164: provide a reference for this definition of a plateau.

Lines 175-179: this information should be in the figure caption.

Line 188-198: suggest changing to ‘Sample 06-1.2 produced very little gas, with low K/Ca values and analyses barely above blank levels, yielding very imprecise ages; the results from this sample have therefore been discarded.’

Table 1: as none of the samples yielded useable plateau or isochron ages, the following columns should be deleted: Plateau Age, ±, MSWD, %39Ar, Inverse Isochron, MSWD. Deleting these columns will free up space in the table.

Line 248: delete ‘closed’. If the system has been partially or wholly reset, it is not closed.

Table 2: numbers are reported with too many digits – limit to significant figures only.

Line 277: what are the ‘various analogues’?

Line 289: what is meant by ‘with variations to pressure’?

Line 300: please explain why that approach was not possible in this study.

Line 315: instead of ‘magmatic’ do the authors mean ‘sedimentary’?

Line 356: here and elsewhere: this should be ‘minimum age’.

General Comments: This study applies the ⁴⁰Ar-³⁹Ar dating technique to crystals of polyhalite from the Salt Range Formation in northern Pakistan. The aim is to determine the age of the formation and to determine diffusion parameters and a closure temperature for Ar in polyhalite. The study did not yield any crystallization ages due to disturbances to the Ar-Ar system, suggested to be from repeated episodes and deformation (as well as the difficulty associated with dating evaporite minerals in general). The authors were able however, to present minimum ages suggested to represent primary crystallization, and a suggested maximum age of deformation. There are several issues with the study that require clarification, further information and revision (see below), but study is still a useful stepping stone, particularly because of the paucity of geochronologic data for evaporite minerals in general. Clarification on the determination, and meaning of, the reported range of closure temperatures determined for polyhalite is required. In the introduction, the authors are suitably cautious “Though these results are semi-quantitative, they are contextualised with the structural history of the host formation to form a speculative interpretation of deformation history” and generally I think this is fair. As reliable Ar-Ar ages for polyhalite would be useful for, e.g., formation ages, reconstructing deformation histories, the qualitative to partially quantitative data provided in this study would likely be of use to future workers pursuing Ar-Ar applications of these complex minerals. As the results are largely qualitative, however, the discussion could be shortened in places.

Specific Comments:

Line 132: Was the “homogenised temperature” determined – was it specifically monitored?

Line 138: It is mentioned that “contemporaneous step heating experiments” using the same parameters as described in the analytical methods were used to determine diffusion parameters. Much more information on these experiments is needed here. It would be very helpful to describe (as above) how the temperature was monitored, e.g, pyrometer?, as this is essential for these experiments.

Line 153: You describe 9 samples but only descriptions for SRLR-05 and SRLR-06 are given in section 2.2. If the 9 samples are aliquots of these two samples, perhaps say nine aliquots or repats from two samples. Looking at the filenames in the supplement, it looks like 7 from 05 and 2 from 06. It might be helpful to list the number (e.g., n=7) for each sample and also explain the uneven distribution (why only 2 analyses from sample 05?).

Line 155: If you denoted each panel with an (a) or (b) the description of data plots here would be less cumbersome.

Line 158: (Figure 5) If the data aren’t used for anything, I would suggest moving these plots to the supplement.

Line 178: Can you explain why the flat K/Ca indicates a single Ar domain?

Line 185-187: Long sentence – a bit unclear, please revise. Also, seems more interpretative rather than “results.”

Looking at Figure 4 and 5, two samples of SRLR-06 have identical K/Ca to SRLR-05 of ~ 0.82 but the remaining 5 aliquots of SRLR-06 are entirely different. Can you shed light on the two populations?

Line 242: It still isn’t clear how single domain diffusion was established – I might be missing something, so please expand/clarify.

Line 296: If the polyhalite is undergoing dehydroxilation at the same T range as the determined closure temperature, then much of this discussion could be shortened and perhaps out of caution the closure temperature shouldn’t be reported in the abstract, or with a caveat.

Line 315: Perhaps step-crushing experiments alongside step-heating experiments could help here.

Line 324-330: Are you suggesting this? It isn’t clear the way it is written. This section seems quite speculative.

Section 5.1/5.2 and section 5.3 could be reversed with the discussion/interpretation of the ages first.

Section 5.1: Relating to the comment above regarding T steps, more information is required here. Also, its quite short to warrant its own section as it currently stands.

Line 333 onwards: The numbered points are confusing – are these possible scenarios, a suggested sequence, etc.? It also seems speculative given the nature of the data.

Line 351: I think 9 samples is a bit misleading, rephrase as above.

Line 354: “profiles consistent with pure diffusion kinetics from a single domain” I don’t think this has been adequately demonstrated. I’m not sure that attributing a specific process to the ~ 500 Ma age is warranted.

Line 370: I would delete “taken with a grain of salt.”

Line 371: “As such, they serve only as a first pass on polyhalite diffusion kinetics and cannot be used for geochronological works with any precision.” It seems this sentence negates all prior discussion. I think with different language you could frame this in a more positive light –it is a first study on very challenging samples and much can be learned from the experiments.

Figure 6 could do with revision. The fonts are too small, there are excessive decimal places in the y-axis, the legend is too small, and most of the data are in at the axis (could do with a zoomed in panel). The symbol colors of 06-1.2 and 06-2.1 are hard to differentiate. I would also remove the title.

Figure 7 would also benefit from revision. The two panels have different scales on both x and y making it difficult to compare visually. The diffusion parameters overlap with the data in panel A. I would also remove the titles.

The formatting of Table 1 makes it really difficult to read, perhaps adjust columns or delete “incalculable” and replace with “nd” for not determined.

Table 2 is a nice summary, but it isn’t exhaustive and many of the mineral phases are not particularly relevant to the geologic with discussion.

Supplement “Arrhenius Final” could be in better shape for a supplementary file. I can see that the required information is there, but it is quite hard to follow. It also isn’t clear how some of the important parameters were determined (e.g., T). This requires clarification and improvement in the main text and in the supplement.

The references need some attention. They are inconsistent in formatting, contain many typos and often have incomplete information.

Technical Corrections: A few minor suggestions to improve clarity and formatting.

• Line 50: could delete radioisotope
• Line 56: could delete “process in an attempt”
• Line 60: I would remove (stratigraphy, composition, samples) from the Header
• Line 116: Superscript 38Ar
• Line 120: Space, neutron fluence
• Line 131: Argon
• Line 132: Superscript -14, also line 136
• Line 240: “Coincidentally these samples coincide” is a bit awkward, perhaps revise
• Line 254: I would use different notation here, e.g., 2.62 x 10⁷
• Line 256: “Ar datable minerals" sounds a bit awkward, perhaps revise.
• Section 4.2, lines 220, would suggest not using “E” notation in the main text.
• Line 276: delete repeated degree symbol
• Line 338: “Deformation events resulting in deformation” could be rewritten