the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
02 Jun 2021
02 Jun 2021
Attenuation of beta radiation in granular matrices: implications for trapped-charge dating
- 1Department of Physics, Technical University of Denmark, Risø Campus, Roskilde, Denmark
- 2Department of Geoscience, Aarhus University, Risø Campus, Roskilde, Denmark
- 1Department of Physics, Technical University of Denmark, Risø Campus, Roskilde, Denmark
- 2Department of Geoscience, Aarhus University, Risø Campus, Roskilde, Denmark
Abstract. Mineral grains within sediment or rock absorb a radiation dose from the decay of radionuclides in the host matrix. For the beta dose component, the estimated dose rate must be adjusted for the attenuation of beta particles within the mineral grains. Standard calculations, originally designed for thermoluminescence dating of pottery, assume that the grain is embedded in a homogenous medium. However, most current applications of trapped-charge dating concern sand- or silt-sized dosimeters embedded in granular sediment. In such cases, the radionuclide sources are not homogeneous, but are localized in discrete grains or held on grain surfaces. We show here that the mean dose rate to dosimeter grains in a granular matrix is dependent on the grain-size distributions of the source grains, and of the bulk sediment, as well as on the grain size of the dosimeters. We further argue that U and Th sources are likely to be held primarily on grain surfaces, which causes the dose rate to dosimeter grains to be significantly higher than for sources distributed uniformly throughout grains. For a typical well-sorted medium sand, the beta dose rates derived from surface U and Th sources are higher by 9 % and 14 %, respectively, compared to a homogenous distribution of sources. We account for these effects using an expanded model of beta attenuation, and validate the model against Monte Carlo radiation transport simulations within a geometry of packed spheres.
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Alastair Charles Cunningham et al.
Status: closed (peer review stopped)
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RC1: 'Comment on gchron-2021-17', Guillaume Guérin, 17 Jun 2021
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AC1: 'Reply on RC1', Alastair Cunningham, 10 Sep 2021
Many thanks for the detailed review. You raise a number of points which need addressing, and should lead to an improved submission. Regarding the main issues:
- The modelled dose rate to dosimeters when sources are placed on grain surfaces, which differs from Guérin et al., (2012).
This difference largely comes from an omission on my part. The MC simulations in section 3 address the external dose rate only, i.e. they do not include a self-dose from the dosimeter grains. It was modelled this way for two reasons;
- There are code limitations on the total number of sources in the MCNP6, that prevent every grain from being a source. So if there are 5000 grains in total a simulation, and the number of sources is <1000. Dosimeter grains are selected from the remaining non-sources, hence do not have a self-dose;
- The self-dose is easy to calculate from the simpler MC simulations in section 2; for the complex simulations, it makes no difference whether the doses are modelled at the same time or added later.
Obviously this was not clear in the manuscript. In addition, the self-dose values should have been included when making the summary statements in the results/discussion/abstract. When they are added, the difference with Guérin et al. 2012 numbers is reduced. For the sand-sized sediments with surface sources, the U and Th dose rates are 19 % and 28 % greater than for whole-grain sources. The remainder might be explained by small differences in the input parameters (grains size distributions, etc)
2 On the effects of water content:
I think you are on the right lines with the water content. The analysis in section 4 was done by comparing the effects of water to quartz in the same geometry. However, this is not what is assumed in the standard equation. To do this subject justice would require a much larger set of simulations, which is certainly no room for in the present manuscript. So this section will be removed in the revision.
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AC1: 'Reply on RC1', Alastair Cunningham, 10 Sep 2021
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RC2: 'Comment on gchron-2021-17', Svenja Riedesel, 22 Jun 2021
Review of Cunningham et al. “Attenuation of beta radiation in granular matrices: implications for trapped-charge dating” submitted to the Journal Geochronology
The manuscript submitted by Cunningham et al. presents simulation results on the grain size dependence of the mean dose rate to dosimeter grains in a granular matrix. Additionally, the authors explore the effect of surface or whole grain sources on the dose rates to dosimeter grains. Experiments performed by the authors suggest that U and Th as radioactive sources are primarily being held on grain surfaces, whereas K seems to be a whole grain source. The manuscript shows the need of a refined model to account for variable grain size distributions of dosimeter and source grains. This refined model is presented in the manuscript and the authors provide an excel spreadsheet for potential users, who wish to make use of the new findings in their own research.
