Talk:WikiJournal of Science/Radiocarbon dating

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WikiJournal of Science is an open-access, free-to-publish, Wikipedia-integrated academic journal for science, mathematics, engineering and technology topics. WJS WikiJSci Wiki.J.Sci. WikiJSci WikiSci WikiScience Wikiscience Wikijournal of Science Wikiversity Journal of Science WikiJournal Science Wikipedia Science Wikipedia science journal STEM Science Mathematics Engineering Technology Free to publish Open access Open-access Non-profit online journal Public peer review

<meta name='citation_doi' value='10.15347/wjs/2018.006'>

First submitted: 16 Nov 2017
Accepted: 31 May 2018
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Mike Christie (1 June 2018). "Radiocarbon dating". WikiJournal of Science 1 (1): 6. doi:10.15347/WJS/2018.006. Wikidata Q55120317. ISSN 2470-6345. https://upload.wikimedia.org/wikiversity/en/7/7b/Radiocarbon_dating.pdf. 

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Wikipedia: This work is adapted from the Wikipedia article Radiocarbon dating (CC BY-SA). Content has also subsequently been used to update that same Wikipedia article Radiocarbon dating.

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Submitting author: Mike Christie  
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Recommendation

British Archaeology, the magazine of the Council for British Archaeology, has a note in each issue on its protocol for citing radiocarbon dates. The note refers readers to this article for further information. Dudley Miles (discuss • contribs) 17:40, 13 December 2020 (UTC)

Plagiarism check

Pass. WMF copyvio tool using TurnItIn. Short phrases such as "...received the Nobel Prize in Chemistry in 1960" were similarly used in external pages, but not regarded as plagiarism. T.Shafee(Evo﹠Evo)^talk 10:58, 9 January 2018 (UTC)

Reader Comments

Would it be possible for the authors to include a section on compliance with ethical standards to the end of this manuscript. A suitable section for this paper would be (if there are indeed no conflicts of interest and no studies with human or animal subjects):

Compliance with Ethical Standards

Conflicts of Interest

Mike Christie has not declared any potential conflits of interest

Human and animal Subjects

This article does not contain any studes with human or animal subjects performed by any of the authors

Van Vlijmen (discuss • contribs) 07:15, 15 February 2018 (UTC)

I'd be fine with including this; I'm not sure of the format required, so if there is a example article that has such a section, please post a link so I can copy the format. Mike Christie (discuss • contribs) 20:35, 17 February 2018 (UTC)

Editorial comments

Comments by Marshall Sumter ,

1. In Hemisphere effect, the last use of ¹⁴C shows as end of a line "¹⁴" with "C" on the next line. This may be an artifact of my browser or the template {{chem|14|C}} may not be working correctly here.
2. In Preparation and size, "CO" is separated from ₂ and in line 2 "¹⁴" is separated "C".
3. In Calibration, "(Fig. 6)" should be after "from old wood" rather than after "overlapping sequences".
4. In Calibration, references ^[28][29][69] after "well-established." are separated from end of line. --Marshallsumter (discuss • contribs) 18:34, 22 November 2017 (UTC)

Response

Thanks for these comments. I've fixed point 3; the other points seem to indicate that the markup isn't working on Wikiversity as it does on Wikipedia -- none of these three points appear to be an issue on the Wikipedia page. Is there a MediaWiki expert we can ask about this? I can try asking for technical help on Wikipedia if necessary. Mike Christie (discuss • contribs) 19:18, 22 November 2017 (UTC)

Comments by Marshall Sumter ,


I concur the problem is here! {{chem|14|C}} is working correctly on Wikipedia. "&nbsp" may be required, but multiple references usually work here! I'll do some more checking around. Some customs may have changed for our new formatting. Here's a message I usually leave on author's Discuss page, "I am currently peer reviewing Radiocarbon dating. This is an open process. Please add any comments you wish to make to the talk page only for the resource being reviewed! Thanks! --Marshallsumter (discuss • contribs) 22:25, 22 November 2017 (UTC)"

5. Figures 1, 5 & 7 have no credit line or stated copyright status.

Response

Fixed. Mike Christie (discuss • contribs) 21:39, 25 November 2017 (UTC)

6. All figures use the {{fig}} template which is putting in a vertical line "|" between "Figure #" and caption. --Marshallsumter (discuss • contribs) 21:22, 24 November 2017 (UTC)

Response

Isn't this intentional? Looking at the rotavirus article in the WikiJournal of Medicine it appears to use that formatting. If not, what's the preferred format? Mike Christie (discuss • contribs) 21:42, 25 November 2017 (UTC)

Comments by Thomas Shafee ,


You are correct, the {{fig}} template intentionally includes a vertical line symbol in the style of Nature (example). T.Shafee(Evo﹠Evo)^talk 01:42, 26 November 2017 (UTC)

7. Using ¹⁴C in place of {{chem|14|C}} prevents ¹⁴ C separation. --Marshallsumter (discuss • contribs) 21:58, 24 November 2017 (UTC)

Response

Yes, that's an improvement. I'd like {{chem}} to be available for use here, though, so I will post a note on en-wiki's technical noticeboard asking for assistance. Fixing it here would be the best outcome. Mike Christie (discuss • contribs) 21:19, 25 November 2017 (UTC)

Note posted here. Mike Christie (discuss • contribs) 21:39, 25 November 2017 (UTC)

There's a reply there already, with a solution! Can we try that? Mike Christie (discuss • contribs) 23:11, 25 November 2017 (UTC)

Comments by Marshall Sumter ,


Thanks for posting on Wikipedia! I can access Wikiversity Media Wiki and will insert the code! --Marshallsumter (discuss • contribs) 01:04, 26 November 2017 (UTC)

Code has been inserted! --Marshallsumter (discuss • contribs) 10:26, 26 November 2017 (UTC)

Response

That seems to have worked, for me at least. Thanks! Mike Christie (discuss • contribs) 15:14, 26 November 2017 (UTC)

Suggestions:

1. In the History section, "slow neutrons" are mentioned. Perhaps mentioning what "slow neutrons" and "thermal neutrons" are relative to ¹⁴C atmospheric production is needed. --Marshallsumter (discuss • contribs) 21:42, 24 November 2017 (UTC)

Response

The source gives no more specifics; it's definitely "slow neutrons" for Korff's work, though a related paper speculates about the interaction of thermal neutrons with the ¹⁴
C reaction. I've wikilinked "slow neutrons" to w:neutron temperature; is that enough? I think it would be a distraction for this article to delve into the topic at all. Mike Christie (discuss • contribs) 21:19, 25 November 2017 (UTC)

Comments by Marshall Sumter ,


As the article's first and main author, inclusion of my suggestions is your call! The article to be included in WikiJournal of Science does not have to be identical to the Wikipedia version but should be a good scientific review. I'll see what I can find. Your sources may be all we have. --Marshallsumter (discuss • contribs) 01:04, 26 November 2017 (UTC)

Here's a couple of references regarding "slow neutrons" and "thermal neutrons" with respect to ¹⁴N:

1. "The disintegration of nitrogen by slow neutrons has been studied in photographic emulsions of different sensitivity, which enable an unambiguous distinction to be made between the emission of α-particles and protons. Evidence has been obtained that the disintegration takes place according to the reaction

¹n + ¹⁴
₇N
→ ¹⁴
₅B
+ ⁴
₂He

with a cross-section of about 10−24 cm²."

2. "The fast neutrons from uranium fission can be moderated by elastic collision with graphite or heavy water in a nuclear reactor until their velocity is reduced to that of thermal energies (average 2200 meters/sec = 0.025 electron volts); such very slow neutrons are called thermal neutrons. Unlike fast neutrons, whose principal reaction with matter is one of scattering, thermal neutrons because of their very low energy and velocity are more likely to be captured than scattered by the atoms they encounter. Most of the reactions of biological elements with thermal neutrons are capture reactions. After an atom captures a neutron, it forms a new compound nucleus with an excess of energy. This new compound nucleus may then:

1.) emit a gamma ray immediately to form a stable isotope, e.g.,¹

¹
₁H
+ ¹n → [²
₁H
] → ²
₁H
+ γ;

2.) emit a heavy particle immediately to form a stable isotope, e.g.,

¹⁰
₅B
+ ¹n → [¹¹
₅B
] → ⁷
₃Li
+ α;

3.) emit immediately a capture radiation to form a radioactive daughter which subsequently emits beta or gamma rays at a rate characteristic for the isotope formed, e.g.,

¹⁴
₇N
+ ¹n → [¹⁵
₇N
] → ¹⁴
₆C
* + p (half life = 6,000 years) → ¹⁴
₇N
+ β^-."