The manuscript by Cunningham et al. presents new simulation and experimental results on dosimetry issues in trapped charge dating and updated self-dose values for quartz and feldspar. I enjoyed reading the manuscript and it deserves to be published in the Journal Geochronology after some minor revisions. I hope that my suggestions will help the authors to improve the readability of the manuscript.
Minor comments:
Comment #1: Use of terms
In their manuscript the authors make use of various terms to describe their simulation setup as well as their results. Unfortunately, sometimes new words are introduced for things that have been described by a different term in previous sections. Using the same term throughout the manuscript and explaining the used term on its introduction would help the reader in understanding the manuscript.
Here are some examples:
- Line 38 – 43: Here the terms inactive and inert are used. I would suggest sticking to one of these terms. Also here the term “inert” is used for the first time, whilst its meaning is explained later on (line 79 – 80).
- Line 85: “… external grains …”. It is unclear what “external grains “ are. I assume that here the authors use the term “external grains” as a synonym for the in line 82 described “… presence of other grains in the sediment …”. I find the term “external grains” difficult, especially, because it is not used again at a later stage. I suggest using the term “inert grains”, if this is what the authors actually mean.
- The use of the term “matrix” throughout the manuscript: In the beginning the authors use the term “matrix” for the homogenous surrounding of a dosimeter grain – as which the term matrix has been used in the literature previously. However later on (e.g. line 305-312) the term “matrix” is also used to describe the sediment grains simulated in section 4, including source and dosimeter grains.
Comment #2: Section 2 and section 3
Section 2 introduces the balanced energy model, whilst section 3 does not make use of this model. Additionally, section 2 refers to the tables generated using the simulations presented in section 3. I find this rather confusing, and I would suggest swapping section 2 and 3 for better readability of the manuscript. I also think that presenting section 3 before section 2 could help in justifying the contribution of this paper to the current body of knowledge when presenting the aims of this manuscript at the end of section 1.
Comment # 3: Self-dose values for K-rich feldspar grains
Table 3 is only mentioned once in the entire manuscript (line 165 in section 2). I assume it is generated using the simulations described in section 3, although this is not explicitly stated in this section. I would suggest to also refer to this table in section 3 and explain the simulation setup used for the K-rich feldspar grains, i.e. composition of the grains and matrix.
Comment #4: References needed for some statements
- Line 155 – 159: Here references are needed for the statements on U and Th as surface sources and the low likelihood of K as a surface source. Later on (section 7) references are listed and explanations are given. Maybe some of this could already be used in line 155-159?
- In line 215 the authors state that there is only “little difference in electron stopping powers between the main silicate minerals”. A reference is needed for this statement.
- Line 291: Here a reference should be given for x = 1.2.
Comment #5: Figures
- I really like that the simulation geometries are shown in the manuscript. However, it would be useful if a legend would be given for each geometry used. This should include an explanation for the colours used in the box geometry as well as for the bars shown in the respective grains size distributions, as it is unclear to what distribution the filled and the non-filled bars refer.
- Figure 4: For consistency I would suggest using the same symbols as in figures 2 and 3. A better alternative would be to use different symbols and different colours for U, Th and K in all figures. This would make reading the figures more accessible to everyone, and it might be helpful should the manuscript be printed in greyscales.
- There are a few occasions where a reference to a figure would be helpful, e.g. in line 225, lines 381-384.
Comment #6: Minor typographical errors
- Line 191: ðs is given in the text, but in table 2 self-dose values for surface sources are denoted as ðsurf.
- Line 234: Here the abbreviation BEM is used for the first time. However, the abbreviation is not explained. Please spell BEM out on its first use.
- Line 311: Could you please check the phrasing of the sentence starting with “If conditions…”.
-
AC2: 'Reply on RC2', Alastair Cunningham, 10 Sep 2021
Many thanks for the review. I think I can accommodate most of the points you raise.