The point being that "slow neutrons" do not produce ¹⁴C from ¹⁴N and "thermal neutrons" do. --Marshallsumter (discuss • contribs) 22:38, 26 November 2017 (UTC)

Response

Thanks for finding those. The 1950 paper says "slow neutrons" in the title but talks about "thermal neutrons", so I wonder if "slow" was used back then as a general term, rather than as a specific velocity category separate from "thermal". It seems to me to say that the majority of reactions that occur with thermal neutrons are capture reactions, and that includes the production of ¹⁴
C; but it doesn't say that the majority of neutron captures are with thermal neutrons specifically, does it? I can't access the other paper.

I recalled that an editor had done some more digging into this, so I'm posting a note on w:Talk:Radiocarbon dating asking them to take a look at the relevant paper for me. I think since we're talking about what Korff predicted, we should either use Korff's own language, or, if that's misleading, drop the temperature adjective completely. I'll post here again when I hear back. Mike Christie (discuss • contribs) 02:18, 28 November 2017 (UTC)

Comments by Marshall Sumter ,


Here's another reference that may be helpful:

3. "The sharp dependence on energy of the cadmium cross section for neutrons of energies near 0.35 eV [slow neutrons] has been used to investigate the energy distribution of 0.35-ev neutrons scattered through 90° by lead, aluminum, diamond, and graphite."

Like point 2. it refers to neutrons an order of magnitude higher in energy than thermal neutrons.

"Slow neutrons" does appear to be a general term for energies below fast neutrons like those mentioned in point 2. from the fission of uranium. Subsequent research found as mentioned by the reference that as fast neutrons lose energy through scattering they reach an energy plateau where they are likely to be absorbed (fused) into nuclei such as ¹⁴N; hence, the new designation for such neutrons: "thermal neutrons".

Whether Korff's prediction is correct or not depends on the theoretician's word choice. If by "slow neutrons" was meant any energies below "fast neutrons", then the prediction is false, because of point 1. above. If energies predicted were only those energies of fusion, which it doesn't seem they were, then the prediction was proven. At any rate, the term "thermal neutrons" has become generally accepted for fusional neutrons so it is likely a better term to use, though some later investigators may have yet another term. --Marshallsumter (discuss • contribs) 04:24, 28 November 2017 (UTC)

Response

I have Korff's 1940 paper in hand now, and he uses "slow neutrons", without directly estimating their speed, and then comments that "most probably will be eventually captured by nitrogen". The radiocarbon article currently says "a prediction by Serge A. Korff...that the interaction of slow neutrons with ¹⁴
N in the upper atmosphere would create ¹⁴
C". I don't think we can change this to "thermal neutrons" since that's not what Korff said. I think we should either leave it as slow neutrons, with a footnote at that point saying "Korff used the term slow neutrons without specifying the speed. "Slow neutrons" nowadays refers to a particular range of speeds; neutrons that are likely to interact with ¹⁴
N to create ¹⁴
C would now be described as thermal neutrons, which are slower than slow neutrons"; or else drop "slow". I think the former is preferable, though no doubt the wording could be improved. What do you think? Mike Christie (discuss • contribs) 12:41, 28 November 2017 (UTC)

After thinking about it some more, I've changed it to "thermal neutrons" in the article, and added a footnote explaining that this was not Korff's terminology. Mike Christie (discuss • contribs) 14:56, 29 November 2017 (UTC)

I like it!

2. In the Physical and chemical details section, cosmic rays as incident on the Earth's atmosphere are of three types: solar, galactic and extra-galactic. Perhaps which produces the most ¹⁴C needs to be mentioned and how. --Marshallsumter (discuss • contribs) 01:41, 25 November 2017 (UTC)

Response

The sources I have don't discuss this at all, so I don't think I can expand on it. The discussion of cosmic rays is set around 1939; as I understand it the fact that there are multiple types was not properly understood until at least the 1950s. I'm not aware of any research on which type produces the most neutrons of the relevant temperature. I'd prefer not to expand on this. Mike Christie (discuss • contribs) 21:19, 25 November 2017 (UTC)

Here's an image that may be helpful:

This image shows an overview of the space weather conditions over several solar cycles including the relationship between sunspot numbers and cosmic rays. Credit: Daniel Wilkinson.{{free media}}

Take a close look at sunspot numbers vs. cosmic rays. While the anti-correlation is above 50 % it's not close to 100 %. This next one clarifies the galactic cosmic-ray connection:

File:NeutronMonitor.GIF

Cosmic Ray Intensity (blue) and Sunspot Number (green) is shown from 1951 to 2006 Credit: University of New Hampshire.{{fairuse}}

The graph on the left shows an inverse correlation between sunspot numbers (solar activity) and neutron production from galactic cosmic rays. Solar magnetic field strength which would deflect most galactic cosmic rays correlates strongly with other solar activity, such as solar irradiance and sunspot number.

Response

I've had a look at the graphs, and I'm not clear what language I would add based on them. Are you saying that since sunspots decrease galactic cosmic rays and also decrease neutron pressure, I can say it is primarily galactic cosmic rays that create ¹⁴
C? It looks plausible to me, but I would want to see a paper that actually draws that conclusion before saying so. Or am I missing something here? Mike Christie (discuss • contribs) 13:54, 30 November 2017 (UTC)

Here's a free access reference that addresses galactic cosmic rays and their solar modulation. If you have access to Google Scholar, entering: radiocarbon "galactic cosmic rays", will yield about 1,170 articles. --Marshallsumter (discuss • contribs) 00:54, 1 December 2017 (UTC)

Here's a quote from Bowman's "Radiocarbon Dating" book from 1990, p. 19: "High sunspot activity increases the weak magnetic field that exists between the planets, and at such times there is a greater deflection of cosmic rays and hence ¹⁴C decreases." --Marshallsumter (discuss • contribs) 11:34, 2 December 2017 (UTC)

Here's a quote from Aitken's "Radiocarbon Dating" article from 2000, "Cosmic-ray variations are associated with changes in the strength of the Earth's magnetic field. A weak field allows more cosmic radiation to reach the upper atmosphere, and the production of carbon-14 is consequently enhanced--causing raw radiocarbon ages to be underestimates of calendar ages. The short-term wiggles mentioned above are associated with sunspot activity." While neither Bowman (1990) nor Aitken (2000) mentioned galactic cosmic rays, they were aware of solar activity modulating cosmic rays. --Marshallsumter (discuss • contribs) 23:27, 4 December 2017 (UTC)

"While a variety of causes for the observed temporal variations in natural ¹⁴
C concentrations have been proposed, they can be grouped into two major types. As noted in Section 1.4.1, the first involves changes in the production rate of ¹⁴
C due to such parameters as variations in the intensity and/or composition of galactic cosmic rays, changes in the physical characteristics of elements of the sun's magnetic field (heliomagnetic effects), or variations in the characteristics of the earth's magnetic field (geomagnetic effects).⁶⁶" Taylor & Bar-Yosef (2014), p. 58.

I'm concerned that not even briefly describing the importance of galactic cosmic rays to the production of ¹⁴
C dates this review to b2k. Here's an example of timeliness from a PhD thesis from 2011:

"¹⁴
C is produced in the upper atmosphere by the bombardment of ¹⁴
N by thermal neutrons [...], mainly initiated by high energy galactic cosmic rays, although less energetic solar cosmic rays also contribute to the production of ¹⁴
C (Libby, 1946). These primary cosmic rays lose energy through ionization of molecules and interactions with atomic nuclei as they travel through the Earth’s atmosphere, forming secondary particles: mainly neutrons, protons and muons (Tuniz et al., 1998; Muziker et al., 2003). A proportion of secondary particles, known as fast neutrons, lose further energy through nuclear collisions to form thermal neutrons, which are in vibrational equilibrium with atmospheric gases (Gosse and Phillips, 2001)."

"Rapid circulation of atmospheric ¹⁴
CO
₂, on the order of 4-10 years (Craig, 1957a; Nydal and Lövseth, 1970), ensures an almost uniform global atmospheric ¹⁴
C concentration at any point in time, although certain factors can influence the rate of production of ¹⁴
C (and consequently ¹⁴
CO
₂) over time, including latitude, altitude and solar activity. Understanding these variations in ¹⁴
C concentration is fundamental to the calculation of accurate ¹⁴
C ages, and their subsequent interpretation."

"Magnetic fields induced by solar activity also affect ¹⁴
C production, as high solar activity increases the flux of solar magnetic particles that deflect cosmic rays away from the Earth, thus decreasing ¹⁴
C production rates in the Earth’s atmosphere (Stuiver et al., 1997). Changes in solar activity therefore correlate with ¹⁴
C activity, and the periodicity is evident throughout the solar cycles that affect irradiance on the Earth. Therefore, regular variations in the flux of high energy galactic cosmic rays are evident in the ¹⁴
C record. 11 year Schwabe variations involve one cycle of increasing/decreasing sunspot activity and one reversal of the solar magnetic field, with ¹⁴
C production reaching a maximum of 1.15 times the normal production rate during periods of minimum solar activity (Masarik and Beer, 1999). 210 year Suess cycles (Masuda et al., 2009) and 2300 year Hallstatt cycles (Tobias et al., 2004; Clilverd et al., 2003, 2004) have similar effects, modulating ¹⁴
C production in inverse proportion to solar activity."

Response

I've added a clarification that it is primarily galactic rays that create ¹⁴
C; for now I've cited it to Russell, but I'd prefer to find a better source than a Ph.D. thesis and will replace it when I do.

3. In the Physical and chemical details section regarding "Once produced, the ¹⁴
C quickly combines with the oxygen in the atmosphere to form carbon dioxide (CO
₂)." Atmospheric (tropospheric or stratospheric) nitrogen is in the form of N
₂. The fusional thermal neutron creates ¹⁴N¹⁵N, which likely goes to H¹⁴C*¹⁴N (hydrogen cyanide). The hydrogen cyanide ¹⁴N¹⁴C*H + 2O
₂ → (CO
₂) + HNO₂ (nitrous acid). Hydrogen cyanide gas in air is explosive at concentrations over 5.6%. So it's highly reactive! No readily available reference so point is moot unless addressed by another reviewer! --Marshallsumter (discuss • contribs) 00:21, 1 December 2017 (UTC)

"Initially, the ¹⁴
C atoms get oxidized to ¹⁴
CO, primarily (Pandow et al. 1960; MacKay et al. (1963):"

1. C(g) + O₂ ⟶ CO + O: ∆H = –138.96kcal

"In the atmosphere, initially 90–100% of the ¹⁴
C produced is oxidized to ¹⁴
CO (Pandow et al. 1960)."

"In the atmosphere, the main removal process for ¹⁴
CO is oxidation by OH radicals (cf. Jockel et al. 1999). Because of the low abundance of CO in the atmosphere, and the formation of ¹⁴
CO initially, the ¹⁴
C/¹²
C ratio in the atmospheric CO is much higher than in the atmospheric CO
₂; by about two orders of magnitude in the lower stratosphere (Brenninkmeijer et al. 1995)." --Marshallsumter (discuss • contribs) 17:44, 6 December 2017 (UTC)

Response

Thanks for the ref. I expanded the relevant slightly to point out that CO is created first. I didn't mention other pathways to CO
₂; instead I just said it "ultimately" forms CO
₂, since that's the main point. Mike Christie (discuss • contribs) 00:54, 7 December 2017 (UTC)

4. In the Principles section, the mean-life of 8,267 appears awkwardly. The experimentally determined half-life of 5,370 occurs afterward. This section may be clearer by starting with the half-life to derive the mean-life. As the experimentally determined half-life appears to only have three significant digits so too must have the mean-life. --Marshallsumter (discuss • contribs) 03:12, 30 November 2017 (UTC)

Response

The discussion in Aitken (1990) gives the mean-life first, since that's the term that appears in the equation, and it makes sense to me to do it that way round -- otherwise one has to start with the half-life, derive the mean-life, and only then explain why you're doing the calculation. The significant figures point is interesting -- the most recent paper I can find on the experimental determination of the half-life is from 1962, and it gives +/- 40 years as the error, implying there are indeed only three significant figures. Aitken however gives 8267 as the mean-life, and I'm reluctant to truncate his number without a source for doing so, since that would impact the rest of the calculation. I suspect that, if there is no more precise value for the half-life, what Aitken did is to derive the mean-life from the half-life, and use it as if all four digits were significant in order that the calculation to rederive the half-life comes out correctly. This seems reasonable to me, given that this is an article about radiocarbon dating rather than about the isotope itself. Mike Christie (discuss • contribs) 11:55, 1 December 2017 (UTC)

Here's what you've written:

"The mean-life, denoted by τ, of ¹⁴
C is 8,267 years, so the equation above can be rewritten as:

$t{\text{=}}8267\cdot \ln(N_{0}/N){\text{ years}}$"

This can be written as:

"The mean-life is denoted by τ so the equation above can be rewritten as:

$t{\text{=}}\tau \cdot \ln(N_{0}/N){\text{ years}}$",

then after note 2 and "The currently accepted value for the half-life of ¹⁴
C is 5,730 years. This means that after 5,730 years, only half of the initial ¹⁴
C will remain; a quarter will remain after 11,460 years; an eighth after 17,190 years; and so on.", τ of ¹⁴
C is 5,730/ln 2 = 8,267 years.

Response

I'm not clear what you're suggesting should be changed here -- can you clarify? Mike Christie (discuss • contribs) 19:31, 1 December 2017 (UTC)

I mentioned: The "weighted mean of these three determinations, 5568 ± 30, is probably accurate to within 50 years and almost certainly within 100 years." When converting to 1950 via the specific activity of the absolute international standard a Libby half-life of 5568 yrs is used by convention. --Marshallsumter (discuss • contribs) 18:24, 1 December 2017 (UTC), both to show the error on Libby's half-life and the reason your seeing absolute numbers like 5730, 8267, 5568 and 8033 is by international convention, which you describe later. But, here you're describing principles. --Marshallsumter (discuss • contribs) 20:56, 1 December 2017 (UTC)

Response

Marshall, sorry if I'm being thick here, but I still don't see the problem. The start of the "Principles" section doesn't use Libby's data, and the mean-life and the half-life are both explained before being used. When the Libby data is introduced it's explained why it's still used in calculations. What do you see as the problem here? Mike Christie (discuss • contribs) 15:18, 2 December 2017 (UTC)

It's the same here with 8267 as with 8033 below. When I was reading through the principles section "8267" pops up in the equation and I was thinking much as a reader would: "Where did that 8267 in the equation come from?" In a principles section a number unlike ln2, for example, is expected but not something like 8267. I was expecting a half-life determination first because I've performed half-life research. Once we experimentally determine a half-life then we use the equation presented in the principles section to obtain the mean-life and, of course, they both have associated errors. Then, as has unfortunately happened with ¹⁴C, Libby's team did not obtain the correct half-life the first time. So now as you've described later a convention has been set up to convert older ages to correct ages, that's why the author you're mentioning above put 8267 and 8033 into the respective equations. I hope this helps! A more recent reader who has not performed half-life research may not think anything of 8267 popping up in an equation such as it does. --Marshallsumter (discuss • contribs) 22:52, 2 December 2017 (UTC)

Response

OK, I see where you're coming from now. Thanks for the explanation. As it stands the first use of 8267 is in "The mean-life, denoted by τ, of ¹⁴
C is 8,267 years, so the equation above can be rewritten as..." just preceding the equation itself. I was hoping that would be enough, but if it's not, I could mention the half-life there. I don't currently have any source on the half-life determination but could find some if you think it's important, but I think it would be a distraction to go too far down that road. In Wikipedia terms, I would say that it belongs in the radiocarbon article, not in the radiocarbon dating article; I'm aware this is a different context, but perhaps it still applies. Mike Christie (discuss • contribs) 01:05, 3 December 2017 (UTC)

In case of interest here's the half-life references:

1. "The half-life of C¹⁴ has been found to be 5720±47 years by means of the use of mass spectrometrically analyzed C¹⁴O₂ as a part of the counter gas in brass wall Geiger counters."
2. In 1952, the "weighted mean of these three determinations, 5568 ± 30, is probably accurate to within 50 years and almost certainly within 100 years."
3. In 1962, "A more accurate half-life has been measured as 5730±40 years (Godwin, 1962)."