The placement of section 3 is not so easy… the section is necessary but boring, so it looks out-of-place wherever it is put. When designing the structure of the MS, our main concern was in keeping the flow of the argument progressing in a logical fashion. An earlier draft had the phi-values as the second section, as you suggest, but this created an interruption to the reader because at that point it is not clear why phi-values are necessary. We explain phi fully in the model section, so after that the necessity should be obvious.
On the use of language: clearly there has been some confusion on the term ‘matrix’; I am not sure this is really justified, because the term is qualified in most cases (bulk matrix, homogenous matrix etc). I will take a close look and clarify where possible. The word ‘sediment’ was avoided, because the arguments apply to rock as well.
- AC4: 'Reply on RC2', Alastair Cunningham, 10 Sep 2021
-
AC2: 'Reply on RC2', Alastair Cunningham, 10 Sep 2021
-
CC1: 'Comment on gchron-2021-17', Barbara Mauz, 13 Jul 2021
With extending the luminescence dating practice towards heterogeneous materials and changing measurement geometry accordingly, microdosimetry has become important. This study is therefore highly appreciated. My comment is mainly about the conceptual approach illustrated in Fig. 1 and the grain-size dependence of radioactivity.
A new approach may well be introduced by way of a first order approximation, but Fig. 1A does not look like a first order approximation or I am missing something here. Fig. 1A illustrates a giant source (red region) hosting a small dosimeter. In nature this would be, for instance, the lattice of a pyroxene mineral (e.g., zircon, olivine, etc) in which a quartz grain is embedded or, as illustrated in Fig. 1B and 1C the pyroxene host carries a quartz grain together with a number of inert grains. In nature, however, quartz and pyroxene are not mixed and a re-melting of a pyroxene-bearing rock in the way that quartz and zircon get in contact as illustrated in Fig 1A can be ruled out. In contrast, Fig 1D looks realistic: the quartz dosimeter is surrounded by active and inactive grains of variable size. In the text the use of the term ‘matrix’ was puzzling: the matrix is composed of quartz and feldspar grains hence granular as illustrated in Fig 1D. Elsewhere it says the matrix is (or is not) homogeneous or it is a ‘bulk matrix’ for which the 1-φ approach should be used. Is the bulk matrix assumed to be inert, hence the opposite of Fig. 1A? Equally, “sources that are held on grain surfaces” is not illustrated in Fig. 1 and only briefly mentioned in the text as “secondary mineral coatings formed on grain surfaces”. What is a secondary mineral coating and how likely is it that it includes radioisotopes? Last, what is the relationship between Fig. 1 and the geometries depicted in Fig. 3 and what is a source distribution that equals sediment distribution in geometries B and C?
The dependence of radionuclide concentration on grain size is tested using gamma spectrometry. If the samples were wet sieved and settled in distilled water with the aid of a dispersing agent, then the secondary mineral coating on grain surfaces is altered or it has disappeared completely. The data shown in Fig. 5 would then reflect the grain size of the radioisotope-bearing mineral.
In sec. 6 there are typos regarding the daughters of Ra-226. With Murray et al. (2015; 2018) in mind, I suggest to indicate (a) the energy line with which the respective radioisotope was determined, the measurement geometry and (c) the reference material used to ensure reliability of the estimate.
I suggest to re-write the text by first illustrating the Mejdahl approach using figure, text and equation and then add one after the other element of complexity, e.g. sources held on grain surfaces, each time keeping nomenclature and notations constant.
-
AC3: 'Reply on CC1', Alastair Cunningham, 10 Sep 2021
Babara – many thanks for the comments, I will address these as best I can here:
Figure 1 is not intended to be realistic. It is a schematic illustration designed to help the reader visualise the concepts and arguments of Section 2. In Section 2, the argument progresses from the highly simplified assumption of a homogenous matrix, towards the more realistic scenario of the granular matrix. So this argument actually progresses in the way you suggest it should- beginning by explaining the standard (Mejdahl) approach and then explaining what needs to change to accommodate the granular matrix. The figure placement is a bit early, however, so I will address that when I see the proofs.