Although it may distract the reader, including also informs, and including what's in w:Radiocarbon makes for a better scientific review of radiocarbon dating. --Marshallsumter (discuss • contribs) 16:05, 8 December 2017 (UTC)

Response

I've added a note that gives the ref to Libby for his statement of the earlier value, and the Godwin and van der Plicht refs for the later value. This is partly repeated a few sentences later in the text, but I take your point that the reader is going to be curious as soon as the number is mentioned, and I think the note is a good way to separate the comment from the main thread of the article. Does that address your concern? Mike Christie (discuss • contribs) 16:00, 9 December 2017 (UTC)

5. In the Calculations section the number 8033 pops up without derivation. "Radiocarbon age = τln F where τ is the Libby mean life of 8033 years."

Response

Good point. This is the Libby mean-life; I've added a clarification. How does that look? Mike Christie (discuss • contribs) 19:30, 1 December 2017 (UTC)

Better! If you want you can add "(8033)" after mean-life to help the reader. --Marshallsumter (discuss • contribs) 20:56, 1 December 2017 (UTC)

Response

I tweaked it a bit. Mike Christie (discuss • contribs) 14:58, 2 December 2017 (UTC)

6. In the Physical and chemical details section, the ¹⁴
C produced by fast neutrons in the reaction ¹⁶O(n,³He)¹⁴C in the stratosphere isn't mentioned. As oxygen composes 28 % of the atmosphere, 25-28 % more ¹⁴
C is likely to be produced because fast neutrons are much more plentiful higher up. --Marshallsumter (discuss • contribs) 11:33, 3 December 2017 (UTC)

Response

I had a look for papers that cover this (my own sources don't) and couldn't find anything I had access to. If you have access to something I could use as a source, could you email it to me? Thanks. Mike Christie (discuss • contribs) 01:04, 5 December 2017 (UTC)

"Spallation of atmospheric oxygen nuclei might contribute up to 20% to production of ¹⁴
C produced in the atmosphere (Lal and Peters 1967)." --Marshallsumter (discuss • contribs) 16:09, 6 December 2017 (UTC)

Response

I'd like some editorial guidance on this one, so pinging Thomas as well. Walker's Quaternary Dating Methods cites this paper for other points it makes, but he passes over this point, only giving the pathway from ¹⁴
N to ¹⁴
C. I'm aware that the rules here about original research are not the same as on Wikipedia, but as you know I am not a subject matter expert, so I'm hesitant to pass over the statement in the secondary source in order to use a primary source that says oxygen "might" contribute to ¹⁴
C production. What would you recommend? Mike Christie (discuss • contribs) 01:06, 7 December 2017 (UTC)

Comments by Thomas Shafee ,


I can't say whether the secondary source is omitting the information on oxygen nuclei just for brevity, or whether it is being cautious over genuine uncertainty. If it's a well-accepted fact, I'd expect that it should appear in a secondary source somewhere. Since the intention for this article is for updates after review to be re-integrated into Wikipedia, I would recommend a secondary source if possible, however WP:SCIRS does allow for primary sources to be used when necessary (e.g. secondary sources skim over detail). T.Shafee(Evo﹠Evo)^talk 04:04, 8 December 2017 (UTC)

Lal is an expert on in situ ¹⁴
C, otherwise known as ¹⁴
C produced by "spallation of atmospheric oxygen". I don't have access to Lal and Peters 1967. To me the phrase "might contribute up to 20% to production of ¹⁴
C produced in the atmosphere" means no one has tested the atmosphere in the stratosphere for ¹⁴
C produced by "spallation of atmospheric oxygen", but Lal and Peters know of no reason this method of producing ¹⁴
C won't occur in rough correspondence with the oxygen concentration in the stratosphere. Another way of writing it is "Spallation of atmospheric oxygen nuclei may produce up to 20% (oxygen percent of the stratosphere) of ¹⁴
C in the atmosphere." --Marshallsumter (discuss • contribs) 03:32, 7 December 2017 (UTC)

Response

I just tried putting something together and was unable to find a convincing form of words that uses this. The best I could come up with was to add (after the sentence giving the nuclear reaction with ¹⁴
N) something like: "Another nuclear reaction that creates ¹⁴
C is the spallation of atmospheric oxygen, which might contribute as much as 20% of the total ¹⁴
C production. I don't like this because it is unspecific as regards the nuclear reacion, and vague because of the uncertainty of the numbers. In the end I changed the nuclear reaction sentence to start: "The following nuclear reaction is the main pathway by which ¹⁴
C is created", and added a cite to Lal & Jull. That removes the implication that this is the only pathway, without distracting the reader with a vague statement. Mike Christie (discuss • contribs) 23:09, 7 December 2017 (UTC)

Just FYI, you left in after the cite to Lal & Jull: "It is possible that". I'm still looking at this! I find it hard to believe that all these researchers chose to ignore this source without a valid reason. And, I may have found a clue. The cross section for thermal neutron capture, in barns, for ¹⁷
O is 0.235 for the reaction ¹⁷O(n,α)¹⁴C, whereas for ¹⁴N it is 1.81 for the reaction ¹⁴N(n,p)¹⁴C. These are for the absorption of thermalized (approximately the same temperature as the gases) neutrons. The knock-on reaction for fast neutrons likely has a cross section even smaller than 0.235. This suggests that the reaction ¹⁴N(n,p)¹⁴C is about 8 times more likely to occur than the reaction ¹⁶
O(n,³
He)¹⁴
C for equal atomic concentrations, but nitrogen is 2.5 times more prevalent than oxygen. So the likely amount of ¹⁴
C produced from oxygen, which does not like neutrons like nitrogen does, may be as low or lower than 5 %. Not insignificant but small within any error analysis. If this "back-of-the-envelope" calculation is close, it would explain part of it. Lal estimates 13 such knock-on collisions on average before thermalization per neutron. That's only a 0.65 probability of success per neutron per the reaction ¹⁶
O(n,³
He)¹⁴
C. This is probably why Lal stated such knock-on reactions might produce up to 20 % of ¹⁴
C. "the main pathway" is a good compromise without experimental support. Many balloon flights have measured the main pathway production at latitudes and altitudes, but none appear to have tested the spallation reaction anywhere. --Marshallsumter (discuss • contribs) 03:22, 8 December 2017 (UTC)

Response

Oops; removed the fragment; thanks for spotting that. Interesting that, as you say, nobody appears to have tested the production of this pathway. I might email a radiocarbon researcher I know and ask about that. Glad you like the compromise wording. Mike Christie (discuss • contribs) 03:31, 8 December 2017 (UTC)

7. In the History section, there is the following: "Libby and James Arnold proceeded to test the radiocarbon dating theory by analyzing samples with known ages. For example, two samples taken from the tombs of two Egyptian kings, Zoser and Sneferu, independently dated to 2625 BC plus or minus 75 years, were dated by radiocarbon measurement to an average of 2800 BC plus or minus 250 years." Once it became known that Libby's team had the wrong half-life for ¹⁴
C, was the calibration curve correction applied to these dates for Zoser and Sneferu, and if so how much did their dates change? --Marshallsumter (discuss • contribs) 01:16, 5 December 2017 (UTC)

Response

There's an article in Science that might answer this question; I don't have access to it, though. It's Bronk Ramsey et al, 2010, "Radiocarbon-based chronology for dynastic Egypt", Science 328:1554-7. However, they may not have redated the original samples; the owner of the material from which the samples were taken may not have given more samples. If you have access to the article, could you let me have a copy? Otherwise I'll request one on Wikipedia at w:WP:RX. Mike Christie (discuss • contribs) 03:37, 5 December 2017 (UTC)

This also looks like it would be relevant. Mike Christie (discuss • contribs) 03:41, 5 December 2017 (UTC)

Now requested on w:WP:RX. Mike Christie (discuss • contribs) 01:12, 6 December 2017 (UTC)

I have the papers now; it appears that Libby's date range -- 3050 to 2550 BC -- includes all the dates that modern analyses produce, but Libby's error bars are quite large, so that's not surprising. None of the papers says that the same material was retested. Libby's dates were for samples of known age -- the chronology was fairly well-known, and the whole point of the testing was to validate the method, not to determine a date that had previously been unknown. Hence it's unremarkable that the dates were right. Given that the range he gives is so broad, I don't think this is worth further comment in the article. Mike Christie (discuss • contribs) 13:36, 6 December 2017 (UTC)

8. In the Carbon exchange reservoir section, the ice-covered reservoir is not mentioned. Ice covers 10 % of the surface of the Earth, about 7 % at or near the poles. As it is composed of H
₂O it entraps about 2 % ¹⁴
CO
₂ and produces in situ ¹⁴
C from fast neutron spallation of the oxygen in the ice. Here are some quotes:

1. "THE first suggestion that appreciable ¹⁴
   C might be produced in situ in polar ice was made by Fireman and Norris¹, who studied ¹⁴
   C in CO₂ extracted from both accumulation and ablation samples. In some ablation samples they observed ¹⁴
   C activities between four and six times higher than those expected due to trapped atmospheric CO₂."
2. "The ¹⁴C is produced mainly by nuclear spallations of oxygen in ice. The observed concentration of ¹⁴C in ablation ice samples is 1–3 x 10³ atom per g ice— three orders of magnitude higher than expected from the amount of trapped atmospheric CO₂ in this ice."
3. "The in situ ¹⁴C has a unique signature: about 60% exists as ¹⁴CO and the remainder as ¹⁴CO₂."
4. "Significant in situ production of radiocarbon by fast neutrons is restricted to the first ~15 m of firn, while the pore closure at this site occurs at 71 m depth [7]. So it is to be expected that most of the in situ produced ¹⁴
   CO
   ₂ and ¹⁴
   CO will diffuse out of the firn matrix and subsequently escape via the pores before these are closed, although a small fraction may stay behind."
5. "The ¹⁴
   C activities of the CO fractions are close to the background value for CO blanks. A mean concentration of 9 ± 6 molecules ¹⁴
   CO/g ice was deduced for the three ice samples. The relatively large error is primarily caused by the observed fluctuations in the background level. When this result is combined with the in situ ¹⁴
   CO
   ₂/¹⁴
   CO ratio of 3.8 [4], this leads to approximately 40 in situ produced ¹⁴
   C atoms per gram of ice. For ice still containing all in situ produced ¹⁴
   C atoms (no escape before pore closure), the ¹⁴
   C concentration can be calculated using the model by Lal et al. [1]. For the altitude, latitude and meteorological data [7,9] of the present location we find approximately 2400 at./g. So we observe that ~98% of the in situ produced ¹⁴
   C escaped from the firn before pore closure. This result compares well with the ~3% retained in situ ¹⁴
   C, obtained by Wilson and Donahue [5] on two ice samples of the GISP ice core."
6. Disregarding "in situ production of radiocarbon would make the correlation worse: the radiocarbon ages would become younger. The large uncertainty in radiocarbon AD age for the youngest samples is mainly caused by the radiocarbon calibration curve."
7. "To compare our radiocarbon ages with ages derived from volcanic horizon identification with di-electrical profiling (DEP)/electrical DC conductivity (ECM) measurements, the age difference between trapped air and the ice matrix must be known. The age of the ice matrix at pore closure, at this site, can be calculated from the accumulation rate (62 mm water equivalent/yr), the -10 m temperature (-38.5°C) and the initial density of the snow pack (325 kg/m³) [7,9,11], which leads to 740 yr. According to Schwander and Stauffer [12], the average age difference between the air captured in the ice and the ice matrix is equal to the age of the ice matrix at a density of 815 kg/m³. For this site [Dronning Maud Land, Antarctica], this leads to 670 yr (estimated error ± 100 yr), [...]. (At 815 kg/m³ ca. 50% of the air which will be eventually in the ice has been trapped.)"
8. The "results obtained at this site by radiocarbon dating of ice at shallow depth cannot compete in accuracy with those obtained by the DEP/ECM methods. However, for drill sites with very low accumulation rates, sites where hiati exist, or at greater depth where stratigraphical methods become more uncertain due to layer thinning, ¹⁴
   C measurements can provide absolute age estimates of the captured air from which ages of the ice matrix can be approximated."
9. "The Earth's magnetic field deflects incoming charged particles so that the equatorial cosmic-ray flux is four times less than the polar flux [...]."
10. "The fraction of cosmogenic ¹⁴
    C produced below the atmosphere at the earth’s surface is estimated to be less than 0.1% of the total (Lal 1988a, 1992b)."

Response

Thank you! This is very helpful. I'll read this through a couple of times and figure out the best way to add something based on this, today or tomorrow. Mike Christie (discuss • contribs) 16:05, 9 December 2017 (UTC)

Now done. Mike Christie (discuss • contribs) 03:27, 10 December 2017 (UTC)

9. Regarding the Hemisphere effect: "One such [atmospheric] variation is the 56 ± 24 ¹⁴
C yr offset noted between the Northern and Southern Hemispheres (McCormac et al., 2004). This offset remains broadly constant, although some temporal variations do occur. Known as the North/South Hemisphere effect, it occurs because the Southern Hemisphere contains an area of ocean c 40% greater than that of the Northern (Aitken, 1990, Levin et al., 1987). This results in the Southern Hemisphere having a greater area of ocean / air interface available for exchange between atmospheric CO
₂ and oceanic bicarbonate. Oceanic bicarbonate is depleted in ¹⁴
C relative to atmospheric CO
₂ because of the extended residence time of ¹⁴
C in the marine environment known as the marine reservoir effect (MRE). [...] This is accounted for during the calibration process with separate calibration curves (IntCal09 [now IntCal13?] for the Northern Hemisphere (Reimer et al., 2009), SHCal04 [now SHCal13?] for the Southern Hemisphere (McCormac et al., 2004))." --Marshallsumter (discuss • contribs) 11:14, 11 December 2017 (UTC)

Response

Looks like the SHCAL13 number is ~40 years; see [1]. I'll add something based on this and post a note here when done. Mike Christie (discuss • contribs) 11:21, 11 December 2017 (UTC)

Now done. Mike Christie (discuss • contribs) 11:59, 11 December 2017 (UTC)

10. Regarding the Marine effect: "Separate calibration curves have been constructed for the atmospheric (terrestrial) environment (INTCAL09 (Reimer et al., 2009)) and the marine environment (MARINE 09 (Reimer et al., 2009) [MARINE 13 calibration dataset (Reimer et al., 2013)]) to account for the large offset in ¹⁴
C concentration between the two reservoirs caused by the MRE." --Marshallsumter (discuss • contribs) 21:43, 11 December 2017 (UTC)

Response

I think this is covered in the calibration section, isn't it? The marine curve is mentioned there. Or is there some additional point that needs to be made? Mike Christie (discuss • contribs) 22:54, 11 December 2017 (UTC)

I was suggesting including "MARINE 13 calibration dataset (Reimer et al., 2013)", i.e., MARINE 13 for the readers benefit indicating the calibration has it's own name. --Marshallsumter (discuss • contribs) 23:28, 11 December 2017 (UTC)

Response

Good point; done. I also saw your comment below about putting material in notes rather than in the main text, and have moved the mention of SHCAL13 up into the body of the article. Mike Christie (discuss • contribs) 17:37, 13 December 2017 (UTC)

11. In the Principles section is stated, "Calculating radiocarbon ages also requires the value of the half-life for ¹⁴
C, which for more than a decade after Libby's initial work was thought to be 5,568 years." But, in Libby's 1949 Science article the half-life for ¹⁴
C is stated as 5720 ±47 years. In Libby's book, Libby, Willard F. (1965) [1952], Radiocarbon Dating (2nd (1955) ed.), Chicago: Phoenix, the half-life is stated as 5568 years. Then, in 1962 the half-life was reconfirmed as 5730. Apparently, from 1949 up to 1952, the half-life was 5720. While this is about a decade (1952 to 1962), the way this is described suggests to the reader that Libby had the half-life wrong from the beginning, but instead, for reasons hopefully described somewhere in the book he changed it after the 1949 Science article which established the technique for archaeology. This is not an easy thing to include, but it should be clarified for the reader. --Marshallsumter (discuss • contribs) 23:28, 11 December 2017 (UTC)