With regard to the surface held activity, there are certainly unresolved questions on the nature of the chemical bonds, which could be resolved in future by sequential leaching experiments. Your assertion that distilled water would remove all surface-held nuclides is a pretty strong one; it would need to be backed up with evidence, and would need to explain why the residual activity concentrations are proportional to surface-to-volume ratio, in four different samples. From the work that I know of – particularly Olley’s thesis, it is most likely that the U and Th nuclides are co-precipitated with iron and manganese oxides, and would not be affected by distilled water.
With regards to gamma spectrometry: Murray et al. (2018) gives full details of the measurement and analysis procedures, including calibration material and comparisons to reference samples. Typos: yes, it should be Pb-214 and Bi-214.
-
AC3: 'Reply on CC1', Alastair Cunningham, 10 Sep 2021
Status: closed (peer review stopped)
-
RC1: 'Comment on gchron-2021-17', Guillaume Guérin, 17 Jun 2021
-
AC1: 'Reply on RC1', Alastair Cunningham, 10 Sep 2021
Many thanks for the detailed review. You raise a number of points which need addressing, and should lead to an improved submission. Regarding the main issues:
- The modelled dose rate to dosimeters when sources are placed on grain surfaces, which differs from Guérin et al., (2012).
This difference largely comes from an omission on my part. The MC simulations in section 3 address the external dose rate only, i.e. they do not include a self-dose from the dosimeter grains. It was modelled this way for two reasons;
- There are code limitations on the total number of sources in the MCNP6, that prevent every grain from being a source. So if there are 5000 grains in total a simulation, and the number of sources is <1000. Dosimeter grains are selected from the remaining non-sources, hence do not have a self-dose;
- The self-dose is easy to calculate from the simpler MC simulations in section 2; for the complex simulations, it makes no difference whether the doses are modelled at the same time or added later.
Obviously this was not clear in the manuscript. In addition, the self-dose values should have been included when making the summary statements in the results/discussion/abstract. When they are added, the difference with Guérin et al. 2012 numbers is reduced. For the sand-sized sediments with surface sources, the U and Th dose rates are 19 % and 28 % greater than for whole-grain sources. The remainder might be explained by small differences in the input parameters (grains size distributions, etc)
2 On the effects of water content:
I think you are on the right lines with the water content. The analysis in section 4 was done by comparing the effects of water to quartz in the same geometry. However, this is not what is assumed in the standard equation. To do this subject justice would require a much larger set of simulations, which is certainly no room for in the present manuscript. So this section will be removed in the revision.
-
AC1: 'Reply on RC1', Alastair Cunningham, 10 Sep 2021
-
RC2: 'Comment on gchron-2021-17', Svenja Riedesel, 22 Jun 2021
Review of Cunningham et al. “Attenuation of beta radiation in granular matrices: implications for trapped-charge dating” submitted to the Journal Geochronology
The manuscript submitted by Cunningham et al. presents simulation results on the grain size dependence of the mean dose rate to dosimeter grains in a granular matrix. Additionally, the authors explore the effect of surface or whole grain sources on the dose rates to dosimeter grains. Experiments performed by the authors suggest that U and Th as radioactive sources are primarily being held on grain surfaces, whereas K seems to be a whole grain source. The manuscript shows the need of a refined model to account for variable grain size distributions of dosimeter and source grains. This refined model is presented in the manuscript and the authors provide an excel spreadsheet for potential users, who wish to make use of the new findings in their own research.
The manuscript by Cunningham et al. presents new simulation and experimental results on dosimetry issues in trapped charge dating and updated self-dose values for quartz and feldspar. I enjoyed reading the manuscript and it deserves to be published in the Journal Geochronology after some minor revisions. I hope that my suggestions will help the authors to improve the readability of the manuscript.
Minor comments:
Comment #1: Use of terms
In their manuscript the authors make use of various terms to describe their simulation setup as well as their results. Unfortunately, sometimes new words are introduced for things that have been described by a different term in previous sections. Using the same term throughout the manuscript and explaining the used term on its introduction would help the reader in understanding the manuscript.