Here's why the half-life was changed and when: "The value, 5568 ± 30 years, was finally secured (Engelkemeir and Libby, 1950; Engelkemeir, et al, 1949. It has been confirmed in two other laboratories (Jones, 1948; Miller, et al, 1950)." Why all these efforts proved to be wrong might make a good history of science article but that's not relevant now for your article. But mentioning the half-life used in the Arnold and Libby Science article probably should be even if only in one of your "notes". --Marshallsumter (discuss • contribs) 02:03, 12 December 2017 (UTC)

Each review article bears the distinctness of its authors. Yours currently is its well-balanced treatment of both the subtopics of radiocarbon dating and its notable contributions to archaeology. It's not up to me to limit it by "Why all these efforts proved to be wrong might make a good history of science article but that's not relevant now for your article." Sorry! If you want to include this, go for it! --Marshallsumter (discuss • contribs) 16:16, 13 December 2017 (UTC)

Response

I've included the details in the "Principles" section. I looked this up in Taylor and Bar-Yosef, and they do mention it (p. 287); I missed it. They also comment that there were some other values determined in the early 1950s that were substantially different and not included in Libby's half-life: ~6,090 years, and 5900 ± 250 years (Caswell RS, Brabant JM, Schwebel. 1954. "Disintegration rate of Carbon-14". Journal of Research of the National Bureau of Standards 53: 27-28.) I don't think this needs to be mentioned, but it might be worth pointing out that these number, probably seen back then as outliers, were in fact about as close to the modern value as the three values used to calculate Libby's half-life. 17:37, 13 December 2017 (UTC)

Marshall, thanks for your comment above; I went ahead and mentioned the values omitted from the calculation, though this time I did leave them in a note since they don't have any direct effect on the narrative. Mike Christie (discuss • contribs) 18:19, 13 December 2017 (UTC)

Good note! In the Principles section I'd like you to consider mentioning, perhaps also in a note, the half-life measurement of C¹⁴, 5720 ± 47 years used in the Arnold and Libby Science article. These measurements were actually the only ones performed by Engelkemeir and they were performed at Argonne National Laboratory in the Chemistry division. I checked all publications by Engelkemeir. While I worked in the Materials Sciences division, different buildings same cafeteria, about that time, the article was published in Physical Review, not an Argonne-based journal. Physical Review like Nature uses extensive and intense peer review. Engelkemeir got the best answer the first time. As the article reads it suggests that Libby's group and many others were unsuccessful in obtaining the best half-life, but not so. While COI could be claimed for this request, there isn't any. But, I do think leaving it out is an injustice to good work performed well the first time and again by Godwin in 1962. --Marshallsumter (discuss • contribs) 21:08, 13 December 2017 (UTC)

Response

I agree, worth adding. I've reworked this a bit as I had the information distributed over a couple of places. It's now in the main text, but to do that I had to reduce the explanation at the first point the mean-life value of 8267 is mentioned. I think this works better; let me know if you disagree. Mike Christie (discuss • contribs) 21:44, 13 December 2017 (UTC)

I like it! --Marshallsumter (discuss • contribs) 22:38, 13 December 2017 (UTC)

12. Radiocarbon dating is used in fields outside archaeology, a short section with some recent examples would be good. --Marshallsumter (discuss • contribs) 11:24, 12 December 2017 (UTC)

Response

I looked for examples outside archaeology when I wrote the article, and didn't find anything I thought was worth highlighting, perhaps because much of what I found is also often of interest to archaeologists. Dating pollen, for example, is used by archaeologists as well as palaeoclimatologists and palaeobotanists. However, that does make it clear that it's not only archaeologists who are interested in the results. How about this, which is about the application of radiocarbon dating to Quaternary stratigraphy? Mike Christie (discuss • contribs) 18:06, 13 December 2017 (UTC)

Thanks for the pdf on radiocarbon dating by Godwin applied to stratigraphy! It's a good choice although b2k. But, it extensively covers the subject! --Marshallsumter (discuss • contribs) 21:08, 13 December 2017 (UTC)

Response

Added a paragraph based mostly on Godwin. Mike Christie (discuss • contribs) 22:04, 13 December 2017 (UTC)

Nice! --Marshallsumter (discuss • contribs) 22:44, 13 December 2017 (UTC)

First review summary:

1. Generally, I found the article well-balanced in its treatment of both the subtopics of radiocarbon dating and its notable contributions to archaeology.
2. The article has already been reviewed and rated a Feature Article on Wikipedia. As such, this may have created some inertia against "Up to date, aware of latest research".
3. One criteria currently being discussed by the WJS for a review article is "Up to date, aware of latest research". With some nudging, the authors have made some improvements along this line. But, is it enough? --Marshallsumter (discuss • contribs) 23:21, 12 December 2017 (UTC)

Response

I agree I've been slightly hesitant to expand scope to add some of the newer material, but I think the main reason is that I am not a subject matter expert and so am trying to be cautious about not adding material unless I fully understand it, and can be clear on its relevance. For a Wikipedia article I would look for secondary sources that cover the material to reassure me of relevance; here, I have to make more of a judgement call. I've no objection to the expansion -- I just don't want to add something a professional in the field would regard as low-value. So if any of my responses above fall short, please let me know, and I'll go back and take another look. Mike Christie (discuss • contribs) 18:24, 13 December 2017 (UTC)

13. "14C" rather than ¹⁴
C occurs twice, do you want the latter? "column can be used to for this purpose." to "column can be used for this purpose."? --Marshallsumter (discuss • contribs) 19:55, 26 May 2018 (UTC)

Response

Thanks for spotting those! All fixed. Mike Christie (discuss • contribs) 21:29, 26 May 2018 (UTC)

References

First peer reviewer

Review by anonymous peer reviewer ,
These assessment comments were submitted on 14 Feb 2018, and refer to this previous version of the article

Sections reviewed: History, Use in archaeology and elsewhere

Content: The submitted article contains extensive, clear and accurate information on the history of radiocarbon dating, and the science behind this important archaeological tool.

References: The referencing reflects the research, accurate and expansive; multiple scholarly sources are used and the referencing style is consistent throughout.

Style: Well written, clear and engaging, the author has used simple but accurate language to layout complex scientific endeavours and a historical account of the use of radiocarbon dating.

Second peer reviewer

Review by Timothy Jull , Professor, University of Arizona, Editor-in-Chief of the journal Radiocarbon
These assessment comments were submitted on 17 Apr 2018, and refer to this previous version of the article

This discussion on radiocarbon dating is well-written and conveys a good general view of the subject. I have some minor comments, additions and corrections to improve the discussion.

Response

Thank you very much. I will work through these points shortly, and add notes below. Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

1. P.2. In the abstract, it says that “more recently, accelerator mass spectrometry has become the method of choice…”. This is true, although AMS has been established for about 40 years and is certainly the “method of choice” since about 1990. So, perhaps reword this?

Response

Done; I made it "Accelerator mass spectrometry has since become the method of choice". Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

2. P.3. A recent paper by Jull et al. (2018) remeasured some of Libby’s original samples and confirmed most of the results.

Response

I'd like to cite that; can you give me the reference? Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

Now cited. Mike Christie (discuss • contribs) 10:29, 1 May 2018 (UTC)

3. P.3, Physical and chemical details. I think the 14C/12C ratio is about 1.2 parts per 1012, not 1.5.

Response

Updated to 1.25, using a 1997 reference; if there's a more recent and precise reference I'd be glad of a pointer. Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

4. P. 3, Principles. I would reword the first sentence as follows: “During its life, a plant or animal is in equilibrium with its surroundings by exchanging carbon either with the atmosphere, or through its diet. It will therefore have the same proportion of 14C as the atmosphere, or in the case of marine animals or plants, with the ocean”.

Response

Done. Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

5. P.4. In the third paragraph, you say “This is done by calibration curves which convert a measurement of 14C in a sample into an estimate calendar age”. This is true, but you don’t discuss this until much later. I would add that this is now done through open-access software such as calib.org or oxcal.

Response

I added "(discussed below)" to make it clearer that the topic is going to be covered; I want to keep the reference to the curve here because a reader who's understood the discussion will realize some correction must be made, and I don't want to leave them hanging. The current Wikipedia article on calibration of radiocarbon dates gives a more detailed discussion of calibration with examples; I cut that from this article for space reasons but could re-add some or all of that material if you think it would be useful. Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

6. P.4, paragraph 4. I would reword the sentence beginning “For consistency…”, as follows: “For consistency with these early papers, it was agreed at the 1962 Radiocarbon Conference in Cambridge (UK) to use the “Libby half-life” of 5568 years. Radiocarbon ages are still calculated using this half-life. A correction for the half-life is incorporated into the calibration software so that the final reported calibrated age is correct.”. Comment: At the 1982 Seattle Conference, a proposal was made to change to the correct half-life, but it was not agreed at the business meeting.

Response

Done. The point about the 1982 proposal is interesting but perhaps a historical detail, rather than something that needs to be included here, since this is not primarily a historical article. Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

7. I think figure 1 is from Bowman (1995)?

Response

Yes, with a couple of the boxes eliminated for simplicity. I cited Bowman, but have added "redrawn from Bowman (1995)" to the caption to be completely clear. Mike Christie (discuss • contribs) 11:29, 19 April 2018 (UTC)

8. P.5. I think that most people say the radiocarbon age of surface marine life is about 400 years, but I guess 440 years is fine. It is important perhaps to add here that there is a software package (calib.org/marine) that can estimate the marine reservoir correction for different locations.

Response

I added a comment about CALIB, but to the "Marine effect" paragraph, further down the article, which goes into the effect in a bit more detail. Mike Christie (discuss • contribs) 21:53, 19 April 2018 (UTC)

Updated to 400; the sources are not new enough for the extra precision to be worth mentioning. Mike Christie (discuss • contribs) 00:28, 8 May 2018 (UTC)

9. P. 6, figure 2. I think that figure 2 can easily be extended to much more recent time by using the figure from Hua et al. (2013) Radiocarbon 55(4): 2059-2072. https://www.cambridge.org/core/journals/radiocarbon/article/atmospheric-radiocarbon-for-the-period-19502010/6BD120B674D0467B648CE1B8DF6428B8

Response

I'd have to redraw the graph (I can't reuse the image), but the URL for the supplemental materials (which presumably include the graph data) still refers to the U of Arizona website where the journal was once hosted. I've looked for the supplemental materials on the new journal website, but can't find them; would you know how to locate them? Mike Christie (discuss • contribs) 01:40, 20 April 2018 (UTC)

Now done. Mike Christie (discuss • contribs) 00:28, 8 May 2018 (UTC)

10. P.6, last paragraph. I would say that coal or oil contains little or no detectable 14C.

Response

Done. Mike Christie (discuss • contribs) 21:53, 19 April 2018 (UTC)

P. 7, para 2. The level in figure 2 has dropped to about 1.02-1.03 in 2017. It is anticipated to drop below 1.0 by earlier 2020’s (Graven et al. 2012, Journal of Geophysical Research 117: D02303. https://doi.org/10.1029/2011JD016535.

Response

Rather than give these details I think the extension of the graph, per the response to point 9 above, is enough to tell the reader that the level is close to pre-bomb levels. Mike Christie (discuss • contribs) 00:31, 8 May 2018 (UTC)

11. p. 9, 3rd paragraph. The statement about dormant volcanoes is misleading. It’s true that volcanoes that are emitting CO2 can add dead CO2 to the local atmosphere. However, this is a very localized effect. It’s not proven for Santorini, although several authors speculate about it. I don’t think there are any plants that show this there – maybe on the new small island in the center of the crater. The fact that the Akrotiri samples do NOT show any effects (next sentence) contradicts this statement. I would recommend adding an article that shows this effect (elsewhere), e.g. Pasquier-Cardina et al. (1999), Journal of Volcanology and Thermal Research 92(1): 195-207. https://www.sciencedirect.com/science/article/pii/S0377027399000761. There are several other articles that can easily be found at scholar.google.com.

Response

Done; I dropped the discussion of Santorini and referenced Pasquier-Cardina instead. Mike Christie (discuss • contribs) 10:54, 20 April 2018 (UTC)

12. Material considerations. In the section about soils, I think it’s important to note that the other problem with soils is that they contain organic components of different age. The carbon can be stored for some period of time, and may be different in the organic (A) horizon compared to the clay (B) horizons.

Response

Added "and the fact that the organic components can be of different ages". Mike Christie (discuss • contribs) 10:56, 20 April 2018 (UTC)

13. Preparation and size. I think the use of thermal diffusion for enrichment hasn’t been used for a long time, except in some very special case. It’s certainly not a routine method.

Response

Reworded to make it clear it's rarely done. Mike Christie (discuss • contribs) 21:53, 19 April 2018 (UTC)

14. p. 10. I don’t think iron carbide has been used for quite some time as a target, although it was in the period 1982-1995.

Response

Cut. Mike Christie (discuss • contribs) 21:53, 19 April 2018 (UTC)

15. p.12. Figure 5 and Accelerator Mass Spectrometry. Although the first AMS machines used the C3+ charge state, this is no longer the only situation. Many modern AMS machines at lower energies use the C+ charge state (e.g. 200-500kV machines) and others (1MV) run with C2+, some higher-energy machines even use C4+.

Response

Clarified. Mike Christie (discuss • contribs) 21:53, 19 April 2018 (UTC)

16. p.12. “Some AMS facilities are also able to evaluate a sample’s fractionation…”. This isn’t quite right. Most AMS facilities measure the d13C value either on the machine (most labs at this point) or off-line and correct the radiocarbon date to -25 per mil, which is the convention. Anyway, I suggest rewording this sentence.

Response

Reworded to "Most AMS machines also measure the sample's δ13C, for use in calculating the sample's radiocarbon age." Mike Christie (discuss • contribs) 21:53, 19 April 2018 (UTC)

17. p13, Errors and reliability. I think the first sentence should say that doubling the counting time with the same amount of sample should increase the precision by a factor of 1.4 (i.e. √2), but this assumes that the errors are purely due to counting statistics. Since there are other sources of error, this may not always be the case. Most laboratories also estimate and include other sources of error, e.g. from the blank, from variability of the machine, etc.

Response

Reworded to "then doubling the counting time with the same size sample will increase the precision by a factor of √2, though this increase in precision only addresses errors in the counting statistics, and would not reduce other sources of error from elsewhere in the calculations". The article doesn't include a lot of detail about the use of e.g. processing blanks, so I didn't want to introduce something that is not fully explained. Mike Christie (discuss • contribs) 01:36, 20 April 2018 (UTC)

18. p. 15, wiggles. I think the discussion here is not completely clear. I would reword “For a set of samples forming a sequence with a known separation in time, these samples form a subset of the calibration curve. The sequence can be compared to the calibration curve and the best match to the sequence established. This “wiggle-matching” technique can lead to more precise dating…”

Response

Used the suggested wording. Mike Christie (discuss • contribs) 22:01, 19 April 2018 (UTC)

19. p. 15. I think the Bayesian discussion could be improved. I suggest “For example, if a series of radiocarbon dates is taken from different levels in a stratigraphic sequence, Bayesian analysis can be used to evaluate dates which are outliers, and can calculate improved probability distributions, based on the prior information that the sequence should be ordered in time.”

Response

Used the suggested wording. Mike Christie (discuss • contribs) 22:01, 19 April 2018 (UTC)

20. p. 15. Van de Graaff…

Response

Oops. Fixed. Mike Christie (discuss • contribs) 22:01, 19 April 2018 (UTC)

21. p. 17. I think there are lots of applications outside archaeology, e.g. to geology, geomorphology, oceanography, sedimentology, lake studies…

Response

I mentioned a couple more in the introductory part of the sentence, but have not found a good example worth adding to the ones already in the article, so I've left it at that. If there's a good application that would be interesting to describe in one of these fields I'd love to get a pointer. Mike Christie (discuss • contribs) 22:01, 19 April 2018 (UTC)

22. p. 18. I think the statement that “in may cases the scrolls were determined to be older than the paleographically-determined age” is not correct. If you read the papers, they in general were in reasonable agreement.