Here are some examples:
- Line 38 – 43: Here the terms inactive and inert are used. I would suggest sticking to one of these terms. Also here the term “inert” is used for the first time, whilst its meaning is explained later on (line 79 – 80).
- Line 85: “… external grains …”. It is unclear what “external grains “ are. I assume that here the authors use the term “external grains” as a synonym for the in line 82 described “… presence of other grains in the sediment …”. I find the term “external grains” difficult, especially, because it is not used again at a later stage. I suggest using the term “inert grains”, if this is what the authors actually mean.
- The use of the term “matrix” throughout the manuscript: In the beginning the authors use the term “matrix” for the homogenous surrounding of a dosimeter grain – as which the term matrix has been used in the literature previously. However later on (e.g. line 305-312) the term “matrix” is also used to describe the sediment grains simulated in section 4, including source and dosimeter grains.
Comment #2: Section 2 and section 3
Section 2 introduces the balanced energy model, whilst section 3 does not make use of this model. Additionally, section 2 refers to the tables generated using the simulations presented in section 3. I find this rather confusing, and I would suggest swapping section 2 and 3 for better readability of the manuscript. I also think that presenting section 3 before section 2 could help in justifying the contribution of this paper to the current body of knowledge when presenting the aims of this manuscript at the end of section 1.
Comment # 3: Self-dose values for K-rich feldspar grains
Table 3 is only mentioned once in the entire manuscript (line 165 in section 2). I assume it is generated using the simulations described in section 3, although this is not explicitly stated in this section. I would suggest to also refer to this table in section 3 and explain the simulation setup used for the K-rich feldspar grains, i.e. composition of the grains and matrix.
Comment #4: References needed for some statements
- Line 155 – 159: Here references are needed for the statements on U and Th as surface sources and the low likelihood of K as a surface source. Later on (section 7) references are listed and explanations are given. Maybe some of this could already be used in line 155-159?
- In line 215 the authors state that there is only “little difference in electron stopping powers between the main silicate minerals”. A reference is needed for this statement.
- Line 291: Here a reference should be given for x = 1.2.
Comment #5: Figures
- I really like that the simulation geometries are shown in the manuscript. However, it would be useful if a legend would be given for each geometry used. This should include an explanation for the colours used in the box geometry as well as for the bars shown in the respective grains size distributions, as it is unclear to what distribution the filled and the non-filled bars refer.
- Figure 4: For consistency I would suggest using the same symbols as in figures 2 and 3. A better alternative would be to use different symbols and different colours for U, Th and K in all figures. This would make reading the figures more accessible to everyone, and it might be helpful should the manuscript be printed in greyscales.
- There are a few occasions where a reference to a figure would be helpful, e.g. in line 225, lines 381-384.
Comment #6: Minor typographical errors
- Line 191: ðs is given in the text, but in table 2 self-dose values for surface sources are denoted as ðsurf.
- Line 234: Here the abbreviation BEM is used for the first time. However, the abbreviation is not explained. Please spell BEM out on its first use.
- Line 311: Could you please check the phrasing of the sentence starting with “If conditions…”.
-
AC2: 'Reply on RC2', Alastair Cunningham, 10 Sep 2021
Many thanks for the review. I think I can accommodate most of the points you raise.
The placement of section 3 is not so easy… the section is necessary but boring, so it looks out-of-place wherever it is put. When designing the structure of the MS, our main concern was in keeping the flow of the argument progressing in a logical fashion. An earlier draft had the phi-values as the second section, as you suggest, but this created an interruption to the reader because at that point it is not clear why phi-values are necessary. We explain phi fully in the model section, so after that the necessity should be obvious.
On the use of language: clearly there has been some confusion on the term ‘matrix’; I am not sure this is really justified, because the term is qualified in most cases (bulk matrix, homogenous matrix etc). I will take a close look and clarify where possible. The word ‘sediment’ was avoided, because the arguments apply to rock as well.