Response

Yes, the source I used (Taylor and Bar-Yosef) doesn't support this. Fixed, I think. Mike Christie (discuss • contribs) 01:27, 20 April 2018 (UTC)

23. I would recommend checking all the weblinks in the reference section. Probably the doi should be cited instead of some of the complex links.

Response

I've gone through every external link and checked that they all work. I think everything that has a doi has a doi link, and they all seem to be correct. Mike Christie (discuss • contribs) 10:38, 1 May 2018 (UTC)

Third peer review

Review by anonymous peer reviewer ,
These assessment comments were submitted on 30 May 2018, and refer to this previous version of the article

Introductory Part

“Conversely, nuclear testing increased the amount of 14C in the atmosphere, which attained a maximum in 1963 of almost twice what it had been before the testing began.”

The maximum occurred at different years in the Northern and Southern Hemispheres. Check Hua et al. (2013).

Response

The dates are 1964 for the Northern hemisphere and 1966 for the Southern Hemisphere; changed to "about 1965" in the abstract, with the details given in the body of the article. Mike Christie (discuss • contribs) 09:09, 1 June 2018 (UTC)

“Accelerator mass spectrometry has since become the method of choice; it counts all the 14C atoms in the sample and not just the few that happen to decay during the measurements;”

It does not count all the atoms.

Response

Changed to "it counts ¹⁴
C atoms in the sample directly, rather than just the few that happen to decay during the measurements". Mike Christie (discuss • contribs) 09:13, 1 June 2018 (UTC)

Background

“...they were able to demonstrate that they contained radioactive 14C.”

This sounds a bit odd to me as if 14C could be both radioactive and non-radioactive.

Response

Removed "radioactive". Mike Christie (discuss • contribs) 09:15, 1 June 2018 (UTC)

Physical Chemical Details

Here if you call the section “details” you could include the reactions for the formation of 14CO2.

Response

Added. Mike Christie (discuss • contribs) 10:42, 4 June 2018 (UTC)

Principles

“It will therefore have the same proportion of 14C...”

Should be 14C.

Response

I assume you mean ¹⁴
C; fixed. Mike Christie (discuss • contribs) 09:16, 1 June 2018 (UTC)

“the calculations for radiocarbon years assume that the 14C/

12C ratio has not changed over time.”

Add “the atmospheric 14C/12C ratio has not...”

Response

Added. Mike Christie (discuss • contribs) 09:17, 1 June 2018 (UTC)

“Since the calibration curve (IntCal) also reports past 14C radioactivity using this conventional...”

You need to add references for the IntCal curves and replace 14C with 14C. I also think 14C radioactivity sounds odd. Perhaps atmospheric 14C concentration?

Response

Fixed; added a reference and made the suggested change to the wording. Mike Christie (discuss • contribs) 09:25, 1 June 2018 (UTC)

Carbon Exchange Reservoir

“...if another reservoir has a lower ratio of 14C to 12C, it indicates that the carbon is older and hence that some of the 14C has decayed.”

Not necessarily. See for example the case of reservoir effects. There may be situations in which a lower 14C/C ratio does not mean radiocarbon decay but rather 14C not entering the system, a lack of replenishment. Alternatively, an input of 12C and 13C would also lower the ratio 14C/C in a given system.

Response

Changed to "it indicates that the carbon is older and hence that either some of the ¹⁴
C has decayed, or the reservoir is receiving carbon that is not at the atmospheric baseline"; the following sentences discuss upwelling from the deep ocean, which is an example.

“Creatures living at the ocean surface have the same 14C ratios as the water they live in...”

Provided corrections for the isotopic fractionation are performed.

“...the atmosphere and have the same 14C/12C ratio as the atmosphere.”

Again provided corrections for the isotopic fractionation are performed.

Response

There was a footnote giving this qualification; I've reworded it and moved it to after the second sentence so it's clear it covers both. Mike Christie (discuss • contribs) 16:11, 2 June 2018 (UTC)

Dating considerations

Isotopic Fractionation

“...so that direct measurements of 14C radiation are similar to measurements for the rest of the biosphere.”

It is better to say measurements of 14C concentration. Measuring 14C radiation implies using the conventional technique.

Response

Done. Mike Christie (discuss • contribs) 10:04, 1 June 2018 (UTC)

Reservoir Effects Marine

“These deviations can be accounted in calibration, and software such as CALIB can estimate the appropriate correction for different locations.”

This is misleading. Although CALIB, OxCal and other calibration software are able to estimate ∆R corrections based on radiocarbon ages provided by the user, they cannot estimate appropriate ∆R corrections for different locations to be used during calibration. When one needs to calibrate a marine radiocarbon age, they need to have the appropriate ∆R correction

PRIOR calibration. The software will not give this value to you.

Check Ascough et al. (2005) and Alves et al. (2018) for information that can strengthen this section and other sections in the paper.

Response

Changed to "These deviations can be accounted for in calibration, and users of software such as CALIB can provide as an input the appropriate correction for the location of their samples." Mike Christie (discuss • contribs) 15:55, 2 June 2018 (UTC)

Other Effects

Here you should also discuss the case in which modern organic material is incorporated into freshwater systems.

Response

Expanded the sentence mentioning humus to "...other sources of carbon such as humus can produce similar results, and can also reduce the apparent age if they are of more recent origin than the sample". Mike Christie (discuss • contribs) 16:04, 2 June 2018 (UTC)

Samples

“Alkali and acid washes can be used to remove humic acid and carbonate contamination, but care has to be taken to avoid destroying or damaging the sample.”

Here you are describing the treatment of an organic sample. Also, of course there is nothing wrong with damaging or destructing the sample since 14C-AMS is a destructive technique. You probably mean something like care should be taken not to lose the sample? Sometimes, when removing contaminants, we can also remove the original carbon atoms that we want to date.

Response

Reworded to "but care has to be taken to avoid removing the part of the sample that contains the carbon to be tested". Mike Christie (discuss • contribs) 10:26, 1 June 2018 (UTC)

Preparation and size

Accelerator mass spectrometry (AMS)

The acronym is only defined in the last lines but the technique has been mentioned before.

Response

Moved the acronym to the first mention of the technique. Mike Christie (discuss • contribs) 09:57, 1 June 2018 (UTC)

“Accelerator mass spectrometry (AMS) is much more sensitive, and samples as small as 0.5 milligrams can be used”

Make it clear you are talking about 0.5 mg OF CARBON. Not 0.5 mg of the original sample!

Response

Done. Mike Christie (discuss • contribs) 09:59, 1 June 2018 (UTC)

Accelerator mass spectrometry

“The ions are accelerated and passed through a stripper, which removes several electrons so

that the ions emerge with a positive charge.”

It is important to mention that the stripper is used to break molecular isobars such as 13CH.

Response

Done. Mike Christie (discuss • contribs) 10:38, 1 June 2018 (UTC)

Calculations

“...which was prepared by NIST”

Define what NIST is.

Response

Done. Mike Christie (discuss • contribs) 10:01, 1 June 2018 (UTC)

REFERENCES

Alves, E. Q., Macario, K., Ascough, P., Bronk Ramsey, C. (2018).The worldwide marine radiocarbon reservoir effect: Definitions, mechanisms, and prospects. Reviews of Geophysics, 56. https://doi.org/10.1002/2017RG000588

Hua, Q., Barbetti, M., & Rakowski, A. Z. (2013). Atmospheric radiocarbon for the period 1950–2010. Radiocarbon, 55(4), 2059–2072.

Ascough, P., Cook, G., & Dugmore, A. (2005). Methodological approaches to determining the marine radiocarbon reservoir effect. Progress in Physical Geography: Earth and Environment, 29(4), 532–547.

Reference error

Reference number 13 (Russell, 2011) is giving an error. Can this be corrected? Andrew Z. Colvin • Talk 07:08, 22 June 2018 (UTC)

Done. It was an issue with the |month= parameter in the {{cite book}} template. T.Shafee(Evo﹠Evo)^talk 09:31, 22 June 2018 (UTC)