- AC4: 'Reply on RC2', Alastair Cunningham, 10 Sep 2021
-
AC2: 'Reply on RC2', Alastair Cunningham, 10 Sep 2021
-
CC1: 'Comment on gchron-2021-17', Barbara Mauz, 13 Jul 2021
With extending the luminescence dating practice towards heterogeneous materials and changing measurement geometry accordingly, microdosimetry has become important. This study is therefore highly appreciated. My comment is mainly about the conceptual approach illustrated in Fig. 1 and the grain-size dependence of radioactivity.
A new approach may well be introduced by way of a first order approximation, but Fig. 1A does not look like a first order approximation or I am missing something here. Fig. 1A illustrates a giant source (red region) hosting a small dosimeter. In nature this would be, for instance, the lattice of a pyroxene mineral (e.g., zircon, olivine, etc) in which a quartz grain is embedded or, as illustrated in Fig. 1B and 1C the pyroxene host carries a quartz grain together with a number of inert grains. In nature, however, quartz and pyroxene are not mixed and a re-melting of a pyroxene-bearing rock in the way that quartz and zircon get in contact as illustrated in Fig 1A can be ruled out. In contrast, Fig 1D looks realistic: the quartz dosimeter is surrounded by active and inactive grains of variable size. In the text the use of the term ‘matrix’ was puzzling: the matrix is composed of quartz and feldspar grains hence granular as illustrated in Fig 1D. Elsewhere it says the matrix is (or is not) homogeneous or it is a ‘bulk matrix’ for which the 1-φ approach should be used. Is the bulk matrix assumed to be inert, hence the opposite of Fig. 1A? Equally, “sources that are held on grain surfaces” is not illustrated in Fig. 1 and only briefly mentioned in the text as “secondary mineral coatings formed on grain surfaces”. What is a secondary mineral coating and how likely is it that it includes radioisotopes? Last, what is the relationship between Fig. 1 and the geometries depicted in Fig. 3 and what is a source distribution that equals sediment distribution in geometries B and C?
The dependence of radionuclide concentration on grain size is tested using gamma spectrometry. If the samples were wet sieved and settled in distilled water with the aid of a dispersing agent, then the secondary mineral coating on grain surfaces is altered or it has disappeared completely. The data shown in Fig. 5 would then reflect the grain size of the radioisotope-bearing mineral.
In sec. 6 there are typos regarding the daughters of Ra-226. With Murray et al. (2015; 2018) in mind, I suggest to indicate (a) the energy line with which the respective radioisotope was determined, the measurement geometry and (c) the reference material used to ensure reliability of the estimate.
I suggest to re-write the text by first illustrating the Mejdahl approach using figure, text and equation and then add one after the other element of complexity, e.g. sources held on grain surfaces, each time keeping nomenclature and notations constant.
-
AC3: 'Reply on CC1', Alastair Cunningham, 10 Sep 2021
Babara – many thanks for the comments, I will address these as best I can here:
Figure 1 is not intended to be realistic. It is a schematic illustration designed to help the reader visualise the concepts and arguments of Section 2. In Section 2, the argument progresses from the highly simplified assumption of a homogenous matrix, towards the more realistic scenario of the granular matrix. So this argument actually progresses in the way you suggest it should- beginning by explaining the standard (Mejdahl) approach and then explaining what needs to change to accommodate the granular matrix. The figure placement is a bit early, however, so I will address that when I see the proofs.
With regard to the surface held activity, there are certainly unresolved questions on the nature of the chemical bonds, which could be resolved in future by sequential leaching experiments. Your assertion that distilled water would remove all surface-held nuclides is a pretty strong one; it would need to be backed up with evidence, and would need to explain why the residual activity concentrations are proportional to surface-to-volume ratio, in four different samples. From the work that I know of – particularly Olley’s thesis, it is most likely that the U and Th nuclides are co-precipitated with iron and manganese oxides, and would not be affected by distilled water.
With regards to gamma spectrometry: Murray et al. (2018) gives full details of the measurement and analysis procedures, including calibration material and comparisons to reference samples. Typos: yes, it should be Pb-214 and Bi-214.
-
AC3: 'Reply on CC1', Alastair Cunningham, 10 Sep 2021
Alastair Charles Cunningham et al.
Alastair Charles Cunningham et al.
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